Pre-ecat 2019 (Group: F.Sc Pre Engineering)

1. The addition of unsymmetrical reagents to an unsymmetrical alkenes is in the accordance with rule:

Hund's Rule

Markownikov's Rule

Pauli- Exclusion Prinicple

Aufau- Principle

Markownikov's Rule states that when an unsymmetrical reagent adds to an unsymmetrical alkene, the hydrogen atom of the reagent attaches to the carbon atom that already has more hydrogen atoms bonded to it. This rule is based on the observation that in the addition reaction, the more stable carbocation intermediate is formed when the positive charge is on the carbon atom that already has more alkyl groups attached to it. Therefore, the correct answer is Markownikov's Rule.

Explanation

Markownikov's Rule states that when an unsymmetrical reagent adds to an unsymmetrical alkene, the hydrogen atom of the reagent attaches to the carbon atom that already has more hydrogen atoms bonded to it. This rule is based on the observation that in the addition reaction, the more stable carbocation intermediate is formed when the positive charge is on the carbon atom that already has more alkyl groups attached to it. Therefore, the correct answer is Markownikov's Rule.

2. Hydrogen bond is the strongest between the molecules of:

HF

HCl

HBr

HI

Hydrogen bond is the strongest between the molecules of HF because HF has the highest electronegativity difference between hydrogen and fluorine atoms. This large electronegativity difference results in a highly polarized bond, with the hydrogen atom carrying a partial positive charge and the fluorine atom carrying a partial negative charge. This creates a strong electrostatic attraction between the hydrogen atom of one HF molecule and the fluorine atom of another HF molecule, leading to the formation of strong hydrogen bonds. In comparison, HCl, HBr, and HI have lower electronegativity differences, resulting in weaker hydrogen bonds.

Explanation

Hydrogen bond is the strongest between the molecules of HF because HF has the highest electronegativity difference between hydrogen and fluorine atoms. This large electronegativity difference results in a highly polarized bond, with the hydrogen atom carrying a partial positive charge and the fluorine atom carrying a partial negative charge. This creates a strong electrostatic attraction between the hydrogen atom of one HF molecule and the fluorine atom of another HF molecule, leading to the formation of strong hydrogen bonds. In comparison, HCl, HBr, and HI have lower electronegativity differences, resulting in weaker hydrogen bonds.

3. When water freezes, it occupies;

9% more space

9% less space

Same amount of space

None of these

When water freezes, it expands and occupies 9% more space. This is because the water molecules arrange themselves in a crystalline structure when they freeze, causing them to spread out and take up more volume. As a result, the density of ice is lower than that of liquid water. Therefore, when water freezes, it increases in volume and occupies more space.

Explanation

When water freezes, it expands and occupies 9% more space. This is because the water molecules arrange themselves in a crystalline structure when they freeze, causing them to spread out and take up more volume. As a result, the density of ice is lower than that of liquid water. Therefore, when water freezes, it increases in volume and occupies more space.

4. What makes the detective sure that the robber did not come through the windows?

The windows are locked

The windows face the police station.

The windows have not been used in months.

The windows are too small for a person to fit through.

The detective is sure that the robber did not come through the windows because they have not been used in months. This suggests that there has been no recent activity or signs of entry through the windows, making it unlikely that the robber used them as an access point.

Explanation

The detective is sure that the robber did not come through the windows because they have not been used in months. This suggests that there has been no recent activity or signs of entry through the windows, making it unlikely that the robber used them as an access point.

5. Two vectors $P=ai+aj+3k\, and\, Q=ai-2j-k$ are perpendicular to each other. The positive value of "a" will be:

4

3

9

13

When two vectors are perpendicular to each other, their dot product is equal to zero. The dot product of two vectors is calculated by multiplying their corresponding components and adding the results. Let's assume the two vectors are a = (a1, a2, a3) and b = (b1, b2, b3). If a and b are perpendicular, then a1*b1 + a2*b2 + a3*b3 = 0. In this case, the only option that satisfies this condition is a = (0, 1, 0), which corresponds to the number 3. Therefore, the positive value of "a" is 3.

Explanation

When two vectors are perpendicular to each other, their dot product is equal to zero. The dot product of two vectors is calculated by multiplying their corresponding components and adding the results. Let's assume the two vectors are a = (a1, a2, a3) and b = (b1, b2, b3). If a and b are perpendicular, then a1*b1 + a2*b2 + a3*b3 = 0. In this case, the only option that satisfies this condition is a = (0, 1, 0), which corresponds to the number 3. Therefore, the positive value of "a" is 3.

6. Chemistry (Question 61 to 90) $N{H}_{3}\, burns\, in\, {O}_{2}\, according\, to\, the\, following\, reaction:$ $4N{H}_{3\, (g)}+{3O}_{2\, (g)}\to 2{N}_{2\, (g)}+{6H}_{2}{O}_{(g)}$

It shows that 1 mole of will produce 1/2 mole of

1 mole of will produce the 6 moles of

For the complete reaction of 2 moles of are required

None of these

not-available-via-ai

Explanation

not-available-via-ai

7. Solve for x, if $\frac {{2}^{x-3}} {{8}^{-x}}=\frac {32} {{4}^{x/2}}$

5/8

-5/8

8/5

-8/5

The given equation is asking to solve for x. The equation consists of four fractions: 5/8, -5/8, 8/5, and -8/5. The answer to the equation is 8/5.

Explanation

The given equation is asking to solve for x. The equation consists of four fractions: 5/8, -5/8, 8/5, and -8/5. The answer to the equation is 8/5.

8. Why do educationists consider philosophy a ‘weak and woolly’ field?

Its theoretical concepts are easily understood

It is not practically applicable

It is irrelevant for education

None of the above

Educationists consider philosophy a 'weak and woolly' field because it is not practically applicable. While philosophy deals with theoretical concepts and ideas, it does not provide practical solutions or tangible outcomes that can be directly applied in the field of education. Educationists often prioritize practical and concrete approaches that can be implemented in classrooms and educational settings, making philosophy seem irrelevant and ineffective in their eyes.

Explanation

Educationists consider philosophy a 'weak and woolly' field because it is not practically applicable. While philosophy deals with theoretical concepts and ideas, it does not provide practical solutions or tangible outcomes that can be directly applied in the field of education. Educationists often prioritize practical and concrete approaches that can be implemented in classrooms and educational settings, making philosophy seem irrelevant and ineffective in their eyes.

9. Two forces of magnitudes 12 N and 13 N act on a body. Which one of the following is not possible resultant of these two vectors?

1 N

20 N

25 N

31 N

Range of the resultant of two vectors A and B can be found by:

|A-B| ≤ Resultant ≤ |A+B|

In this case, A= 12 N and B=13 N

so, range of the resultant is given by:

|12-13| ≤ Resultant ≤ |12+13|

|-1| ≤ Resultant ≤ 25

1 ≤ Resultant ≤ 25

Hence, resultant of two vectors 12 N and 13 must be in range of 1 to 25. Here, in the given options 31 N is the which can't be possible resultant of the given vectors.

Explanation

Range of the resultant of two vectors A and B can be found by:

|A-B| ≤ Resultant ≤ |A+B|

In this case, A= 12 N and B=13 N

so, range of the resultant is given by:

|12-13| ≤ Resultant ≤ |12+13|

|-1| ≤ Resultant ≤ 25

1 ≤ Resultant ≤ 25

Hence, resultant of two vectors 12 N and 13 must be in range of 1 to 25. Here, in the given options 31 N is the which can't be possible resultant of the given vectors.

10. You have 15 capacitors available with you, each of 15 nF. You need a capacitance of around 150 nF in a circuit. You can achieve this value by connecting:

10 capacitors in series

10 capacitors in parallel

12 capacitors in series

8 capacitors in parallel

Connecting capacitors in parallel increases the total capacitance. In this case, since each capacitor has a capacitance of 15 nF, connecting 10 capacitors in parallel will give a total capacitance of 10 * 15 nF = 150 nF, which is the desired value.

Explanation

Connecting capacitors in parallel increases the total capacitance. In this case, since each capacitor has a capacitance of 15 nF, connecting 10 capacitors in parallel will give a total capacitance of 10 * 15 nF = 150 nF, which is the desired value.

11. At Murree hills, water will boil at about:

102 °C

98 °C

69 °C

100 °C

At higher altitudes, the atmospheric pressure decreases, which in turn lowers the boiling point of water. In Murree hills, which are located at a high altitude, the atmospheric pressure is lower compared to sea level. As a result, water will boil at a lower temperature. The correct answer, 98 °C, indicates that water boils at a lower temperature in Murree hills compared to the standard boiling point of 100 °C at sea level.

Explanation

At higher altitudes, the atmospheric pressure decreases, which in turn lowers the boiling point of water. In Murree hills, which are located at a high altitude, the atmospheric pressure is lower compared to sea level. As a result, water will boil at a lower temperature. The correct answer, 98 °C, indicates that water boils at a lower temperature in Murree hills compared to the standard boiling point of 100 °C at sea level.

12. If $\frac {x+10} {{x}^{2}-4}=\frac {a} {(x+2)}+\frac {b} {(x-2)}$ then a+b is

3

-2

1

-1

The statement "If a then b" implies that if a certain condition is true, then another condition, b, will also be true. In this case, the condition a is not specified, so it can be any value. However, the condition b is given as "a+b". Since the answer is 1, it suggests that the condition a is equal to 0. Therefore, when a is 0, the sum of a and b will be 1.

Explanation

The statement "If a then b" implies that if a certain condition is true, then another condition, b, will also be true. In this case, the condition a is not specified, so it can be any value. However, the condition b is given as "a+b". Since the answer is 1, it suggests that the condition a is equal to 0. Therefore, when a is 0, the sum of a and b will be 1.

13. Two lines, $L:\, y=\frac {2} {3}x+7\, and\, M:\, y=\frac {-3} {2}+8\, \, are;$

L and M are parallel to each other

L and M are perpendicular to each other

Both L and M are perpendicular and parallel to each other

Neither L and M are perpendicular nor parallel to each other

The given answer states that lines L and M are perpendicular to each other. This means that the two lines intersect at a right angle, forming a 90-degree angle. If two lines are perpendicular, they cannot be parallel because parallel lines do not intersect. Therefore, the statement "Both L and M are perpendicular and parallel to each other" is incorrect. Additionally, the statement "Neither L and M are perpendicular nor parallel to each other" is also incorrect because it contradicts the given information that the lines are perpendicular.

Explanation

The given answer states that lines L and M are perpendicular to each other. This means that the two lines intersect at a right angle, forming a 90-degree angle. If two lines are perpendicular, they cannot be parallel because parallel lines do not intersect. Therefore, the statement "Both L and M are perpendicular and parallel to each other" is incorrect. Additionally, the statement "Neither L and M are perpendicular nor parallel to each other" is also incorrect because it contradicts the given information that the lines are perpendicular.

14. If the coordinates given in the table represents a line $\frac {x} {a}+\frac {y} {b}=1$ , then values of a and b are:

x	0	1	2	3	-1
y	4	10/3	8/3	2	14/3

A=4 and b=6

A=6 and b=4

A=2 and b=3

A=3 and b=2

The given coordinates represent a line. To find the equation of the line, we can use the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept. By observing the table, we can see that the slope of the line is (10/3 - 4) / (1 - 0) = 6/3 = 2. Therefore, the value of a is 2. To find the y-intercept, we can substitute the values of x and y from the table into the equation and solve for b. Using the point (0, 4), we get 4 = 2(0) + b, which gives us b = 4. Therefore, the correct values of a and b are a = 2 and b = 4.

Explanation

The given coordinates represent a line. To find the equation of the line, we can use the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept. By observing the table, we can see that the slope of the line is (10/3 - 4) / (1 - 0) = 6/3 = 2. Therefore, the value of a is 2. To find the y-intercept, we can substitute the values of x and y from the table into the equation and solve for b. Using the point (0, 4), we get 4 = 2(0) + b, which gives us b = 4. Therefore, the correct values of a and b are a = 2 and b = 4.

15. What does Ms. Gervis do with her cakes?

She eats them

She sells them.

She hides them

She gives them away

Ms. Gervis gives away her cakes. This implies that she does not eat them herself, sell them, or hide them. Giving them away suggests that she is generous and enjoys sharing her cakes with others.

Explanation

Ms. Gervis gives away her cakes. This implies that she does not eat them herself, sell them, or hide them. Giving them away suggests that she is generous and enjoys sharing her cakes with others.

16. In the following fig. is shown the flow of liquid through a horizontal pipe. Three tubes A, B and C are connected to the pipe. The radii of the tubes A, B and C at the junction are respectively 2 cm 1 cm and 2 cm, it can be said that the

Height of the liquid in the tube A is maximum

Height of the liquid in the tubes A and B is the same

Height of the liquid in all the three tubes is the same

Height of the liquid in the tubes A and C is the same

The height of the liquid in the tubes A and C is the same because the radii of the tubes A and C at the junction are the same. According to the principle of continuity, the flow rate of the liquid is constant at every point in the pipe. Since the radii of tubes A and C are the same, the flow rate of the liquid through these tubes will also be the same. Therefore, the height of the liquid in tubes A and C will be the same.

Explanation

The height of the liquid in the tubes A and C is the same because the radii of the tubes A and C at the junction are the same. According to the principle of continuity, the flow rate of the liquid is constant at every point in the pipe. Since the radii of tubes A and C are the same, the flow rate of the liquid through these tubes will also be the same. Therefore, the height of the liquid in tubes A and C will be the same.

17. A mixture of two gas at constant temperature contains the molecules of two kinds. The first kind of mass m₁and root mean square speed c₁and the second molecule of mass m₂ and rms speed c₂. The ratio of $\frac {{c}_{1}} {{c}_{2}}$ is:

M1/m2

M2/m1

The ratio of the masses of the two kinds of molecules is m1/m2. This can be inferred from the given information that the mixture contains molecules of two kinds with different masses.

Explanation

The ratio of the masses of the two kinds of molecules is m1/m2. This can be inferred from the given information that the mixture contains molecules of two kinds with different masses.

18. Aqua Regia is employed to dissolve the gold or silver. It is when formed, the volume of concentrated $HN{O}_{3}$ is mixed with volume of concentrated HCl is in ratio :

1:1

3:1

1:3

3:2

Aqua Regia is a mixture of concentrated nitric acid (HNO3) and concentrated hydrochloric acid (HCl). When it is formed, the volume of concentrated HNO3 is mixed with three times the volume of concentrated HCl. This ratio of 1:3 is necessary to dissolve gold or silver effectively. The strong oxidizing properties of nitric acid, combined with the chloride ions from hydrochloric acid, create a powerful solvent that can dissolve noble metals like gold and silver.

Explanation

Aqua Regia is a mixture of concentrated nitric acid (HNO3) and concentrated hydrochloric acid (HCl). When it is formed, the volume of concentrated HNO3 is mixed with three times the volume of concentrated HCl. This ratio of 1:3 is necessary to dissolve gold or silver effectively. The strong oxidizing properties of nitric acid, combined with the chloride ions from hydrochloric acid, create a powerful solvent that can dissolve noble metals like gold and silver.

19. Why did Aquinas propose a model of education which did not lay much emphasis on facts?

Facts do not lead to holistic education

Facts change with the changing times

Facts are frozen in time

Facts are not important

Aquinas proposed a model of education that did not lay much emphasis on facts because he believed that facts are not static and can change with the changing times. He understood that knowledge is not limited to a fixed set of facts, but rather requires a deeper understanding and critical thinking skills. By focusing on the ability to adapt and analyze new information, Aquinas aimed to provide a more holistic education that would enable individuals to navigate the complexities of an ever-changing world.

Explanation

Aquinas proposed a model of education that did not lay much emphasis on facts because he believed that facts are not static and can change with the changing times. He understood that knowledge is not limited to a fixed set of facts, but rather requires a deeper understanding and critical thinking skills. By focusing on the ability to adapt and analyze new information, Aquinas aimed to provide a more holistic education that would enable individuals to navigate the complexities of an ever-changing world.

20. Three particles A,B and C are thrown from the top of a tower with the same speed. A is thrown up, B is thrown down and C is thrown horizontally. They hit the ground with speeds V_A, V_B, and V_Crespectively;

VA=VB=VC

VA=VB>VC

VB>VC>VA

VA>VB=VC

The given answer, "VA=VB=VC," means that the speeds at which particles A, B, and C hit the ground are equal. This implies that the initial speed with which each particle was thrown did not affect their final speeds when they hit the ground. It suggests that the vertical motion of particle A (thrown up) and particle B (thrown down) did not have any impact on their final speeds. Similarly, the horizontal motion of particle C did not affect its final speed. Therefore, all three particles hit the ground with the same speed.

Explanation

The given answer, "VA=VB=VC," means that the speeds at which particles A, B, and C hit the ground are equal. This implies that the initial speed with which each particle was thrown did not affect their final speeds when they hit the ground. It suggests that the vertical motion of particle A (thrown up) and particle B (thrown down) did not have any impact on their final speeds. Similarly, the horizontal motion of particle C did not affect its final speed. Therefore, all three particles hit the ground with the same speed.

21. What does the detective seem to think will happen if he solves the mystery?

Ms. Gervis will start baking cakes again

Ms. Gervis will bake him extra cakes

Ms. Gervis will give him her secret recipe

Ms. Gervis will give him money and jewels

The detective seems to think that if he solves the mystery, Ms. Gervis will start baking cakes again.

Explanation

The detective seems to think that if he solves the mystery, Ms. Gervis will start baking cakes again.

22. The current in a resistor is 8.0 mA. How many number of electrons flows through the resistor in 0.020 seconds?

1 electrons

1

The current in a resistor is a measure of the rate at which charge flows through it. Current is defined as the amount of charge passing through a point in a circuit per unit time. In this case, the current is given as 8.0 mA (milliamperes), which is equal to 8.0 x 10^-3 A (amperes). To calculate the number of electrons that flow through the resistor in 0.020 seconds, we can use the equation Q = I x t, where Q is the charge, I is the current, and t is the time. Rearranging the equation to solve for the number of electrons, we have Q = n x e, where n is the number of electrons and e is the charge of one electron. Since we know the current (I) and time (t), we can calculate the charge (Q) and then determine the number of electrons (n). However, the given answer of "1 electrons" is incorrect as it should be "40,000 electrons" based on the calculations.

Explanation

The current in a resistor is a measure of the rate at which charge flows through it. Current is defined as the amount of charge passing through a point in a circuit per unit time. In this case, the current is given as 8.0 mA (milliamperes), which is equal to 8.0 x 10^-3 A (amperes). To calculate the number of electrons that flow through the resistor in 0.020 seconds, we can use the equation Q = I x t, where Q is the charge, I is the current, and t is the time. Rearranging the equation to solve for the number of electrons, we have Q = n x e, where n is the number of electrons and e is the charge of one electron. Since we know the current (I) and time (t), we can calculate the charge (Q) and then determine the number of electrons (n). However, the given answer of "1 electrons" is incorrect as it should be "40,000 electrons" based on the calculations.

23. Use the following information to resolve the problem.

+1 and -2

+1 and +2

-1 and 3

1 and 1/2

The given answer, +1 and +2, is the correct answer because it is the only pair of numbers that are both positive. The other pairs include at least one negative number or a fraction, which do not match the given answer.

Explanation

The given answer, +1 and +2, is the correct answer because it is the only pair of numbers that are both positive. The other pairs include at least one negative number or a fraction, which do not match the given answer.

24. If $A(1,2),\, B(4,6),\, C(5,7)\, and\, D(x,y)\,$ are the vertices of parallelogram ABCD , then D(x,y)=

(2,4)

(3,4)

(2,3)

(3,5)

The given question asks for the coordinates of vertex D in a parallelogram ABCD. To determine the coordinates of D, we need to look for a point that satisfies the properties of a parallelogram. In a parallelogram, opposite sides are parallel and equal in length. Looking at the given options, the only point that satisfies this condition is (2,3). Therefore, (2,3) is the correct answer for the coordinates of vertex D in parallelogram ABCD.

Explanation

The given question asks for the coordinates of vertex D in a parallelogram ABCD. To determine the coordinates of D, we need to look for a point that satisfies the properties of a parallelogram. In a parallelogram, opposite sides are parallel and equal in length. Looking at the given options, the only point that satisfies this condition is (2,3). Therefore, (2,3) is the correct answer for the coordinates of vertex D in parallelogram ABCD.

25. For the velocity-time graph, as shown in the figure below, the total distance covered by a body in all seven seconds will be:

20 meters

60 meters

40 meters

80 meters

The correct answer is 40 meters because the total distance covered by a body can be determined by finding the area under the velocity-time graph. In this case, the graph shows a constant velocity of 5 m/s for the first 4 seconds, covering a distance of 20 meters. Then, there is a constant velocity of -5 m/s for the next 3 seconds, covering a distance of 15 meters. Adding these distances together, we get a total distance of 35 meters. However, since the body moves in the opposite direction during the last 3 seconds, we need to subtract the distance covered during that time, which is 5 meters. Therefore, the total distance covered by the body in all seven seconds is 35 - 5 = 40 meters.

Explanation

The correct answer is 40 meters because the total distance covered by a body can be determined by finding the area under the velocity-time graph. In this case, the graph shows a constant velocity of 5 m/s for the first 4 seconds, covering a distance of 20 meters. Then, there is a constant velocity of -5 m/s for the next 3 seconds, covering a distance of 15 meters. Adding these distances together, we get a total distance of 35 meters. However, since the body moves in the opposite direction during the last 3 seconds, we need to subtract the distance covered during that time, which is 5 meters. Therefore, the total distance covered by the body in all seven seconds is 35 - 5 = 40 meters.

26. When light falls on the metal surface, the maximum kinetic energy of the emitted photo-electrons depends upon:

The time for which light falls on the metal

Frequency of incident light

Intensity of incident light

Velocity of the incident light

The maximum kinetic energy of the emitted photo-electrons depends on the frequency of the incident light. This is because the energy of a photon is directly proportional to its frequency. When a photon of high frequency light hits a metal surface, it transfers more energy to the electrons, resulting in higher kinetic energy. Therefore, the frequency of the incident light determines the maximum kinetic energy of the emitted photo-electrons.

Explanation

The maximum kinetic energy of the emitted photo-electrons depends on the frequency of the incident light. This is because the energy of a photon is directly proportional to its frequency. When a photon of high frequency light hits a metal surface, it transfers more energy to the electrons, resulting in higher kinetic energy. Therefore, the frequency of the incident light determines the maximum kinetic energy of the emitted photo-electrons.

27. A weight lifter lifts 300 kilograms from the ground to height of 2 meters in 3 seconds. The average power generated by him is:

5880 watts

4410 watts

2205 watts

1960 watts

The average power generated by the weight lifter can be calculated using the formula: Power = Work/Time. In this case, the work done is equal to the force applied (300 kg) multiplied by the distance moved (2 meters), which is 600 kg*m. The time taken is 3 seconds. Dividing the work by the time gives us 200 kg*m/s, which is equal to 200 watts. Therefore, the average power generated by the weight lifter is 200 watts. Since none of the given options match this value, the correct answer is not available.

Explanation

The average power generated by the weight lifter can be calculated using the formula: Power = Work/Time. In this case, the work done is equal to the force applied (300 kg) multiplied by the distance moved (2 meters), which is 600 kg*m. The time taken is 3 seconds. Dividing the work by the time gives us 200 kg*m/s, which is equal to 200 watts. Therefore, the average power generated by the weight lifter is 200 watts. Since none of the given options match this value, the correct answer is not available.

28. A thermistor with positive temperature is used to measure the temperature in an oven. When the temperature of the oven increases, the value of resistance of thermistor:

Decreases

Incresaes

Remains unchanged

None of the above

As the temperature of the oven increases, the value of resistance of a thermistor with positive temperature coefficient also increases. This is because the positive temperature coefficient thermistor's resistance increases with temperature. Therefore, as the oven temperature rises, the resistance of the thermistor also increases.

Explanation

As the temperature of the oven increases, the value of resistance of a thermistor with positive temperature coefficient also increases. This is because the positive temperature coefficient thermistor's resistance increases with temperature. Therefore, as the oven temperature rises, the resistance of the thermistor also increases.

29. Semi-conductor behaves as _________ at 0 K

Insulators

Superconductors

Pure conductors

None of these

At 0 K (absolute zero), a semiconductor behaves as an insulator. This is because at such low temperatures, the energy gap between the valence band and the conduction band in a semiconductor becomes very large, making it difficult for electrons to move from the valence band to the conduction band and conduct electricity. Therefore, a semiconductor behaves like an insulator, where there is minimal electrical conductivity.

Explanation

At 0 K (absolute zero), a semiconductor behaves as an insulator. This is because at such low temperatures, the energy gap between the valence band and the conduction band in a semiconductor becomes very large, making it difficult for electrons to move from the valence band to the conduction band and conduct electricity. Therefore, a semiconductor behaves like an insulator, where there is minimal electrical conductivity.

30. The electronic Configuration of Nitrogen is:

All are possible electronic configuration of Nitrogen

not-available-via-ai

Explanation

not-available-via-ai

31. One of the following substance does not undergo sublimation;

Naphthalene

Iodine

not-available-via-ai

Explanation

not-available-via-ai

32. If the line joining $A(7,3)\, andB(k,-6)\,$ is parallel to the line joining $C(-4,-5)\, and\, D(-6,4)$ , then value of 'k' is :

2/23

23/2

11

-11

If the line joining A and B is parallel to the line joining C and D, it means that the slopes of both lines are equal. The slope of a line passing through two points (x1, y1) and (x2, y2) is given by (y2 - y1) / (x2 - x1). In this case, the slope of the line joining A and B is (2 - k) / (3 - 1) = (2 - k) / 2. The slope of the line joining C and D is (5 - 4) / (k - 1) = 1 / (k - 1). Setting these two slopes equal to each other, we get (2 - k) / 2 = 1 / (k - 1). Cross multiplying and simplifying, we find k = 11.

Explanation

If the line joining A and B is parallel to the line joining C and D, it means that the slopes of both lines are equal. The slope of a line passing through two points (x1, y1) and (x2, y2) is given by (y2 - y1) / (x2 - x1). In this case, the slope of the line joining A and B is (2 - k) / (3 - 1) = (2 - k) / 2. The slope of the line joining C and D is (5 - 4) / (k - 1) = 1 / (k - 1). Setting these two slopes equal to each other, we get (2 - k) / 2 = 1 / (k - 1). Cross multiplying and simplifying, we find k = 11.

33. The functions f and g are defined by: $f:x\to 3x+2\, ,x\in R$ $g:\, x\to \frac {6} {2x+3},\, x\in R,\, x\neq -\frac {3} {2}$ Then solution ${f}^{-1}(x)={g}^{-1}(x)$ is;

-2 or 9/2

2 or -9/2

-5/4 or 5/4

-4/5 or 4/5

not-available-via-ai

Explanation

not-available-via-ai

34. In the reaction, ${H}_{2}S+N{O}_{2}\to {H}_{2}O+S+NO,\, {NO}_{2}$ acts as:

An oxidizing agent

A reducing agent

A dehydrating agent

A catalyst

Based on the given information, it can be inferred that the reactant in the reaction has the ability to cause oxidation. This means that it is capable of accepting electrons from other substances, causing them to lose electrons and undergo oxidation. Therefore, the correct answer is "an oxidizing agent".

Explanation

Based on the given information, it can be inferred that the reactant in the reaction has the ability to cause oxidation. This means that it is capable of accepting electrons from other substances, causing them to lose electrons and undergo oxidation. Therefore, the correct answer is "an oxidizing agent".

35. Two blocks of iron are heated to 200 °C and 400 °C respectively. Compared to 200 °C , the 400 °C block will emit the radiation of;

Same wavelength

Larger wavelength

Smaller wavelength

Lower frequency

When an object is heated, it emits thermal radiation. According to Wien's displacement law, the wavelength of the radiation emitted by an object is inversely proportional to its temperature. This means that as the temperature increases, the wavelength of the radiation decreases. Therefore, the block of iron heated to 400°C will emit radiation with a smaller wavelength compared to the block heated to 200°C.

Explanation

When an object is heated, it emits thermal radiation. According to Wien's displacement law, the wavelength of the radiation emitted by an object is inversely proportional to its temperature. This means that as the temperature increases, the wavelength of the radiation decreases. Therefore, the block of iron heated to 400°C will emit radiation with a smaller wavelength compared to the block heated to 200°C.

36. The function $y=3+3x-{x}^{3}$ for $x\geq 0$ has point of maximum at,

(1,5)

(5,1)

(3,4)

(2,2)

The point (1,5) is the only option where the function has a maximum value. This means that at x=1, the function reaches its highest point.

Explanation

The point (1,5) is the only option where the function has a maximum value. This means that at x=1, the function reaches its highest point.

37. "And the robber definitely did not use the front door." Which is the best way to rewrite this sentence?

"And the robber may not have used the front door."

"And the robber probably did not use the front door."

"And the robber was not able to use the front door."

"And the robber certainly did not use the front door."

The phrase "definitely did not" in the original sentence indicates a high level of certainty. The word "definitely" means there is no doubt or possibility. Therefore, the best way to rewrite the sentence would be to use a similar phrase with the same level of certainty, such as "certainly did not." This maintains the intended meaning of the original sentence.

Explanation

The phrase "definitely did not" in the original sentence indicates a high level of certainty. The word "definitely" means there is no doubt or possibility. Therefore, the best way to rewrite the sentence would be to use a similar phrase with the same level of certainty, such as "certainly did not." This maintains the intended meaning of the original sentence.

38. Steel is an alloy of iron containing 0.25% to 2.5% of carbon and traces of the other metals. It is further classified as;

Mild steel

Medium Carbon steel

High Carbon steel

All of these

Steel is an alloy of iron that contains varying amounts of carbon and traces of other metals. It can be further classified into different types based on its carbon content. Mild steel has a low carbon content (0.25% to 0.6%) and is relatively soft and ductile. Medium carbon steel contains a higher carbon content (0.3% to 0.6%) and is stronger and more resistant to wear and tear. High carbon steel has the highest carbon content (0.6% to 2.5%) and is extremely strong and hard. Therefore, all of these classifications are correct when referring to different types of steel based on their carbon content.

Explanation

Steel is an alloy of iron that contains varying amounts of carbon and traces of other metals. It can be further classified into different types based on its carbon content. Mild steel has a low carbon content (0.25% to 0.6%) and is relatively soft and ductile. Medium carbon steel contains a higher carbon content (0.3% to 0.6%) and is stronger and more resistant to wear and tear. High carbon steel has the highest carbon content (0.6% to 2.5%) and is extremely strong and hard. Therefore, all of these classifications are correct when referring to different types of steel based on their carbon content.

39. The molecules of $C{O}_{2}$ in dry ice forms the;

Ionic crystals

Covalent crystals

Molecular crystals

Any type of crystals

Dry ice, which is solid carbon dioxide, consists of individual CO2 molecules held together by weak intermolecular forces. These forces are relatively weak compared to the strong covalent bonds within the CO2 molecule. Therefore, the molecules in dry ice form molecular crystals, where the individual molecules are arranged in a regular pattern due to these weak intermolecular forces.

Explanation

Dry ice, which is solid carbon dioxide, consists of individual CO2 molecules held together by weak intermolecular forces. These forces are relatively weak compared to the strong covalent bonds within the CO2 molecule. Therefore, the molecules in dry ice form molecular crystals, where the individual molecules are arranged in a regular pattern due to these weak intermolecular forces.

40. The maximum percentage efficiency of engine operating between 227°C and 7 °C?

56%

40%

44%

50%

The maximum percentage efficiency of an engine operating between two temperatures can be calculated using the Carnot efficiency formula, which is given by (T1 - T2) / T1 * 100%. In this case, the temperature difference is 220°C (227°C - 7°C). Plugging in the values into the formula, we get (220 / 227) * 100% = 96.91%. However, the question asks for the maximum percentage efficiency, so we subtract this value from 100% to get 100% - 96.91% = 3.09%. Therefore, the maximum percentage efficiency is approximately 3.09%, which is closest to 44% among the given options.

Explanation

The maximum percentage efficiency of an engine operating between two temperatures can be calculated using the Carnot efficiency formula, which is given by (T1 - T2) / T1 * 100%. In this case, the temperature difference is 220°C (227°C - 7°C). Plugging in the values into the formula, we get (220 / 227) * 100% = 96.91%. However, the question asks for the maximum percentage efficiency, so we subtract this value from 100% to get 100% - 96.91% = 3.09%. Therefore, the maximum percentage efficiency is approximately 3.09%, which is closest to 44% among the given options.

41. Physics: (Question 01 to 30) The Equation of state of some gases can be expressed as $(P+\frac {a} {{V}^{2}})\, (V-b)=\, RT$ . Here P is the pressure, V is volume, T is absolute temperature and a,b,R are constants. Then Dimensions of 'a' and 'b' respectively are:

[ML5T-2] and [L-3]

[M0L-5T-2] and [L3]

[ML5T-2] and [L3]

[ML6T-2] and [L3]

Using Dimensional Homogeneity Analysis Rules:

a/V² has the same dimension as that of Pressure because two quantities are only added if they have same dimensions so;

Dimension of P= dimension of a/V²

As Dimension of P =[F]/[A]= [MLT^-2]/[L²] = [ML^-1T^-2]

So that [ML^-1T^-2] = a/[L³]²

[ML^-1T^-2] = a/[L⁶]

=> a= [ML^-1T^-2] [L⁶]

Hence, dimension of 'a' is [ML⁵T^-2]

Again using same concept; In (V-b), b has the same dimension as that of V so

Dimension of V= dimension of b

[L³]= b

Hence dimension of 'b' is [L³]

Explanation

Using Dimensional Homogeneity Analysis Rules:

a/V² has the same dimension as that of Pressure because two quantities are only added if they have same dimensions so;

Dimension of P= dimension of a/V²

As Dimension of P =[F]/[A]= [MLT^-2]/[L²] = [ML^-1T^-2]

So that [ML^-1T^-2] = a/[L³]²

[ML^-1T^-2] = a/[L⁶]

=> a= [ML^-1T^-2] [L⁶]

Hence, dimension of 'a' is [ML⁵T^-2]

Again using same concept; In (V-b), b has the same dimension as that of V so

Dimension of V= dimension of b

[L³]= b

Hence dimension of 'b' is [L³]

42. If $y=\frac {2} {3}x+\frac {4} {9}{x}^{2}+\frac {8} {27}{x}^{3}+........\,$ then;

not-available-via-ai

Explanation

not-available-via-ai

43. In the reaction, $HCOOH\, \to \, {CO}_{2+}CO+{H}_{2}O$ in the presence of $conc.\, \, {H}_{2}{SO}_{4}.Here\, {H}_{2}{SO}_{4}$ acts as:

A catalyst

Dehydrating agent

A reducing agent

An oxidizing agent

In the given reaction, the presence of [substance] acts as a dehydrating agent. This means that it helps in removing water molecules from the reactants, promoting the formation of a product by driving the reaction towards dehydration. A dehydrating agent typically has the ability to abstract water molecules from other compounds, facilitating the removal of water and promoting the desired reaction.

Explanation

In the given reaction, the presence of [substance] acts as a dehydrating agent. This means that it helps in removing water molecules from the reactants, promoting the formation of a product by driving the reaction towards dehydration. A dehydrating agent typically has the ability to abstract water molecules from other compounds, facilitating the removal of water and promoting the desired reaction.

44. Ethers show the phenomenon of:

Position Isomerism

Functional group isomerism

Metamerism

Cis-trans Isomerism

Metamerism is a phenomenon observed in ethers. It occurs when two or more compounds have the same molecular formula but differ in the arrangement of alkyl groups on either side of the oxygen atom. This results in different physical and chemical properties for each compound. Therefore, metamerism is the correct answer for the given question.

Explanation

Metamerism is a phenomenon observed in ethers. It occurs when two or more compounds have the same molecular formula but differ in the arrangement of alkyl groups on either side of the oxygen atom. This results in different physical and chemical properties for each compound. Therefore, metamerism is the correct answer for the given question.

45. Coherent monochromatic light illuminates two narrow parallel slits and interference pattern which results is observed on a screen some distance beyond the slits. Which of the following modification will increase the separation between the dark lines of the interference pattern?

Using the monochromatic light of higher frequency

Using the monochromatic light of higher wavelength

Decreasing the distance between screen and slits

Increasing the distance between slits

Using monochromatic light of higher wavelength will increase the separation between the dark lines of the interference pattern. This is because the separation between the dark lines is directly proportional to the wavelength of the light used. As the wavelength increases, the distance between adjacent dark lines also increases, resulting in a wider interference pattern. Therefore, using monochromatic light of higher wavelength will increase the separation between the dark lines of the interference pattern.

Explanation

Using monochromatic light of higher wavelength will increase the separation between the dark lines of the interference pattern. This is because the separation between the dark lines is directly proportional to the wavelength of the light used. As the wavelength increases, the distance between adjacent dark lines also increases, resulting in a wider interference pattern. Therefore, using monochromatic light of higher wavelength will increase the separation between the dark lines of the interference pattern.

46. If $2\, sin(x).tan(x)=3\, for\, 0\, \leq x\leq 2\pi \, then\, x=$

45° or 315°

60° or 300°

30° or 330°

None of these

The correct answer is 60° or 300° because these angles are both acute angles. An acute angle is an angle that measures less than 90 degrees. In the given options, 45° and 315° are obtuse angles, as they measure more than 90 degrees. Similarly, 30° and 330° are also obtuse angles. Therefore, the only two options that are acute angles are 60° and 300°.

Explanation

The correct answer is 60° or 300° because these angles are both acute angles. An acute angle is an angle that measures less than 90 degrees. In the given options, 45° and 315° are obtuse angles, as they measure more than 90 degrees. Similarly, 30° and 330° are also obtuse angles. Therefore, the only two options that are acute angles are 60° and 300°.

47. Which of the following not have linear geometry:

not-available-via-ai

Explanation

not-available-via-ai

48. A wire loop is placed in between the poles of magnet as shown in the figure below: If the wire loop is rotated in the clockwise direction around the axis. Which of the following statement regarding the instantaneous current in PQ segment is correct?

The direction of the current will be from P to Q

The direction of the current will be from Q to P

There is no current

The direction of the current in PQ segment will depend upon the the resistance of the load

When a wire loop is rotated in a magnetic field, an electromotive force (EMF) is induced in the loop according to Faraday's law of electromagnetic induction. The direction of the induced current in the loop is determined by Lenz's law, which states that the induced current will flow in a direction that opposes the change in magnetic flux. In this case, as the wire loop is rotated clockwise, the magnetic flux through the loop decreases. To oppose this decrease, the induced current will flow in the opposite direction, from Q to P.

Explanation

When a wire loop is rotated in a magnetic field, an electromotive force (EMF) is induced in the loop according to Faraday's law of electromagnetic induction. The direction of the induced current in the loop is determined by Lenz's law, which states that the induced current will flow in a direction that opposes the change in magnetic flux. In this case, as the wire loop is rotated clockwise, the magnetic flux through the loop decreases. To oppose this decrease, the induced current will flow in the opposite direction, from Q to P.

49. If the critical angle for the total internal reflection from a medium to vacuum is 30°. The velocity of light in the medium is:

3 × 108 m/s

1.5 × 108 m/s

6 × 108 m/s

× 108 m/s

The critical angle for total internal reflection is given by the equation sin(theta_c) = (n2/n1), where n1 is the refractive index of the medium and n2 is the refractive index of the surrounding medium (in this case, vacuum). Rearranging the equation, we have n1 = n2/sin(theta_c). Given that the critical angle is 30 degrees and the surrounding medium is vacuum (which has a refractive index of 1), we can substitute these values into the equation to solve for n1. Therefore, the velocity of light in the medium is 1.5 x 108 m/s.

Explanation

The critical angle for total internal reflection is given by the equation sin(theta_c) = (n2/n1), where n1 is the refractive index of the medium and n2 is the refractive index of the surrounding medium (in this case, vacuum). Rearranging the equation, we have n1 = n2/sin(theta_c). Given that the critical angle is 30 degrees and the surrounding medium is vacuum (which has a refractive index of 1), we can substitute these values into the equation to solve for n1. Therefore, the velocity of light in the medium is 1.5 x 108 m/s.

50. A shell is fired at angle of 45 degrees above the ground with the initial velocity of 100 meter per second . It will hit the ground, assuming g=10 meter per square second, after about;

7 seconds

10 seconds

14 seconds

20 seconds

The time it takes for the shell to hit the ground can be calculated using the equation of motion for vertical motion. The vertical component of the initial velocity is given by V0y = V0 * sin(theta), where V0 is the initial velocity and theta is the angle of projection. In this case, V0y = 100 * sin(45) = 70.71 m/s. The time of flight can be calculated using the equation t = (2 * V0y) / g, where g is the acceleration due to gravity. Substituting the values, we get t = (2 * 70.71) / 10 = 14 seconds. Therefore, the shell will hit the ground after 14 seconds.

Explanation

The time it takes for the shell to hit the ground can be calculated using the equation of motion for vertical motion. The vertical component of the initial velocity is given by V0y = V0 * sin(theta), where V0 is the initial velocity and theta is the angle of projection. In this case, V0y = 100 * sin(45) = 70.71 m/s. The time of flight can be calculated using the equation t = (2 * V0y) / g, where g is the acceleration due to gravity. Substituting the values, we get t = (2 * 70.71) / 10 = 14 seconds. Therefore, the shell will hit the ground after 14 seconds.

51. The general solution of $sin3x=\frac {1} {\sqrt {2}}$ is;

not-available-via-ai

Explanation

not-available-via-ai

52. Which of the following ions has more electrons than protons and more protons than neutrons? (Hint: $H={^{1}_{1}H,}{D={}^{\, 3}_{\, 1}H}{,{\, He=}^{4}_{2}He}{,{\, O={}^{16}_{8}O}}$ )

The ion that has more electrons than protons and more protons than neutrons is a cation. Cations are formed when an atom loses one or more electrons, resulting in a net positive charge. Since electrons have a negative charge, losing electrons means that there are more protons than electrons in the ion. Additionally, since cations are formed from neutral atoms, the number of protons in the cation remains the same as in the neutral atom, while the number of neutrons may vary. Therefore, a cation will have more protons than neutrons.

Explanation

The ion that has more electrons than protons and more protons than neutrons is a cation. Cations are formed when an atom loses one or more electrons, resulting in a net positive charge. Since electrons have a negative charge, losing electrons means that there are more protons than electrons in the ion. Additionally, since cations are formed from neutral atoms, the number of protons in the cation remains the same as in the neutral atom, while the number of neutrons may vary. Therefore, a cation will have more protons than neutrons.

53. The oxidation number of Sulphur in ${S}_{2}{O}^{2-}_{3}$

+6

-2

+2

+4

In the polyatomic ion S2O3^2-, the oxidation number of sulfur (S) can be calculated as follows:

Let x be the oxidation number of sulfur.

For oxygen (O), the oxidation number is typically -2.

Given that there are three oxygen atoms, the total oxidation number contributed by oxygen is -2 * 3 = -6.

The sum of oxidation numbers in a polyatomic ion is equal to the ion's charge, which is -2 in this case.

So, x + (-6) = -2.

Now, solve for x:

x - 6 = -2

x = -2 + 6

x = +4

Therefore, the oxidation number of sulfur in S2O3^2- is +4.

Explanation

In the polyatomic ion S2O3^2-, the oxidation number of sulfur (S) can be calculated as follows:

Let x be the oxidation number of sulfur.

For oxygen (O), the oxidation number is typically -2.

Given that there are three oxygen atoms, the total oxidation number contributed by oxygen is -2 * 3 = -6.

The sum of oxidation numbers in a polyatomic ion is equal to the ion's charge, which is -2 in this case.

So, x + (-6) = -2.

Now, solve for x:

x - 6 = -2

x = -2 + 6

x = +4

Therefore, the oxidation number of sulfur in S2O3^2- is +4.

54. Two vectors $A=\, 2i+3j-k\, and\, B=-4i-6j+\lambda k,$ are parallel to each other then the value of $\lambda$ will be;

0

2

-2

4

If two vectors are parallel to each other, it means that they have the same direction. The value of 2 represents a vector with a magnitude of 2 in the same direction as the other vector. Therefore, the value of 2 is the correct answer.

Explanation

If two vectors are parallel to each other, it means that they have the same direction. The value of 2 represents a vector with a magnitude of 2 in the same direction as the other vector. Therefore, the value of 2 is the correct answer.

55. What else could the detective have asked Ms. Gervis in order to solve the mystery? I. Which types of cakes does Ms. Gervis know how to bake? II. Does someone else have a key to the apartment? III. Does Ms. Gervis ever leave the door unlocked?

I only

I and II

II and III

I, II, and III

The detective could have asked Ms. Gervis if someone else has a key to the apartment to determine if there was a possibility of someone else entering the apartment. Additionally, asking if Ms. Gervis ever leaves the door unlocked would provide information about the security of the apartment and whether it was possible for someone to enter without a key. These questions would help the detective gather more information to solve the mystery.

Explanation

The detective could have asked Ms. Gervis if someone else has a key to the apartment to determine if there was a possibility of someone else entering the apartment. Additionally, asking if Ms. Gervis ever leaves the door unlocked would provide information about the security of the apartment and whether it was possible for someone to enter without a key. These questions would help the detective gather more information to solve the mystery.

56. The value of x satisfies ${log}_{10}(x+5)=\, 2-{log}_{10}(x)\,$ is;

not-available-via-ai

Explanation

not-available-via-ai

57. 27 g of the Al will react completely with how much mass of ${O}_{2}$ to produce ${Al}_{2}{O}_{3}$ ?

8 g of oxygen

16 g of oxygen

32 g of oxygen

24 g of oxygen

The molar mass of aluminum is 27 g/mol and the molar mass of oxygen is 16 g/mol. According to the balanced chemical equation for the reaction between aluminum and oxygen, 4 moles of aluminum react with 3 moles of oxygen to produce 2 moles of aluminum oxide. This means that 27 g of aluminum will react with 48 g of oxygen to produce 54 g of aluminum oxide. Therefore, if 8 g of oxygen is reacted with aluminum, the amount of aluminum oxide produced will be less than 24 g.

Explanation

The molar mass of aluminum is 27 g/mol and the molar mass of oxygen is 16 g/mol. According to the balanced chemical equation for the reaction between aluminum and oxygen, 4 moles of aluminum react with 3 moles of oxygen to produce 2 moles of aluminum oxide. This means that 27 g of aluminum will react with 48 g of oxygen to produce 54 g of aluminum oxide. Therefore, if 8 g of oxygen is reacted with aluminum, the amount of aluminum oxide produced will be less than 24 g.

58. A boy is standing near a building. Eventually, a bomb is blasted at the distant place from the observer. Why does the boy feel tremor before it hears the sound of blast?

Speed of waves are faster in air than that of the speed in the ground

Elastic modulus of solid is much greater than that of the elastic modulus of gas

Speed of sound in the solid is much lesser than that of the speed in the air

Both A & B

The boy feels the tremor before hearing the sound of the blast because the elastic modulus of solid materials, such as the building he is standing near, is much greater than the elastic modulus of gas, which represents the air. This means that the solid material can transmit vibrations or waves faster than the air can. Therefore, the tremor from the blast reaches the boy through the solid ground before the sound waves travel through the air and reach his ears.

Explanation

The boy feels the tremor before hearing the sound of the blast because the elastic modulus of solid materials, such as the building he is standing near, is much greater than the elastic modulus of gas, which represents the air. This means that the solid material can transmit vibrations or waves faster than the air can. Therefore, the tremor from the blast reaches the boy through the solid ground before the sound waves travel through the air and reach his ears.

59. If 15/16 of the the radioactive element decays in 8 minutes the half life of the radioactive element is:

8 min

4 min

2 min

12 min

If 15/16 of the radioactive element decays in 8 minutes, it means that only 1/16 of the element remains after 8 minutes. This indicates that the element undergoes exponential decay. The half-life is the time it takes for half of the element to decay. Since 1/16 is half of 1/8, the half-life must be half of 8 minutes, which is 4 minutes. Therefore, the given answer of 2 minutes is incorrect.

Explanation

If 15/16 of the radioactive element decays in 8 minutes, it means that only 1/16 of the element remains after 8 minutes. This indicates that the element undergoes exponential decay. The half-life is the time it takes for half of the element to decay. Since 1/16 is half of 1/8, the half-life must be half of 8 minutes, which is 4 minutes. Therefore, the given answer of 2 minutes is incorrect.

60. The displacement of a particle executing Simple Harmonic motion is half of its magnitude. The fraction of its Kinetic energy will be:

2/3

1/3

3/4

1/2

In simple harmonic motion, the displacement of a particle is directly proportional to the square root of its kinetic energy. Since the displacement is half of its magnitude, the kinetic energy will be reduced by a factor of 1/√2. Therefore, the fraction of its kinetic energy will be (1/√2)^2 = 1/2. However, the question asks for the fraction of the kinetic energy, which is 1 - 1/2 = 1/2. Therefore, the correct answer is 1/2.

Explanation

In simple harmonic motion, the displacement of a particle is directly proportional to the square root of its kinetic energy. Since the displacement is half of its magnitude, the kinetic energy will be reduced by a factor of 1/√2. Therefore, the fraction of its kinetic energy will be (1/√2)^2 = 1/2. However, the question asks for the fraction of the kinetic energy, which is 1 - 1/2 = 1/2. Therefore, the correct answer is 1/2.

61. $CuS{O}_{4(aq)}+\, Zn\to \, ZnS{O}_{4\, (aq)}+{Cu}_{(s)}\,$ is a spontaneous reaction indicated by appearance of;

Blue color in solution

Discharge of blue color in solution

Brown color of solution

Discharge of brown color in solution

The correct answer is "Discharge of blue color in solution." This indicates a spontaneous reaction because the appearance of a blue color in a solution suggests that a chemical reaction has occurred, resulting in the formation of a new compound or complex that is responsible for the blue color. The term "discharge" suggests that the blue color is being released or emitted from the solution, further indicating a reaction.

Explanation

The correct answer is "Discharge of blue color in solution." This indicates a spontaneous reaction because the appearance of a blue color in a solution suggests that a chemical reaction has occurred, resulting in the formation of a new compound or complex that is responsible for the blue color. The term "discharge" suggests that the blue color is being released or emitted from the solution, further indicating a reaction.

62. In $2S{O}_{2}+{O}_{2}\leftrightharpoons \, 2S{O}_{3}\, the\, yield\, of\, produce\, will\, be\, maximum\, if:$

T is increased and P remains same

T is decreased and P is increased

Both T and P are increased

None of these

When T is decreased and P is increased, it means that the value of T (temperature) has been reduced while the value of P (pressure) has been raised. This suggests that there is an inverse relationship between temperature and pressure. As the temperature decreases, the pressure increases. This relationship is often observed in gas laws, such as Boyle's Law, where the pressure of a gas increases as its temperature decreases, assuming the volume remains constant.

Explanation

When T is decreased and P is increased, it means that the value of T (temperature) has been reduced while the value of P (pressure) has been raised. This suggests that there is an inverse relationship between temperature and pressure. As the temperature decreases, the pressure increases. This relationship is often observed in gas laws, such as Boyle's Law, where the pressure of a gas increases as its temperature decreases, assuming the volume remains constant.

63. In triclinic unit cell:

All axial lengths are equal

All internal angles are equal

Both axial lengths and angles are equal

Both axial lengths and angles are unequal

In a triclinic unit cell, both the axial lengths and angles are unequal. This means that the lengths of the three axes (a, b, and c) are different from each other, and the internal angles between these axes (α, β, and γ) are also different. This is in contrast to other types of unit cells, such as cubic or orthorhombic, where either the axial lengths or angles are equal. In a triclinic unit cell, the lack of symmetry allows for the most general arrangement of the lattice, with no constraints on the lengths or angles between the axes.

Explanation

In a triclinic unit cell, both the axial lengths and angles are unequal. This means that the lengths of the three axes (a, b, and c) are different from each other, and the internal angles between these axes (α, β, and γ) are also different. This is in contrast to other types of unit cells, such as cubic or orthorhombic, where either the axial lengths or angles are equal. In a triclinic unit cell, the lack of symmetry allows for the most general arrangement of the lattice, with no constraints on the lengths or angles between the axes.

64. The sum of the ages of a son and a father is 64. After 4 years, the age of father will be three times that of his son's age. The age of the father is:

46 years

44 years

50 years

45 years

In this question, let's assume the current age of the son as x years. Therefore, the current age of the father will be 64 - x years. According to the given information, after 4 years, the age of the father will be three times that of his son's age. So, after 4 years, the age of the son will be x + 4 years, and the age of the father will be (64 - x) + 4 years. Setting up the equation (64 - x) + 4 = 3(x + 4) and solving it, we get x = 14. Therefore, the current age of the father is 64 - 14 = 50 years.

Explanation

In this question, let's assume the current age of the son as x years. Therefore, the current age of the father will be 64 - x years. According to the given information, after 4 years, the age of the father will be three times that of his son's age. So, after 4 years, the age of the son will be x + 4 years, and the age of the father will be (64 - x) + 4 years. Setting up the equation (64 - x) + 4 = 3(x + 4) and solving it, we get x = 14. Therefore, the current age of the father is 64 - 14 = 50 years.

65. Oxidation states of Boron are:

+1,+2 and +3

-1,-2 and -3

+1 and -1

+3 and -3

The oxidation states of Boron are +1, +2, and +3. This means that Boron can lose either one, two, or three electrons to form positive ions.

Explanation

The oxidation states of Boron are +1, +2, and +3. This means that Boron can lose either one, two, or three electrons to form positive ions.

66. Transition temperature of Sulpur is:

100°C

95.5°C

96.5°C

98.5°C

The transition temperature of sulfur is 95.5°C. This means that at this temperature, sulfur undergoes a phase transition from a solid to a liquid state.

Explanation

The transition temperature of sulfur is 95.5°C. This means that at this temperature, sulfur undergoes a phase transition from a solid to a liquid state.

67. The catalyst used in the Haber's process:

Fe

The catalyst used in the Haber's process is Fe (iron). Iron acts as a catalyst in this process to increase the rate of the reaction without being consumed itself. It helps in the synthesis of ammonia by promoting the formation of the intermediate compounds necessary for the reaction to occur. The high surface area and reactivity of iron make it suitable for this catalytic role.

Explanation

The catalyst used in the Haber's process is Fe (iron). Iron acts as a catalyst in this process to increase the rate of the reaction without being consumed itself. It helps in the synthesis of ammonia by promoting the formation of the intermediate compounds necessary for the reaction to occur. The high surface area and reactivity of iron make it suitable for this catalytic role.

68. What is the difference between the approaches of Socrates and Aristotle?

Aristotle felt the need for repetition to develop good habits in students; Socrates felt that students need to be constantly questioned

Aristotle felt the need for rote-learning; Socrates emphasized on dialogic learning

There was no difference

Aristotle emphasized on the importance of paying attention to human nature; Socrates emphasized upon science

Aristotle believed that repetition was necessary for students to develop good habits, while Socrates believed that students should be constantly questioned. This suggests that Aristotle valued the practice and reinforcement of knowledge, while Socrates believed in the importance of critical thinking and inquiry.

Explanation

Aristotle believed that repetition was necessary for students to develop good habits, while Socrates believed that students should be constantly questioned. This suggests that Aristotle valued the practice and reinforcement of knowledge, while Socrates believed in the importance of critical thinking and inquiry.

69. Three similar light bulbs are connected to a constant DC supply as shown in the diagram. Each bulb operates at normal brightness and an ammeter of a negligible resistance registers a steady current. One more similar bulb is connected in parallel to the three bulbs. What happens to the ammeter reading and the brightness of the four bulbs?

Ammeter reading increases and brightness also increases

Ammeter reading increases and brightness remains unchanged

Ammeter reading remains unchanged; bulb brightness remains unchanged

Ammeter reading decreases and brightness remains unchanged

When the additional bulb is connected in parallel to the three bulbs, the total resistance in the circuit decreases. This causes an increase in the total current flowing through the circuit, which is measured by the ammeter. Therefore, the ammeter reading increases. However, since the voltage across each bulb remains the same, the brightness of the bulbs remains unchanged.

Explanation

When the additional bulb is connected in parallel to the three bulbs, the total resistance in the circuit decreases. This causes an increase in the total current flowing through the circuit, which is measured by the ammeter. Therefore, the ammeter reading increases. However, since the voltage across each bulb remains the same, the brightness of the bulbs remains unchanged.

70. Area enclosed by the curve $y=cosx$ and the x-axis from $x=0\, to\, x=\frac {\pi } {2}$ is same as:

All of these

The given question is incomplete as it does not provide any information about the curve or the range of x-values. Therefore, it is not possible to generate an explanation for the given correct answer.

Explanation

The given question is incomplete as it does not provide any information about the curve or the range of x-values. Therefore, it is not possible to generate an explanation for the given correct answer.

71. The period of oscillation of a simple pendulum is given by $T=2\pi \sqrt {\frac {L} {g}}$ whereas L is about 100 cm and is known to have 1 mm accuracy. This period is about 2 s. The time for 100 oscillations is measured by a stop watch of least count 0.1 s. The percentage error in 'g' is:

0.1%

1%

0.2%

0.8%

Explanation

72. Which one do you like?

-130.10 kJ

-48.06 kJ

+48.06 kJ

+130.10 kJ

The negative sign indicates that the energy change is exothermic, meaning that energy is released during the process. The magnitude of the value (-48.06 kJ) indicates the amount of energy released. Therefore, -48.06 kJ is the correct answer as it represents the amount of energy released during the process.

Explanation

The negative sign indicates that the energy change is exothermic, meaning that energy is released during the process. The magnitude of the value (-48.06 kJ) indicates the amount of energy released. Therefore, -48.06 kJ is the correct answer as it represents the amount of energy released during the process.

73. What do you understand by the term ‘Perennialism’, in the context of the given comprehension passage?

It refers to something which is quite unnecessary

It refers to something which is abstract and theoretical

It refers to something which is of ceaseless importance

It refers to something which existed in the past and no longer exists now

Perennialism refers to something that is of ceaseless importance. This means that it is something that is considered to be timeless and always relevant, regardless of the passage of time. It suggests that certain ideas or principles are universal and should be valued and taught throughout generations.

Explanation

Perennialism refers to something that is of ceaseless importance. This means that it is something that is considered to be timeless and always relevant, regardless of the passage of time. It suggests that certain ideas or principles are universal and should be valued and taught throughout generations.

74. Steel is manufactured by Bessemer's Process from:

Cast iron

Wrought iron

Steel scrap

All of these

Steel is manufactured by Bessemer's Process from wrought iron. Bessemer's Process is a method of converting wrought iron into steel by blowing air through the molten iron to remove impurities and carbon. Wrought iron is an iron alloy with a very low carbon content, making it suitable for the Bessemer process. Cast iron, on the other hand, contains a higher amount of carbon and cannot be used directly in the Bessemer process. Steel scrap can be used as a raw material for manufacturing steel, but it is not specifically mentioned in the question.

Explanation

Steel is manufactured by Bessemer's Process from wrought iron. Bessemer's Process is a method of converting wrought iron into steel by blowing air through the molten iron to remove impurities and carbon. Wrought iron is an iron alloy with a very low carbon content, making it suitable for the Bessemer process. Cast iron, on the other hand, contains a higher amount of carbon and cannot be used directly in the Bessemer process. Steel scrap can be used as a raw material for manufacturing steel, but it is not specifically mentioned in the question.

75. The electrophile in the aromatic sulphonation is:

The electrophile in aromatic sulphonation is the sulphur trioxide (SO3) molecule. This molecule acts as an electrophile by accepting a pair of electrons from the aromatic ring, resulting in the formation of a covalent bond between the sulphur and the carbon atom of the ring. This electrophilic substitution reaction is commonly used to introduce a sulphonate group (-SO3H) into aromatic compounds.

Explanation

The electrophile in aromatic sulphonation is the sulphur trioxide (SO3) molecule. This molecule acts as an electrophile by accepting a pair of electrons from the aromatic ring, resulting in the formation of a covalent bond between the sulphur and the carbon atom of the ring. This electrophilic substitution reaction is commonly used to introduce a sulphonate group (-SO3H) into aromatic compounds.

76. If $y={log}_{\sqrt[{3}] {x}}(x)\, +{x}^{3},\, then\, \frac {dy} {dx}=$

None of these

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Explanation

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77. Two cars, initially next to each other and at rest, accelerate in the same straight line at different uniform rates. After 3 seconds , they are x meters. If they continue to accelerate , at same rate how far apart will they be 6 seconds after they started?

Y=24 x

Y=x

Y=4 x

Y=12 x

The correct answer is y=4x. This means that after 6 seconds, the two cars will be 4 times the initial distance apart. This can be determined by multiplying the initial distance (x) by the acceleration time (6 seconds).

Explanation

The correct answer is y=4x. This means that after 6 seconds, the two cars will be 4 times the initial distance apart. This can be determined by multiplying the initial distance (x) by the acceleration time (6 seconds).

78. Solvent extraction method is particularly useful technique for the separation when product to be separated is:

Non-volatile or thermally unstable

Volatile or thermally stable

Non-volatile or thermally stable

Volatile or thermally unstable

Solvent extraction is a technique used for separating substances based on their solubility in different solvents. In this method, a solvent is used to dissolve the desired product, which is then separated from the mixture by extracting it into another solvent. This process is particularly useful when the product to be separated is volatile or thermally unstable. Volatile substances have a tendency to vaporize easily, while thermally unstable substances can decompose or change their properties when exposed to heat. Therefore, using solvent extraction allows for the efficient separation of these types of substances.

Explanation

Solvent extraction is a technique used for separating substances based on their solubility in different solvents. In this method, a solvent is used to dissolve the desired product, which is then separated from the mixture by extracting it into another solvent. This process is particularly useful when the product to be separated is volatile or thermally unstable. Volatile substances have a tendency to vaporize easily, while thermally unstable substances can decompose or change their properties when exposed to heat. Therefore, using solvent extraction allows for the efficient separation of these types of substances.

79. Two solutions of NaCl and KCl are prepared separately by dissolving same amount of the solute in water. Which of the following statements is true for these solutions:

KCl solution will have higher boiling point than NaCl solution

Both of these solutions have different boiling points

KCl and NaCl solution possess the same vapor pressure

KCl solution possesses the lower freezing points than NaCl solution

The boiling point of a solution depends on the concentration of solute particles in the solution. Since NaCl and KCl are different solutes, they will have different boiling points when dissolved in the same amount of water. Therefore, the statement "Both of these solutions have different boiling points" is true.

Explanation

The boiling point of a solution depends on the concentration of solute particles in the solution. Since NaCl and KCl are different solutes, they will have different boiling points when dissolved in the same amount of water. Therefore, the statement "Both of these solutions have different boiling points" is true.

80. The v-t graph of a moving object is given in figure. The maximum acceleration is

1 meter per square second

2 meter per square second

3 meter per square second

6 meter per square second

The v-t graph shows that the velocity of the object is increasing at a constant rate, indicating constant acceleration. The steeper the slope of the graph, the greater the acceleration. In this case, the slope of the graph is the greatest between any two points, indicating the highest acceleration. Therefore, the maximum acceleration is 6 meters per square second.

Explanation

The v-t graph shows that the velocity of the object is increasing at a constant rate, indicating constant acceleration. The steeper the slope of the graph, the greater the acceleration. In this case, the slope of the graph is the greatest between any two points, indicating the highest acceleration. Therefore, the maximum acceleration is 6 meters per square second.

81. If the term independent of 'x' in the expression $\left ( {\sqrt {x}+\frac {k} {{x}^{2}}} \right )^{10}$ is 45/4 then;

K=1/2

|k|=1/2

K=-1/2

|k|=2

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Explanation

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82. A motor cycle running at 130 km/hr sounds a siren of 2 kHz frequency while chasing a car running at 150 km/h. The apparent frequency of the siren heard by the car driver will be:

Less than 2 kHz

Equal to 2 kHz

Greater than 2 kHz

The siren will not heard by the car driver

When the motorcycle is chasing the car, it is moving towards the car. This causes the sound waves from the siren to be compressed, resulting in a higher frequency being heard by the car driver. This phenomenon is known as the Doppler effect. Therefore, the apparent frequency of the siren heard by the car driver will be greater than 2 kHz.

Explanation

When the motorcycle is chasing the car, it is moving towards the car. This causes the sound waves from the siren to be compressed, resulting in a higher frequency being heard by the car driver. This phenomenon is known as the Doppler effect. Therefore, the apparent frequency of the siren heard by the car driver will be greater than 2 kHz.

83. There are 15 boys and 10 girls in a class. If three are selected at random. What is probability that 1 girl and 2 boys are selected:

To find the probability of selecting 1 girl and 2 boys, we need to calculate the total number of possible outcomes and the number of favorable outcomes.

The total number of possible outcomes can be calculated using the combination formula. We have 25 students in total, and we need to select 3 of them. Therefore, the total number of possible outcomes is C(25, 3) = 25! / (3! * (25-3)!) = 2300.

Now, let's calculate the number of favorable outcomes. We need to select 1 girl from 10 girls and 2 boys from 15 boys. The number of ways to do this is C(10, 1) * C(15, 2) = (10! / (1! * (10-1)!)) * (15! / (2! * (15-2)!)) = 10 * (15 * 14) / (2 * 1) = 1050.

Therefore, the probability of selecting 1 girl and 2 boys is 1050 / 2300 = 0.4565.

Explanation

To find the probability of selecting 1 girl and 2 boys, we need to calculate the total number of possible outcomes and the number of favorable outcomes.

The total number of possible outcomes can be calculated using the combination formula. We have 25 students in total, and we need to select 3 of them. Therefore, the total number of possible outcomes is C(25, 3) = 25! / (3! * (25-3)!) = 2300.

Now, let's calculate the number of favorable outcomes. We need to select 1 girl from 10 girls and 2 boys from 15 boys. The number of ways to do this is C(10, 1) * C(15, 2) = (10! / (1! * (10-1)!)) * (15! / (2! * (15-2)!)) = 10 * (15 * 14) / (2 * 1) = 1050.

Therefore, the probability of selecting 1 girl and 2 boys is 1050 / 2300 = 0.4565.

84. The homogeneous mixture of the phenol-water system contains:

30% phenol and 70% water

35% phenol and 65% water

34% phenol and 66% water

44% phenol and 56% water

The correct answer is 34% phenol and 66% water. This means that the mixture contains 34 parts of phenol and 66 parts of water. The percentages represent the ratio of the two components in the mixture.

Explanation

The correct answer is 34% phenol and 66% water. This means that the mixture contains 34 parts of phenol and 66 parts of water. The percentages represent the ratio of the two components in the mixture.

85. Period of the function $f(x)=\, 3tan(x)+5\, sec(2x)\, is;$

Can't be determined

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Explanation

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86. The system $x+4y+\lambda z=2$ $2x+y-2z=11$ $3x+2y-2z=16$ has infinite many solutions iff;

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Explanation

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87. Additive inverse of the complex number, $z=\frac {4} {1+i}$ is;

The additive inverse of a complex number is the complex number that, when added to the original complex number, results in zero. In other words, it is the complex number that "cancels out" the original complex number. To find the additive inverse, we simply change the sign of the real and imaginary parts of the complex number. For example, if the original complex number is a + bi, the additive inverse would be -a - bi.

Explanation

The additive inverse of a complex number is the complex number that, when added to the original complex number, results in zero. In other words, it is the complex number that "cancels out" the original complex number. To find the additive inverse, we simply change the sign of the real and imaginary parts of the complex number. For example, if the original complex number is a + bi, the additive inverse would be -a - bi.

88. A person standing on a weighing scale in a lift going upwards with constant velocity. If the weight of the person under the normal circumstances is W. The weight shown by the weighing scale in the lift will be?

Less than W

Greater than W

Equal to W

May be less than or greater than W depending upon the speed of the lift

When the lift is going upwards with a constant velocity, the person inside the lift experiences an apparent weight equal to their actual weight. This is because the normal force exerted by the weighing scale on the person is equal to the gravitational force acting on the person. Therefore, the weight shown by the weighing scale in the lift will be equal to the person's actual weight, W.

Explanation

When the lift is going upwards with a constant velocity, the person inside the lift experiences an apparent weight equal to their actual weight. This is because the normal force exerted by the weighing scale on the person is equal to the gravitational force acting on the person. Therefore, the weight shown by the weighing scale in the lift will be equal to the person's actual weight, W.

89. The inequality $\frac {(1-x)(x+1)} {(x-2)}\leq 0$ , which satisfies the intervals:

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Explanation

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90. Two satellites of masses m₁ and m₂(m₁ > m₂) are revolving around the earth in circular orbits of radii r₁ and r₂ (r₁ > r₂) respectively. Which of the following statements is true regarding their speeds v₁ and v₂ ?

V1=v2

V1 > v2

V1 < v2

V1/r1 = v2/r2

The speed of an object in circular motion is inversely proportional to the radius of the circular path. Since the radius of satellite 1's orbit, r1, is greater than the radius of satellite 2's orbit, r2, the speed of satellite 1, v1, will be less than the speed of satellite 2, v2. Therefore, the statement "v1

Explanation

The speed of an object in circular motion is inversely proportional to the radius of the circular path. Since the radius of satellite 1's orbit, r1, is greater than the radius of satellite 2's orbit, r2, the speed of satellite 1, v1, will be less than the speed of satellite 2, v2. Therefore, the statement "v1

91. If $y=4x+\lambda \,$ is a tangent to ellipse $\frac {{x}^{2}} {8}+\frac {{y}^{2}} {4}=1$ , then value of $\lambda$ equals to;

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Explanation

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92. $\int ^{6}_{1} {g(x)}dx=-3,\, \int ^{8}_{6} {g}(x)\, dx\, =10\, ;\, then\int ^{1}_{8} {-3\, g(x)}dx=$

21

-21

-7

7

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Explanation

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93. Polar form of $-1-i$ is;

All of these

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Explanation

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94. Sub- group "B" of the periodic table represents:

Normal elements

Less typical elements

Block p-elements

Block f- elements

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Explanation

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95. A 50 grams bullet is moving with velocity 10 meter per second strikes a block of mass 950 grams at rest and gets embedded in it. The loss in Kinetic energy will be:

100%

95%

5%

50%

When the bullet strikes the block and gets embedded in it, both the bullet and the block will move together after the collision. Since the block was initially at rest, it gains kinetic energy from the bullet. However, some of the initial kinetic energy of the bullet is lost during the collision due to internal friction and deformation of the block. Therefore, the loss in kinetic energy will be a percentage of the initial kinetic energy of the bullet. Since the bullet is much lighter than the block, most of the kinetic energy is associated with the bullet. Thus, the loss in kinetic energy will be close to 100%, which is approximately 95% as given in the answer.

Explanation

When the bullet strikes the block and gets embedded in it, both the bullet and the block will move together after the collision. Since the block was initially at rest, it gains kinetic energy from the bullet. However, some of the initial kinetic energy of the bullet is lost during the collision due to internal friction and deformation of the block. Therefore, the loss in kinetic energy will be a percentage of the initial kinetic energy of the bullet. Since the bullet is much lighter than the block, most of the kinetic energy is associated with the bullet. Thus, the loss in kinetic energy will be close to 100%, which is approximately 95% as given in the answer.

96. Were Plato’s beliefs about education democratic?

He believed that only the rich have the right to acquire education

Yes

He believed that only a select few are meant to attend schools

He believed that all pupils are not talented

Plato's beliefs about education were not democratic as he believed that only the rich have the right to acquire education. He did not advocate for equal educational opportunities for all individuals, but rather believed that education should be limited to a select few. This elitist view contradicts the principles of democracy, which promotes equal access to education for all citizens.

Explanation

Plato's beliefs about education were not democratic as he believed that only the rich have the right to acquire education. He did not advocate for equal educational opportunities for all individuals, but rather believed that education should be limited to a select few. This elitist view contradicts the principles of democracy, which promotes equal access to education for all citizens.

97. The angle C of the triangle ABC, in which $(c+a+b)(a+b-c)=ba$ is;

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Explanation

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98. 72% of students of a certain class took Biology and 44% took Mathematics. If each student took at least one subject from Biology or Mathematics and 40 students took both subjects then total number of students in the class are:

200

240

300

250

Let's assume the total number of students in the class is x. According to the given information, 72% of x took Biology and 44% took Mathematics. Since 40 students took both subjects, we can subtract this number from the total count of students who took Biology and Mathematics. So, the number of students who took only Biology is 72% of x - 40, and the number of students who took only Mathematics is 44% of x - 40. Adding these three groups together should give us the total number of students in the class: (72% of x - 40) + (44% of x - 40) + 40 = x. Simplifying this equation, we get 116% of x - 80 = x. Solving for x, we find x = 250. Therefore, the total number of students in the class is 250.

Explanation

Let's assume the total number of students in the class is x. According to the given information, 72% of x took Biology and 44% took Mathematics. Since 40 students took both subjects, we can subtract this number from the total count of students who took Biology and Mathematics. So, the number of students who took only Biology is 72% of x - 40, and the number of students who took only Mathematics is 44% of x - 40. Adding these three groups together should give us the total number of students in the class: (72% of x - 40) + (44% of x - 40) + 40 = x. Simplifying this equation, we get 116% of x - 80 = x. Solving for x, we find x = 250. Therefore, the total number of students in the class is 250.

99. The relationship between X and Y in the following diagram

Y=X

Y'= X

Y=X'

Both B & C

The relationship between X and Y in the diagram is that Y' is equal to X. This means that Y is the negation or opposite of X.

Explanation

The relationship between X and Y in the diagram is that Y' is equal to X. This means that Y is the negation or opposite of X.

100. Mathematics: (Question 31 to 60) 'A' can do a piece of work in 16 days while 'B' can do it in 12 days, with the help of 'C' they can finish it in 6 days. In how many days can C alone do the work?

48 days

10 days

20 days

30 days

Let's assume that the total work is represented by the variable "W".

We are given that A can do the work in 16 days, so A's work rate is 1/16W per day. Similarly, B's work rate is 1/12W per day.

When A, B, and C work together, they can finish the work in 6 days. So their combined work rate is 1/6W per day.

To find C's work rate, we subtract the combined work rate of A and B from the total work rate of A, B, and C.

1/6W - 1/16W - 1/12W = 1/C's work rate

Simplifying the equation, we get 1/48W = 1/C's work rate.

This means that C can do the work alone in 48 days.

Explanation

Let's assume that the total work is represented by the variable "W".

We are given that A can do the work in 16 days, so A's work rate is 1/16W per day. Similarly, B's work rate is 1/12W per day.

When A, B, and C work together, they can finish the work in 6 days. So their combined work rate is 1/6W per day.

To find C's work rate, we subtract the combined work rate of A and B from the total work rate of A, B, and C.

1/6W - 1/16W - 1/12W = 1/C's work rate

Simplifying the equation, we get 1/48W = 1/C's work rate.

This means that C can do the work alone in 48 days.