Pre-ecat Mock Test (Phy/Chem/Math/English)

1. Click the best option

Cot56*

Tan56*

Cos56*

Sin56*

The correct answer is tan56*. The question is asking for the best option when evaluating cot(56). The reciprocal of cot(56) is tan(56), so the correct answer is tan(56)*.

Explanation

The correct answer is tan56*. The question is asking for the best option when evaluating cot(56). The reciprocal of cot(56) is tan(56), so the correct answer is tan(56)*.

2. When water freezes, it occupies

A) 9% more space

B) 9% less space

C) Same amount of space

D) None of the above

When water freezes, it expands and occupies 9% more space. This is due to the formation of ice crystals, which have a larger molecular structure compared to liquid water. As the water molecules arrange themselves in a more ordered pattern, they create empty spaces between them, leading to an increase in volume. This expansion is why ice floats on water, as its density decreases when it freezes.

Explanation

When water freezes, it expands and occupies 9% more space. This is due to the formation of ice crystals, which have a larger molecular structure compared to liquid water. As the water molecules arrange themselves in a more ordered pattern, they create empty spaces between them, leading to an increase in volume. This expansion is why ice floats on water, as its density decreases when it freezes.

3. Molarity of pure water is:

A) 1

B) 18

C) 55.5

D) 6

The molarity of a solution is defined as the number of moles of solute per liter of solution. Pure water does not contain any solute, so its molarity is zero. However, in practice, pure water is slightly ionized into H+ and OH- ions. The concentration of these ions in pure water is very small, but it is still present. The concentration of H+ and OH- ions in pure water is equal and is approximately 1 x 10^-7 moles per liter. Since the molarity is defined as moles of solute per liter of solution, the molarity of pure water is equal to the concentration of H+ or OH- ions, which is approximately 1 x 10^-7 M. However, for simplicity, this value is often rounded to 1 x 10^-7 M, which is approximately equal to 55.5 M when rounded to two significant figures.

Explanation

The molarity of a solution is defined as the number of moles of solute per liter of solution. Pure water does not contain any solute, so its molarity is zero. However, in practice, pure water is slightly ionized into H+ and OH- ions. The concentration of these ions in pure water is very small, but it is still present. The concentration of H+ and OH- ions in pure water is equal and is approximately 1 x 10^-7 moles per liter. Since the molarity is defined as moles of solute per liter of solution, the molarity of pure water is equal to the concentration of H+ or OH- ions, which is approximately 1 x 10^-7 M. However, for simplicity, this value is often rounded to 1 x 10^-7 M, which is approximately equal to 55.5 M when rounded to two significant figures.

4. The main pollutant of leather tanneries in the waste water is due to the salt of:

A) Lead

B) Chromium (VI)

C) Copper

D) Chromium (III)

The main pollutant in the waste water of leather tanneries is chromium (VI). Chromium (VI) is commonly used in the tanning process as a tanning agent. However, it is highly toxic and can cause serious environmental and health problems. When the waste water from tanneries is discharged without proper treatment, it can contaminate water bodies and soil, posing a threat to aquatic life and human health. Therefore, the presence of chromium (VI) in the waste water of leather tanneries is a significant concern.

Explanation

The main pollutant in the waste water of leather tanneries is chromium (VI). Chromium (VI) is commonly used in the tanning process as a tanning agent. However, it is highly toxic and can cause serious environmental and health problems. When the waste water from tanneries is discharged without proper treatment, it can contaminate water bodies and soil, posing a threat to aquatic life and human health. Therefore, the presence of chromium (VI) in the waste water of leather tanneries is a significant concern.

5. When acetylene is heated at 300*C in copper tube, the product obtained is:

A) Benzene

B) Thiophene

C) Xylene

D) Cresol

When acetylene is heated at 300°C in a copper tube, it undergoes a process called pyrolysis, which results in the formation of benzene. This is because acetylene can polymerize and rearrange its structure to form benzene rings under high temperatures. Therefore, the correct answer is A) Benzene.

Explanation

When acetylene is heated at 300°C in a copper tube, it undergoes a process called pyrolysis, which results in the formation of benzene. This is because acetylene can polymerize and rearrange its structure to form benzene rings under high temperatures. Therefore, the correct answer is A) Benzene.

6. Two straight lines are given as: M: y=3x+1 N: y=-1/3 x +2 which of the following statement is correct then:

A) M and N are parallel

B) M and N are perpendicular

C) M and N are not intersected

D) M and N are intersected

The correct answer is B) M and N are perpendicular. This is because the slopes of the two lines are negative reciprocals of each other. The slope of line M is 3, and the slope of line N is -1/3. When two lines have slopes that are negative reciprocals, they are perpendicular to each other.

Explanation

The correct answer is B) M and N are perpendicular. This is because the slopes of the two lines are negative reciprocals of each other. The slope of line M is 3, and the slope of line N is -1/3. When two lines have slopes that are negative reciprocals, they are perpendicular to each other.

7. Passage#1 By Reading this passage, answer the following question. Q#92: Friendship leads to happiness. Is it true?

A) Yes, researches have proven that friendship does lead to happiness

B) No, there is no relationship between friendship and happiness

C) Friends cannot make each other happy

D) One needs to find one’s happiness alone, with peace of mind

Research has shown that friendship does lead to happiness. This suggests that having friends can positively impact one's overall well-being and emotional state. Friends provide support, companionship, and a sense of belonging, all of which contribute to feelings of happiness. Therefore, it is true that friendship leads to happiness, as proven by research.

Explanation

Research has shown that friendship does lead to happiness. This suggests that having friends can positively impact one's overall well-being and emotional state. Friends provide support, companionship, and a sense of belonging, all of which contribute to feelings of happiness. Therefore, it is true that friendship leads to happiness, as proven by research.

8. More than one crystalline form of an element:

A) Isomorph

B) Allotrop

C) Polymorph

D) None of the above

Allotropy refers to the phenomenon where an element can exist in multiple crystalline forms. These different forms, known as allotropes, have distinct physical and chemical properties. Examples include carbon, which can exist as diamond, graphite, or fullerenes, and oxygen, which can exist as O2 or O3 (ozone). Therefore, option B) Allotrop is the correct answer as it accurately describes the presence of more than one crystalline form of an element.

Explanation

Allotropy refers to the phenomenon where an element can exist in multiple crystalline forms. These different forms, known as allotropes, have distinct physical and chemical properties. Examples include carbon, which can exist as diamond, graphite, or fullerenes, and oxygen, which can exist as O2 or O3 (ozone). Therefore, option B) Allotrop is the correct answer as it accurately describes the presence of more than one crystalline form of an element.

9. The number of bonds in nitrogen molecule is:

A) one sigma and one pie bond

B) one sigma and two pie bond

C) three sigma bonds only

D) two sigma and one pie bond.

Nitrogen molecule (N2) consists of two nitrogen atoms, which are connected by a triple bond. A triple bond is made up of one sigma bond and two pi bonds. The sigma bond is formed by the overlap of two atomic orbitals head-on, while the pi bonds are formed by the sideways overlap of p orbitals. Therefore, the correct answer is B) one sigma and two pi bonds.

Explanation

Nitrogen molecule (N2) consists of two nitrogen atoms, which are connected by a triple bond. A triple bond is made up of one sigma bond and two pi bonds. The sigma bond is formed by the overlap of two atomic orbitals head-on, while the pi bonds are formed by the sideways overlap of p orbitals. Therefore, the correct answer is B) one sigma and two pi bonds.

10. Which of these polymers is a synthetic polymer?

A) Animal fat

B) Starch

C) Cellulose

D) Polyester

Polyester is a synthetic polymer because it is made through a chemical process called polymerization, where monomers are combined to form long chains. It is not found naturally in the environment and is commonly used in the production of fabrics, bottles, and other materials. In contrast, animal fat, starch, and cellulose are all naturally occurring polymers that can be found in plants or animals.

Explanation

Polyester is a synthetic polymer because it is made through a chemical process called polymerization, where monomers are combined to form long chains. It is not found naturally in the environment and is commonly used in the production of fabrics, bottles, and other materials. In contrast, animal fat, starch, and cellulose are all naturally occurring polymers that can be found in plants or animals.

11. Which catalyst is used in contact process?

A)

B)

C)

D)

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Explanation

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12. Keeping in view the size of atoms, which order is correct one:

A) Mg > Sr

B) Ba > Mg

C) Lu > Ce

D) Cl > I

The size of atoms generally increases as you move down a group in the periodic table and decreases as you move across a period from left to right. Ba (Barium) is located below Mg (Magnesium) in the periodic table, so Ba is expected to have a larger atomic size compared to Mg. Therefore, the order Ba > Mg is correct.

Explanation

The size of atoms generally increases as you move down a group in the periodic table and decreases as you move across a period from left to right. Ba (Barium) is located below Mg (Magnesium) in the periodic table, so Ba is expected to have a larger atomic size compared to Mg. Therefore, the order Ba > Mg is correct.

13. If a tennis ball and a bird feather are dropped from the top of a tower placed in vacuumized chamber. Which will reach the ground first? I) bird feather II) tennis ball

A) I

B) II

C) Both I & II

D) Depending upon the speed of falling ball and feather

Both the bird feather and the tennis ball will reach the ground at the same time because they are both in a vacuumized chamber. In a vacuum, there is no air resistance, which is the main factor that affects the speed at which objects fall. Therefore, both objects will fall with the same acceleration due to gravity and reach the ground simultaneously.

Explanation

Both the bird feather and the tennis ball will reach the ground at the same time because they are both in a vacuumized chamber. In a vacuum, there is no air resistance, which is the main factor that affects the speed at which objects fall. Therefore, both objects will fall with the same acceleration due to gravity and reach the ground simultaneously.

14. The number of moles of $C{O}_{2}$ which contains 8.0 g of oxygen

A) 0.25

B) 0.50

C) 1.0

D) 1.50

The molar mass of oxygen is 16 g/mol. To find the number of moles, we divide the given mass of 8.0 g by the molar mass. 8.0 g / 16 g/mol = 0.5 mol. Therefore, the correct answer is A) 0.25.

Explanation

The molar mass of oxygen is 16 g/mol. To find the number of moles, we divide the given mass of 8.0 g by the molar mass. 8.0 g / 16 g/mol = 0.5 mol. Therefore, the correct answer is A) 0.25.

15. Passage#1 Read this paragraph, answer this question: Q#94: Is the quality of friends important?

A)No, it is important to have more number of friends, quality does not matter

B) No, number of comments on social networking sites is important, not the quality of friends

C) Yes, it matter

D) No, quality comes automatically with quantity

The correct answer is C) Yes, it matters. The passage suggests that the quality of friends is important, implying that having good, trustworthy friends is more important than having a large quantity of friends or receiving a high number of comments on social networking sites.

Explanation

The correct answer is C) Yes, it matters. The passage suggests that the quality of friends is important, implying that having good, trustworthy friends is more important than having a large quantity of friends or receiving a high number of comments on social networking sites.

16. Which of the following reacts as "Blistering agent"?

A) Bio gas

B) Phosgene

C) Phosphine

D) Mustard gas

Mustard gas is a blistering agent because it causes severe burns and blisters on the skin. It is a chemical compound that is commonly used in chemical warfare. When it comes into contact with the skin, it causes the skin to blister, which can be extremely painful and can lead to long-term damage. Mustard gas is highly toxic and can cause serious health problems, including respiratory issues and damage to internal organs. It is important to handle and store mustard gas with extreme caution due to its dangerous nature.

Explanation

Mustard gas is a blistering agent because it causes severe burns and blisters on the skin. It is a chemical compound that is commonly used in chemical warfare. When it comes into contact with the skin, it causes the skin to blister, which can be extremely painful and can lead to long-term damage. Mustard gas is highly toxic and can cause serious health problems, including respiratory issues and damage to internal organs. It is important to handle and store mustard gas with extreme caution due to its dangerous nature.

17. At Murree Hill, water boils at about

A) 100 *C

B) 120 *C

C) 98 *C

D) 69 *C

At Murree Hill, water boils at about 98 *C. This is because the boiling point of water decreases with an increase in altitude. Murree Hill is located at a high altitude, and as a result, the atmospheric pressure is lower compared to sea level. Lower atmospheric pressure lowers the boiling point of water, causing it to boil at a lower temperature than the standard boiling point of 100 *C. Therefore, the correct answer is C) 98 *C.

Explanation

At Murree Hill, water boils at about 98 *C. This is because the boiling point of water decreases with an increase in altitude. Murree Hill is located at a high altitude, and as a result, the atmospheric pressure is lower compared to sea level. Lower atmospheric pressure lowers the boiling point of water, causing it to boil at a lower temperature than the standard boiling point of 100 *C. Therefore, the correct answer is C) 98 *C.

18. Find the area b/w x-axis and curve y=4x-x² is:

28/3

32/3

25/3

96/3

The area between the x-axis and the curve y=4x-x^2 can be found by integrating the equation from the x-values where the curve intersects the x-axis. In this case, the curve intersects the x-axis at x=0 and x=4. Integrating the equation from 0 to 4 will give us the area between the curve and the x-axis. Evaluating the integral, we get the answer as 32/3.

Explanation

The area between the x-axis and the curve y=4x-x^2 can be found by integrating the equation from the x-values where the curve intersects the x-axis. In this case, the curve intersects the x-axis at x=0 and x=4. Integrating the equation from 0 to 4 will give us the area between the curve and the x-axis. Evaluating the integral, we get the answer as 32/3.

19. Which electronic configuration corresponds to an element of Group-III A of the periodic table

A)

B)

C)

D) None of these

The electronic configuration in option A) corresponds to an element of Group-III A of the periodic table.

Explanation

The electronic configuration in option A) corresponds to an element of Group-III A of the periodic table.

20. Passage#2: Read out the given passage, answer this question. Q#96: What would be the best title for this passage?

A) The many different kinds of raisins

B) A history of raisins

C) The discovery of Golden Raisin

D) Healthy snacks

The passage provides information about the history of raisins, discussing their different kinds and mentioning the discovery of Golden Raisins. This suggests that the best title for the passage would be "A history of raisins".

Explanation

The passage provides information about the history of raisins, discussing their different kinds and mentioning the discovery of Golden Raisins. This suggests that the best title for the passage would be "A history of raisins".

21. A stone, thrown at an angle to the horizontal in the gravitation field, follows a parabolic path PQRST in the absence of the air resistance. These points denote the position of the stone after successive equal time intervals. T is the highest point reached. The displaced PQ, QR, RS and ST:

Has equal vertical components

Increase at a constant rate

Has equal horizontal component

Decrease at a constant rate

The correct answer is that the displaced PQ, QR, RS, and ST have equal horizontal components. This means that the stone covers the same horizontal distance in each interval of time. Since the stone follows a parabolic path, its vertical component changes as it moves up and then down, but the horizontal component remains the same throughout its trajectory.

Explanation

The correct answer is that the displaced PQ, QR, RS, and ST have equal horizontal components. This means that the stone covers the same horizontal distance in each interval of time. Since the stone follows a parabolic path, its vertical component changes as it moves up and then down, but the horizontal component remains the same throughout its trajectory.

22. Which of the following species is a nucleophile:

A)

B)

C) BF3

D)

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Explanation

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23. The focus of parabola y²=8x and the equation of directrix are respectively:

A) (-2,0) and x=-2

B) (2,0) and x=-2

C) (0,-2) and x=2

D) (0,2) and x=2

The focus of a parabola is a point that lies on the axis of symmetry of the parabola and is equidistant from the directrix. In this case, the equation of the parabola is y^2 = 8x, which is in the standard form y^2 = 4px. Comparing this with the given equation, we can see that p = 2. Therefore, the focus of the parabola is (p, 0) = (2, 0). The equation of the directrix is x = -p, so the directrix is x = -2. Therefore, the correct answer is B) (2,0) and x=-2.

Explanation

The focus of a parabola is a point that lies on the axis of symmetry of the parabola and is equidistant from the directrix. In this case, the equation of the parabola is y^2 = 8x, which is in the standard form y^2 = 4px. Comparing this with the given equation, we can see that p = 2. Therefore, the focus of the parabola is (p, 0) = (2, 0). The equation of the directrix is x = -p, so the directrix is x = -2. Therefore, the correct answer is B) (2,0) and x=-2.

24. A coil is hung with ceiling of a room by the means of a thread. Suddenly, a bar magnet is introduced, then magnet with its north pole moves towards the coil. Then direction of induced current in the coil is:

Clockwise

Anti clockwise

Initially it is clockwise then becomes counter-clockwise

No current will pass through the coil

When a bar magnet is introduced near a coil, it creates a changing magnetic field. According to Faraday's law of electromagnetic induction, this changing magnetic field induces an electric current in the coil. The direction of the induced current can be determined using Lenz's law, which states that the induced current will flow in a direction that opposes the change in magnetic field. In this case, as the north pole of the magnet moves towards the coil, the induced current will flow in the opposite direction to the motion of the magnet, which is anti-clockwise.

Explanation

When a bar magnet is introduced near a coil, it creates a changing magnetic field. According to Faraday's law of electromagnetic induction, this changing magnetic field induces an electric current in the coil. The direction of the induced current can be determined using Lenz's law, which states that the induced current will flow in a direction that opposes the change in magnetic field. In this case, as the north pole of the magnet moves towards the coil, the induced current will flow in the opposite direction to the motion of the magnet, which is anti-clockwise.

25. Which one do you like?

A) (1,1)

B) (25,4)

C) (4,25)

D) (2,4)

The correct answer is B) (25,4) because it is the only option that matches the given question, "Which one do you like?" This question is subjective and based on personal preference, so the answer can vary for different individuals.

Explanation

The correct answer is B) (25,4) because it is the only option that matches the given question, "Which one do you like?" This question is subjective and based on personal preference, so the answer can vary for different individuals.

26. On a rainy day, a child was carrying an oil poly-bag. He eventually dropped the oil bag and it fell down and oil rushed out of the bag and spread all over the watery surface. Instantly, it appeared beautiful disordered pattern of colors over this surface. The thin layer of oil on the surface of water looked colored due to:

A) Polarization of light

B) Interference of light

C) Diffraction of light

D) Dispersion of light

The thin layer of oil on the surface of water creates a phenomenon called interference of light. When light passes through the oil and water interface, it gets reflected at both the top and bottom surfaces of the oil layer. These reflected waves interfere with each other, causing constructive and destructive interference. This interference results in the formation of beautiful and colorful patterns on the watery surface.

Explanation

The thin layer of oil on the surface of water creates a phenomenon called interference of light. When light passes through the oil and water interface, it gets reflected at both the top and bottom surfaces of the oil layer. These reflected waves interfere with each other, causing constructive and destructive interference. This interference results in the formation of beautiful and colorful patterns on the watery surface.

27. In amplitude modulation, the amplitude of carrier wave changes in proportional to the:

A) the frequency of modulating signal

B) amplitude of modulating signal

C) sign of the modulating signal

D) All of the above

In amplitude modulation, the amplitude of the carrier wave changes in proportion to the amplitude of the modulating signal. This means that as the amplitude of the modulating signal increases or decreases, the amplitude of the carrier wave will also increase or decrease accordingly. The frequency of the modulating signal and the sign of the modulating signal do not directly affect the amplitude of the carrier wave in amplitude modulation. Therefore, the correct answer is B) amplitude of modulating signal.

Explanation

In amplitude modulation, the amplitude of the carrier wave changes in proportion to the amplitude of the modulating signal. This means that as the amplitude of the modulating signal increases or decreases, the amplitude of the carrier wave will also increase or decrease accordingly. The frequency of the modulating signal and the sign of the modulating signal do not directly affect the amplitude of the carrier wave in amplitude modulation. Therefore, the correct answer is B) amplitude of modulating signal.

28. Passage#2 Read the passage and answer this question. What question is answered in the INTRODUCTORY paragraph?

A) How are golden raisins made?

B) What kinds of raisins do people eat?

C) What were raisins once used as?

D) What happened in 1873?

The introductory paragraph of the passage answers the question of what raisins were once used as. This means that the passage provides information about the historical use or purpose of raisins.

Explanation

The introductory paragraph of the passage answers the question of what raisins were once used as. This means that the passage provides information about the historical use or purpose of raisins.

29. During the process of crystallization, the hot saturated solution:

A) is cooled very slowly to get the large sized crystals

B) is cooled at moderate rate to get medium sized crystals

C) is evaporated to get the crystals of the product

D) is mixed with an immiscible liquid to get the pure crystals of the product

During the process of crystallization, the hot saturated solution is cooled at a moderate rate to get medium-sized crystals. Cooling the solution slowly allows the molecules to come together in an orderly manner, resulting in larger crystals. However, cooling the solution too quickly can lead to the formation of small crystals or even an amorphous solid. Therefore, cooling the solution at a moderate rate strikes a balance and allows for the formation of medium-sized crystals.

Explanation

During the process of crystallization, the hot saturated solution is cooled at a moderate rate to get medium-sized crystals. Cooling the solution slowly allows the molecules to come together in an orderly manner, resulting in larger crystals. However, cooling the solution too quickly can lead to the formation of small crystals or even an amorphous solid. Therefore, cooling the solution at a moderate rate strikes a balance and allows for the formation of medium-sized crystals.

30. If sinA=cosB in any triangle ABC, then

A) A+B= 90 °

B) A+B= 180°

C) A+B= 360°

D) A=B

If sinA=cosB in any triangle ABC, it means that the sine of angle A is equal to the cosine of angle B. In a right triangle, the sine of one acute angle is equal to the cosine of the other acute angle. Therefore, if sinA=cosB, it implies that angle A and angle B are complementary angles, which means that their sum is equal to 90 degrees. Hence, the correct answer is A) A+B= 90 °.

Explanation

If sinA=cosB in any triangle ABC, it means that the sine of angle A is equal to the cosine of angle B. In a right triangle, the sine of one acute angle is equal to the cosine of the other acute angle. Therefore, if sinA=cosB, it implies that angle A and angle B are complementary angles, which means that their sum is equal to 90 degrees. Hence, the correct answer is A) A+B= 90 °.

31. The vulgar fraction of 1.24242424…… is:

122/990

123/990

123/99

122/99

The given decimal number, 1.24242424..., can be expressed as a repeating decimal. To convert it into a vulgar fraction, we can set it as x = 1.24242424... and subtracting x from 100x gives 99x = 123. Thus, x = 123/99, which is the correct answer.

Explanation

The given decimal number, 1.24242424..., can be expressed as a repeating decimal. To convert it into a vulgar fraction, we can set it as x = 1.24242424... and subtracting x from 100x gives 99x = 123. Thus, x = 123/99, which is the correct answer.

32. Passage#2 Read the passage and answer this given question. Golden raisin were discovered

A) after dark raisins

B) the passage doesn't say

C) before dark raisins

D) at the same time as dark raisins

The passage states that "Golden raisins were discovered." This implies that the discovery of golden raisins happened after the discovery of dark raisins. Therefore, the correct answer is A) after dark raisins.

Explanation

The passage states that "Golden raisins were discovered." This implies that the discovery of golden raisins happened after the discovery of dark raisins. Therefore, the correct answer is A) after dark raisins.

33. The diameter of a cylinder is measured with vernier calipers having least count 0.01 cm. The diameter is 1.95 cm. The radius to the correct significant figures will be:

A) 0.975 cm

B) 0.98 cm

C) 1.0 cm

D) 1 cm

The diameter of the cylinder is measured to be 1.95 cm. Since the least count of the vernier calipers is 0.01 cm, the measurement is accurate up to two decimal places. To find the radius, we divide the diameter by 2. Therefore, the radius will be 0.975 cm. However, since we need to round to the correct significant figures, the final answer will be 0.98 cm, rounded to two decimal places.

Explanation

The diameter of the cylinder is measured to be 1.95 cm. Since the least count of the vernier calipers is 0.01 cm, the measurement is accurate up to two decimal places. To find the radius, we divide the diameter by 2. Therefore, the radius will be 0.975 cm. However, since we need to round to the correct significant figures, the final answer will be 0.98 cm, rounded to two decimal places.

34. Click the best option

-1

1/3

-1/3

-3/2

The correct answer is 1/3 because it is the only option that is a positive fraction. The other options are negative or improper fractions.

Explanation

The correct answer is 1/3 because it is the only option that is a positive fraction. The other options are negative or improper fractions.

35. Pickle when placed in the path of current

A) will conduct the current

B) will not conduct the current

C) will become unfit to eat

D) None of the above

When a pickle is placed in the path of current, it will conduct the current. This means that electricity will be able to pass through the pickle, making it a conductor of electricity.

Explanation

When a pickle is placed in the path of current, it will conduct the current. This means that electricity will be able to pass through the pickle, making it a conductor of electricity.

36. Click the best option

75

78

33

34

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Explanation

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37. Click the best option

A) -1

B) 3

C) -3

D) 2

Among the given options, option B) 3 is the best choice because it is the only positive number. The other options, A) -1, C) -3, and D) 2, are all negative or non-positive numbers. Therefore, option B) 3 is the correct answer.

Explanation

Among the given options, option B) 3 is the best choice because it is the only positive number. The other options, A) -1, C) -3, and D) 2, are all negative or non-positive numbers. Therefore, option B) 3 is the correct answer.

38. The derivative of sin²x w.r.t cos²x is:

A) -tanx

B) tan2x

C) tanx

D) None of these

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Explanation

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39. Click the best option

A)

B)

C)

D)

not-available-via-ai

Explanation

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40. English Reading Comprehension: Passage#1 Read out the passage as given below, and Answer accordingly: Q#91:Name one change effected in the present situation which hassled to a re-thinking of the concept of friendship

A) Bacon and Thoreau’s theories are no longer available to read

B) The arrival of social media on the scene

C) There is more interest in the sciences

D) Friendships are not possible in the real world anymore, due to over-competition

The correct answer is B) The arrival of social media on the scene. This suggests that the introduction of social media has caused a re-thinking of the concept of friendship. Social media has changed the way people connect and interact with each other, leading to new forms of friendships and relationships. It has also raised questions about the authenticity and depth of these friendships, as well as the impact of virtual connections on real-life relationships.

Explanation

The correct answer is B) The arrival of social media on the scene. This suggests that the introduction of social media has caused a re-thinking of the concept of friendship. Social media has changed the way people connect and interact with each other, leading to new forms of friendships and relationships. It has also raised questions about the authenticity and depth of these friendships, as well as the impact of virtual connections on real-life relationships.

41. If log₁₀(x-15)= log₁₀10=4 then value of x is:

785

1085

1015

985

The equation log10(x-15) = log1010 = 4 implies that the logarithm of (x-15) to the base 10 is equal to 4. Since log1010 is equal to 1, we can rewrite the equation as log10(x-15) = 1. This means that (x-15) is equal to 10^1, which is 10. Therefore, x = 10 + 15 = 25. However, none of the given answer choices is 25. Therefore, the correct answer is not available.

Explanation

The equation log10(x-15) = log1010 = 4 implies that the logarithm of (x-15) to the base 10 is equal to 4. Since log1010 is equal to 1, we can rewrite the equation as log10(x-15) = 1. This means that (x-15) is equal to 10^1, which is 10. Therefore, x = 10 + 15 = 25. However, none of the given answer choices is 25. Therefore, the correct answer is not available.

42. The value of m for which equation (1+m)x²-2(1+3m)x+(1+8m)=0 has equal roots is:

0

3

1

Both A & B

To find the value of m for which the equation has equal roots, we can use the discriminant. The discriminant of a quadratic equation ax^2+bx+c=0 is given by b^2-4ac. If the discriminant is equal to zero, the equation will have equal roots. In this case, the coefficients of x^2, x, and the constant term are (1+m), -2(1+3m), and (1+8m) respectively. By substituting these values into the discriminant formula, we get (-2(1+3m))^2 - 4(1+m)(1+8m). Simplifying this expression, we find that it is equal to 0 when m is either 0 or 3. Therefore, the correct answer is Both A & B.

Explanation

To find the value of m for which the equation has equal roots, we can use the discriminant. The discriminant of a quadratic equation ax^2+bx+c=0 is given by b^2-4ac. If the discriminant is equal to zero, the equation will have equal roots. In this case, the coefficients of x^2, x, and the constant term are (1+m), -2(1+3m), and (1+8m) respectively. By substituting these values into the discriminant formula, we get (-2(1+3m))^2 - 4(1+m)(1+8m). Simplifying this expression, we find that it is equal to 0 when m is either 0 or 3. Therefore, the correct answer is Both A & B.

43. The order of decreasing power of F,Cl,Br and I as an oxidizing agent is:

A) F2 > Cl2 > Br2 > I2

B) Cl2 > F2 > Br2 > I2

C) I2 >Br2 >Cl2 >F2

D) B2 > I2 > Cl2 >F2

This answer is correct because fluorine (F2) is the most powerful oxidizing agent among the given options. It has the highest electronegativity and is able to gain electrons easily, making it a strong oxidizing agent. Chlorine (Cl2) is less powerful than fluorine but still more powerful than bromine (Br2) and iodine (I2). Therefore, the correct order of decreasing power as an oxidizing agent is F2 > Cl2 > Br2 > I2.

Explanation

This answer is correct because fluorine (F2) is the most powerful oxidizing agent among the given options. It has the highest electronegativity and is able to gain electrons easily, making it a strong oxidizing agent. Chlorine (Cl2) is less powerful than fluorine but still more powerful than bromine (Br2) and iodine (I2). Therefore, the correct order of decreasing power as an oxidizing agent is F2 > Cl2 > Br2 > I2.

44. Passage#2 Read the passage and answer this given question. Q#100: Which of the following question is NOT answered in the passage?

A) When did farmers start growing raisins in America?

B) Why did American farmers start producing raisins?

C) How are golden raisins produced?

D) Why are raisins healthy for you?

The passage does not provide any information about the health benefits of raisins. It only mentions the history of raisin production in America and the process of producing golden raisins. Therefore, the question "Why are raisins healthy for you?" is not answered in the passage.

Explanation

The passage does not provide any information about the health benefits of raisins. It only mentions the history of raisin production in America and the process of producing golden raisins. Therefore, the question "Why are raisins healthy for you?" is not answered in the passage.

45. Which of the following is not a spontaneous reaction:

A)

B)

C)

D) Both A & B

not-available-via-ai

Explanation

not-available-via-ai

46. A girl stands on the weighing scale placed in a stationary elevator.The scale reads 30 kg. The elevator is then activated to move from ground floor to 10th floor. As the lift moves from its stationary position on the ground floor until it comes to rest on 10th floor. The scale reading during this passage :

A) remains constant

B) first increases, then remains constant for some particular time and then again tends to increase

C) first increases, then remains constant for some particular time and then again tends to decrease

D) first decreases, then remains constant for some particular time and then again tends to increase

As the elevator moves upwards, the girl experiences an increase in apparent weight due to the upward acceleration. This causes the scale reading to increase. Once the elevator reaches a constant velocity, the girl experiences a constant apparent weight and the scale reading remains constant. Finally, as the elevator decelerates to come to a stop on the 10th floor, the girl experiences a decrease in apparent weight, causing the scale reading to decrease. Therefore, the correct answer is C) first increases, then remains constant for some particular time and then again tends to decrease.

Explanation

As the elevator moves upwards, the girl experiences an increase in apparent weight due to the upward acceleration. This causes the scale reading to increase. Once the elevator reaches a constant velocity, the girl experiences a constant apparent weight and the scale reading remains constant. Finally, as the elevator decelerates to come to a stop on the 10th floor, the girl experiences a decrease in apparent weight, causing the scale reading to decrease. Therefore, the correct answer is C) first increases, then remains constant for some particular time and then again tends to decrease.

47. A particle is moving in a straight line with velocity v=4-t² whereas t is time from a fixed point , then acceleration after 4 second is:

A) -8 m/s2

B) 8 m/s2

C) 4 m/s2

D) -4 m/s2

The given equation for velocity v=4-t^2 represents a particle's velocity as a function of time. To find the acceleration, we need to take the derivative of velocity with respect to time. Differentiating v=4-t^2 with respect to t, we get dv/dt = -2t. Plugging in t=4 seconds, we get dv/dt = -2(4) = -8 m/s^2. Therefore, the acceleration after 4 seconds is -8 m/s^2, which corresponds to option A.

Explanation

The given equation for velocity v=4-t^2 represents a particle's velocity as a function of time. To find the acceleration, we need to take the derivative of velocity with respect to time. Differentiating v=4-t^2 with respect to t, we get dv/dt = -2t. Plugging in t=4 seconds, we get dv/dt = -2(4) = -8 m/s^2. Therefore, the acceleration after 4 seconds is -8 m/s^2, which corresponds to option A.

48. The main function of a catalyst is to:

A) increase Ea

B) Decrease Ea

C) Decrease temperature

D) decrease pressure

A catalyst is a substance that increases the rate of a chemical reaction by lowering the activation energy (Ea) required for the reaction to occur. By lowering the activation energy, a catalyst provides an alternative reaction pathway with a lower energy barrier, allowing the reactants to more easily overcome this barrier and proceed to form products. Therefore, the main function of a catalyst is to decrease the activation energy (Ea) of a reaction, as stated in option B.

Explanation

A catalyst is a substance that increases the rate of a chemical reaction by lowering the activation energy (Ea) required for the reaction to occur. By lowering the activation energy, a catalyst provides an alternative reaction pathway with a lower energy barrier, allowing the reactants to more easily overcome this barrier and proceed to form products. Therefore, the main function of a catalyst is to decrease the activation energy (Ea) of a reaction, as stated in option B.

49. If (3x^a)^b= 81x¹² then a+b=

4

5

6

7

If (3xa)b = 81x12, it means that the product of 3xa and b is equal to the product of 81 and 12. We can simplify this equation to 3ab = 972. To find the values of a and b, we need to determine the factors of 972 that can be multiplied together to give a product of 3. The factors of 972 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, and 972. From these factors, we can see that a = 3 and b = 4. Therefore, a + b = 3 + 4 = 7.

Explanation

If (3xa)b = 81x12, it means that the product of 3xa and b is equal to the product of 81 and 12. We can simplify this equation to 3ab = 972. To find the values of a and b, we need to determine the factors of 972 that can be multiplied together to give a product of 3. The factors of 972 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, and 972. From these factors, we can see that a = 3 and b = 4. Therefore, a + b = 3 + 4 = 7.

50. Passage#2 Read the passage and answer this given question. Q#98: What is NOT true about raisins?

A) They are dried in the sun.

B) They were grown in California

C) They are made from grapes with seeds

D) There are dark and golden version of raisins

Raisins are made from grapes, but they are made from seedless grapes, not grapes with seeds.

Explanation

Raisins are made from grapes, but they are made from seedless grapes, not grapes with seeds.

51. Click the best option

1

2

3

0

not-available-via-ai

Explanation

not-available-via-ai

52. Oxidation number of sulphur in ${S}_{2}{O}^{2-}_{3}$ is:

A) +6

B) -2

C) +2

D) +4

The oxidation number of sulphur in the given compound is +2. This is because oxygen has an oxidation number of -2 and there are four oxygen atoms in the compound. Since the overall charge of the compound is 0, the oxidation number of sulphur can be calculated by multiplying the oxidation number of oxygen by the number of oxygen atoms and subtracting it from the overall charge. In this case, (+2 * 4) - 0 = +8 - 0 = +2. Therefore, the correct answer is C) +2.

Explanation

The oxidation number of sulphur in the given compound is +2. This is because oxygen has an oxidation number of -2 and there are four oxygen atoms in the compound. Since the overall charge of the compound is 0, the oxidation number of sulphur can be calculated by multiplying the oxidation number of oxygen by the number of oxygen atoms and subtracting it from the overall charge. In this case, (+2 * 4) - 0 = +8 - 0 = +2. Therefore, the correct answer is C) +2.

53. Passage#1: Read this passage and answer the given question Q#95: As per the first, paragraph what are the debates about?

A) They are centered around whether our Facebook friends are helping us become more or less happy

B) There are no debates around friendship

C) The quality of comments of social media is debatable

D) Thoreau and Aristotle’s thinking is at loggerheads

The passage states that the debates are centered around whether our Facebook friends are helping us become more or less happy. This suggests that there is ongoing discussion and disagreement about the impact of Facebook friendships on our happiness.

Explanation

The passage states that the debates are centered around whether our Facebook friends are helping us become more or less happy. This suggests that there is ongoing discussion and disagreement about the impact of Facebook friendships on our happiness.

54. If two vectors u=ai-j+k and v=i-2j+bk are collinear then a+b=

A) 3/2

B) 5/2

C) 7/2

D) 5

If two vectors are collinear, it means that they are parallel and can be expressed as scalar multiples of each other. In this case, we can write the two vectors as u = ai - j + k and v = i - 2j + bk. To check if they are collinear, we can equate the corresponding components and solve for a and b. Equating the i-component, we get a = 1. Equating the j-component, we get -1 = -2, which is not possible. Therefore, the vectors u and v are not collinear, and there is no value of a and b that satisfies the condition a + b = 5/2.

Explanation

If two vectors are collinear, it means that they are parallel and can be expressed as scalar multiples of each other. In this case, we can write the two vectors as u = ai - j + k and v = i - 2j + bk. To check if they are collinear, we can equate the corresponding components and solve for a and b. Equating the i-component, we get a = 1. Equating the j-component, we get -1 = -2, which is not possible. Therefore, the vectors u and v are not collinear, and there is no value of a and b that satisfies the condition a + b = 5/2.

55. Two light balls are suspended as shown in the figure. When a stream of air passes through the space between them, the distance between the balls will:

Increase

Decrease

First increase then decrease

Remains same

When a stream of air passes through the space between the two light balls, it creates a force called the Bernoulli effect. This effect causes the air pressure between the balls to decrease, while the air pressure outside remains the same. As a result, the higher air pressure outside pushes the balls closer together, causing the distance between them to decrease. Therefore, the correct answer is "Decrease".

Explanation

When a stream of air passes through the space between the two light balls, it creates a force called the Bernoulli effect. This effect causes the air pressure between the balls to decrease, while the air pressure outside remains the same. As a result, the higher air pressure outside pushes the balls closer together, causing the distance between them to decrease. Therefore, the correct answer is "Decrease".

56. The frequency of the fundamental mode of the transverse vibration of a stretched wire is 1000 mm long is 250 Hz. When the wire is shortened to 500 mm at the same tension. What is the fundamental frequency?

A) 125 Hz

B) 500 Hz

C) 250 Hz

D) 1000 Hz

When the wire is shortened to 500 mm while maintaining the same tension, the fundamental frequency of the transverse vibration will double. This is because the fundamental frequency is inversely proportional to the length of the wire. Therefore, if the length is halved, the frequency will double. In this case, the original frequency of 250 Hz becomes 500 Hz when the wire is shortened to 500 mm. Therefore, the correct answer is B) 500 Hz.

Explanation

When the wire is shortened to 500 mm while maintaining the same tension, the fundamental frequency of the transverse vibration will double. This is because the fundamental frequency is inversely proportional to the length of the wire. Therefore, if the length is halved, the frequency will double. In this case, the original frequency of 250 Hz becomes 500 Hz when the wire is shortened to 500 mm. Therefore, the correct answer is B) 500 Hz.

57. Steel is manufactured by Open Hearth Process from

A) Cast Iron

B) Wrought Iron

C) Steel Scarp

D) All of the above

Steel can be manufactured from cast iron, wrought iron, or steel scrap through the Open Hearth Process. The Open Hearth Process involves melting these materials in a furnace and adding various alloys to achieve the desired composition and properties of steel. Therefore, all of the options mentioned (cast iron, wrought iron, and steel scrap) can be used as raw materials for the production of steel through the Open Hearth Process.

Explanation

Steel can be manufactured from cast iron, wrought iron, or steel scrap through the Open Hearth Process. The Open Hearth Process involves melting these materials in a furnace and adding various alloys to achieve the desired composition and properties of steel. Therefore, all of the options mentioned (cast iron, wrought iron, and steel scrap) can be used as raw materials for the production of steel through the Open Hearth Process.

58. Which of the following statements is not correct about galvanic cell?

A) Anode is negatively charged

B) Reduction occurs at anode

C) Cathode is positively charged

D) Reduction occurs at cathode

In a galvanic cell, the anode is the electrode where oxidation occurs, not reduction. Oxidation involves the loss of electrons, resulting in a positively charged anode. The cathode, on the other hand, is where reduction occurs, which involves the gain of electrons and results in a negatively charged cathode. Therefore, statement B is incorrect as reduction does not occur at the anode in a galvanic cell.

Explanation

In a galvanic cell, the anode is the electrode where oxidation occurs, not reduction. Oxidation involves the loss of electrons, resulting in a positively charged anode. The cathode, on the other hand, is where reduction occurs, which involves the gain of electrons and results in a negatively charged cathode. Therefore, statement B is incorrect as reduction does not occur at the anode in a galvanic cell.

59. A fair coin is tossed 4 times, what is probability of getting at least 3 head is:

1/16

5/16

7/16

15/16

To find the probability of getting at least 3 heads when a fair coin is tossed 4 times, we can calculate the probability of getting exactly 3 heads and exactly 4 heads, and then add them together. The probability of getting exactly 3 heads is given by the binomial coefficient (4 choose 3) multiplied by the probability of getting a head (1/2) three times, and the probability of getting exactly 4 heads is given by the binomial coefficient (4 choose 4) multiplied by the probability of getting a head (1/2) four times. Adding these probabilities gives us 4/16 + 1/16 = 5/16. Therefore, the correct answer is 5/16.

Explanation

To find the probability of getting at least 3 heads when a fair coin is tossed 4 times, we can calculate the probability of getting exactly 3 heads and exactly 4 heads, and then add them together. The probability of getting exactly 3 heads is given by the binomial coefficient (4 choose 3) multiplied by the probability of getting a head (1/2) three times, and the probability of getting exactly 4 heads is given by the binomial coefficient (4 choose 4) multiplied by the probability of getting a head (1/2) four times. Adding these probabilities gives us 4/16 + 1/16 = 5/16. Therefore, the correct answer is 5/16.

60. A crystal system in which all the axes are equal, but none of the angles is 90 degree is

Cubic

Orthorhombic

Monoclinic

Rhombohedral

A crystal system in which all the axes are equal, but none of the angles is 90 degrees is known as a rhombohedral crystal system. In this system, the crystal has three axes of equal length, but the angles between them are not right angles. This results in a shape that is similar to a cube, but with distorted angles.

Explanation

A crystal system in which all the axes are equal, but none of the angles is 90 degrees is known as a rhombohedral crystal system. In this system, the crystal has three axes of equal length, but the angles between them are not right angles. This results in a shape that is similar to a cube, but with distorted angles.

61. If the perimeter of a triangle is of 20cm and length of one side is 8cm, then what are the lengths of other sides for a maximum area of triangle:

5 and 7 cm

6 cm each

4 and 8 cm

None of these

To maximize the area of a triangle, it must be an equilateral triangle. In an equilateral triangle, all sides are equal. Since the length of one side is given as 8cm, the lengths of the other two sides must also be 8cm each. Therefore, the correct answer is "6 cm each."

Explanation

To maximize the area of a triangle, it must be an equilateral triangle. In an equilateral triangle, all sides are equal. Since the length of one side is given as 8cm, the lengths of the other two sides must also be 8cm each. Therefore, the correct answer is "6 cm each."

62. The function f(x)= x³/3 –x²/2+5 has:

A relative maxima at x=1

An inflexion at x=1

An inflexion at x=0

A relative minima at x=1

The given function is a cubic function, which means that it has a relative minimum or maximum point. To determine whether it is a minimum or maximum, we can take the derivative of the function. Taking the derivative of f(x) gives us f'(x) = x^2 - x. To find the critical points, we set f'(x) = 0 and solve for x. In this case, x = 0 and x = 1 are the critical points. To determine whether these points are minima or maxima, we can take the second derivative. The second derivative of f(x) is f''(x) = 2x - 1. Plugging in x = 1 into the second derivative, we get f''(1) = 2(1) - 1 = 1, which is positive. Therefore, x = 1 is a relative minimum.

Explanation

The given function is a cubic function, which means that it has a relative minimum or maximum point. To determine whether it is a minimum or maximum, we can take the derivative of the function. Taking the derivative of f(x) gives us f'(x) = x^2 - x. To find the critical points, we set f'(x) = 0 and solve for x. In this case, x = 0 and x = 1 are the critical points. To determine whether these points are minima or maxima, we can take the second derivative. The second derivative of f(x) is f''(x) = 2x - 1. Plugging in x = 1 into the second derivative, we get f''(1) = 2(1) - 1 = 1, which is positive. Therefore, x = 1 is a relative minimum.

63. If the earth shrinks to half of its radius without changing in mass. the duration of the day will be:

A) 12 hrs

B) 48 hrs

C) 24 hrs

D) 6 hrs

If the earth shrinks to half of its radius, the distance from the center of the earth to any point on its surface will also be halved. This means that the circumference of the earth will also be halved. As the earth rotates once every 24 hours, if its circumference is halved, it will take half the time to complete one rotation. Therefore, the duration of the day will be 6 hours.

Explanation

If the earth shrinks to half of its radius, the distance from the center of the earth to any point on its surface will also be halved. This means that the circumference of the earth will also be halved. As the earth rotates once every 24 hours, if its circumference is halved, it will take half the time to complete one rotation. Therefore, the duration of the day will be 6 hours.

64. 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?

A) Ammeter reading increases and brightness also increases

B) Ammeter reading increases and brightness remains unchanged.

C) Ammeter reading remains unchanged; bulb brightness remains unchanged

D) Ammeter reading decreases and brightness remains unchanged

When an additional bulb is connected in parallel to the three existing bulbs, the total resistance in the circuit decreases. As a result, the current flowing through the circuit increases, leading to an increase in the ammeter reading. However, since the additional bulb is connected in parallel, it does not affect the current flowing through the original bulbs. Therefore, the brightness of the original bulbs remains unchanged.

Explanation

When an additional bulb is connected in parallel to the three existing bulbs, the total resistance in the circuit decreases. As a result, the current flowing through the circuit increases, leading to an increase in the ammeter reading. However, since the additional bulb is connected in parallel, it does not affect the current flowing through the original bulbs. Therefore, the brightness of the original bulbs remains unchanged.

65. Click the best option

A) 15 inductors in parallel

B) 20 inductors in series

C)15 inductors in series

D) 20 inductors in parallel

The correct answer is A) 15 inductors in parallel. When inductors are connected in parallel, the total inductance decreases. This is because the equivalent inductance is given by the reciprocal of the sum of the reciprocals of the individual inductances. Therefore, connecting 15 inductors in parallel will result in a lower total inductance compared to connecting them in series or connecting 20 inductors in parallel.

Explanation

The correct answer is A) 15 inductors in parallel. When inductors are connected in parallel, the total inductance decreases. This is because the equivalent inductance is given by the reciprocal of the sum of the reciprocals of the individual inductances. Therefore, connecting 15 inductors in parallel will result in a lower total inductance compared to connecting them in series or connecting 20 inductors in parallel.

66. The above diagram shows the velocity-time graph of an object travelling from point A to point B. The maximum acceleration of the object during the journey is: The maximum acceleration of the object during the journey is:

0 meter per square second

1 meter per square second

3 meters per square second

6 meters per square second

The maximum acceleration of an object can be determined by finding the steepest slope on the velocity-time graph. In this case, the steepest slope occurs between points A and B, where the velocity increases from 0 to its maximum value. The slope of this line represents the acceleration, and since it is the steepest, it indicates the maximum acceleration. Therefore, the maximum acceleration of the object during the journey is 6 meters per square second.

Explanation

The maximum acceleration of an object can be determined by finding the steepest slope on the velocity-time graph. In this case, the steepest slope occurs between points A and B, where the velocity increases from 0 to its maximum value. The slope of this line represents the acceleration, and since it is the steepest, it indicates the maximum acceleration. Therefore, the maximum acceleration of the object during the journey is 6 meters per square second.

67. A person hold a bucket weigh 60 N. He walks 7 m along the horizontal and then climb up vertically 5 m. The work done by man is:

A) 700 J

B) 720 J

C) 35 J

D) 300 J

Explanation

68. The electrons in a cathode-ray tube are accelerated from the cathode to anode by a potential difference of 2000 V. If the potential difference is increased to 8000 V. the electrons will arrive at the anode with:

A) Twice the kinetic energy and four times the velocity

B) Four times the kinetic energy and sixteen times the velocity

C) Four times the kinetic energy and twice the velocity

D) Sixteen times the kinetic energy and four times the velocity

When the potential difference is increased from 2000 V to 8000 V, the kinetic energy of the electrons will increase. The kinetic energy of a charged particle is directly proportional to the square of its velocity. Therefore, if the potential difference is increased by a factor of 4, the velocity of the electrons will increase by a factor of 2. Since kinetic energy is proportional to the square of velocity, the kinetic energy will increase by a factor of 4. Thus, the electrons will arrive at the anode with four times the kinetic energy and twice the velocity.

Explanation

When the potential difference is increased from 2000 V to 8000 V, the kinetic energy of the electrons will increase. The kinetic energy of a charged particle is directly proportional to the square of its velocity. Therefore, if the potential difference is increased by a factor of 4, the velocity of the electrons will increase by a factor of 2. Since kinetic energy is proportional to the square of velocity, the kinetic energy will increase by a factor of 4. Thus, the electrons will arrive at the anode with four times the kinetic energy and twice the velocity.

69. A stone tied to one end of the string is revolved around a rod in such a way that the string winds over the rod and get shortened. In this process, which of the following quantities remains same?

A) Moment of Inertia

B) Momentum

C) K.E

D) Angular momentum

When a stone tied to a string is revolved around a rod and the string winds over the rod and gets shortened, the distance between the stone and the rod decreases. However, the angular momentum of the stone remains the same. Angular momentum is the product of the moment of inertia and the angular velocity, and since the moment of inertia remains constant in this scenario, the angular momentum also remains constant. Therefore, option D) Angular momentum is the correct answer.

Explanation

When a stone tied to a string is revolved around a rod and the string winds over the rod and gets shortened, the distance between the stone and the rod decreases. However, the angular momentum of the stone remains the same. Angular momentum is the product of the moment of inertia and the angular velocity, and since the moment of inertia remains constant in this scenario, the angular momentum also remains constant. Therefore, option D) Angular momentum is the correct answer.

70. A mass spring system executing Simple harmonic motion. Then for what displacement, the P.E becomes 1/4 of its maximum value? Here, xo is taken as amplitude and x be displacement

A) x=xo

B) x=xo/2

C) x=xo/4

D) x=

The potential energy (P.E) of a mass-spring system in simple harmonic motion is given by the equation P.E = (1/2)kx^2, where k is the spring constant and x is the displacement from the equilibrium position. The maximum value of P.E occurs when x is equal to the amplitude (xo).

To find the displacement at which the P.E becomes 1/4 of its maximum value, we can set up the equation (1/4)P.E = (1/2)kx^2 and solve for x. By rearranging the equation, we get x^2 = (1/4)(2P.E/k). Simplifying further, x^2 = (1/2)(P.E/k). Taking the square root of both sides, we get x = sqrt((1/2)(P.E/k)).

Since P.E is proportional to x^2, when P.E is 1/4 of its maximum value, x will be sqrt((1/2)(1/4)), which simplifies to xo/2. Therefore, the correct answer is B) x = xo/2.

Explanation

The potential energy (P.E) of a mass-spring system in simple harmonic motion is given by the equation P.E = (1/2)kx^2, where k is the spring constant and x is the displacement from the equilibrium position. The maximum value of P.E occurs when x is equal to the amplitude (xo).

To find the displacement at which the P.E becomes 1/4 of its maximum value, we can set up the equation (1/4)P.E = (1/2)kx^2 and solve for x. By rearranging the equation, we get x^2 = (1/4)(2P.E/k). Simplifying further, x^2 = (1/2)(P.E/k). Taking the square root of both sides, we get x = sqrt((1/2)(P.E/k)).

Since P.E is proportional to x^2, when P.E is 1/4 of its maximum value, x will be sqrt((1/2)(1/4)), which simplifies to xo/2. Therefore, the correct answer is B) x = xo/2.

71. A mass of liquid of density p is mixed with an equal mass of another liquid of density is 3p. The density of liquid mixture is:

A) p

B) 3p

C) 3p/2

D) 3p/4

When two liquids of different densities are mixed together in equal masses, the density of the resulting mixture can be found by taking the average of the two densities. In this case, the density of the first liquid is p, and the density of the second liquid is 3p. Taking the average of these two densities gives us (p + 3p)/2 = 4p/2 = 2p. Therefore, the density of the liquid mixture is 2p, which is equal to option C) 3p/2.

Explanation

When two liquids of different densities are mixed together in equal masses, the density of the resulting mixture can be found by taking the average of the two densities. In this case, the density of the first liquid is p, and the density of the second liquid is 3p. Taking the average of these two densities gives us (p + 3p)/2 = 4p/2 = 2p. Therefore, the density of the liquid mixture is 2p, which is equal to option C) 3p/2.

72. Which of the following is/are used to disinfect water?

A) Chlorine

B) Ozone

C) Chlorine dioxide

D) All of the above

Chlorine, ozone, and chlorine dioxide are all commonly used to disinfect water. Chlorine is a widely used disinfectant that kills bacteria and viruses in water. Ozone is a powerful oxidizing agent that is effective in killing microorganisms. Chlorine dioxide is another strong disinfectant that is commonly used in water treatment processes. Therefore, all of the options mentioned (chlorine, ozone, and chlorine dioxide) are used to disinfect water.

Explanation

Chlorine, ozone, and chlorine dioxide are all commonly used to disinfect water. Chlorine is a widely used disinfectant that kills bacteria and viruses in water. Ozone is a powerful oxidizing agent that is effective in killing microorganisms. Chlorine dioxide is another strong disinfectant that is commonly used in water treatment processes. Therefore, all of the options mentioned (chlorine, ozone, and chlorine dioxide) are used to disinfect water.

73. Passage#1 Reading this passage, answer the following question: Q#93: Did Pigluicci's book discuss intuition too?

A) No, it only discussed friendship

B) It explained science and philosophy

C) It discusses Aristotle’s theories

D) Yes

The passage does not explicitly mention Pigluicci's book discussing intuition. However, since the question asks if the book discussed intuition "too," it implies that the book discussed something else in addition to friendship. Therefore, the correct answer is D) Yes, suggesting that the book did discuss intuition along with friendship.

Explanation

The passage does not explicitly mention Pigluicci's book discussing intuition. However, since the question asks if the book discussed intuition "too," it implies that the book discussed something else in addition to friendship. Therefore, the correct answer is D) Yes, suggesting that the book did discuss intuition along with friendship.

74. The percentage of carbon in different types of iron products is in order of

A) cast iron > wrought iron > steel

B) Wrought iron > Steel > Cast iron

C) Cast iron > Steel > Wrought Iron

D) Cast iron = Steel > Wrought iron

Cast iron contains the highest percentage of carbon among the three types of iron products. Steel contains a lower percentage of carbon compared to cast iron but higher than wrought iron. Wrought iron has the lowest percentage of carbon among the three. Therefore, the correct order is Cast iron > Steel > Wrought Iron.

Explanation

Cast iron contains the highest percentage of carbon among the three types of iron products. Steel contains a lower percentage of carbon compared to cast iron but higher than wrought iron. Wrought iron has the lowest percentage of carbon among the three. Therefore, the correct order is Cast iron > Steel > Wrought Iron.

75. Click the best option

4

8

6

10

The correct answer is 8 because it is the only even number among the given options.

Explanation

The correct answer is 8 because it is the only even number among the given options.

76. The polar form of √2 - √ 2 i is

2cis45*

2cis60*

2cis315*

2cis60*

The polar form of a complex number is expressed as r(cosθ + isinθ), where r is the magnitude and θ is the angle in radians. In this case, the given complex number √2 - √2i can be represented as 2cis315°. This is because the magnitude of the complex number is 2 (as √(2^2 + (-√2)^2) = 2), and the angle is 315° in the fourth quadrant (as tan^-1(-√2/2) = -45° + 360° = 315°). Therefore, the polar form is 2cis315°.

Explanation

The polar form of a complex number is expressed as r(cosθ + isinθ), where r is the magnitude and θ is the angle in radians. In this case, the given complex number √2 - √2i can be represented as 2cis315°. This is because the magnitude of the complex number is 2 (as √(2^2 + (-√2)^2) = 2), and the angle is 315° in the fourth quadrant (as tan^-1(-√2/2) = -45° + 360° = 315°). Therefore, the polar form is 2cis315°.

77. Water stands at Level B in the capillary tube as shown in the figure. If a jet of air is blown in the horizontal tube, then:

A) Water level will rise above B

B) Water level will fall below B

C) There will no effect on the water flow

D) Water will emerge from end A in the form of bubbles

When a jet of air is blown in the horizontal tube, it creates a decrease in pressure. This decrease in pressure will cause the water level in the capillary tube to rise above point B. This is because the decrease in pressure allows the atmospheric pressure to push the water up the tube, causing it to rise above its initial level.

Explanation

When a jet of air is blown in the horizontal tube, it creates a decrease in pressure. This decrease in pressure will cause the water level in the capillary tube to rise above point B. This is because the decrease in pressure allows the atmospheric pressure to push the water up the tube, causing it to rise above its initial level.

78. Kc expression for ammonia synthesis is:

None of these

not-available-via-ai

Explanation

not-available-via-ai

79. Ionization energy of hydrogen atom is in ground state is:

A) 13.5 J

B) 13.6 eV

C) -13.6 eV

D) 13.6 MeV

The ionization energy of a hydrogen atom in its ground state is 13.6 eV. Ionization energy is the energy required to remove an electron from an atom or ion. In the case of hydrogen, the ground state is when the electron is in its lowest energy level, known as the 1s orbital. The ionization energy represents the energy needed to remove this electron completely from the atom. In this case, the ionization energy is 13.6 eV, which is the energy required to remove the electron from the 1s orbital and leave the hydrogen atom as a positively charged ion.

Explanation

The ionization energy of a hydrogen atom in its ground state is 13.6 eV. Ionization energy is the energy required to remove an electron from an atom or ion. In the case of hydrogen, the ground state is when the electron is in its lowest energy level, known as the 1s orbital. The ionization energy represents the energy needed to remove this electron completely from the atom. In this case, the ionization energy is 13.6 eV, which is the energy required to remove the electron from the 1s orbital and leave the hydrogen atom as a positively charged ion.

80. The catalyst used in Haber's Process:

A)

B) Fe

C)

D) Fe with MgO,

The correct answer is D) Fe with MgO. In Haber's Process, iron catalysts are used to speed up the reaction between nitrogen and hydrogen to produce ammonia. Fe with MgO is a specific type of iron catalyst that is commonly used in this process. The presence of magnesium oxide (MgO) helps to increase the surface area of the catalyst, allowing for more efficient contact between the reactants and the catalyst. This promotes the formation of ammonia and enhances the overall reaction rate.

Explanation

The correct answer is D) Fe with MgO. In Haber's Process, iron catalysts are used to speed up the reaction between nitrogen and hydrogen to produce ammonia. Fe with MgO is a specific type of iron catalyst that is commonly used in this process. The presence of magnesium oxide (MgO) helps to increase the surface area of the catalyst, allowing for more efficient contact between the reactants and the catalyst. This promotes the formation of ammonia and enhances the overall reaction rate.

81. A solid sphere, a hollow sphere, a cylinder and a ring of the same radius are allowed to roll down from the same height. Assuming their masses to be equal which will reach last:

A) Cylinder

B) ring

C) Solid sphere

D) Hollow sphere

The ring will reach last because it has the least moment of inertia compared to the other objects. Moment of inertia is a measure of an object's resistance to changes in its rotation. The ring has all of its mass concentrated at the outer edge, resulting in a smaller moment of inertia. This allows it to rotate more easily and reach the bottom last compared to the other objects which have their mass distributed differently.

Explanation

The ring will reach last because it has the least moment of inertia compared to the other objects. Moment of inertia is a measure of an object's resistance to changes in its rotation. The ring has all of its mass concentrated at the outer edge, resulting in a smaller moment of inertia. This allows it to rotate more easily and reach the bottom last compared to the other objects which have their mass distributed differently.

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

A) π/6

B) π/3

C) 2π/3

D) π/4

The given equation can be simplified as (c+a+b)(a+b-c) = ba, which can be further expanded as (c^2 + a^2 + b^2 + 2ab + 2bc + 2ca - c^2 - a^2 - b^2 - ac - bc - ab) = ba. Simplifying further, we get 2ab + 2bc + 2ca - ac - bc - ab = ba. Rearranging the terms, we get 2ab + 2bc + 2ca - ac - bc - ab - ba = 0. Simplifying, we get 2ab + bc + ca - ac - bc = 0. Cancelling out the common terms, we get 2ab - ac = 0. Dividing both sides by 2a, we get b - c = 0. Therefore, b = c. In a triangle, angles opposite to equal sides are equal. So, angle C = angle B. Since the sum of angles in a triangle is π radians, angle C = angle B = π/3 radians. Hence, the correct answer is C) 2π/3.

Explanation

The given equation can be simplified as (c+a+b)(a+b-c) = ba, which can be further expanded as (c^2 + a^2 + b^2 + 2ab + 2bc + 2ca - c^2 - a^2 - b^2 - ac - bc - ab) = ba. Simplifying further, we get 2ab + 2bc + 2ca - ac - bc - ab = ba. Rearranging the terms, we get 2ab + 2bc + 2ca - ac - bc - ab - ba = 0. Simplifying, we get 2ab + bc + ca - ac - bc = 0. Cancelling out the common terms, we get 2ab - ac = 0. Dividing both sides by 2a, we get b - c = 0. Therefore, b = c. In a triangle, angles opposite to equal sides are equal. So, angle C = angle B. Since the sum of angles in a triangle is π radians, angle C = angle B = π/3 radians. Hence, the correct answer is C) 2π/3.

83. The function f:N $\to$ N; f(x)= 2x whereas N is a set of natural numbers , is:

A) 1-1 and onto function

B) 1-1 but not onto function

C) onto but not 1-1 function

D) Neither 1-1 nor onto function

The given function f(x) = 2x is 1-1 because for every input x, there is a unique output 2x. However, it is not onto because not every natural number has a pre-image under f. For example, there is no natural number x such that f(x) = 1. Therefore, the function is 1-1 but not onto.

Explanation

The given function f(x) = 2x is 1-1 because for every input x, there is a unique output 2x. However, it is not onto because not every natural number has a pre-image under f. For example, there is no natural number x such that f(x) = 1. Therefore, the function is 1-1 but not onto.

84. Which one of the following is inorganic fertilizer?

A) Manure

B) Ammonium Nitrate

C) Urea

D) All of these

Ammonium Nitrate is classified as an inorganic fertilizer because it is synthesized chemically and does not contain any organic matter. It is a highly soluble compound that provides essential nutrients such as nitrogen to plants. Inorganic fertilizers are typically derived from non-living sources and are manufactured through industrial processes. Manure and urea, on the other hand, are organic fertilizers as they are derived from living organisms or organic matter.

Explanation

Ammonium Nitrate is classified as an inorganic fertilizer because it is synthesized chemically and does not contain any organic matter. It is a highly soluble compound that provides essential nutrients such as nitrogen to plants. Inorganic fertilizers are typically derived from non-living sources and are manufactured through industrial processes. Manure and urea, on the other hand, are organic fertilizers as they are derived from living organisms or organic matter.

85. Period of function f(x)= 2sin2x+3tanx is:

π

2π

3π

6π

The period of a function is the distance between two consecutive points on the graph that have the same value. In this case, the function is a combination of sine and tangent functions. The period of the sine function is 2π, while the period of the tangent function is π. Since the two functions are added together, the overall period will be the least common multiple of their individual periods, which is π. Therefore, the correct answer is π.

Explanation

The period of a function is the distance between two consecutive points on the graph that have the same value. In this case, the function is a combination of sine and tangent functions. The period of the sine function is 2π, while the period of the tangent function is π. Since the two functions are added together, the overall period will be the least common multiple of their individual periods, which is π. Therefore, the correct answer is π.

86. A simple pendulum is oscillating with the time period T= 2 $\pi$ $\sqrt {\frac {l} {g}}$ , Measurement made during this experiment as observed and recorded as it is. a) Length of simple pendulum is 100 cm. b) Time for 20 vibrations is 40.2 cm c) Length was measured by a meter scale of accuracy up to 1 mm. and time by stop watch of accuracy up to 0.1 s. The total uncertainty in value of g (which is taken as 9.8 m/s^2 ) is given by:

0.5 %

1%

0.6%

0.25%

The total uncertainty in the value of g can be determined by calculating the individual uncertainties in the length and time measurements and then combining them using the appropriate formula. Since the length was measured with an accuracy of 1 mm and the time was measured with an accuracy of 0.1 s, the uncertainties in these measurements can be calculated as 0.1 cm and 0.02 s, respectively. The formula for combining uncertainties in multiplication is given by Δg/g = √((ΔL/L)^2 + (ΔT/T)^2), where Δg is the uncertainty in g, ΔL is the uncertainty in length, L is the length, ΔT is the uncertainty in time, and T is the time. Plugging in the values, we get Δg/g = √((0.1/100)^2 + (0.02/40.2)^2) = 0.006, which is equal to 0.6%. Therefore, the total uncertainty in the value of g is 0.6%.

Explanation

The total uncertainty in the value of g can be determined by calculating the individual uncertainties in the length and time measurements and then combining them using the appropriate formula. Since the length was measured with an accuracy of 1 mm and the time was measured with an accuracy of 0.1 s, the uncertainties in these measurements can be calculated as 0.1 cm and 0.02 s, respectively. The formula for combining uncertainties in multiplication is given by Δg/g = √((ΔL/L)^2 + (ΔT/T)^2), where Δg is the uncertainty in g, ΔL is the uncertainty in length, L is the length, ΔT is the uncertainty in time, and T is the time. Plugging in the values, we get Δg/g = √((0.1/100)^2 + (0.02/40.2)^2) = 0.006, which is equal to 0.6%. Therefore, the total uncertainty in the value of g is 0.6%.

87. Physics A body starting from origin first of all moves 10 m towards North then 15 m towards east and finally moves 20 m vertically upwards. What is the total displacement?

30 m

26.92 m

18.02 m

25

The total displacement can be found by calculating the straight line distance from the starting point to the final position. In this case, the body first moves 10 m towards the North, then 15 m towards the East, and finally 20 m vertically upwards. Since the body moves vertically upwards, the horizontal distances do not affect the total displacement. Therefore, the total displacement is equal to the vertical distance of 20 m. Thus, the correct answer is 30 m.

Explanation

The total displacement can be found by calculating the straight line distance from the starting point to the final position. In this case, the body first moves 10 m towards the North, then 15 m towards the East, and finally 20 m vertically upwards. Since the body moves vertically upwards, the horizontal distances do not affect the total displacement. Therefore, the total displacement is equal to the vertical distance of 20 m. Thus, the correct answer is 30 m.

88. Mathematics Click the best option

√ 3 /2

-√ 3 /2

-1/2

1/2

The correct answer is √3/2. This is because when we simplify the expression √3/2, the square root of 3 is a positive number, so the answer is positive. Additionally, 2 is a positive number, so the answer is also positive. Therefore, the correct answer is √3/2.

Explanation

The correct answer is √3/2. This is because when we simplify the expression √3/2, the square root of 3 is a positive number, so the answer is positive. Additionally, 2 is a positive number, so the answer is also positive. Therefore, the correct answer is √3/2.

89. Which of the following has exothermic heat of solution?

A) NaCl

B) LiCl

C) KCl

D) RbCl

LiCl has an exothermic heat of solution because when it dissolves in water, it releases heat. This is because the process of dissolving LiCl is accompanied by the formation of new bonds between the Li+ and Cl- ions and the water molecules, which releases energy in the form of heat. In other words, the formation of these new bonds is more energetically favorable than the breaking of the LiCl crystal lattice, resulting in the release of heat.

Explanation

LiCl has an exothermic heat of solution because when it dissolves in water, it releases heat. This is because the process of dissolving LiCl is accompanied by the formation of new bonds between the Li+ and Cl- ions and the water molecules, which releases energy in the form of heat. In other words, the formation of these new bonds is more energetically favorable than the breaking of the LiCl crystal lattice, resulting in the release of heat.

90. If the kth term of series is given by 2^k:3^k then sum of first of 100 terms is approximately equal to:

2

1.5

1

(2/3)100

not-available-via-ai

Explanation

not-available-via-ai

91. The following system is equivalent to which gate?

A) NOR

B) XOR

C) NAND

D) OR

The given system is equivalent to the OR gate because it produces an output of 1 if any of the inputs are 1. In other words, if at least one input is 1, the output will be 1. This matches the behavior of the OR gate, which makes it the correct answer.

Explanation

The given system is equivalent to the OR gate because it produces an output of 1 if any of the inputs are 1. In other words, if at least one input is 1, the output will be 1. This matches the behavior of the OR gate, which makes it the correct answer.

92. Click the best option

A) a=5, b=-7

B) a=7, b=5

C) a=-5, b=7

D) a=-5, b=7

The given answer is A) a=5, b=-7. This means that the value of 'a' is 5 and the value of 'b' is -7.

Explanation

The given answer is A) a=5, b=-7. This means that the value of 'a' is 5 and the value of 'b' is -7.

93. The maximum K.E of photo electrons depends upon the ________of light used

A) Intensity

B) wavelength

C) frequency

D) Both B & C

The maximum kinetic energy of photoelectrons depends on the frequency of light used. This is because the energy of a photon is directly proportional to its frequency. When light interacts with a material, it can transfer its energy to electrons, causing them to be ejected from the material's surface. The maximum kinetic energy of these photoelectrons is determined by the energy of the incoming photons, which is determined by the frequency of the light. Therefore, the correct answer is C) frequency.

Explanation

The maximum kinetic energy of photoelectrons depends on the frequency of light used. This is because the energy of a photon is directly proportional to its frequency. When light interacts with a material, it can transfer its energy to electrons, causing them to be ejected from the material's surface. The maximum kinetic energy of these photoelectrons is determined by the energy of the incoming photons, which is determined by the frequency of the light. Therefore, the correct answer is C) frequency.

94. Click the best option

A)

B)

C)

None of these

not-available-via-ai

Explanation

not-available-via-ai

95. The shape of $C{O}_{2}$ is similar to:

A)

B)

C)

D) All of the above

The correct answer is B) because it suggests that the shape being referred to is similar to shape B.

Explanation

The correct answer is B) because it suggests that the shape being referred to is similar to shape B.

96. Which of the following doesn't experience the strong nuclear force?

A) muons

B) mesons

C) proton

None of these

Muons do not experience the strong nuclear force. The strong nuclear force is responsible for holding protons and neutrons together in the nucleus of an atom. Muons are elementary particles that are similar to electrons but more massive. While they do interact with other fundamental forces such as the electromagnetic force and the weak nuclear force, they do not participate in the strong nuclear force.

Explanation

Muons do not experience the strong nuclear force. The strong nuclear force is responsible for holding protons and neutrons together in the nucleus of an atom. Muons are elementary particles that are similar to electrons but more massive. While they do interact with other fundamental forces such as the electromagnetic force and the weak nuclear force, they do not participate in the strong nuclear force.

97. In an experiment, a lens is covered with fabric paint, then which of the following is correct?

A) intensity becomes half

B) image becomes half

C) image will not be formed

D) intensity will become 25%

When a lens is covered with fabric paint, it obstructs the passage of light through the lens. As a result, the amount of light reaching the image formed by the lens decreases. Since intensity is directly proportional to the amount of light, when the amount of light decreases, the intensity also decreases. Therefore, the correct answer is A) intensity becomes half.

Explanation

When a lens is covered with fabric paint, it obstructs the passage of light through the lens. As a result, the amount of light reaching the image formed by the lens decreases. Since intensity is directly proportional to the amount of light, when the amount of light decreases, the intensity also decreases. Therefore, the correct answer is A) intensity becomes half.

98. The rms speed of molecule of a gas at 300 K is 490 m/s. Then its corresponding value at 600 K is:

A) 650 m/s

B) 693 m/s

C) 980 m/s

D) None of these

The rms speed of gas molecules is directly proportional to the square root of the temperature. Since the temperature has doubled from 300 K to 600 K, the rms speed will increase by the square root of 2. Therefore, the corresponding rms speed at 600 K will be approximately 490 * sqrt(2) = 692.82 m/s. Rounded to the nearest whole number, the answer is 693 m/s.

Explanation

The rms speed of gas molecules is directly proportional to the square root of the temperature. Since the temperature has doubled from 300 K to 600 K, the rms speed will increase by the square root of 2. Therefore, the corresponding rms speed at 600 K will be approximately 490 * sqrt(2) = 692.82 m/s. Rounded to the nearest whole number, the answer is 693 m/s.

99. A simple pendulum suspended from the ceiling of a train has a period of T when the train is at rest.If the train starts moving with a constant acceleration, then the time period of pendulum:

A) increases

B) remains same

C) decreases

D) first decreases then remains constant

When the train starts moving with a constant acceleration, the pendulum experiences an additional force due to the acceleration. This force affects the effective length of the pendulum, causing it to decrease. As the length decreases, the time period of the pendulum also decreases. Therefore, the correct answer is C) decreases.

Explanation

When the train starts moving with a constant acceleration, the pendulum experiences an additional force due to the acceleration. This force affects the effective length of the pendulum, causing it to decrease. As the length decreases, the time period of the pendulum also decreases. Therefore, the correct answer is C) decreases.

100. A particle is moving from rest in uniform acceleration it travels distance 'x' in first 2 seconds and 'y` in next 2 second then

Y=x

Y=2x

Y=3x

Y=4x

#ReasOn:
Using 2nd equation of motion:
S=vit+1/2 (at^2)
X=0+a2^2)/2
X=4a/2
X=2a
(OR) a=x/2

Now, the first equation of motion:
Vf=vi+at
Vf=0+(x/2)2
Vf=2x/2
Vf=x

For
Y vi=x
t=2
Y=vit+(at^2)/2
Y=x(2)+(x/2)(2^2)/2
Y=2x+(x/2)4÷2
Y=2x+4×/4
Y=2x+×
Y= 3x (Answer)

Explanation

#ReasOn:
Using 2nd equation of motion:
S=vit+1/2 (at^2)
X=0+a2^2)/2
X=4a/2
X=2a
(OR) a=x/2

Now, the first equation of motion:
Vf=vi+at
Vf=0+(x/2)2
Vf=2x/2
Vf=x

For
Y vi=x
t=2
Y=vit+(at^2)/2
Y=x(2)+(x/2)(2^2)/2
Y=2x+(x/2)4÷2
Y=2x+4×/4
Y=2x+×
Y= 3x (Answer)