1.
Reading Comprehension (Question 91-95)
Philosophy of Education is a label applied to the study of the purpose, process, nature and ideals of education. It can be considered a branch of both philosophy and education. Education can be defined as the teaching and learning of specific skills, and the imparting of knowledge, judgment and wisdom, and is something broader than the societal institution of education we often speak of.
Many educationalists consider it a weak and woolly field, too far removed from the practical applications of the real world to be useful. But philosophers dating back to Plato and the Ancient Greeks have given the area much thought and emphasis, and there is little doubt that their work has helped shape the practice of education over the millennia.
Plato is the earliest important educational thinker, and education is an essential element in "The Republic" (his most important work on philosophy and political theory, written around 360 B.C.). In it, he advocates some rather extreme methods: removing children from their mothers' care and raising them as wards of the state, and differentiating children suitable to the various castes, the highest receiving the most education, so that they could act as guardians of the city and care for the less able. He believed that education should be holistic, including facts, skills, physical discipline, music and art. Plato believed that talent and intelligence is not distributed genetically and thus is be found in children born to all classes, although his proposed system of selective public education for an educated minority of the population does not really follow a democratic model.
Aristotle considered human nature, habit and reason to be equally important forces to be cultivated in education, the ultimate aim of which should be to produce good and virtuous citizens. He proposed that teachers lead their students systematically, and that repetition be used as a key tool to develop good habits, unlike Socrates' emphasis on questioning his listeners to bring out their own ideas. He emphasized the balancing of the theoretical and practical aspects of subjects taught, among which he explicitly mentions reading, writing, mathematics, music, physical education, literature, history, and a wide range of sciences, as well as play, which he also considered important.
During the Medieval period, the idea of Perennialism was first formulated by St. Thomas Aquinas in his work "De Magistro". Perennialism holds that one should teach those things deemed to be of everlasting importance to all people everywhere, namely principles and reasoning, not just facts (which are apt to change over time), and that one should teach first about people, not machines or techniques. It was originally religious in nature, and it was only much later that a theory of secular perennialism developed.
During the Renaissance, the French skeptic Michel de Montaigne (1533 - 1592) was one of the first to critically look at education. Unusually for his time, Montaigne was willing to question the conventional wisdom of the period, calling into question the whole edifice of the educational system, and the implicit assumption that university-educated philosophers were necessarily wiser than uneducated farm workers, for example.
2.
“Something is very wrong,” says the detective. “I know!” says Ms. Gervis. “It is wrong that someone has stolen from me!” The detective looks around Ms. Gervis’ apartment. “That is not what I am talking about, ma’am. What is wrong is that I do not understand how the robber got in and out.” Ms. Gervis and the detective stand in silence. Ms. Gervis’ eyes are full of tears. Her hands are shaking. “The robber did not come through the window,” says the detective. “These windows have not been opened or shut in months.” The detective looks at the fireplace. “The robber did not squeeze down here.” The detective walks to the front door. He examines the latch. “And since there are no marks or scratches, the robber definitely did not try to break the lock.” “I have no idea how he did it,” says a bothered Ms. Gervis. “It is a big mystery.” “And you say the robber stole nothing else?” asks the detective. “No money, no jewelry, no crystal?” “That’s right, detective. He took only what was important to me,” Ms. Gervis says with a sigh. “There is only one thing I can do now.” “And what is that?” the detective asks with surprise. “I will stop baking cakes,” Ms. Gervis says. “They are mine to give away. They are not for someone to steal.” “You can’t do that!” says the detective with alarm. “Who will bake those delicious cakes?” “I am sorry. I do not know,” says Ms. Gervis. “I must solve this case immediately!” says the detective.
3.
Physics: (Question 01 to 30)
The Equation of state of some gases can be expressed as . 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:
Correct Answer
C. [ML^{5}T^{-2}] and [L^{3}]
Explanation
Using Dimensional Homogeneity Analysis Rules:
a/V2Â 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]Â
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' isÂ [L3]Â
4.
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?
Correct Answer
D. 31 N
Explanation
Range of the resultant of two vectors A and B can be found by:
|A-B|Â â‰¤ ResultantÂ â‰¤ |A+B|
In this case, A= 12 N and B=13 N
so, range of the resultant is given by:
|12-13|Â â‰¤ ResultantÂ â‰¤ |12+13|
|-1|Â â‰¤Â ResultantÂ â‰¤ 25
1Â â‰¤Â ResultantÂ â‰¤ 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.
5.
The period of oscillation of a simple pendulum is given by 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:
Correct Answer
C. 0.2%
6.
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:
Correct Answer
B. 95%
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.
7.
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?
Correct Answer
C. y=4 x
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).
8.
A mixture of two gas at constant temperature contains the molecules of two kinds. The first kind of mass m_{1 }and root mean square speed c_{1 }and the second molecule of mass m_{2} and rms speed c_{2}. The ratio of is:
Correct Answer
D.
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.
9.
For the velocity-time graph, as shown in the figure below, the total distance covered by a body in all seven seconds will be:
Correct Answer
C. 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.
10.
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;
Correct Answer
C. 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.
11.
The v-t graph of a moving object is given in figure. The maximum acceleration is
Correct Answer
D. 6 meter 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.
12.
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?
Correct Answer
B. Elastic modulus of solid is much greater than that of the elastic modulus of gas
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.
13.
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_{C }respectively;
Correct Answer
A. V_{A}=V_{B}=V_{C}
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.
14.
A weight lifter lifts 300 kilograms from the ground to height of 2 meters in 3 seconds. The average power generated by him is:
Correct Answer
D. 1960 watts
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.
15.
Two satellites of masses m_{1} and m_{2 }(m_{1} > m_{2}) are revolving around the earth in circular orbits of radii r_{1} and r_{2} (r_{1} > r_{2}) respectively. Which of the following statements is true regarding their speeds v_{1} and v_{2} ?
Correct Answer
C. V_{1 }< v_{2}
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 < v2" is true.
16.
If the critical angle for the total internal reflection from a medium to vacuum is 30°. The velocity of light in the medium is:
Correct Answer
B. 1.5 × 10^{8} 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.
17.
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
Correct Answer
D. Height of the liquid in the tubes A and C is 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.
18.
The maximum percentage efficiency of engine operating between 227°C and 7 °C?
Correct Answer
C. 44%
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 220Â°C (227Â°C - 7Â°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.
19.
The displacement of a particle executing Simple Harmonic motion is half of its magnitude. The fraction of its Kinetic energy will be:
Correct Answer
C. 3/4
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/âˆš2. Therefore, the fraction of its kinetic energy will be (1/âˆš2)^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.
20.
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:
Correct Answer
C. 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.
21.
If 15/16 of the the radioactive element decays in 8 minutes the half life of the radioactive element is:
Correct Answer
C. 2 min
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.
22.
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:
Correct Answer
B. Incresaes
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.
23.
The relationship between X and Y in the following diagram
Correct Answer
B. Y'= 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.
24.
The current in a resistor is 8.0 mA. How many number of electrons flows through the resistor in 0.020 seconds?
Correct Answer
B. 1 electrons
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.
25.
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:
Correct Answer
B. 10 capacitors in parallel
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.
26.
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?
Correct Answer
B. Ammeter reading increases and brightness 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.
27.
Semi-conductor behaves as _________ at 0 K
Correct Answer
A. Insulators
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.
28.
When light falls on the metal surface, the maximum kinetic energy of the emitted photo-electrons depends upon:
Correct Answer
B. Frequency of incident light
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.
29.
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?
Correct Answer
B. The direction of the current will be 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.
30.
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?
Correct Answer
B. Using the monochromatic light of higher wavelength
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.
31.
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;
Correct Answer
C. Smaller wavelength
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 400Â°C will emit radiation with a smaller wavelength compared to the block heated to 200Â°C.
32.
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?
Correct Answer
C. Equal to 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.
33.
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?
Correct Answer
A. 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.
34.
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:
Correct Answer
C. 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.
35.
Two vectors are perpendicular to each other. The positive value of "a" will be:
Correct Answer
B. 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.
36.
Two vectors are parallel to each other then the value of will be;
Correct Answer
B. 2
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.
37.
Additive inverse of the complex number, is;
Correct Answer
C.
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.
38.
Polar form of is;
Correct Answer
C.
39.
Two lines,
Correct Answer
B. L and M are perpendicular to each other
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.
40.
The function for has point of maximum at,
Correct Answer
A. (1,5)
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.
41.
The general solution of is;
Correct Answer
A.
42.
If the line joining is parallel to the line joining , then value of 'k' is :
Correct Answer
C. 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.
43.
The angle C of the triangle ABC, in which is;
Correct Answer
A.
44.
If
Correct Answer
B. 60° or 300°
Explanation
The correct answer is 60Â° or 300Â° because these angles are both acute angles. An acute angle is an angle that measures less than 90 degrees. In the given options, 45Â° and 315Â° are obtuse angles, as they measure more than 90 degrees. Similarly, 30Â° and 330Â° are also obtuse angles. Therefore, the only two options that are acute angles are 60Â° and 300Â°.
45.
If the term independent of 'x' in the expression is 45/4 then;
Correct Answer
B. |k|=1/2
46.
If then;
Correct Answer
C.
47.
Ifthen a+b is
Correct Answer
C. 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.
48.
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:
Correct Answer
B.
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.
49.
The inequality , which satisfies the intervals:
Correct Answer
C.
50.
Area enclosed by the curve and the x-axis from is same as:
Correct Answer
D. All of these
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.