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QUESTION: 1

Two charges q and – q are fixed at distance ‘d’ apart. Then another charge of some magnitude can be placed such that it will be in equilibrium :

Solution:

QUESTION: 2

An electric current passes through non uniform cross-section wire made of homogeneous and isotropic material. If the j_{A} and j_{B} be the current densities and E_{A} and E_{B} be the electric field intensities at A and B respectively, then

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QUESTION: 3

A and B are two metallic rings placed at opposite sides of an infinitely long straight conducting wire as shown. If current in the wire is slowly decreased, the direction of induced current will be:

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QUESTION: 4

N atoms of a radioactive element emit n alpha particles per second at an instant. Then the half - life of the element is

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QUESTION: 5

Two small balls, each having equal positive charge Q are suspended by two insulating strings of equal length L from a hook fixed to a stand. If the whole set-up is transferred to a satellite in orbit around the earth, the tension in equilibrium in each string is equal to

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QUESTION: 6

Assume that gravitational lines of forces represent gravitational field just like electric lines of forces represent electric field. Which of the following diagram correctly represents the gravitational field lines for a pair of point masses shown in options below ?

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QUESTION: 7

Figure shows a uniformly charged hemispherical shell. The direction of electric field at point p, that is off-centre (but in the plane of the largest circle of the hemisphere), will be along

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QUESTION: 8

In which of the following cases the total number of decays will be maximum in a time interval of t = 0 to t = 4 hr. The first term represents the number of nuclei at time t = 0 and the second represents the half life of the radionuclide.

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QUESTION: 9

An electron of mass m , when accelerated through a potential V has de-Broglie wavelength λ. The de-Broglie wavelength associated with a proton of mass M accelerated through the same potential difference will be :

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QUESTION: 10

The plates of a parallel plate capacitor have charges Q and -2Q. Its capacitance is C. The potential difference between its plates will be

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QUESTION: 11

Acceleration of a particle under projectile motion at the highest point of its trajectory is :

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QUESTION: 12

Three resistances are arranged as shown. The potential of the point O is:

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QUESTION: 13

A battery of internal resistance 2 ? is connected to a variable resistor whose value can vary from 4 ? to 10?. The resistance is initially set at 4 ? If the resistance is now increased then

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QUESTION: 14

Two identical conducting rings A & B of radius R are in pure rolling over a horizontal conducting plane with same speed (of center of mass)v but in opposite direction. A constant magnetic field B is present pointing inside the plane of paper. Then the potential difference between the highest points of the two rings, is :

Solution:

QUESTION: 15

Two hydrogen atoms are in excited state with electrons residing in n = 2. First one is moving towards left and emits a photon of energy E_{1} towards right. Second one is moving towards left with same speed and emits a photon of energy E_{2} towards left. Taking recoil of nucleus into account during emission process

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QUESTION: 16

Entropy change for 2 moles of an ideal monoatomic gas when it undergoes the change in state from (4 atm, 300K) to (1 atm, 150 K) is

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QUESTION: 17

Which of following is responsible for temporary hardness of water ?

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QUESTION: 18

A solution turns red litmus blue, its pH is likely to be :

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QUESTION: 19

10 mL of a solution of NaOH is found to be completely neutralised by 8 mL of a given solution of HCl. If we take 20 mL of the same solution of NaOH, the amount of H_{2}SO_{4} solution (having the same molarity as that of initial HCl solution) required to neutralise it will be :

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QUESTION: 20

Consider the following equilibrium situation and identify the correct statement :

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QUESTION: 21

What is the pH of 0.01M NaOH aqueous solution ?

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QUESTION: 22

How many α and β particles will be emitted when this conversion occurs ?

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QUESTION: 23

A mixture of a definite composition of ethanol and water forms

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QUESTION: 24

the major product P is

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QUESTION: 25

x, y, z are respectively :

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QUESTION: 26

The solution set of the equation =9 is

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QUESTION: 27

The number of ordered pairs (x, y) satisfying |y| = cosx and y = sin^{-1} (sinx) where are

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QUESTION: 28

The domain of definition of function is

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QUESTION: 29

A function f has domain [–1, 2] and range [0, 1]. The domain and range respectively of the function g defined by g(x) = 1 – f(x 1) is

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QUESTION: 30

The curve y - e^{xy} x = 0 has a vertical tangent at

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QUESTION: 31

The function f(x) is defined as follows What must be the values of a, b, c so that is continuous everywhere ?

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QUESTION: 32

If f(x) = 1 – x – x^{3} , then all real values of x satisfying the inequality 1 – f(x) – f ^{3}(x) > f(1 – 5x) are in

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QUESTION: 33

If a sequence < a_{n} > is such that a_{1} = 1, and exists, then is equals to

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QUESTION: 34

Let where a is constant. In which of the following intervals is decreasing

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QUESTION: 35

If = sin x – A (sin x)^{-1} – B tan^{-1} (sinx) C, (C being arbitrary constant) , then A B is equal to

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QUESTION: 36

Two dice were thrown and it is known that the numbers which come up were different. The probability that the sum of the two numbers is 6, is

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QUESTION: 37

A vector has components 2p and 1 with respect to a rectangular cartesian system. The system is rotated through a certain angle about the origin in the counterclockwise sense. If with respect to the new system has components p 1 and 1, then

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QUESTION: 38

The value of is ([x] stands for greatest integer less than or equal to x)

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QUESTION: 39

dx is equal to

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QUESTION: 40

Solution of differential equation f(x) is

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QUESTION: 41

Find missing term ?

1, 3, 7, 25, 103, ?

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QUESTION: 42

Find missing term ?

ABCA, BCDB, CDEC, DEFD, ?

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QUESTION: 43

Find the missing term?

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QUESTION: 44

Assume the following :

A @ B means A is greater than B ;

A B means A is either greater than or equal to B;

A $ B means A is equal to B ;

A B means A is smaller than B ;

A # B means A is either smaller than or equal to B;

In each question, two statements followed by two conclusions I and II are given. Assuming the statement to be true, state which of the conclusions I and II is / are definitely true ?

Statements : P # Q, M N $ P

Conclusions : I. M @ P II. N # Q

Solution:

QUESTION: 45

Assume the following :

A @ B means A is greater than B ;

AB means A is either greater than or equal to B;

A $ B means A is equal to B ;

A B means A is smaller than B ;

A # B means A is either smaller than or equal to B;

In each question, two statements followed by two conclusions I and II are given. Assuming the statement to be true, state which of the conclusions I and II is / are definitely true ?

Statements : L M, R T $ L

Conclusions :I. T M II. R @ L

Solution:

QUESTION: 46

How many squares does the figure have ?

Solution:

QUESTION: 47

Introducing a girl, Vipin said, Her mother is the only daughter of my mother – in – law. How is Vipin related to the girl ?

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QUESTION: 48

Ram is to the South-East of Mukesh, Shyam is to the East of Mukesh and North-East of Ram. If Suresh is to the North of Ram and North-West of Shyam, in which direction of Mukesh is Suresh located ?

Solution:

QUESTION: 49

The year next to 1996 having the same Calendar will be -

Solution:

QUESTION: 50

At what time between 12 and 1 will the hands of a clock be in the straight line but not together

Solution:

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