Question Paper (Section wise)

A convex lens is put 10 cm from a light source and it makes a sharp image on a screen, kept 10 cm from the lens. Now a glass block (refractive index 1.5) of 1.5 cm thickness is placed in contact with the light source. To get the sharp image again, the screen is shifted by a distance d. Then d is:

A resistance is shown in the figure. Its value and tolerance are given respectively by:

A plane electromagnetic wave of frequency 50 MHz travels in free space along the positive x-direction. At a particular point in space and time,  The corresponding magnetic field , at that point will be

Two identical spherical balls of mass M and radius R each are stuck on two ends of a rod of length 2R and mass M (See figure.) The moment of inertia of system about the axis passing perpendicularly through the centre of the rod is:

Consider a Young’s double slit experiment as shown in figure. What should be the slit separation d in terms of Wavelength λ such that the first minima occurs directly in front of the slit (S₁)?

The electric field of a plane polarized electromagnetic wave in free space at time t = 0 is given by an expression. The magnetic field (x, z, t) is given by: (c is the velocity of light)

A body is projected at t = 0 with a velocity 10ms^-1 at an angle of 60° with the horizontal. The radius of curvature of its trajectory at t=1s is R. Neglecting air resistance and taking acceleration due to gravity g=10 ms^-2. The radius of R is

The force of interaction between two atoms is given by; where x is the distance, k is the Boltzmann constant and T is temperature and α and β are two constants. The dimension of β is:

A body of mass 1 kg falls freely from a height of 100 m, on a platform of masses 3kg which is mounted on a spring having constant k = 1.25 × 10⁶ N/m. The body sticks to the platform and the spring’s maximum compression is found to be x. Given that g=10 ms^-2 the value of x will be close to:

An ideal gas is enclosed in a cylinder at pressure of 2 atm and temperature, 300K. The mean time between two successive collisions is 6 × 10^-8 s. if the pressure is doubled and temperature is increased to 500 K, the mean time between two successive collisions will be close to:

A 10 m long horizontal wire extends from North East to South West. It is falling with a speed of 5.0 ms^-1, at right angles to the horizontal component of the earth’s magnetic of field, 0.3 × 10^-4 Wb/m². The value of the induced emf in wire is:

The mean intensity of radiation on the surface of the sun is about 10⁸ W/m². The rms value of the corresponding magnetic field is closet to:

If Surface tension (S), Moment of Inertia (I) and Planck’s constant (h), were to be taken as the fundamental units, the dimensional formula for linear momentum would be:

Two magnetic dipoles X and Y are placed at a separation d, with their axes perpendicular to each other. The dipole moment of Y is twice that of X. A particle of charge q is passing through their mid-point P, at angle Ѳ =45° with the horizontal line as shown in the figure. What would be the magnitude of force on the particle at that instant? (d is much larger than the dimension of the dipole)

A positive point charge is released from rest at a distance r₀ from a positive line charge with uniform density. The speed (V) of the point charge, as a function of instantaneous distance r from line charge, it proportional to

The following bodies are made to roll up (without slipping) the same inclined plane from a horizontal place: (i) a ring of radius R, (ii) a solid cylinder of radius and (iii) a solid sphere of radius . If, in each case, the speed of the center of mass at bottom of the incline is same, the ratio of the maximum heights they climb is:

A rectangular coil (Dimension 5 cm × 2 cm) with 100 100 turns, carrying a current of 3 A in the clock-wise direction, is kept centered at the origin and in the X-Z plane. A magnetic field of 1 T is applied along X-axis. If the coil is tilted through 45° about Z-axis, then the torque on the coil is:

The magnetic field of a plane electromagnetic wave is given by:

Where B₀= 3 × 10^-5 T and B₁ = 2 ×10^-6 T. The rms value of the force experienced by a stationary charge Q = 10^-4 = C at z = 0 is closet to:

One mole of ideal gas passes through a process where pressure and volume obey the relation

Here P₀ and V₀ are constant. Calculate the change in the temperature of the gas if its volume change from V₀ to 2V₀

The correct figure that shows, schematically, the wave pattern produced by superposition of two waves of frequencies 9 Hz and 11 Hz,

A 2 mW laser operates at a wavelength of 500 nm. The approximate number photons that will be emitted per second is ______ × 10¹⁵.

[Given Planck’s constant h = 6.6 × 10-³⁴ Js, speed of light c = 3.0 × 10⁸ m/s]

An excited He⁺ ion emits two photons in succession, with wavelength 108.5 nm and 30.4 nm, in making a transition to ground state. The quantum number n, corresponding to its initial excited state is ______.

(For photon of wavelength λ, energy )

The resistive network shown below is connected to a D. C. source of 16 V. The power consumed by the network is 4 Watt. The value of R is _____ Ω.

An amplitude modulated waves is represented by expression v_m = 5 (1 + 0.6 cos 6280t) sin (211 × 10⁴t) volts. The maximum amplitudes of the amplitude modulated wave is _______.

A galvanometer, whose resistance is 50 Ω has 25 divisions in it. When a current of 0.4 mA passes through it, its needle (pointer) deflects by one division. To use this galvanometer as a voltmeter of range 2.5 V, it should be connected to a resistance of ____ Ω.

In general, the properties that decrease and increase down a group in the periodic table respectively are

The anodic half-cell of lead- acid battery is recharged using electricity of 0.05 Faraday. The amount of PbSO₄ electrolyzed in gm during the process is:

(Molar mass of PbSO₄ = 303 g mol^-1)

The alkaline earth metal nitrate that does not crystallise with water molecules is

The 71^st electron of an element X with an atomic number of 71 enters into the orbital:

An aromatic compound ‘A’ having molecular formula C₇H₆O₂ on treating with aqueous ammonia and heating forms compound ‘B’. The compound ‘B’ on reaction with molecular bromine and potassium hydroxide provides compound ‘C’ having molecular formula C₆H₇N. The structure of ‘A’ is:

What is the IUPAC name of the following compound?

The correct match between items I and II is:

The concentration of dissolved oxygen (DO) is cold water can go upto:

If a reaction follows the Arrhenius equation, the plot Ink v 1/ (RT) gives straight line with a gradient (-y) unit. The energy required to activate the reactant is:

The element that does NOT show catenation is:

Among the following, the false statement is:

The major product of the following reaction is:

The percentage composition of carbon by mole in methane is:

The Mond process is used for the:

Fructose and glucose can be distinguished by:

Magnesium powder burns in air to give:

The number of water molecule(s) not coordinated to copper ion directly in CuSO₄.5H₂O, is:

Among the following, the molecule expected to be stabilized by anion formation is:

The major product obtained in the given reaction is

Total number of the correct statements among (a) to (d) are:

a.    Saline hydrides produce H₂ gas when reacted with H₂O.

b.    Reaction of LiAH₄ with BF₃ leads to B₂H₆.

c.    PH₃ and CH₄ are electron - rich and electron-precise hydrides, respectively.

d.    HF and CH₄ are called as molecular hydrides.

Number of noble gas/gases that does NOT occur in the atmosphere

Number of carbon atoms in product which is having higher molecular weight in following reaction are:

Total number of functional group present in the major product of the following addition reaction is:

Complete removal of both the axial ligands (along the z-axis) from an octahedral complex leads to the following splitting patterns (relative orbital energies not on scale).

Correct number of patterns is-

Glucose on prolonged heating with HI gives an alkane. Total number of carbons in this alkane is-

The value of  dx is:

The maximum volume (in. cu. m) of the right circular cone having slant height 3 m is

Axis of a parabola lies along x – axis. If its vertex and focus are at distance 2 and 4 respectively from the origin on the positive x – axis, then which of the following points does not lie on it?

The value of is:

The positive value of λ for which the co-efficient of x² in the expression  is 720, is:

, then K is equal to:

If the system of linear equation

2x + 2y + 3z = a

3x – y + 5z = b

x - 3y +2z = c

Where a, b, c, are non-zero real numbers, has more than one solution, then:

The outcome each of 30 item was observed; 10 items gave an outcome  each, 10 items gave outcome  each and the remaining 10 items gave outcome  each. If the variance of this outcome data is  then |d| equals:

If one real root of the quadratic equation 81x² + kx + 256 = 0 is cube of the other root, then a value of k is:

Let  be three unit vectors, out of which vectors  are non-parallel. If α and β are the angles which vector  makes with vectors  respectively and

If an angle between the line,  and the plane, x - 2y – kz = 3 is  then a value of k is:

The expression ∼(∼ p → q) is logically equivalent to:

Let f(x) = a^x (a > 0) be written as f(x) = f₁(x) + f₂(x), where f₁(x) is an even function and f₂(x) is an odd function.

Then f₁(x + y) + f₁(x - y) equals

Let f: [-1, 3] → R is defined as

Where [t] denotes the greatest integer less than or equal to t. Then f is discontinuous at:

The sum  is equal to:

A committee of 11 members is to be formed from 8 males and 5 females. If m is the number of ways the committee is formed with at least 6 males and n is the number of ways the committee is formed with at least 3 females, then:

All the points in the set  lie on a ______

The solution of the differential equation (x≠ 0) with y(1) = 1, is:

Lines are drawn parallel to the line 4x - 3y + 2 = 0 at a distance from the origin. Then which one of the following points lies on any of these lines?

If the area (in sq. units) of the region bounded by the curves y = 2^x and y = |X + 1| in the first quadrant is  The value of k is equal to __________.

If three of the six vertices of a regular hexagon are chosen at random, the probability that the triangle formed with these chosen vertices is equilateral is  Then the value of m is equal to ____________.

If the area (in sq. units) of the region {(x, y): y² ≤ 4x, x + y ≤ 1, x ≥ 0, y ≥ 0} is a √2 + b, then a – b is equal to _________.

The number of solutions of the equation 1 + sin⁴x = cos²3x,  is equal to __________.

If the value of the integral

The value of ‘a’ is equal to _________.