Question Paper (Section wise)

Mobility of electron in a semiconductor is defined as the ratio of their velocity to the applied electric field. If, for an n-type semiconductor, the density of electrons is 1019 m^-3 and their mobility is 1.6 m² / (V. s) then the resistivity of the semiconductor (since it is an n-type semiconductor contribution of holes is ignored) is close to:

A copper wire is stretched to make it 0.5% longer. The percentage change in its electric resistance if its volume remains unchanged is

When the switch S, in the circuit shown is closed, then the value of current I will be

Consider the nuclear fission Ne²⁰ → 2He⁴ + C¹². Given that the binding energy/ nucleon of Ne²⁰, He⁴ and C¹² are, respectively, 8.03 MeV, 7.07 MeV, and 7.86 MeV, Identify the correct statement:

Charges – q and + q located at A and B, respectively, constitute an electric dipole. Distance AB = 2a, O is the mid-point of the dipole OP is perpendicular to AB. A charge Q is placed at P where OP = y and y >> 2a. The charge Q experience an electrostatic force F. If Q is now moved along the equatorial line to P’ such that , the force on Q will be close to:

A rigid massless road of length 3I has tow masses attached at each end as shown in the figure. The rod is pivoted at point P on the horizontal axis ( see figure). When released from initial horizontal position, its instantaneous angular acceleration will be :

There are two long co – axial solenoids of same length I. The inner and outer coils have radii r₁ and r₂ and number of turns per unit length n₁ and n₂ respectively. The ratio of mutual inductance to the self – inductance of the inner – coil is:

The resistance of the meter bridge AB in given figure is 4Ω With a cell emf ε=005 V and rheostat resistance R_h =2Ω the full point is obtained at some point J. When the cell is replaced by another one of emf ε = ε₂ the same null point J is found for R_n=6 Ω. The emf ε₂ is:

If the de Broglie wavelength of an electron is equal to  10^-3 times the wavelength of a photon of frequency 6 × 10¹⁴ Hz, then the speed of electron is equal to: (Speed of light=3 × 10=8=m/s; Planck’s constant=6.63 × 10^-34J.s; Mass of electron=9.1 × 10^-31Kg)

Two satellites, A and B, have masses m and 2m respectively. A is in a circular orbit of radius R, and B is in a circular orbit of radius 2R around the earth. The ratio of their kinetic energies, T_A / T_B, is:

A block kept on a rough inclined plane, as shown in the figure, remains at rest upto a maximum force 2 N down the inclined plane. The maximum external force up the inclined plane that does not move the block is 10 N. the coefficient of static friction between the block and the plane is:

[Take g = 10 m / s²]

Two particles A, B are moving on two concentric circles of radii R₁ and R₂ with equal angular speed ω. At t = 0, their positions and direction of motion are shown in the figure:

The relative velocity is given by:

A parallel plate capacitor has 1_µF capacitance. One of its two plates is given + 2_µC charge and the other plate, +4_µC charge. The potential difference developed across the capacitor is:

In a line of sight radio communication, a distance of about 50 km is kept between the transmitting and receiving antennas. If the height of the receiving antenna is 70m, then the minimum height of the transmitting antenna should be: (Radius of the Earth = 6.4×10⁶m)

The very long, straight and insulated are kept at 90° angle from each other In xy – plane as shown in the figure.

These wires cary currently of equal magnitude I, whose directions are shown in the figure. The met magneti field at point P will be:

The figure shows a Young’s double slit experimental setup. It is observed that when a thin transparent sheet of thickness t and refractive index μ is put in front of one of the slits, the central maximum gets shifted by a distance equal to n fringe widths. If the wavelength of light used is λ, t will be:

The stream of a river is flowing with a speed of 2 km/h. A swimmer can swim at a speed of 4 km/h. What should be the direction of the swimmer with respect to the flow of the river to cross the river straight?

The pressure wave, P = 0.01 sin [1000t – 3x] NM^–2, corresponds to the sound produced by a vibrating blade on a day when atmospheric temperature is 0°C. On some other day when temperature is T, the speed of sound produced by the same blade and at the same frequency is found to be 336 ms^–1. Approximate value of T is:

Two blocks A and B of masses m_A = 1kg and m_B = 3 kg are kept on the table as shown in figure. The coefficient of friction between A and B is 0.2 and between B and the surface of the table is also 0.2. The maximum force F that can be applied on B horizontal, so that the block A does not slide over the block B is:

The formula X = 5YZ² X and Z have dimensions of capacitance and magnetic field respectively. What are the dimensions of Y in Sl units?

In a Young’s double slit experiment the ratio of the slit’s width is 4:1. The approximate value of ratio of the intensity of maxima to minima, close to central fringe on the screen will be _______.

A man (mass = 50 kg) and his son (mass = 20 kg) are standing on a frictionless surface facing each other. The man pushes his son so that he starts moving at a speed of 6 ms^-1 with respect to the man. The speed of the man with respect to the surface is ______ m/s.

The transfer characteristic curve of a transistor, having input and output resistance 100 Ω and 100 kΩ respectively, is shown in the figure. For the given case the Voltage gain is ________ kV.

A gas can be transported from point A to point B using one of two processes: ACB or ADB. When the path ACB is used, 40 J of heat enters the system. If path ADB is used, the system's work down is 10 J, and the heat flow into the system in path ADB is _____ J.

A conducting circular loop made of a thin wire, has area 3.5 × 10^-3 m² resistance 40 Ω. It is placed perpendicular to a time dependent magnetic field B(t) = (0.4T) sin (50πt). The field is uniform in space. Then the net charge flowing through the loop during t = 0 s and t = 10 ms is close to ______ μC.

Adsorption of a gas follows Freundlich adsorption isotherm. In the given plot, x is the mass of gas adsorbed on mass m of the adsorbent at pressure. is proportional to

The ore that contains both iron and copper is

Aluminium is usually found in + 3 oxidation state. In contrast, thallium exists in + 1 and + 3 oxidation states. This is due to

The major product 'Y' in the following reaction is:

An ideal gas undergoes isothermal compression from 5 m³ to 1m³ against a constant external pressure of 4 NM^-2. Heat released in this process is used to increase the temperature of 1 mole of Al. If molar heat capacity of AI is 24 Jmol^-1K^-1, the temperature of Al is increase by:

The major product of the following reaction is:

The correct match between item I and item II is:

The freezing point of diluted milk sample is found to be – 0.2°C, while it should have been 0.5°C for pure milk. How much water been added to pure milk to make the diluted sample?

The complex ion that will lose its crystal field stabilization energy upon oxidation of its metal to +3 state is

The combination of plots which do not represent isothermal expansion of an ideal gas is:

(a)

(b)

(c)

(d)

The major product in the following conversion is:

The idea of froth floatation method came from a person X and this method is related to the process Y of ores. X and Y, respectively, are:

In the following reaction; xA→ yB

‘A’ and ‘B’ respectively can be:

The major product in the following reaction is:

The compound that inhibits the growth of tumors is:

For 1 molal aqueous solution of the following compounds, which one will show the highest freezing point?

The major product of the following reaction is:

Sodium salt of an organic acid ‘X’ produces effervescence with conc. H₂SO₄. ‘X’ reacts with the acidified aqueous CaCl₂ solution to give a white precipitate which decolourises acidic solution of KMnO₄. ‘X’ is:

Points I, II and III in the following plot respectively correspond to (V_mp : most probable velocity)

Compound A (C₉H₁₀O) shows positive iodoform test. Oxidation of A with KMnO₄/KOH gives acid B(C₈H₆O₄). Anhydride of B is used for the preparation of phenolphthalein. Compound A is:

The amount of sugar (C₁₂H₂₂O₁₁) in grams required to prepare 2 L of its 0.1 M aqueous solution is:

Number of ‘Br’ will be added to product of the following reactions is/are

If K_sp of Ag₂CO₃ is 8 × 10^-12, the molar solubility of Ag₂CO₃ in 0.1 M AgNO₃ is 8 ×10^-x M, x is

In the IUPAC name of the following compounds the position of carbon for nitro group is carbon no.____

Number of –Cl present in the product of the following reaction is:

The area (in sq. units) bounded by the parabola y = x² – 1, the tangent at the point (2, 3) to it and the y – axis is:

Let a₁, a₂…. a₃₀ be an A. P., . If a₅ = 27 and S – 2T = 75, then a₁₀ is equal to:

The length of the chord of the parabola x² = 4y having equation  is

Let where b > 0. Then the minimum value of is:

A helicopter is flying along the curve given by y - x^3/2  = 7, (x ≥ 0). A solider positioned at the point  wants to shoot down the helicopter when it is nearest to him. Then this nearest distance is:

If q is false and p ∧ q ⟷ r is true, then which one of the following statement is a tautology?

The straight line x + 2y = 1 meets the coordinate axes at A and B. A circle is drawn through A, B and the origin. Then the sum of perpendicular distances from A and B on the tangent to the circle at the origin is:

In a triangle, the sum of lengths of two sides is x and the product of the lengths of the same two sides is y. If x² – c² = y, where c is the length of the third side of the triangle, then the circum-radius of the triangle is:

There are m men and two women participating in a chess tournament. Each participant plays two games with every other participant. If the number of games played by the men between themselves exceed the number of games played between the men and the women by 84, then the value of m is:

Let S be the set of all real values of λ such that a plane passing through the points (-λ ², 1, 1), (1, - λ², 1) and (1, 1, - λ²) also passes through the point (-1, -1, 1). Then S is equal to:-

If the angle of elevation of a cloud from a point P which is 25 m above a lake be 30° and the angle of depression of reflection of the cloud in the lake from P be 60°, then the height of the cloud (in meters) from the surface of the lake is:

Suppose that the points (h, k), (1, 2) and (–3, 4) lie on the line L₁. If a line L₂ passing through the points (h, k) and (4, 3) is perpendicular to L₁, then  equals:

The tangent to the parabola y² = 4x at the point where it intersects the circle x² + y² = 5 in the first quadrant, passes through the point:

Two vertical poles of heights, 20 m and 80m stand apart on a horizontal plane. The height (in meters) of the point of intersection of the lines joining the top of each pole to the foot of the other, from the horizontal plane is:

Let  and  If , where is parallel to  and  is perpendicular to , then  is equal to:

If one end of a focal chord of the parabola, y² = 16x is at (1, 4), then the length of this focal chord is:

Let α and β be the roots of the equation x² + x + 1 = 0. Then for y ≠ 0 in R,  is equal to:

Let a₁, a₂, a₃,…. be an A. P with a₆ = 2. Then the common difference of this A. P., which maximizes the product a₁a₄a₅ is:

The smallest natural number n, such that the coefficient of x in the expansion of is:

Let  where a ∈ R. Suppose Q = [q_ij ] is a matrix satisfying PQ = kI₃ for some non – zero k ∈ R. If q₂₃ = –k/8 and |Q| = k²/2, then a² + k² is equal to __________.

The coefficie0nt of x¹⁸ in the product

(1+x)(1-x)¹⁰ (1+x+x²)⁹is:

A 2m ladder leans against a vertical wall. The top of the ladder begins to slide down the wall at the rate 25 cm/sec. If the rate (in cm/sec.) at which the bottom of the ladder slides away from the wall on the horizontal ground when the top of the ladder is 1m above the ground is  then (p – q) is equal to ___________.

Let are two vectors. The magnitude of a unit vector which is perpendicular to both the vectors  is _______.

If the curves y² = 6x, 9x² + by² =16 intersect each other at right angles, then the value of 2b is: