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Consider the function f : R → R defined by f(x) = [latex]left{begin{matrix} (2-sin(1/x)|x|), &xneq 0 \ 0&x=0 end{matrix}right.[/latex]. Then f is

a. monotonic on (0, ∞) only b. Not monotonic on (–∞, 0) and (0, ∞) c. monotonic on (–∞, 0)... View Article

If the equation of the plane passing through the mirror image of a point

If the equation of the plane passing through the mirror image of a point (2, 3, 1) with respect to... View Article

The number of solutions of the equation x + 2 tanx = π / 2 in the interval [0, 2π] is

a. 5 b. 2 c. 4 d. 3 Answer: (d) x + 2 tan x = π / 2 in... View Article

Let a computer program generate only the digits 0 and 1

Let a computer program generate only the digits 0 and 1 to form a string of binary numbers with a... View Article

Let the tangent to the circle x² + y² = 25 at the point R (3, 4)

Let the tangent to the circle x2 + y2 = 25 at the point R (3, 4) meet the x-axis... View Article

A transmitting station releases waves of wavelength 960 m. A capacitor of 256 μF is used in the resonant circuit. The self inductance of coil necessary for resonance is _____ × 10^–8H.

Answer: 10 At resonance ωr = 1/√(Lc) ∴ 2πf = 1/√(Lc) ∴ 4π2c2/λ2 = 1/Lc ∴4π2×3×108×3×108/960×960 = 1/L×2.56×10-6 L =... View Article

A coil of inductance 2 H having negligible resistance is connected to a source of supply whose voltage is given by V = 3t volt. (where t is in second). If the voltage is applied when t = 0, then the energy stored in the coil after 4 s is _______ J.

Answer: 144 L di/dt = ε = 3t L ∫di = 3 ∫t dt Li = 3t2/2 i = 3t2/2L... View Article

A monoatomic gas of mass 4.0 u is kept in an insulated container. Container is moving with a velocity 30 m/s. If container is suddenly stopped then change in temperature of the gas (R=gas constant) is x/3R. Value of x is ______.

Answer: 3600 ΔKE = ΔU ΔU = nCVΔT ½ mv2 = (3/2) nRΔT mv2/3nR = ΔT 4×(30)2/3×1×R = ΔT ΔT... View Article

Circuit of potentiometer

In the given circuit of potentiometer, the potential difference E across AB (10 m length) is larger than E1 and... View Article

In a certain thermodynamic process, the pressure of a gas depends on its volume as kV³. The work done when the temperature changes from 100⁰C to 300⁰C will be ____ nR, where n denotes number of moles of a gas.

Answer: 50 P = kv3 pv–3 = k x = –3 w = nR(T1 – T2)/(x – 1) = nR(100-300)/(-3... View Article

A small bob tied at one end of a thin string of length 1m is describing a vertical circle so that the maximum and minimum tension in the string are in the ratio 5 : 1. The velocity of the bob at the highest position is ______ m/s. (take g = 10 m/s²)

Answer: 5 By conservation of energy, v2min = V2 – 4gl ….(1) Tmax = mg + mv2/l ….(2) Tmin =... View Article

The potential energy (U) of a diatomic molecule is a function dependent on r (interatomic distance) as U= α/r¹⁰– β/r⁵– 3. Where, a and b are positive constants. The equilibrium distance between two atoms will (2α/β)^a/b. Where a =_______

Answer: 1 F = -dU/dr F = -[-10α/r11 + 5β/r6] for equilibrium, F = 0 10α/r11 = 5β/r6 2α/β =... View Article

512 identical drops of mercury are charged to a potential of 2 V each. The drops are joined to form a single drop. The potential of this drop is ____ V.

Answer: 128 Let charge on each drop = q Radius = r V = kq/r 2 = kq/r Radius of... View Article

The electric field in a region is given by [latex]left ( frac{3}{5}E_{o}hat{i}+ frac{4}{5}E_{o}hat{j}right )frac{N}{C}[/latex]. The ratio of flux of reported field through the rectangular surface of area 0.2 m2 (parallel to y-z plane) to that of the surface of area 0.3 m2(parallel to x-z plane) is a : 2, where a = ________

[Here i, j and k are unit vectors along x, y and z-axes respectively] Answer: 1 Therefore, a = 1

The same size images are formed by a convex lens when the object is placed at 20 cm or at 10 cm from the lens. The focal length of a convex lens is ______ cm.

Answer: 15 1/v – 1/u = 1/f …(1) m = v/u ….(2) from (1) and (2) we get m =... View Article

Magnetic fields at two points on the axis of a circular coil at a distance of 0.05 m and 0.2 m from the centre are in the ratio 8 : 1. The radius of coil is ______

a. 0.15 m b. 0.2 m c. 0.1 m d. 1.0 m Answer: (c) B = μ0NiR2/2(R2 + x2)3/2 at... View Article

Two coherent light sources having intensities in the ratio 2x produce an interference pattern. The ratio (I_max – I_min)/(I_max + I_min) will be:
a. 2√(2x)/(x + 1)b. √(2x)/(2x + 1)c. 2√(2x)/(2x + 1)d. √(2x)/(x + 1)

a. 2√(2x)/(x + 1) b. √(2x)/(2x + 1) c. 2√(2x)/(2x + 1) d. √(2x)/(x + 1) Answer: (c) Let I1... View Article

The angular frequency of alternating current in a L-C-R circuit is 100 rad/s. The components connected are shown in the figure. Find the value of inductance of the coil and capacity of condenser.

The angular frequency of alternating current in a L-C-R circuit is 100 rad/s. The components connected are shown in the... View Article

Given below are two statements: one is labelled as Assertion A and the other is labelled as reason R

Assertion A: The escape velocities of planet A and B are same. But A and B are of unequal masses.... View Article

An α particle and a proton are accelerated from rest by a potential difference of 200 V. After this, their de Broglie wavelengths are λ_α and λ_p respectively. The ratio λ_p/λ_α is:

a. 8 b. 2.8 c. 3.8 d. 7.8 Answer: (b) λ = h/p = h/√(2mqV) λp/λα = √(mαqα/mpqp) = √(4×2/1×1)... View Article

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