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A parallel plate capacitor is of area 6 cm² and a separation 3 mm. The gap is filled with three dielectric materials of equal thickness (see figure) with dielectric constant K₁=10, K₂ = 12 and K₃ =14. The dielectric constant of a material which when fully inserted in above capacitor, gives same capacitance would be :

a. 34 b. 12 c. 4 d. 14 < strong>Answer: b Let K be the dielectric constant of the material used. So So K = 36/3 = 12... View Article

A train moves towards a stationary observer with speed 34m/s. The train sounds a whistle and its frequency registered by the observer is f₁. If the train’s speed is reduced to 17m/s, the frequency registered is f₂. If the speed of sound of 340m/s, then the ratio f₁/f₂is

a. 18/7 b. 21/20 c. 20/19 d. 19/18 Answer: d f1 = f(v/v-vs) = f(340/340-34) = f(340/306) f2 = f(340/340-17) = f(340/323) f1/f2 =... View Article

A string of length 1 m and mass 5 g is fixed at both ends. The tension in the string is 8.0 N. The siring is set into vibration using an external vibrator of frequency 100 Hz. The separation between successive nodes on the string is close to __?

a. 10 cm b. 16.6 cm c. 20 cm d. 33.3 cm Answer: c The velocity of wave on string, V = √(T/μ) = √(8×1000/5) = 40 m/s The wavelength... View Article

A heat source at T = 10³ K is connected to another heat reservoir at T = 10² K by a copper slab which is 1 m thick. Given that the thermal conductivity of copper is 0.1 WK^-1m^-1, the energy flux through it in steady state is :

a. 90 W/m2 b. 120 W/m2 c. 65 W/m2 d. 200 W/m2 Answer: a (dQ/dt) = kAΔt/l (1/A)(dQ/dt) = (0.1×900)/1 = 90W/m2... View Article

Three Carnot engines operate in series between a heat source at a temperature T₁ and a heat sink at temperature T₄ (see figure). There are two other reservoirs at temperature T₂ and T₃, as shown, with T₁ >T₂ >T₃ >T₄. The three engines are equally efficient if :

a. T2 = (T1T42)1/3 ; T3 = (T12 T4)1/3 b. T2 = (T1T4)1/2 ; T3 = (T12 T4)1/3 c. T2 = (T12 T4)1/3 ; T3 = (T1 T42)1/3 d. T2 = (T13 T4)1/4 ;... View Article

Water flows into a large tank with flat bottom at the rate of 10⁻⁴m³s⁻¹. Water is also leaking out of a hole of area 1 cm² at its bottom. If the height of the water in the tank remains steady, then this height is

a. 5.1 cm b. 4 cm c. 2.9 cm d. 1.7 cm Answer: a Water inflow rate = water outflow rate Water inflow rate = 10-4 Water outflow rate =... View Article

A satellite is moving with a constant speed v in circular orbit around the earth. An object of mass m is ejected from the satellite such that it just escapes from the gravitational pull of the earth. At the time of ejection, the kinetic energy of the object is

a. (1/2)mv2 b. mv2 c. (3/2)mv2 d. 2mv2 Answer: b Orbital velocity = v Escape velocity = Ve v = √(GM/R) g = GM/R2 gR2 = GM v = √gR... View Article

To mop-clean a floor, a cleaning machine presses a circular mop of radius R vertically down with a total force F and rotates it with a constant angular speed about its axis. If the force F is distributed uniformly over the mop and the floor is μ, the torque, applied by the machine on the mop is :

a. μFR/6 b. μFR/3 c. μFR/2 d. 2μFR/3 Answer: d Force per unit length = F/πR2)2πxdx Torque = F×r = = = =... View Article

A homogeneous solid cylindrical roller of radius R and mass M is pulled on a cricket pitch by a horizontal force. Assuming rolling without slipping, angular acceleration of the cylinder is:

a. 2F/3mR b. 3F/2mR c. F/3mR d. F/2mR Answer: a Considering pure rolling, acm = Rα FR = (mR2 +(1/2) mR2 ) α =... View Article

A block of mass m is kept on a platform which starts from rest with constant acceleration g/2 upward, as shown in fig. Work done by normal reaction on block in time t is :

a. 3mg2t2/8 b. -mg2t2/8 c. mg2t2/8 d. 0 Answer: a S = ut+(1/2)at2 ut = 0 a = g/2 S = (1/4)gt2 N-mg = mg/2 N = 3mg/2 Work... View Article

A piece of wood of mass 0.03 kg is dropped from the top of a building 100 m high. At the same time, a bullet of mass 0.02 kg is fired vertically upward with a velocity of 100 m/s from the ground the bullet gets embedded in the wooded piece after striking. Then the maximum height to which the combined system reaches above the building before falling below is: (take g = 10ms^-2).

a. 40 b. 30 c. 20 d. 10 Answer: a Time taken by the particles to collide, t = d/Vrel = 100/100 = 1 sec Before collision, speed of... View Article

In the cube of side ‘a’ shown in the figure, the vector from the central point of the face ABOD to the central point of the face BEFO will be

a. b. c. d. Answer: c Position vector of G is Position vector of H is... View Article

Two guns A and B can fire bullets at speeds 1 km/s and 2 km/s respectively. From a point on a horizontal ground, they are fired in all possible directions. The ratio of maximum areas covered by the bullets fired by the two guns, on the ground is :

a. 1:2 b. 1:16 c. 1:8 d. 1:4 Answer: b R = u2sin 2θ/g For gun A, (Rmax)A = uA2/g For gun B, (Rmax)B = uB2/g (Area)A/(Area)B =... View Article

The density of a material in SI units is 128 kg m^-3. In certain units in which the unit of length is 25 cm and the unit of mass is 50 g, the numerical value of density of the material is :

a. 40 b. 410 c. 640 d. 16 Answer: a Density = mass/volume δ = M/V = M/L3 n1u1 = n2u2 n1 = 128 128[M1L1-3] = n2[M2L2-3] n2 =... View Article

On dissolving 0.5 g of non-volatile, non-ionic solute to 39 g of benzene, its vapour pressure decreases from 650 mm of Hg to 640 mm of Hg. The depression of freezing point of benzene (in K) upon addition of the solute is __________________. [Given data: Molar mass & molar freezing point depression of benzene is 78 g mol^-1 & 5.12 K Kg mol^-1]

Answer: (1.03 or 1.02) Therefore, M = 64 g... View Article

Consider the kinetic data given in the following table for the reaction A + B + C → Product

When [A] = 0.15 [B] = 0.25 [C] = 0.15 Rate of reaction is Y × 10-5 m/s. Find Y. Answer: (6.75) Let From (1), (2) -> y = 0 (1),... View Article

Which of the following compounds contain bond between same type of atoms.

N2O4, B3 N3H6, H2S2O3, N2O, H2S2O8, B2H6 Answer: N2O4, H2S2O3, N2O, H2S2O8... View Article

Schemes 1 and 2 describe the conversion of P to Q and R to S, respectively. Scheme 3 describes the synthesis of T from Q and S. The total number of Br atoms in a molecule of T is _____

Answer: (4) Total Br atoms = 4... View Article

For the following reaction, equilibrium constant K_c at 298 K is 1.6 × 10¹⁷.

When equal volume of 0.06 M Fe+2 and 0.2 M S-2 solution are mixed, then equilibrium concentration of Fe+2 is found to be Y × 10-17 M. Y is:... View Article

At 143 K, the reaction of XeF₄ with O₂F₂ produces a xenon compound Y. The total number of lone pair(s) of electron present on the whole molecule of Y is ____

Answer: (19) Distorted octahedral shape. Total no. of lone pair present on the whole molecule of Y = 1 ℓ. p. in Xe + 18. ℓ. p. in F = 19... View Article