A 800 kg car can accelerate from rest to a speed of 30 m/s in 10s. Neglecting friction loss, the average power of the engine of the car required is:
1. 42 kw
2. 36 kw
3.32 kw
4. 30 kw

The equation of a stationary wave along a stretched string is given by $$y= 5 \sin\lgroup \dfrac{\pi x}{3} \rgroup \cos(40 \pi t)$$ Where x and y are in cm and t is in sec. The separation between two adjacent nodes is:

1) 3
2) 1.5
3) 6
4) 4

A uniform wire of resistance 12Ω  is bent in the form of a square. A cell of emf 6 V having negligible internal resistance connected across the diagonal of the square. The magnetic induction at its centre is (in T)

1) 0
2) 10^−7?
3) 5×10⁻⁷
4) $$\dfrac{\mu _{0}}{4\pi }\times 5\times 10^{-7}$$

The distance to which an electron of a hydrogen atom is to be removed from the atom so that the force of electrostatic attraction is equal to six times the weight of the atom, will be :

[Take g=10 m/s² and number of atoms in 1 kg1 kg of monoatomic hydrogen is 66 x 10²⁶]

1) 1.2 cm

2) 4.8 cm

3) 2.4 cm

4) 3.6 cm

 A 10 m long potentiometer wire is connected to a battery having a steady voltage. A Leclanche cell is balanced at 4 m length of the wire. If the length is kept the same, but its cross-section is doubled, the null point will be obtained at:

(1) 8 m

(2) 4m

(3) 2m

(4) none

 In the definition of 'calorie', the heat required to raise the temperature of 1 gram of water through 1°C in the range of temperature and pressure.

(1) 3.5 to 4.5°C, 76mm of Hg
(2) 13.5 to 14.5°C 76mm of Hg
(3) 14.5 to 15.5°C 760mm of Hg
(4) 98.5 to 99.5°C 760mm of Hg

A certain color of light towards the purple end of the visible spectrum has a wavelength of 420 nm in a vacuum.
What is the frequency of this light?
The speed of light in a vacuum is 3.00×10⁸m/s

1) 126Hz
2) 7.1×10¹⁴Hz
3) 1.26×10¹¹Hz
4) 1.4×10⁻¹⁵Hz

Thin semi-circular part ABC has mass m1 and diameter AOC has mass m2. Here, axis passes through mid-point of diameter and the axis is perpendicular to plane ABC.
Here, AO=OC=R. The moment of inertia of this composite system about the axis is:

1) $$\dfrac {m_{1}R^{2}}{2} + \dfrac {m_{2}R^{2}}{3}$$
2) $$\dfrac {m_{1}R^{2}}{2} + \dfrac {m_{2}R^{2}}{6}$$
3) $$m_{1}R^{2} + \dfrac {m_{2}R^{2}}{3}$$
4) $$m_{1}R^{2} + \dfrac {m_{2}R^{2}}{12}$$

The potential difference VV and the current II flowing through an instrument in an AC circuit are given by V=5cosωt volt,I=2sinωtAmp . The power dissipated in the circuit is

1) 5 watt
2) 10 watt
3) 2.5 watt
4) 0