The resultant magnitude of two vectors of same magnitude is equal to magnitude of either. The angle between the two vectors is

Two balls of charge \(q_1\) and \(q_2\) initially have a velocity of the same magnitude and direction. After a uniform electric field has been applied during a certain time, the direction of the velocity of the first ball changes by \(60^{\circ}\), and the velocity magnitude is reduced by half. The direction of the velocity of the second ball changes thereby by \(90^{\circ}\).
In what proportion will the velocity of the second ball change? Determine the magnitude of the charge-to-mass ratio for the second ball if it is equal to \(k_1\) for the first ball. The electrostatic interaction between the balls should be neglected.

A Carnot engine whose heat sink is at $27°\mathrm{C}$ has an efficieny of $40\%$. By how much should its source temperature be changed so as to increase its efficiency to $60\%$?

A diving board is at a height of ' \(h\) ' from the water surface, A swimmer standing on this board thrown a stone vertically upward with a velocity \(16 \mathrm{~ms}^{-1}\). It reaches the water surface in a time of 5 s . In the next 0.2 s , the diver can hear the sound from water surface. The speed of sound is (acceleration due to gravity \(\mathrm{g}=10 \mathrm{~ms}^{-2}\) )

A body of mass 30 kg moving with a velocity \(20 \mathrm{~ms}^{-1}\) undergoes one dimensional elastic collision with another ball of same mass moving in the opposite direction with a velocity of \(30 \mathrm{~ms}^{-1}\). After collision the velocities of first and second bodies respectively are

The angle between the axes of a polariser and an analyser is \(45^{\circ}\). If the intensity of the unpolarized light incident on the polariser is 1 , then the intensity of the light emerged from the analyser is

A galvanometer may be converted into ammeter or a voltmeter. In which of the following cases the resistance of the devices, so obtained will be largest?

\(\left(\frac{1+i}{1-i}\right)^4+\left(\frac{1-i}{1+i}\right)^4\) is equal to

A force of \(10 \mathrm{~N}\) acting at an angle on a particle produces a displacement of \((3 \hat{i}-4 \hat{\jmath}) \mathrm{m}\). Due to this force, if the kinetic energy of the particle is decreased by 25 joule, then the angle between the force and the displacement is

The roots of the equation \(\left|x^2-x-6\right|=x+2\) are

If \(\mathrm{Q}(h, k)\) is the inverse point of the point \(\mathrm{P}(1,2)\) with respect to the circle \(x^2+y^2-4 x+1-0\), then \(2 h+k=\)

The ten's digit in \(1 !+4 !+7 !+10 !+12 !+13 !+15 !+16 !+17 !\) is divisible by

Which of the following statements is not correct?