A message signal of frequency \(8 \mathrm{kHz}\) and peak voltage \(12 \mathrm{~V}\) is used to modulate a carrier of frequency 1.2 MHz and peak voltage \(20 \mathrm{~V}\). The modulation index is

When a body is heated, then maximum rise will be in its

When 40 J of heat is absorbed by a monatomic gas, the increase in the internal energy of the gas is

Two towers \(A\) and \(B\), each of height \(20 \mathrm{~m}\) are situated a distance \(200 \mathrm{~m}\) apart. A body thrown horizontally from the top of the tower \(A\) with a velocity \(20 \mathrm{~ms}^{-1}\) towards the tower \(B\) hits the ground at point \(P\) and another body thrown horizontally from the top of tower \(B\) with a velocity \(30 \mathrm{~ms}^{-1}\) towards the tower \(A\) hits the ground at point \(Q\). If a car starting from rest from \(P\) reaches \(Q\) in 10 seconds, then the acceleration of the car is \(\left(\right.\) acceleration due to gravity \(\left.=10 \mathrm{~ms}^{-2}\right)\)

The force required to stop a body of mass \(10 \mathrm{~kg}\) moving along a straight line path with a velocity of \(10 \mathrm{~ms}^{-1}\) in a time of \(10 \mathrm{~s}\) is

A coil of resistance \(200 \Omega\) is placed in a magnetic field. If the magnetic flux \(\phi\) (in weber) linked with the coil varies with time ' \(t\) ' (in second) as per the equation \(\phi=50 \mathrm{t}^2+4\), then the current induced in the coil at a time \(\mathrm{t}=2 \mathrm{~s}\) is

Assertion (a) : A particle of mass \(m\) dropped into a hole made along the diameter of the earth from one end to the other and possess simple harmonic motion.Reason (R) : Gravitational force between any two particles is inversely proportional to the square of the distance between them.

If \(\sqrt{9 x^2+6 x+1} < (2-x)\), then:

Phenol on oxidation in air gives

If \(\alpha, \beta\) are the roots of \(x^2-2 x+4=0\), for \(n \in \mathbf{N}\), what is the value of \(\alpha^n+\beta^n=\)

The sum of the maximum and the minimum values of \(2\left(\cos ^{-1} x\right)^2-\pi \cos ^{-1} x+\frac{\pi^2}{4}\), is

Locus of the centroid of a triangle whose vertices are \((1,0) .(a \cos t, a \sin t)\), \((b \sin t,-b \cos t)\) is \(9 x^2+9 y^2-6 x=k\). Then, the value of \(k\) is equal to

Match the following
\begin{array}{llll}
& List I & & List II \\
& (Group 13 element) & & (metallic radius, pm) \\
A & \mathrm{Al} & I & 135 \\
\mathrm{~B} & \mathrm{Ga} & II & 143 \\
\mathrm{C} & In & III & 170 \\
\mathrm{D} & \mathrm{Tl} & IV & 167
\end{array}
The correct answer is