Three thin uniform rods each of mass M and length L are placed along the three axes of a cartesian coordinate system with one end of all the rods at origin. The moment of inertia of the system of the rods about z -axis 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 \(\left.=10 \mathrm{~ms}^{-2}\right)\)

In the following diagram, the work done in moving a point charge from point P to point \(\mathrm{A}, \mathrm{B}\) and C are \(\mathrm{W}_{\mathrm{A}}, \mathrm{W}_{\mathrm{B}}\) and \(\mathrm{W}_{\mathrm{C}}\) respectively. Then (A, B, C are points on semicircle and point charge \(q\) is at the centre of semicircle)

When a spiral spring is stretched by suspending a load with it, the strain produced is called strain.

If a solid sphere is rolling without slipping on a horizontal plane, then the ratio of its rotational and total kinetic energies is

A circuit containing inductance of \(\frac{1}{6 \pi} \mathrm{H}\) and a resistance of \(15 \Omega\) in series. If an \(A C\) voltage of \(100 \mathrm{~V}\) and \(60 \mathrm{~Hz}\) is applied to above circuit, then the current in the circuit and phase difference between voltage and current respectively are

A thin circular ring and a circular disc of equal mass are rolling without sliding. If their linear velocities are equal and the total kinetic energy of the disc is 6 J, then the total kinetic energy of the ring is

Energy required to remove an electron from aluminum surface is 4.2 eV . If light of wavelength \(2000 Å\) falls on the surface, the velocity of the fastest electron ejected from the surface will be

The maximum amplitude of an amplitude modulated wave is \(16 \mathrm{~V}\), while the minimum amplitude is \(4 \mathrm{~V}\). The modulation index is

The type of bond connecting two nucleotides is

A molecule \((X)\) has (i) four sigma bonds formed by the overlap of \(s p^2\) and \(s\) orbitals (ii) one sigma bond formed by \(s p^2\) and \(s p^2\) orbitals and (iii) one \(\pi\) bond formed by \(p_x\) and \(p_z\) orbitals. Which of the following is \(X\) ?

If \(\left(\frac{1}{10}, \frac{-1}{5}\right)\) is the inverse point of a point \((-1,2)\) with respect to the circle \(x^2+y^2-2 x+4 y+c=0\) then \(c=\)

Assertion (A): \(\int_0^{\frac{\pi}{2}}\left(\sin ^6 x+\cos ^6 x\right) d x\) lies in the interval \(\left(\frac{\pi}{8}, \frac{\pi}{2}\right)\)
Reason (R): \(\sin ^6 x+\cos ^6 x\) is a periodic function with period \(\frac{\pi}{2}\)