Let '\(a\)' and '\(b\)' be two numbers where \(a < b\). The geometric mean of these numbers exceeds the smaller number by 12 and the arithmetic mean is smaller than the larger number by 24. Then the value of \(|b - a|\) is:

The equation of the circle having \(x-y-2=0\) and \(x-y+2=0\) as two tangents and \(x+y=0\) as a diameter is

The value of \(\left|\begin{array}{lll}x & p & q \\ p & x & q \\ p & q & x\end{array}\right|\) is

The absolute maximum and minimum values of the function \(f(x) = \sin x + \sqrt{3}\cos x\) in \([0, \pi]\) are

Domain of the function \(f(x)=\sqrt{\sin ^{-1}(2 x)+\dfrac{\pi}{6}}\) for real valued of \(x\) is

\(\text { If } 6^{\text {th }} \text { term of a geometric progression is }-\dfrac{1}{32} \text { and } 9^{\text {th }} \text { term is } \dfrac{1}{256} \text { then } r \text { is }\)

If \(y=\cos ^{2} \frac{3 x}{2}-\sin ^{2} \frac{3 x}{2}\), then \(\frac{d^{2} y}{d x^{2}}\) is

If \(A=\left[\begin{array}{lll}a & 0 & 0 \\ 0 & a & 0 \\ 0 & 0 & a\end{array}\right]\), then \(|A|| \operatorname{adj} A \mid\) is equal to

The current through a conductor is '\(\mathrm{a}\)' when the temperature is \(0^{\circ} \mathrm{C}\). It is '\(\mathrm{b}\)' when the temperature is \(100^{\circ} \mathrm{C}\). The current through the conductor at \(220^{\circ} \mathrm{C}\) is

An electric dipole of dipole moment \(p\) is lying along a uniform electric field \(E\). The work done in rotating the dipole from \(60^{\circ}\) to \(90^{\circ}\) from the direction of electric field, is

A proton is moving along negative X axis. If a uniform magnetic field is applied parallel to the positive Z axis, then choose the correct answer from the following options;
1. The proton will experience magnetic force along positive Y direction and will move along a circular path in the XY plane
2. The proton will experience magnetic force along negative Y direction and will move along a circular path in the XY plane
3. The proton will experience magnetic force along positive Y direction and will move along a circular path in the XZ plane
4. The proton will experience magnetic force along negative Y direction and will move along a circular path in the XZ plane

The SI unit of electrical conductivity is :

Which one of the following is the correct statement?