In the circuit shown below, the ammeter reading is zero. Then the value of the resistance \(R\) is

The particle having zero mass is

A force-time \((F-t)\) graph for a linear motionis shown in following figure. The segments shown are circular. The linear momentum gained between 0 and \(8 \mathrm{~s}\) is

The current gain for a transistor working as common base amplifier is 0.96 . If the emitter current is \(7.2 \mathrm{~mA}\), then the base current is

In the figure shown, \(\mathrm{AB}\) is a rod of length \(30 \mathrm{~cm}\), area of cross-section \(1 \mathrm{~cm}^2\) and thermal conductivity \(336 \mathrm{SI}\) units. The ends \(\mathrm{A}\) and \(\mathrm{B}\) are at constant temperatures \(20^{\circ} \mathrm{C}\) and \(40^{\circ} \mathrm{C}\) respectively. A point \(\mathrm{C}\) of the rod is connected to ice at \(0^{\circ} \mathrm{C}\) in a thermally insulated box \(\mathrm{D}\) through a highly conducting wire of negligible heat capacity. The rate at which ice melts in the box is \(\left(\mathrm{L}_{\mathrm{ice}}=80 \mathrm{cal} \mathrm{g}^{-1}\right)\)

A quarter horse power motor runs at a speed of $600 \mathrm{rpm}.$ Assuming $60\%$ efficiency, the work done by the motor in one rotation is

A sphere of surface area $4 {\mathrm{m}}^2$ at temperature $400 \mathrm{K}$ and having emissivity $0.5$ is located in an environment of temperature $200 \mathrm{K}$. The net rate of energy exchange of the sphere is (Stefan Boltzmann constant $\sigma =5.67\times {10}^{-8} \mathrm{W} {\mathrm{m}}^{-2} {\mathrm{K}}^4$)

If $f\left(x\right)=\left|\begin{array}{ccc}x& x^2& x^3\\ 1& 2x& 3x^2\\ 0& 2& 6x\end{array}\right|$, then the ratio $f^{\text{'}\text{'}}\left(x\right) : f^{\text{'}}\left(x\right)=$

Which one of the following does not undergo disproportionation reaction?

If \(I_n=\int \sin ^n x d x\), then \(n I_n-(n-1) I_{n-2}\) equals

Number of unit vectors of the form $a\hat{\mathrm{i}}+b\hat{\mathrm{j}}+c\hat{\mathrm{k}},$ where $a, b, c\in W$ is

If the inverse point of the point \((3,2)\) with respect to the circle \(\mathrm{x}^2+\mathrm{y}^2-2 \mathrm{x}+4 \mathrm{y}-4=0\) is \((l, \mathrm{~m})\) then \((2 l+19 \mathrm{~m})=\)

Find \(|\mathbf{a} \times \mathbf{b}|^2\), if \(|\mathbf{a}|=2,|\mathbf{b}|=3\) and \((\mathbf{a}, \mathbf{b})=\frac{\pi}{6}\)