For the circuit shown, the value of current at time \({t}=3.2\, {s}\) will be ...... \({A}\). [Voltage distribution \(V(t)\) is shown by Fig. \((1)\) and the circuit is shown in Fig. \((2)\)]

The induced \(emf\) can be produced in a coil by \(A.\) moving the coil with uniform speed inside magnetic field \(B.\) moving the coil with non-uniform speed inside uniform magnetic field \(C.\) rotating the coil inside the uniform magnetic field \(D.\) changing the area of the coil inside the uniform magnetic field Choose the correct answer from the options given below:

The velocity of a small ball of mass \(0.3\,g\) and density \(8\,g / cc\) when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is \(1.3\,g / cc\), then the value of viscous force acting on the ball will be \(x \times 10^{-4}\,N\), the value of \(x\) is [use \(g=10\,m / s ^{2}\) ] 

A screw gauge with a pitch of \(0.5 \ mm\) and a circular scale with \(50\) divisions is used to measure the thickness of a thin sheet of Aluminium. Before starting the measurement, it is found that wen the two jaws of the screw gauge are brought in contact, the \(45^{th} \)division coincides with the main scale line and the zero of the main scale is barely visible. What is the thickness of the sheet (in \(mm\)) if the main scale reading is \(0.5\ mm\) and the \(25^{th}\) division coincides with the main scale line 

In photoelectric effect, the stopping potential \(\left(\mathrm{V}_0\right) \mathrm{v} / \mathrm{s}\) frequency \((\nu)\) curve is plotted.
( h is the Planck's constant and \(\phi_0\) is work function of metal )
(A) \(\mathrm{V}_0 \mathrm{v} / \mathrm{s} \nu\) is linear.
(B) The slope of \(\mathrm{V}_0 \mathrm{v} / \mathrm{s} \nu\) curve \(=\frac{\phi_0}{\mathrm{~h}}\)
(C) h constant is related to the slope of \(\mathrm{V}_0 \mathrm{v} / \mathrm{s} \nu\) line.
(D) The value of electric charge of electron is not required to determine \(h\) using the \(V_0 \mathrm{v} / \mathrm{s} \nu\) curve.
(E) The work function can be estimated without knowing the value of \(h\).
Choose the correct answer from the options given below :

The figure shows a region of length \('l'\) with a uniform magnetic field of \(0.3\, T\) in it and a proton entering the region with velocity \(4 \times 10^{5}\, ms ^{-1}\) making an angle \(60^{\circ}\) with the field. If the proton completes \(10\) revolution by the time it cross the region shown, \(l\) is close to....... \(m\) (mass of proton \(=1.67 \times 10^{-27} \,kg ,\) charge of the proton \(\left.=1.6 \times 10^{-19}\, C \right)\)

The formula \(X = 5YZ^2\),  \(X\) and \(Z\) have dimensions of capacitance and magnetic field respectively. What are the dimensions of \(Y\) in \(SI\) units?

Let \(a_1, a_2, \ldots . a_{10}\) be \(10\) observations such that \(\sum_{\mathrm{k}=1}^{10} \mathrm{a}_{\mathrm{k}}=50\) and \(\sum_{\forall \mathrm{k}<\mathrm{j}} \mathrm{a}_{\mathrm{k}} \cdot \mathrm{a}_{\mathrm{j}}=1100\). Then the standard deviation of \(a_1, a_2, \ldots, a_{10}\) is equal to :

Let \(\mathrm{a}\) and \(\mathrm{b}\) be real constants such that the function \(f\) defined by \(f(x)=\left\{\begin{array}{cc}x^2+3 x+a & x \leq 1 \\ b x+2, & x>1\end{array}\right.\) be differentiable on \(R\). Then, the value of \(\int_{-2}^2 f(x) d x\) equals

The centre of a circle C is at the centre of the ellipse \(E: \frac{x^2}{a^2}+\frac{y^2}{b^2}=1, a \gt b\). Let \(C\) pass through the foci \(F_1\) and \(F_2\) of \(E\) such that the circle \(C\) and the ellipse \(E\) intersect at four points. Let P be one of these four points. If the area of the triangle \(\mathrm{PF}_1 \mathrm{~F}_2\) is 30 and the length of the major axis of E is 17 , then the distance between the foci of E is :

Let \(x=2\) be a root of the equation \(x^2+p x+q=0\) and \(f(x)=\left\{\begin{array}{cc}\frac{1-\cos \left(x^2-4 p x+q^2+8 q+16\right)}{(x-2 p)^4}, & x \neq 2 p \\ 0, & x=2 p\end{array}\right.\) Then \(\lim _{x \rightarrow 22^{+}}[f(x)]\) where [. ] denotes greatest integer function, is \(........\)

A random variable \(X\) has the following probability distribution

\(X\)	\(0\)	\(1\)	\(2\)	\(3\)	\(4\)
\(P(X)\)	\(k\)	\(2k\)	\(4k\)	\(6k\)	\(8k\)

The value of \(P (1< X <4 \mid X \leq 2)\) is equal to

Let a circle \(C\) have its centre in the first quadrant, intersect the coordinate axes at exactly three points and cut off equal intercepts from the coordinate axes. If the length of the chord of \(C\) on the line \(x + y = 1\) is \(\sqrt{14}\), then the square of the radius of \(C\) is _______.