As shown in the figure, in an experiment to determine Young's modulus of a wire, the extension-load curve is plotted. The curve is a straight line passing through the origin and makes an angle of \(45^{\circ}\) with the load axis. The length of wire is \(62.8\,cm\) and its diameter is \(4\,mm\). The Young's modulus is found to be \(x \times\) \(10^4\,Nm ^{-2}\). The value of \(x\) is

A rectangular parallelopiped is measured as \(1\,cm \times 1\,cm \times 100\,cm\). If its specific resistance is \(3 \times 10^{-7}\,\Omega\,m\), then the resistance between its two opposite rectangular faces will be \(..........x^{-7} \Omega\).

A circuit is arranged as shown in figure. The output voltage \({V}_{0}\) is equal to \(\ldots \ldots . {V}\).

Which of the following are correct expression for torque acting on a body?
A. \(\vec{\tau}=\vec{r}\times\vec{L}\)
B. \(\vec{\tau}=\frac{\mathrm{d}}{\mathrm{dt}}(\overrightarrow{\mathrm{r}} \times \overrightarrow{\mathrm{p}})\)
C. \(\vec{\tau}=\overrightarrow{\mathrm{r}} \times \frac{\mathrm{d} \mathrm{p}}{\mathrm{dt}}\)
D. \(\vec{\tau}=\mathrm{I} \vec{\alpha}\)
E. \(\vec{\tau}=\overrightarrow{\mathrm{r}} \times \overrightarrow{\mathrm{F}}\)
( \(\overrightarrow{\mathrm{r}}=\) position vector; \(\overrightarrow{\mathrm{p}}=\) linear momentum;
\(\overrightarrow{\mathrm{L}}=\) angular momentum; \(\vec{\alpha}=\) angular acceleration;
\(I=\) moment of inertia; \(\vec{F}=\) force; \(t=\) time)
Choose the correct answer from the options given below :

The time taken by a block of mass \(m\) to slide down from the highest point to the lowest point on a rough inclined plane is \(50\%\) more compared to the time taken by the same block on identical inclined smooth plane. Both inclined planes are at \(45^\circ\) with the horizontal. The coefficient of kinetic friction between the rough inclined surface and block is _____.

Two conducting circular loops \(A \) and \(B\) are placed in the same plane with their centres coinciding as shown in figure. The mutual inductance between them is _______.

Given below are two statements: One is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion \(A\): If we move from poles to equator, the direction of acceleration due to gravity of earth always points towards the center of earth without any variation in its magnitude. Reason \(R \): At equator, the direction of acceleration due to the gravity is towards the center of earth. In the light of above statements, choose the correct answer from the options given below

Two discs of moment of inertia \(I_1=4 \mathrm{~kg} \mathrm{~m}^2\) and \(\mathrm{I}_2=2 \mathrm{~kg} \mathrm{~m}^2\) about their central axes & normal to their planes, rotating with angular speeds \(10 \mathrm\ {rad} / \mathrm{s}\) & \(4  \mathrm\ {rad} / \mathrm{s}\) respectively are brought into contact face to face with their axe of rotation coincident. The loss in kinetic energy of the system in the process is _______ \(\mathrm{J}\).

Critical angle of incidence for a pair of optical media is \(45^{\circ}\). The refractive indices of first and second media are in the ratio _______.

The number of numbers greater than 5000, less than 9000 and divisible by 3, that can be formed using the digits 0, 1, 2, 5, 9, if the repetition of the digits is allowed, is ___ .

A conductor lies along the \(z-\)axis \(a\) \(-1.5\)\( \le Z < 1.5\,m\) carries a fixed current of \(10.0\ A\) in \( - {\hat a_z}\) direction (see figure). For a field \(\vec B\) \(=\) \(3.0 \times  10^{-4}\)  \(e^{-0.2x}\) \({\hat a_y}\,T\) find the power required to move the conductor at constant speed to \(x = 2.0\ m, y = 0\ m\) in \(5 \times 10^{-3}\ s\). Assume parallel motion along the \(x-\)axis........\( W\)

If the plane \(2x -y + 2z + 3 = 0\) has the distances \(\frac {1}{3}\) and \(\frac {2}{3}\) units from the planes \(4x -2y + 4z + \lambda = 0\) and \(2x -y + 2z + \mu = 0,\) respectively, then the maximum value of \(\lambda + \mu \) us equal to

If the image of the point \(P\left( {1, - 2,3} \right)\) in the plane , \(2x + 3y - 4z + 22 = 0\) measured parallel to line , \(\frac{x}{1} = \frac{y}{4} = \frac{z}{5}\) is \(Q\) , then \(PQ \) is equal to :