The volume flow rate of water flowing out of a tubewell is given by \(Q = \left( 3 t^{2}- 4 t +1\right)~\text{m}^3/\text{sec}  \). What volume of water will flow out of the tubewell in the third second if the volume flow rate is defined as \(Q=\frac{dV}{dt}\)?
1. \(10\) ${\mathrm{m}}^3$
2. \(17\) ${\mathrm{m}}^3$
3. \(36\) ${\mathrm{m}}^3$
4. \(34\) ${\mathrm{m}}^3$

Find \(\frac{dy}{dx}, \) if \(y = t^3+1\) and \(x = t^2+3\):
1. \(\frac{t^2}{3}\)
2. \(\frac{t}{2}\)
3. \(\frac{3t}{2}\)
4. \(t^2\)

A thin wire bent to form a circle and carrying a current I has a magnetic moment M. The shape of the wire is changed to a square and it carries the same current. It will have a magnetic moment

(1) $\frac{\mathrm{\pi M}}{4}$

(2) $\frac{M}{4}$

(3) $M$

(4) $\mathrm{\pi M}$

What is the maximum value of \(5\sin\theta-12\cos\theta\)?

1. \(12\)

2. \(17\)

3. \(7\)

4. \(13\)

If \(\overrightarrow{A} \times \overrightarrow{B} = \overrightarrow{C} + \overrightarrow{D}\), then which of the following statement is correct?

A scalar quantity is one that:

Given below are two statements: 

Given below are two statements: 

Given are two vectors, \(\overrightarrow{A} =   \left(\right. 2 \hat{i}   -   5 \hat{j}   +   2 \hat{k} \left.\right)\) and \(\overrightarrow{B} =   \left(4 \hat{i}   -   10 \hat{j}   +   c \hat{k} \right).\) What should be the value of \(c\) so that vector \(\overrightarrow A \) and \(\overrightarrow B\) would becomes parallel to each other?
1. \(1\)
2. \(2\)
3. \(3\)
4. \(4\)

Two forces of the same magnitude are acting on a body in the East and North directions, respectively. If the body remains in equilibrium, then the third force should be applied in the direction of:

1. North-East

2. North-West

3. South-West

4. South-East