If \(x= 3\tan(t)\) and \(y = \sec (t)\), then the value of \(\frac{d^{2} y}{d x^{2}}~\text{at}~t = \frac{\pi}{4}\) is:
1. \(3\)
2. \(\frac{1}{18\sqrt{2}}\)
3. \(1\)
4. \(\frac{1}{6}\)
A particle's position as a function of time is given by .
The maximum value of the position co-ordinate of the particle is:
1. \(8\)
2. \(12\)
3. \(3\)
4. \(6\)
The equation of position (\(x\)) of a particle is given by The maximum velocity of the particle is, if velocity is defined as :
1. +56 m/s
2. +46 m/s
3. +36 m/s
4. +26 m/s
The current in a circuit is defined as . The charge (q) flowing through a circuit, as a function of time (t), is given by . The minimum charge flows through the circuit at:
1. \(t = 4~\text{s}\)
2. \(t = 2~\text{s}\)
3. \(t = 6~\text{s}\)
4. \(t = 3~\text{s}\)
Work done by a force (\(F\)) in displacing a body by dx is given by W=. If the force is given as a function of displacement (\(x\)) by \(F \left(x\right) = \left( x^{2} - 2 x + 1\right) \text{N}\), then work done by the force from \(x=0\) to \(x=3\) m is:
1. \(3\) J
2. \(6\) J
3. \(9\) J
4. \(21\) J
The impulse due to a force on a body is given by \(I=\int Fdt\). If the force applied on a body is given as a function of time \((t)\) as \(F = \left(3 t^{2} + 2 t + 5\right) \text{N}\), then impulse on the body between \(t = 3~\text{s}\) to \(t =5~\text{s}\) is:
1. \(175\) kg-m/sec
2. \(41\) kg-m/sec
3. \(216\) kg-m/sec
4. \(124\) kg-m/sec
If is the angle between vectors , then which of the following is the unit vector perpendicular to ?
1.
2.
3.
4.
Which of the following option is not true, if and , where \(\mathrm{A}\) and \(\mathrm{B}\) are the magnitudes of ?
1.
2.
3.
4. \(\mathrm{A}=5\)
If is perpendicular to , then which of the following statement is correct?
1.
2.
3.
4.
The angle between the two vectors \(\left(- 2 \hat{i} +3 \hat{j} + \hat{k}\right)\) and \(\left(\hat{i} + 2 \hat{j} - 4 \hat{k}\right)\) is:
1. \(0^{\circ}\)
2. \(90^{\circ}\)
3. \(180^{\circ}\)
4. \(45^{\circ}\)