A particle moves along the X-axis so that its X coordinate varies with time t according to the equation . The initial velocity of the particle is: \(\left(\text{Given;}~ v=\frac{dx}{dt}\right)\)
1. -5 m/s
2. 6 m/s
3. 3 m/s
4. 4 m/s
The maximum value of the function \(7 + 6 x - 9 x^{2}\) is:
1. \(8\)
2. \(-8\)
3. \(4\)
4. \(-4\)
If \(f \left(x\right) = x^{2} - 2 x + 4\), then \(f(x)\) has:
1. | \(x=1\). | a minimum at
2. | \(x=1\). | a maximum at
3. | no extreme point. |
4. | no minimum. |
The resultant of the forces \(\overrightarrow {P}\) and \(\overrightarrow {Q}\) is \(\overrightarrow {R}\). If \(\overrightarrow {Q}\) is doubled, then the resultant also doubles in magnitude. Find the angle between \(\overrightarrow {P}\) and \(\overrightarrow {Q}\)?
1. \(\cos\theta = \frac{Q}{2P}\)
2. \(\cos\theta = \frac{-4Q}{3P}\)
3. \(\cos\theta = \frac{-2Q}{3P}\)
4. \(\cos\theta = \frac{-3P}{4Q}\)
If \(\overrightarrow{A}={2}\hat{i}+\hat{j}\;{\&}\;\overrightarrow{B}=\hat{i}{-}\hat{j},\) then the components of \(\overrightarrow {A}\) along with \(\overrightarrow {B}\) & perpendicular to \(\overrightarrow {B}\) respectively will be:
1. \(\frac{\hat{i} - \hat{j}}{2} ,~\frac{3}{2}\left(\hat i+\hat j\right)\)
2. \(\frac{\hat{i} - \hat{j}}{2} ,~-\frac{2}{3}\left(\hat i+\hat j\right)\)
3. \(\frac{\hat{i} - \hat{j}}{2} ,~-\frac{3}{2}\left(\hat i-\hat j\right)\)
4. \(\frac{\hat{i} - \hat{j}}{2} ,~\frac{2}{3}\left(\hat i-\hat j\right)\)
If \(\overrightarrow{a}\) is a vector and \(x\) is a non-zero scalar, then which of the following is correct?
1. | \(x\overrightarrow{a}\) is a vector in the direction of \(\overrightarrow{a}\). |
2. | \(x\overrightarrow{a}\) is a vector collinear to \(\overrightarrow{a}\). |
3. | \(x\overrightarrow{a}\) and \(\overrightarrow{a}\) have independent directions. |
4. | \(x\overrightarrow{a}\) is a vector perpendicular to \(\overrightarrow{a}\). |
The vector \(\overrightarrow b\) which is collinear with the vector \(\overrightarrow a = \left(2, 1, -1\right)\) and satisfies the condition \(\overrightarrow a. \overrightarrow b=3\) is:
1. \(\left(1, \frac{1}{2}, \frac{-1}{2}\right)\)
2. \(\left(\frac{2}{3}, \frac{1}{3}, \frac{-1}{3}\right)\)
3. \(\left(\frac{1}{2}, \frac{1}{4}, \frac{-1}{4}\right)\)
4. \(\left(1, 1, 0\right)\)
If a, b and c are three non-zero vectors such that , then the value of will be:
1. | Less than zero | 2. | equal to zero |
3. | greater than zero | 4. | 3 |
If \(\overrightarrow P +\overrightarrow Q\)
1. \(\theta = 0^{\circ}\)
2. \(\theta = 90^{\circ}\)
3. \(P=0\)
4. \(Q=0\)
What is the torque of a force newton acting at a point metre about the origin? (Given: )
1.
2.
3.
4.