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.
The momentum of a body moving in a straight line is . Force acting on the body at t=2 sec will be: \(\left(\text{Given:}~ F=\frac{dp}{dt}\right)\)
1. 6 N
2. 8 N
3. 4 N
4. 2 N
Temperature of a body varies with time as , where is the temperature in Kelvin at , then the rate of change of temperature at is:
1. \(8~\text{K}\)
2. \(80~\text{K}\)
3. \(8~\text{K/sec}\)
4. \(80~\text{K/sec}\)
\(\overrightarrow{A}\) and \(\overrightarrow B\) are two vectors and \(\theta\) is the angle between them. If \(\left|\overrightarrow A\times \overrightarrow B\right|= \sqrt{3}\left(\overrightarrow A\cdot \overrightarrow B\right),\) then the value of \(\theta\) will be:
1. | \(60^{\circ}\) | 2. | \(45^{\circ}\) |
3. | \(30^{\circ}\) | 4. | \(90^{\circ}\) |
A particle is moving along the x-axis. The velocity v of this particle varies with its position x as . Find the velocity of the particle as a function of time t given that at t=0, x=1 and v=.
1.
2.
3.
4. None of these
If a curve is governed by the equation y = sinx, then the area enclosed by the curve and x-axis between x = 0 and x = is (shaded region):
1. \(1\) unit
2. \(2\) units
3. \(3\) units
4. \(4\) units