The displacement of a particle is given by . The initial velocity and initial acceleration, respectively, are: (\(Given: v=\frac{dx}{dt}~and~a=\frac{d^2x}{dt^2}\))
1. b, -4d
2. -d, 2c
3. b, 2c
4. 2c, -4d
The position x of the particle varies with time t as . The acceleration of the particle will be zero at a time equal to: (\(Given: a=\frac{d^2x}{dt^2}\))
1.
2.
3.
4. Zero
A body is moving according to the equation where x represents displacement and a, b and c are constants. The acceleration of the body is: (\(Given: a=\frac{d^2x}{dt^2}\))
1.
2.
3.
4.
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: (\(Given; v=\frac{dx}{dt}\))
1. -5 m/s
2. 6 m/s
3. 3 m/s
4. 4 m/s
The maximum value of the function is:
1. 8
2. -8
3. 4
4. -4
If , then f(x) has:
1. a minimum at x=1.
2. a maximum at x=1.
3. no extreme point.
4. no minimum.
The resultant of the forces and is . If is doubled, then the resultant also doubles in magnitude. Find the angle between and .
1.
2.
3.
4.
If \(\overrightarrow{\mathbf{A}}{=}{2}\hat{i}+\hat{j}\;{\&}\;\overrightarrow{\mathbf{B}}{=}\hat{i}{-}\hat{j}\) , then the components of along with & perpendicular to respectively will be:
1.
2.
3.
4.
If \(\vec{a}\) is a vector and \(x\) is a non-zero scalar, then which of the following is correct?
1. \(x\vec{a}\) is a vector in the direction of \(\vec{a}\)
2. \(x\vec{a}\) is a vector collinear to \(\vec{a}\)
3. \(x\vec{a}\) and \(\vec{a}\) have independent directions
4. \(x\vec{a}\) is a vector perpendicular to \(\vec{a}\)
The vector , which is collinear with the vector =(2, 1, -1) and satisfies the condition .=3 is-
1. (1, 1/2, -1/2)
2. (2/3, 1/3, -1/3)
3. (1/2, 1/4, -1/4)
4. (1, 1, 0)