The position x of the particle varies with time t as x=at2-bt3 The acceleration of the particle will be zero at a time equal to: (\(Given: a=\frac{d^2x}{dt^2}\))

1.  ab

2.  2ab

3.  a3b

4.  Zero

Subtopic:  Differentiation |
 84%
From NCERT
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A body is moving according to the equation x=at+bt2-ct3 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.  a+2bt

2.  2b+6ct

3.  2b-6ct

4.  3b-6ct2

Subtopic:  Differentiation |
 86%
From NCERT
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A particle moves along the X-axis so that its X coordinate varies with time t according to the equation x=2-5t+6t2m. 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

Subtopic:  Differentiation |
 85%
From NCERT
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The maximum value of the function 7+6x-9x2 is:

1.  8

2.  -8

3.  4

4.  -4

Subtopic:  Differentiation |
 66%
From NCERT
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If fx=x2-2x+4, then f(x) has:

1.  a minimum at x=1.

2.  a maximum at x=1.

3.  no extreme point.

4.  no minimum.

Subtopic:  Differentiation |
 66%
From NCERT
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The resultant of the forces P and Q is R. If Q is doubled, then the resultant also doubles in magnitude. Find the angle between P and Q.

1.  cos θ=Q2P

2.  cos θ=-4Q3P

3. cos θ=-2Q3P

4.  cos θ=-3P4Q

Subtopic:  Resultant of Vectors |
 56%
From NCERT
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If \(\overrightarrow{\mathbf{A}}{=}{2}\hat{i}+\hat{j}\;{\&}\;\overrightarrow{\mathbf{B}}{=}\hat{i}{-}\hat{j}\) , then the components of A along with B & perpendicular to B respectively will be:
1.  i^-j^2, 32i^+j^

2.  i^-j^2,- 23i^+j^

3.  i^-j^2, -32i^-j^

4.  i^-j^2, 23i^-j^

Subtopic:  Scalar Product |
 54%
From NCERT
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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 \(\vec{a}\)

Subtopic:  Scalars & Vectors |
From NCERT
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The vector b, which is collinear with the vector a=(2, 1, -1) and satisfies the condition a.b=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)

Subtopic:  Scalar Product |
 53%
From NCERT
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If a, b and c are three non-zero vectors such that a+b+c=0, then the value of a.b+b.c+c.a will be:

1.  Less than zero

2.  equal to zero

3.  greater than zero

4.  3

Subtopic:  Scalar Product |
From NCERT
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