# Class 12 Maths Mcqs

Q:

A) 4/27 units | B) 4/23 units |

C) 4/25 units | D) 4/35 units |

Answer & Explanation
Answer: A) 4/27 units

Explanation: Let v be the velocity of the particle at time t seconds after start (that is at a distance s from O). Then,

v = ds/dt = d[(t – 1)²(t – 2)²]/dt

Or v = (t – 2)(3t – 4)

Clearly, v = 0, when (t – 2)(3t – 4) = 0

That is, when t = 2

Or 3t – 4 = 0 i.e., t = 4/3

Now, s = (t – 1)(t – 2)²

Therefore, when t = 4/3, then s = (4/3 – 1)(4/3 – 2)² = 4/27

And when t = 2, then s =(2 – 1)(2 – 2)² = 0

Therefore, the velocity of the particle is zero, when its distance from O is 4/27 units and when it is at O.

Explanation: Let v be the velocity of the particle at time t seconds after start (that is at a distance s from O). Then,

v = ds/dt = d[(t – 1)²(t – 2)²]/dt

Or v = (t – 2)(3t – 4)

Clearly, v = 0, when (t – 2)(3t – 4) = 0

That is, when t = 2

Or 3t – 4 = 0 i.e., t = 4/3

Now, s = (t – 1)(t – 2)²

Therefore, when t = 4/3, then s = (4/3 – 1)(4/3 – 2)² = 4/27

And when t = 2, then s =(2 – 1)(2 – 2)² = 0

Therefore, the velocity of the particle is zero, when its distance from O is 4/27 units and when it is at O.

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Q:

A) 1/v² + 1/u² = 4at | B) 1/v² + 1/u² = -4at |

C) 1/v² – 1/u² = 4at | D) 1/v² – 1/u² = -4at |

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Q:

A) 1/v² = 1/2u² + 2kt | B) 1/v² = 1/2u² – 2kt |

C) 1/v² = 1/u² – 2kt | D) 1/v² = 1/u² + 2kt |

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Q:

A) 11m/sec | B) 31 cm/sec |

C) 21m/sec | D) 41m/sec |

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Q:

A) 30 cm | B) 31 cm |

C) 32 cm | D) 33 cm |

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Q:

A) The retardation of the particle is the cube of its velocity | B) The acceleration of the particle is the cube of its velocity |

C) The retardation of the particle is the square of its velocity | D) The acceleration of the particle is the square of its velocity |

Answer & Explanation
Answer: A) The retardation of the particle is the cube of its velocity

Explanation: Not available for this question

Explanation: Not available for this question

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Q:

A) 21 cm | B) 22 cm |

C) 23 cm | D) 24 cm |

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Q:

A) Uniform retardation | B) Uniform speed |

C) Uniform acceleration | D) Uniform velocity |

Answer & Explanation
Answer: D) Uniform velocity

Explanation: We have, x = a + bt + ct² ……….(1)

Let, v and f be the velocity and acceleration of a particle at time t seconds.

Then, v = dx/dt = d(a + bt + ct²)/dt = b + ct ……….(2)

And f = dv/dt = d(b + ct)/dt = c ……….(3)

Clearly, when c = 0, then f = 0 that is, acceleration of the particle is zero.

Hence in this case the particle moves with an uniform velocity.

Explanation: We have, x = a + bt + ct² ……….(1)

Let, v and f be the velocity and acceleration of a particle at time t seconds.

Then, v = dx/dt = d(a + bt + ct²)/dt = b + ct ……….(2)

And f = dv/dt = d(b + ct)/dt = c ……….(3)

Clearly, when c = 0, then f = 0 that is, acceleration of the particle is zero.

Hence in this case the particle moves with an uniform velocity.

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