Calculus Application MCQ

Test your knowledge with important Calculus Application MCQ and their applications. These MCQs are beneficial for competitive exams too. Explore 30 + more Calculus Application MCQs at Bissoy

• The distance s of a particle moving along a straight line from a fixed-pointO on the line at time t seconds after start is given by x = (t – 1)2(t – 2)2. What will be the distance of the particle from O when its velocity is zero?
  ক

  4/27 units

  খ

  4/23 units

  গ

  4/25 units

  ঘ

  4/35 units
• The distance x of a particle moving along a straight line from a fixed point on the line at time t after start is given by t = ax2 + bx + c (a, b, c are positive constants). If v be the velocity of the particle and u(≠0) be the initial velocity of the particle then which one is correct?
  ক

  1/v2 + 1/u2 = 4at

  খ

  1/v2 + 1/u2 = -4at

  গ

  1/v2 – 1/u2 = 4at

  ঘ

  1/v2 – 1/u2 = -4at
• A particle moves with uniform acceleration along a straight line and describes distances 21m, 43m and 91m at times 2, 4 and 7 seconds, respectively.What is the velocity of the particle in 3 seconds?
  ক

  11m/sec

  খ

  31 cm/sec

  গ

  21m/sec

  ঘ

  41m/sec
• A particle moves with uniform acceleration along a straight line and describes distances 21m, 43m and 91m at times 2, 4 and 7 seconds,respectively.What is the distance described by the particle in 3 seconds?
  ক

  30 cm

  খ

  31 cm

  গ

  32 cm

  ঘ

  33 cm
• A particle moving in a straight line traverses a distance x in time t. If t = x2/2 + x, then which one is correct?
  ক

  The retardation of the particle is the cube of its velocity

  খ

  The acceleration of the particle is the cube of its velocity

  গ

  The retardation of the particle is the square of its velocity

  ঘ

  The acceleration of the particle is the square of its velocity
• A particle moves in a straight line and its velocity v at time t seconds is given byv = 3t2 – 4t + 5 cm/second. What will be the distance travelled by the particle during first 3 seconds after the start?
  ক

  21 cm

  খ

  22 cm

  গ

  23 cm

  ঘ

  24 cm
• A particle moves in a straight-line OA; the distance of the particle from O at time t seconds is x ft, where x = a + bt + ct2 (a, b > 0). What will be the nature of motion of the particle when c = 0?
  ক

  Uniform retardation

  খ

  Uniform speed

  গ

  Uniform acceleration

  ঘ

  Uniform velocity
• A particle moves in a straight-line OA; the distance of the particle from O at time t seconds is x ft, where x = a + bt + ct2 (a, b > 0). What is the meaning of the constant b?
  ক

  Final velocity

  খ

  Initial velocity

  গ

  Mid velocity

  ঘ

  Arbitrary velocity
• A particle moves in a straight-line OA; the distance of the particle from O at time t seconds is x ft, where x = a + bt + ct2 (a, b > 0). What is the meaning of the constant a?
  ক

  Initial position

  খ

  Final position

  গ

  Mid position

  ঘ

  Any arbitrary position
• “It is impossible for a particle to move in a straight line so that its velocity varies at the distance from the commencement of motion”. Which one is correct for the given statement?
  ক

  The above statement is valid

  খ

  The above statement is not valid

  গ

  Data inadequate

  ঘ

  Answer does not exist
• A particle is moving along the straight line OX and its distance x is in metres from O after t seconds from start is given by x = t3 – t2 – 5t. What will be the distance traversed before it comes to rest?
  ক

  -173/27

  খ

  173/27

  গ

  -175/27

  ঘ

  175/27
• A particle is moving in a straight line is at a distance x from a fixed point in the straight line at time t seconds, where x = 2t3 – 12t + 11. What is the displacement of the particle at the end of 2 seconds?
  ক

  1 cm

  খ

  2 cm

  গ

  3 cm

  ঘ

  4 cm
• A particle is moving in a straight line is at a distance x from a fixed point in the straight line at time t seconds, where x = 2t3 – 12t + 11. What is the velocity of the particle at the end of 2 seconds?
  ক

  10 cm/sec

  খ

  12 cm/sec

  গ

  14 cm/sec

  ঘ

  16 cm/sec
• A particle is moving in a straight line and its distance s cm from a fixed point in the line after t seconds is given by s = 12t – 15t2 + 4t3. What will be the distance between the two positions of the particle at two times, when the velocity is instantaneously 0?
  ক

  27/4 cm

  খ

  29/4 cm

  গ

  27/2 cm

  ঘ

  29/2 cm
• A particle is moving in a straight line and its distance s cm from a fixed point in the line after t seconds is given by s = 12t – 15t2 + 4t3. What is the velocity of the particle after 3 seconds?
  ক

  10 cm/sec

  খ

  20 cm/sec

  গ

  30 cm/sec

  ঘ

  40 cm/sec
• A particle starts moving from rest with an acceleration in a fixed direction. If its acceleration at time t be(a – bt2),where a and b are positive constants then which one is correct? max = 4a√a/3√b b) max = 2a√a/3√b c) max = 2a√a/3√b d) max = 4a√a/3√b
  ক

  max = 4a√a/3√b

  খ

  v

  গ

  v

  ঘ

  v
• Two straight railway lines meet at right angles. A train starts from the junction along one line and at the same time instant, another train starts towards the junction from a station on the other line and they move at the same uniform velocity.When will they be nearest to each other?
  ক

  When they are equal distance from the junction

  খ

  When they are in unequal distance from the junction

  গ

  When they form a right angle at the junction

  ঘ

  Data not sufficient
• The distance x of a particle moving along a straight line from a fixed point on the line at time t after start is given by t = ax2 + bx + c (a, b, c are positive constants). If v be the velocity of the particle at the instant, then which one is correct?
  ক

  Moves with retardation 2av2

  খ

  Moves with retardation 2av3

  গ

  Moves with acceleration 2av3

  ঘ

  Moves with acceleration 2av2
• A particle moves in a horizontal straight line under retardation kv3, where v is the velocity at time t and k is a positive constant. If initial velocity be u and x be the displacement at time,then which one is correct?
  ক

  1/v = 1/u + kx

  খ

  1/v = 1/u – 2kx

  গ

  1/v = 1/u – kx

  ঘ

  1/v = 1/u + 2kx
• A particle moves along the straight-line OX, starting from O with a velocity 4 cm/sec. At time t seconds its acceleration is (5 + 6t) cm/sec2. What will be the distance from O after 4 seconds?
  ক

  110 cm

  খ

  120 cm

  গ

  130 cm

  ঘ

  140 cm
• A particle moves along the straight-line OX, starting from O with a velocity 4 cm/sec. At time t seconds its acceleration is (5 + 6t) cm/sec2. What will be the velocity of the particle from O after 4 seconds?
  ক

  70 cm/sec

  খ

  71 cm/sec

  গ

  72 cm/sec

  ঘ

  73 cm/sec
• A particle moves in a straight line and its velocity v at time t seconds is given byv = 3t2 – 4t + 5 cm/second. What will be the acceleration of the particle during first 3 seconds after the start?
  ক

  10cm/sec2

  খ

  12cm/sec2

  গ

  14cm/sec2

  ঘ

  16cm/sec2
• A particle moves in a straight-line OA; the distance of the particle from O at time t seconds is x ft, where x = a + bt + ct2 (a, b > 0). What will be the nature of motion of the particle when c < 0?
  ক

  Uniform retardation

  খ

  Uniform speed

  গ

  Uniform acceleration

  ঘ

  Uniform velocity
• A particle moves in a straight-line OA; the distance of the particle from O at time t seconds is x ft, where x = a + bt + ct2 (a, b > 0). What will be the nature of motion of the particle when c > 0?
  ক

  Uniform retardation

  খ

  Uniform speed

  গ

  Uniform positive acceleration

  ঘ

  Uniform velocity
• A particle moves in a straight-line OA; the distance of the particle from O at time t seconds is x ft, where x = a + bt + ct2 (a, b > 0). What is the meaning of the constant c?
  ক

  Uniform acceleration

  খ

  Non – uniform acceleration

  গ

  Uniform retardation

  ঘ

  Non – uniform retardation
• A particle is moving along the straight line OX and its distance x is in metres from O after t seconds from start is given by x = t3 – t2 – 5t. What will be the acceleration of the particle when it is at a distance 28 metres from O?
  ক

  20 m/sec2

  খ

  22 m/sec2

  গ

  24 m/sec2

  ঘ

  26 m/sec2
• A particle is moving in a straight line is at a distance x from a fixed point in the straight line at time t seconds, where x = 2t3 – 12t + 11. What is the average acceleration of the particle at the end of 3 seconds?
  ক

  28 cm/sec2

  খ

  30 cm/sec2

  গ

  32 cm/sec2

  ঘ

  26 cm/sec2
• A particle is moving in a straight line is at a distance x from a fixed point in the straight line at time t seconds, where x = 2t3 – 12t + 11. What is the acceleration of the particle at the end of 2 seconds?
  ক

  22 cm/sec2

  খ

  24 cm/sec2

  গ

  26 cm/sec2

  ঘ

  28 cm/sec2
• A particle is moving in a straight line and its distance s cm from a fixed point in the line after t seconds is given by s = 12t – 15t2 + 4t3. What is the acceleration of the particle after 3 seconds?
  ক

  41 cm/sec2

  খ

  42 cm/sec2

  গ

  43 cm/sec2

  ঘ

  44 cm/sec2
• A particle is moving in a straight line and its distance x from a fixed point on the line at any time t seconds is given by, x = t4/12 – 2t3/3 + 3t2/2 + t + 15. What is the minimum velocity?
  ক

  1 cm/sec

  খ

  2 cm/sec

  গ

  3 cm/sec

  ঘ

  4 cm/sec