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Class 12 Mathematics: Application of Calculus
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MCQs on calculus applications like increasing and decreasing functions, tangents and normals, straight line motion, motion under gravity, calculus applications like maxima and minima, acceleration and velocity.
 

Class 12 Mathematics: Application of Calculus
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25 Questions

1. 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?
2. If the curves x2/a + y2/b = 1 and x2/c + y2/d = 1 intersect at right angles, then which one is the correct relation?
3. 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?
4. 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?
5. What will be the equation of the circle which touches the line x + 2y + 5 = 0 and passes through the point of intersection of the circle x2 + y2 = 1 and x2 + y2 + 2x + 4y + 1 = 0?
6. A particle moving along a straight line with uniform acceleration, passes successively through three points A, B, C. If t1 = time taken to go from A to B; t2 = time taken to go from B to C and AB = a, BC = b, then what is the value of acceleration?
7. What will be nature of the f(x) = 10 – 9x + 6x2 – x3 for x > 3?
8. What will be the values of x for which the value of cosx is minimum?
9. 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?
10. A particle moving along a straight line with uniform acceleration, passes successively through three points A, B, C. If t1 = time taken to go from A to B; t2 = time taken to go from B to C and AB = a, BC = b. If a = b and the velocities of the particle at A, B, C be p, q, r respectively, then, what is the relation between p2, q2 and r2?
11. Given, f(x) = x3 – 12x2 + 45x + 8. What is the maximum value of f(x)?
12. 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?
13. A particle moving in a straight line with uniform retardation described 7cm in 5th second and after some time comes to rest. If the particle describes 1/64 part of the total path during the last second of its motion, for how long was the particle in motion?
14. What is the equation of the tangent at a specific point of y2 = 4ax at (0, 0)?
15. What will be the co-ordinates of the foot of the normal to the parabola y2 = 5x that makes an angle 45° with the x axis?
16. A particle is projected vertically upwards with a velocity of 196 m/sec. What will be its velocity at the end of 10 seconds?
17. What is the nature of the straight line x + y + 7 = 0 to the hyperbola 3x2 – 4y2 = 12 whose normal is at the point (x1, y1)?
18. What will be the equation of the tangent to the circle x2 + y2 – 6x + 4y – 7 = 0, which are perpendicular to the straight line 2x – y + 3 = 0?
19. If X and Y are given as current co-ordinates, what is the equation of the tangent at a specific point of x3 – 3axy + y3 = 0 at (x, y)?
20. 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?
21. A particle moving in a straight line with uniform acceleration has a velocity 10 cm/sec and 8 seconds later has a velocity 54 cm/sec. What will be the acceleration?
22. What will be the range of the function f(x) = 2x3 – 9x2 – 24x + 5 which decreases with x?
23. What will be the co-ordinates of the foot of the normal to the parabola y2 = 3x which is perpendicular to the line y = 2x + 4?
24. A point starts with the velocity 10 cm/sec and moves along a straight line with uniform acceleration 5cm/sec2. How much time it takes to describe 80 cm?
25. What is the equation of the tangent to the parabola y2 = 8x, which is inclined at an angle of 45° with the x axis?

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