Mathematics – Class 12 Practice Test 10

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

2. 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?

3. 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?

4. 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?

5. If the normal to the ellipse x² + 3y² = 12 at the point be inclined at 60° to the major axis, then at what angle does the line joining the curve to the point is inclined to the same axis?

6. 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 value of space described?

7. Given, f(x) = x³ – 12x² + 45x + 8. At which point does f(x) has its maximum?

8. What is the foot of the normal if the straight line x + y + 7 = 0 is normal to the hyperbola 3x² – 4y² = 12 whose normal is at the point (x₁, y₁)?

9. At which point does f(x) = |x – 1| has itslocal minimum?

10. One motor car A stands 24m in front of a motorcycle B. Both starts from rest along a straight road in the same direction. If A moves with uniform acceleration of 2 m/sec², B runs at a uniform velocity of 11 m/sec how many times will they meet?