Mathematics – Class 12 Mock Test 10

1. What will be the minima for the function f(x) = x⁴ – 8x³ + 22x² – 24x + 8?

2. 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?

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 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?

5. 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)?

6. 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?

7. What is the equation of the tangent at a specific point of y² = 4ax at (0, 0)?

8. A motor car travelling at the rate of 40 km/hr is stopped by its brakes in 4 seconds. How long will it go from the point at which the brakes are first applied?

9. 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 and B runs with a uniform velocity of 9 m/sec, is it possible for B to overtake A?

10. 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?