Mathematics – Class 12 Practice Test 4

1. Find \(\frac{dy}{dx}\), if x=9t⁴ and y=t.

2. Function f is not continuous on [a,b] to satisfy Lagrange’s mean value theorem.

3. What will be the increment of the differentiable function f(x) = 2x² – 3x + 2 when x changes from 3.02 to 3?

4. Find \(\frac{d^2 y}{dx^2}\)-6 \(\frac{dy}{dx}\) if y=4x⁴+2x.

5. The length of a side of a cube is 10cm; if an error of 0.05cm is made in measuring the side, then what is the value of relative error in calculating its volume?

6. Find the interval in which function f(x) = sinx+cosx is increasing.

7. The value of f’(x) is -1 at the point P on a continuous curve y = f(x). What is the angle which the tangent to the curve at P makes with the positive direction of x axis?

8. What will be the differential function of √(x² + 2)?

9. Find the second order derivative of y=3x² 1 + log⁡(4x)

10. What is the formula for Lagrange’s theorem?