DSC - Mathematics Mock Tests

If y = sin⁻¹(2x√(1 − x²)), then dy/dx at x = 1/2 is:

The function f(x) = |x| · sin x is:

The function f(z) = |z|² is differentiable at

If α and β are the zeros of the polynomial p(x) = 2x² - 5x + k, and they satisfy α + β = αβ, find the value of k.

A factory has two machines X and Y. Machine X produces 60% of items and machine Y produces 40%. If 2% of items from X and 1% from Y are defective, the probability that a randomly selected defective item came from machine X is:

In a pie chart, if the entire circle represents 360 students, what angle represents 90 students?

A cylindrical tank has radius 7 m and height 10 m. Its capacity in litres is: (use π = 22/7)

The vector equation r · (î + ĵ − k̂) = 6 represents a plane. The length of the perpendicular from the origin to this plane is: