माना कि f(x) = x3, x ∈ [-1, 1] है। निम्नलिखित में से कौन सा कथन सही है?

What is the value of the definite integral 10∫ x dx?

The value of the double integral ∫12 ∫0y/2 y dx dy is:

If f(x) = x3 - 6x2 + 9x + 1, then the local maximum and local minimum values of f(x) are, respectively:

What is the fourth derivative of the function y = 10x3 + 3x2 - 5x + 6?

The equation of motion of a particle starting from rest along a straight line is x(t) = t3 - 3t2 + 5. The ratio of the accelerations after 5 seconds and 3 seconds will be:

What is the coefficient of x5 in the Taylor series expansion of (1 + x)-1/2 about 0?

Let f(x) = tan(x2) and g(x) = x|x| for |x| < √π2. If p(x) = f(x)g(x), then which of the following statements is/are correct? I. p(x) is continuous at x = 0. II. p(x) is differentiable at x = 0. Select the correct answer using the code given below:

Let f(x) = tan(x2) and g(x) = x|x| for |x| < √π2. If q(x) = (f ○ g)(x), then which of the following statements is/are correct? I. q(x) is continuous at x = 0. II. q(x) is differentiable at x = 0. Select the correct answer using the code given below: