MAH-MHT CET (PCM/PCB) entrance exam Question Bank Solutions for Mathematics

If y = `tan^-1((sqrtx + 1)/(sqrtx - 1)) + tan^-1((sqrtx - 1)/(sqrtx + 1))`, then the value of `dy/dx` = ______

If `y = tan^-1((sqrtx - x)/(1 + x^{3/2}))`, then y'(1) is ______ 

If `y = cot^-1((6cotx - 5)/(5cotx + 6)), "then" dy/dx` = ______ 

The derivative of `cos^-1 (2x^2 - 1)` w.r.t `cos^-1 x` is ______

The angle between the lines represented by the equation ax² + xy + by² = 0 will be 45°, if ______ 

The plane 2x - 3y + 6z - 11 = 0 makes an angle sin^-1 (α) with X-axis. The value of α is equal to ______ 

The derivative of `sin^-1(2xsqrt(1 - x^2))` with respect to `sin^-1(3x - 4x^3)` is ______ 

The negation of "∀, n ∈ N, n + 7 > 6" is ______.

If `tan^-1x + tan^-1y = pi/4`, then ______

`d/dx[cot^-1(sqrtx)]` = ______ 

Derivative of `sin^-1 ("t"/sqrt(1 + "t"^2))` with respect to `cos^-1 (1/sqrt(1 + "t"^2))` is ______.

What is the mean of f(x) = 3x + 2 where x is a random variable with probability distribution

If `intsqrt((x - 7)/(x - 9)) dx = Asqrt(x^2 - 16x + 63) + log|x - 8 + sqrt(x^2 - 16x + 63)| + c`, then A = ______

If `y = sin^-1(1/x^3)`, then `dy/dx` = ______ 

The probability distribution of the random variable X is given by

Then, 4 var (X) - E (X²) is equal to ______ 

If y = `cot^-1(x/(sqrt(1 - x^2)))`, then `dy/dx` is equal to ______ 

Let f (x) > 0 for all x and f '(x) exists for all x. If f is the inverse function of h and h'(x) = `1/(1 + logx)`. Then f'(x) will be ______ 

The probability distribution of X is 

Then P(X is not a natural number) = ______ 

The maximum value of P = 3x + 4y subject to the constraints x + y ≤ 40, x + 2y ≤ 60, x ≥ 0 and y ≥ 0 is ______ 

If the angle between the line x = `("y" - 1)/2 = ("z - 3")/lambda` and the plane x + 2y + 3z = 4 is `cos^-1 (sqrt(5/14))`, then λ equals.