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

The value of `lim_{x→0}{(a^x + b^x + c^x + d^x)/4}^{1/x}` is ______ 

lf y = `2^(x^(2^(x^(...∞))))`, then x(1 - y logx logy)`dy/dx` = ______  

`inte^{2logx}(x^3 + 1)^-1dx` = ____________

If y = `{f(x)}^{phi(x)}`, then `dy/dx` is ______ 

`int e^{3x}/(e^{3x} + 1)`dx = ______

If the function

f(x) = `(("e"^"kx" - 1)tan "kx")/"4x"^2, x ne 0`

= 16 , x = 0

is continuous at x = 0, then k = ?

If f(x) = [x], where [x] is the greatest integer not greater than x, then f'(1') = ______.

A ladder 20 ft Jong leans against a vertical wall. The top-end slides downwards at the rate of 2 ft per second. The rate at which the lower end moves on a horizontal floor when it is 12 ft from the wall is ______ 

`lim_{x→∞} ((3x + 3)^40(9x - 3)^5)/(3x + 1)^45` = ______ 

The function f(x) = x³ - 3x is ______.

If x^y = e^x-y, then `"dy"/"dx"` at x = 1 is ______.

Which of the following statements is contingency?

`int tan^-1((2tanx)/(1 - tan^2x))`dx = ______

`int_0^1 1/(sqrt(3 + 2x - x^2))dx` = ______ 

Which of the following statement pattern is a tautology?

`intx^2/sqrt(1 - x^6)dx` is equal to ______ 

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

If `int1/((x^2 - 1)) log((x - 1)/(x + 1))dx = A[log((x - 1)/(x + 1))]^2 + c,` then ______

The value of `lim_{x→-∞} (sqrt(5x^2 + 4x + 7))/(5x + 4)` is ______ 

The point of intersection of lines given by the equation 2x² + 4xy - 2y² + 4x + 8y + 1 = 0 is ______