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

If `overlinea`, `overlineb` and `overlinec` are three non-coplanar vectors then `(overlinea + overlineb + overlinec).[(overlinea + overlineb) xx (overlinea + overlinec)]` = ______

`lim_{x→0}((3^x - 3^xcosx + cosx - 1)/(x^3))` is equal to ______ 

The following statement (p → q) → [(∼p → q) → q] is ______ 

`int(1 + logx)^3/xdx` = ______

`int_0^2 1/sqrt(4 - x^2)dx` = ______ 

`int 1/(x^2 + 1)^2`dx = __________.

Derivative of log_e² (logx) with respect to x is _______.

`intcosx/((1 + sinx)(2 + sinx))`dx = ______ 

The variance of 6 scores 1, 2, 3, 4, 5, 6 is ______ 

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 ______.