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

If `"x"/sqrt(1 + "x") + "y"/sqrt(1 + "y")` = 0, x ≠ y, then `(1 + "x")^2 "dy"/"dx"` = ____________.

If the foot of perpendicular drawn from the origin to the plane is (3, 2, 1), then the equation of plane is ____________.

If `sqrt("x"/"y") + sqrt("y"/"x")` = 4, then `"dy"/"dx"` = ____________.

`int_e^(e^2)[1/(logx) - 1/(logx)^2]dx` = ______

If `int1/sqrt(16 - 25x^2) dx = a sin^-1(bx) + c`, then `a + 1/b` = ______ 

`int(((x^2 + 2)a^((x + tan^-1x)))/(x^2 + 1))dx` is equal to  ______ 

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 ______ 

`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 = ?