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

If y = `(sin x)^sin x` , then `"dy"/"dx"` = ?

The odds in favour of drawing a king from a pack of 52 playing cards is ______.

The rate at which the metal cools in moving air is proportional to the difference of temperatures between the metal and air. If the air temperature is 290 K and the metal temperature drops from 370 K to 330 K in 1 O min, then the time required to drop the temperature upto 295 K.

For every value of x, the function f(x) = `1/"a"^x`, a > 0 is ______.

The equations of planes parallel to the plane x + 2y + 2z + 8 = 0, which are at a distance of 2 units from the point (1, 1, 2) are ________.

`int "dx"/(x^2 + 4x + 13)` = ?

The area of the square increases at the rate of 0.5 cm²/sec. The rate at which its perimeter is increasing when the side of the square is 10 cm long is ______.

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 = ______