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

The acute angle between the curve x = 2y² and y = 2x² at `(1/2, 1/2)` is ______.

`int (cot(logx))/x "d"x` = ______.

`int "e"^sintheta [log(sin theta) + "cosec"^2theta]costheta "d"theta` = ______.

`int (sec^8x)/("cosec" x)  "d"x` = ______.

A random variable X has the following probability distribution:

Then, the expected value of X is ______.

`int cosx/sqrt(1 + sinx) "d"x` = ______.

Inverse of the function y = 5 – 10x is ______.

Let f(x) = 1 + x, g(x) = x² + x + 1, then (f + g) (x) at x = 0 is ______.

Eccentricity of ellipse `x^2/a^2 + y^2/b^2` = 1, if it passes through point (9, 5) and (12, 4) is ______.

Equation of the ellipse whose axes are along the coordinate axes, vertices are (± 5, 0) and foci at (± 4, 0) is ______.

The equation of set points P such that PA² + PB² = 2K², where A and B are the points (3, 4, 5) and (–1, 3, –7), respectively is ______.

`int ("e"^x(1 + x))/(cos^2 ("e"^x x))"d"x` is equals to ______.

The inverse of f(x) = `2/3 (10^x - 10^-x)/(10^x + 10^-x)` is ______.

The foot of the perpendicular drawn from the origin to a plane is the point (1, –3, 1). What is the intercept cut on the x-axis by the plane?

Three vertices of a parallelogram ABCD are A ( 3, –1, 2), B (1, 2, –4) and C (–1, 1, 2). The coordinates of fourth vertex D are ______.

The equation of the plane containing the line `(x + 1)/(-3) = (y - 3)/2 = (z + 2)/1` and the point (0, 7, –7), is ______.

The co-ordinates of the foot of perpendicular from the point A (1, 1, 1) on the line joining the points B (1, 4, 6) and C (5, 4, 4) are ______.

The distance of the point (1, –2, 3) from the plane x – y + z = 5 measured parallel to the line `x/2 = y/3 = (z - 1)/(-6)` is ______.

A fair coin is tossed 99 times. If X is the number of times head occurs, P(X = r) is maximum when r is ______.

If g(x) is the inverse function of f(x) and f'(x) = `1/(1 + x^4)`, then g'(x) is ______.