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

The negation of the statement "If you don't work bard you will not become successful." is ______ 

If `int (sin2x)/(sin^4x + cos^4x) "d"x = tan^-1["f"(x)] + "c"`, then `"f"(pi/3)` = ______.

The Standard deviation of the following frequency distribution

is ______.

If f(x) =x⁴, g(x) = 6x – 2, then g[f(x)] = ______.

If 4x + 5y ≤ 20, x + y ≥ 3, x ≥ 0, y ≥ 0, maximum 2x + 3y 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` = ______.

The maximum of z = 5x + 2y, subject to the constraints x + y ≤ 7, x + 2y ≤ 10, x, y ≥ 0 is ______.

A random variable X has the following probability distribution:

Then, the expected value of X is ______.

Negation of (∼p → q) is ______.

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

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

The minimum value of z = 7x + 9y subject to 3x + y ≤ 6, 5x + 8y ≤ 40, x ≥ 0, y ≥ 2 is ______.

Negation of (p ∧ q) → (∼p ∨ r) is ______.

The negation of the statement, ∃ x ∈ R, such that x³ + 8 > 0, 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 ______.