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

The area of the Δ ABC is `10sqrt3` cm², angle B is 60° and its perimeter is 20 cm , then l(AC) = ______.

If A and Bare supplementary angles, then `sin^2  "A"/2 + sin^2  "B"/2` = ______.

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

The polar coordinates of the point whose cartesian coordinates are (−2, −2), are given by ____________.

The minimum value of Z = 5x + 8y subject to x + y ≥ 5, 0 ≤ x ≤ 4, y ≥ 2, x ≥ 0, y ≥ 0 is ____________.

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

In a ΔABC, A : B : C = 3 : 5 : 4. Then `a + b + csqrt2` is equal to ______

The modulus of z = `sqrt7` + 3i is ______

Max value of z equals 3x + 2y subject to x + y ≤ 3, x ≤ 2, -2x + y ≤ 1, x ≥ 0, y ≥ 0 is ______ 

If f(x) = 3x³ - 9x² - 27x + 15, then the maximum value of f(x) is _______.

If a r.v. X has p.d.f., f(x) = `1/(xlog3)`, for 1 < x < 3, then E(X) and Var(X) are respectively ______

The modulus and amplitude of 4 + 3i are ______

The p.d.f of a random variable x is given by

f(x) = `1/"4a"`, 0 < x < 4a, (a > 0)

= 0, otherwise

and `"P"(x < "3a"/2) = "kp"(x > "5a"/2)` then k = ?

If R is the circum radius of Δ ABC, then A(Δ ABC) = ______.

If x + iy = `5/(3 + costheta + isintheta)`, then x² + y² is equal to ______ 

The mean and S.D. of the scores of 100 candidates were found to be 80 and 15 respectively. Later, it was discovered that a score of 50 was wrongly read as 40. The correct mean and S.D. respectively are ______ 

The negation of "∀, n ∈ N, n + 7 > 6" is ______.

If z = ax + by; a, b > 0 subject to x ≤ 2, y ≤ 2, x + y ≥ 3, x ≥ 0, y ≥ 0 has minimum value at (2, 1) only, then ______.

The pdf of a random variable X is

f(x) = 3(1 - 2x²), 0 < x < 1

      = 0   otherwise

The P`(1/4 < "X" < 1/3)` = ?

If f(x) = `x + 1/x, x ne 0`, then local maximum and x minimum values of function f are respectively.