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

The mean of the number a, b, 5, 8, 10 is 6 and variance is 6.80. Then, which one of the following gives possible values of a and b?

If log (x + y) = log (xy) + 3, then `dy/dx` = ______. 

If xy = tan^–1 (xy) + cot^–1 (xy), then `(dy/dx)_((4","  2))` = ______.

where (x, y) ∈ R

A plane passes through (1, - 2, 1) and is perpendicular to two planes 2x - 2y + z = 0 and x - y + 2z = 4. The distance of the plane from the point (1, 2, 2) is ______.

If f(x) = px⁵ + qx⁴ + 5x³ - 10 has local maximum and minimum at x = 1 and x = 3 respectively then (p, q) = ______.

The shortest distance between the lines

`bar"r" = (hat"i" + 2hat"j" + hat"k") + lambda (hat"i" - hat"j" + hat"k")` and

`bar"r" = (2hat"i" - hat"j" - hat"k") + mu(2hat"i" + hat"j" + 2hat"k")` is

If the tangent to the curve y = 3x² - 2x + 1 at a point Pis parallel toy = 4x + 3, the co-ordinates of P are

The maximum volume of a right circular cylinder if the sum of its radius and height is 6 m is ______.

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` = ______.

The statement pattern p ∧ ( q v ~ p) is equivalent to ______.

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 ____________.

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

For any two statements p and q, the negation of the expression (p ∧ ∼q) ∧ ∼p is ______ 

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 ______

(p → q) ∨ p is logically equivalent to ______