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

The maximum value of z = 6x + 8y subject to x - y ≥ 0, x + 3y ≤ 12, x ≥ 0, y ≥ 0 is ______.

Equations of planes parallel to the plane x - 2y + 2z + 4 = 0 which are at a distance of one unit from the point (1, 2, 3) are _______.

For L.P.P. maximize z = 4x₁ + 2x₂ subject to 3x₁ + 2x₂ ≥ 9, x₁ - x₂ ≤ 3, x₁ ≥ 0, x₂ ≥ 0 has ______.

In Δ ABC, if tan A + tan B + tan C = 6 and tan A tan B = 2 then tan C = ______.

Using differentiation, approximate value of f(x) = x² - 2x + 1 at x = 2.99 is ______.

`int_"a"^"b" sqrtx/(sqrtx + sqrt("a" + "b" - x)) "dx"` = ______.

`int_0^1 (1 - x)^5`dx = ______.

If `int_0^"a" sqrt("a - x"/x) "dx" = "K"/2`, then K = ______.

Area of the region bounded by y = cos x, x = 0, x = π and X-axis is ______ sq.units.

The length of the latusrectum of an ellipse is `18/5` and eccentncity is `4/5`, then equation of the ellipse is ______.

`int log x * [log ("e"x)]^-2` dx = ?

If y = log `[(x + sqrt(x^2 + 25))/(sqrt(x^2 + 25) - x)]` then `"dy"/"dx"` = ______.

`int_0^(pi/2) sqrt(cos theta) * sin^2 theta "d" theta` = ______.

If `hati - 2hatj + hatk`, `2hati + phatj + 3hatk` and `5hati - 9hatj + 4hatk` are coplanar, then the value of p is equal to ______

Equation of plane parallel to ZX-plane and passing through the point (0, 5, 0) is ______

`sqrt3 sin15^circ + cos15^circ` = ______

`int_0^{pi/4} (sin2x)/(sin^4x + cos^4x)dx` = ____________

`int_0^{pi/4} (sin2x)/(sin^4x + cos^4x)dx` = ____________

In a multiple-choice question, there are three options out of which only one is correct. A person is guessing the answer at random. If there are 7 such questions, then the probability that he will get exactly 4 correct answers is ______ 

If line `(2x - 4)/lambda = ("y" - 1)/2 = ("z" - 3)/1` and `(x - 1)/1 = (3"y" - 1)/lambda = ("z" - 2)/1` are perpendicular to each other then λ = ______.