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

If `int_0^(pi/2) log (cos x) "dx" = - pi/2 log 2,` then `int_0^(pi/2) log (cosec x)`dx = ?

In a ΔABC, c² sin 2B + b² sin 2C = ?

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

A coin is tossed 10 times. The probability of getting exactly six heads is ______.

A square plate is contracting at the uniform rate of 3cm²/sec. The rate at which the perimeter is decreasing when the side of the square is 12 cm long is

The degree of the differential equation `("d"^4"y")/"dx"^4 + sqrt(1 + ("dy"/"dx")^4)` = 0 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

A random variable X has the following probability distribution:

Then the value of k is

The maximum value of Z = 3x + 5y, subject to 3x + 2y ≤ 18, x ≤ a, y ≤ 6, x, y ≥ 0 is ______.

In a ΔABC if 2 cos C = sin B · cosec A, then ______.

The order and degree of the differential equation `[1 + ["dy"/"dx"]^3]^(7/3) = 7 (("d"^2"y")/"dx"^2)` are respectively.

Out of 100 people selected at random, 10 have common cold. If five persons selected at random from the group, then the probability that at most one person will have common cold is ______.

If a = sin 175°+ cos 175°, then ______.

With usual notations, if the angles A, B, C of a Δ ABC are in AP and b : c = `sqrt3 : sqrt2`.

If Xis a.r.v. with c.d.f F (x) and its probability distribution is given by

then, F(1.5) - F(- 0.5) = ?

The LPP to maximize Z = x + y, subject to x + y ≤ 1, 2x + 2y ≥ 6, x ≥ 0, y ≥ 0 has ________.

The order and degree of the differential equation `[1 + 1/("dy"/"dx")^2]^(5/3) = 5 ("d"^2y)/"dx"^2` are respectively.

In a triangle ABC with usual notations, if `(cos "A")/"a" = (cos "B")/"b" = (cos "C")/"c"`, then area of triangle ABC with a = `sqrt6` is ____________.

The area of the region bounded by the curve y = 4x³ − 6x² + 4x + 1 and the lines x = 1, x = 5 and X-axis is ____________.

If f(x) = `(2"x" + 3)/(3"x" - 2)`, `"x" ≠ 2/3`, then the function fof is ____________.