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

If in Δ ABC, 3a = b + c, then `cot ("B"/2) cot ("C"/2)` = ______.

Area under the curve `y=sqrt(4x+1)` between x = 0 and x = 2 is ______.

The differential equation of the family of curves y = e^x (A cos x + B sin x). Where A and B are arbitary constants is ______.

If PQ and PR are the two sides of a triangle, then the angle between them which gives maximum area of the triangle is ______.

The order and degree of the differential equation `("d"^2"y")/"dx"^2 + (("d"^3"y")/"dx"^3) + x^(1/5) = 0` are respectively.

The area enclosed by the parabolas x = y² - 1 and x = 1 - y² is ______.

Two coins are tossed. Then the probability distribution of number of tails is.

In `triangleABC,` if a = 3, b = 4, c = 5, then sin 2B = ______.

If P(α, β) be a point on the line 3x + y = 0 such that the point P and the point Q(1, 1) lie on either side of the line 3x = 4y + 8, then _______.

The order and degree of `(("n + 1")/"n")("d"^4"y")/"dx"^4 = ["n" + (("d"^2"y")/"dx"^2)^4]^(3//5)` are respectively.

In a series of observations, S.D. = 5 and mean is 20, then coefficient of variation is ______.

The c.d.f. of a discrete r.v. x is 

Then P(1 < x ≤ 4) = ______ 

The c.d.f. of a discrete r.v. X is

Then P(X ≤ 4|X > -1) = ?

If `((1 + "i"sqrt3)/(1 - "i"sqrt3))^"n"` is an integer, then n is ______.

If in a `triangle"ABC",` a²cos² A - b² - c² = 0, then ______.

In a series of observations, coefficient of variation is 25 and mean is 20, then the variance is ______.

If m and n are the order and degree of the differential equation `((d^3y)/(dx^3))^6+5((d^3y)/(dx^3))^4/((d^4y)/(dx^4))+(d^4y)/(dx^4)=x^3-1,` then ______.

If function `f(x)={((x^2-9)/(x-3), ",when "xne3),(k, ",when "x =3):}` is continuous at x = 3, then the value of k will be ______.

If in ΔABC, `sin  "B"/2 sin  "C"/2 = sin  "A"/2` and 2s is the perimeter of the triangle, then s is ______.

The order of the differential equation whose general solution is given by `y=C_(1)e^(2x+C_2)+C_3e^x+C_4sin(x+C_5)` is ______.