MHT - CET MCQ

Let X – B (n = 7, p = 0.5). Then P(X = 2) is ______.

In order to get a head at least once probability ~ 0.9, the minimum number of time a unbiased coin needs to be tossed is ______.

The probability distribution of a random variable X is given below.

X = k	0	1	2	3	4
P(X = k)	0.1	0.4	0.3	0.2	0

The variance of X is ______

The rate of growth of bacteria is proportional to the number present. If initially, there are 1000 bacteria and the number doubles in 1 hour, the number of bacteria after `21/2` hours will be ______. `(sqrt(2) = 1.414)`

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

The area of the region bounded by y = |x - 2| and y = 2 is ______

`int_0^log5 (e^xsqrt(e^x - 1))/(e^x + 3)` dx = ______

`int_0^pi x sin^2x dx` = ______

`int_-2^1 dx/(x^2 + 4x + 13)` = ______

`int_0^3 1/sqrt(3x - x^2)"d"x` = ______.

`int sec^6 x tan x "d"x` = ______.

`int ("e"^(7logx) - "e"^(6logx))/("e"^(5logx) - "e"^(4logx)) "d"x` = ______.

If y = `sqrt("e"^x + sqrt("e"^x + sqrt("e"^x + .... oo)`, then `("d"y)/("d"x)` is equal to ______.

If for a function f(x), f'(a) = 0, f"(a) = 0, f"'(a) > 0, then at x = a, f(x) is ______

The maximum value of P = 7x + 6y subject to constraints x + 2y ≤ 24, 2x + y ≤ 30 and x ≥ 0, y ≥ 0 is ______.

The d.r.s of normal to the plane through (1, 0, 0), (0, 1, 0) which makes an angle `pi/4` with plane x + y = 3, are ______.

Equation of the plane passing through A(-2, 2, 2), B(2, -2, -2) and perpendicular to x + 2y - 3z = 7 is ______

If A(1, 3, 2), B(a, b, - 4) and C(5, 1, c) are the vertices of triangle ABC and G(3, b, c) is its centroid, then

If C is the midpoint of AB and P is any point outside AB, then ______

The joint equation of pair of lines having inclinations 60° and 120°and passing through the origin is ______.

The value of `sin^-1(cos (53pi)/5)` is ______

In a triangle ABC, b = `sqrt3`, c = 1 and ∠A = 30°, then the largest angle of the triangle is ______

Which of the following quantified statement is True?

Given 'p' and 'q' as true and 'r' as false, the truth values of p v (q ∧ ~r) and (p → r) ∧ q are respectively

If (p ∧ ~ q) → ~ p is false, the truth values of p and q are respectively.

`lim_(x -> 0) (sin^4 3x)/x^4` = ________.

If f = {(4, 1), (5, 2), (6, 3)} and g = { (3, 9), (1, 7), (2, 8)}, then gof is ______

The number of ways in which a garland can be formed by using 10 identical pink flowers and 9 identical white flowers is ______

Which of the following is the third root of `(1 + i)/sqrt2`?

One page is randomly selected from a book containing 100 pages. The probability that the sum of the digits of the page number of the selected page is 9, is ______.

The variance and mean of distribution are 16 and 7 respectively. If every value is decreased by 3, then ______

In a triangle ABC, A ≡ (0, 2), B ≡ (4, 0). If the centroid of the triangle lies on the locus y = x, then the equation of locus of the third vertex C is ______

1 +cos 20° +cos 30° +cos 50° = ______.