MHT - CET MCQ

The p.m.f. of a r.v. X is

The probability distribution of X is

X = x	-4	-3	-2	-1	0	1	2
P(X = x)	0.25a	0.20a	0.15a	0.10a	0.05a	0.10a	0.15a

Then P(X is not a natural number) = ______

A random variable X has the following probability distribution:

X	1	2	3	4
P(X)	`1/3`	`2/9`	`1/3`	`1/9`

1hen, the mean of this distribution is ______

The solution of the differential equation `dy/dx = ((1 + x)y)/((y - 1)x)` is ______

Let f(x) be a non-negative continuous function such that the area bounded by the curve y = f(x), X-axis and the ordinates x = `pi/4` and x = `beta > pi/4` is `(beta sin beta + pi/4 cos beta + sqrt(2)beta)`. Then `"f"(pi/2)` is ______.

The area bounded by the X-axis, the curve y = f(x) and the lines x = 1, x = b is equal to `sqrt("b"^2 + 1) - sqrt(2)` for all b > 1, then f(x) is ______.

`int_(-pi/4)^(pi/4) 1/(1 - sinx) "d"x` = ______.

`int_(-1)^1 log ((2 - x)/(2 + x)) "dx" = ?`

`int_0^{pi/2} xsinx dx` = ______

`int dx/(sqrt(x + 3) - sqrt(x + 2))` = ______

`int (sec^8x)/("cosec" x) "d"x` = ______.

If `tan^-1x = 2tan^-1((1 - x)/(1 + x))`, then the value of x is ______

`int_3^4 1/(x^2 + 7x + 12) "d"x` = ______.

If f'(x) = `2 - 5/x^4` and f(1) = `14/3`, then f(-1) = ______

If `("f"(x))/(log (sec x)) "dx"` = log(log sec x) + c, then f(x) = ______.

The point which provides the solution to the linear programming problem: Max P = 2x + 3y subject to constraints: x ≥ 0, y ≥ 0, 2x + 2y ≤ 9, 2x + y ≤ 7, x + 2y ≤ 8, is ______

The solution for maximizing the function z = x + 2y under a LPP with constraints x + y ≥ 1, x + 2y ≤ 10, y ≤ 3 and x, y ≥ 0, is ______

If the angle between the planes `overliner . (mhati - hatj + 2hatk) + 3 = 0` and `overliner . (2hati - mhatj - hatk) - 5 = 0` is `pi/3`, then m = ______

If the plane x - 3y + 5z = d passes through the point (1, 2, 4), then the lengths of intercepts cut by it on the axes of X, Y, Z are respectively ______

The shortest distance between the skew lines `overliner= (6hati + 2hatj + 2hatk) + t(hati - 2hatj + 2hatk)` and `overliner = (-4hati - hatk) + s(3hati - 2hatj - 2hatk)` is ______

The direction ratio of the line 2x - 1 = 3y + 2 = z - 2 are ______.

If the vectors `ahat("i")+hat("j")+hat("k"), hat("i")+bhat("j")+hat("k")` and `hat("i")+hat("j")+chat("k")` are coplanar (a ≠ b ≠ c ≠ 1), then the value of abc - (a + b + c) = ______.

The angle between the planes and `bar"r"*(2hat"i" + hat"j" - hat"k") = 3` and `bar"r"*(hat"i" + 2hat"j" + hat"k") = 1` is ______.

If the line `x/(3) = y/(4)` = z is perpendicular to the line `(x - 1)/k = (y + 2)/(3) = (z - 3)/(k - 1)`, then the value of k is ______.

The equation of line passing through the midpoint of the line joining the points (-1, 3, -2) and (-5, 3, -6) and equally inclined to the axes is ______.

The value of cot (- 1110°) is equal to ______.

If in a right-angled triangle ABC, the hypotenuse AB = p, then `overline"AB".overline" AC" + overline"BC".overline" BA" + overline" CA".overline"CB"` is equal to ______

The general solution of the equation tan θ tan 2θ = 1 is given by ______

The logical statement (∼p → q) ∧ (q → p) is equivalent to: ______

If q Λ ∼p is T, then which of the following is correct?

Find out which of the following statements have the same meaning:
i. If Meena makes a software then she is happy.

ii. If Meena does not make a software then she is not happy.

iii. If Meena is not happy then she hasn't made a software.

iv. If Meena is happy then she has made a software.

If f(x) = `{:{(tan^-1|x|; "when" x ≠ 0), (pi/4; "when" x = 0):}`, then ______

`lim_(x -> 0) ((2 + x)^5 - 2)/((2 + x)^3 - 2)` = ______.

If f(x) = `1/sqrt(4 - 3x)`, then dom(f) = ______..

Four mangoes and five apples are in a box. If two fruits are chosen at random, then find the probability that one is a mango and other is an apple ______.

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

The equation of circle whose diameter is the line joining the points (–5, 3) and (13, –3) is ______.

The equation of line equally inclined to co-ordinate axes and passing through (–3, 2, –5) is ______.

The imaginary part of `1/(1 - sintheta + icostheta)` is equal to ______