MHT - CET MCQ

The p.m.f. of a r.v. X is
P(x) = `{:(= 1/13"," "for" x = 1"," 2"," ......"," 14"," 13),(= 0"," "otherwise."):}`
Then, E(X) is equal to ______.

The probability distribution of a random variable X is

X	- 2.5	- 1.5	-0.5	0.5	1.5
P(X)	0.35	0.25	0.2	0.15	0.05

Then the c.d.f. of X is

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

The population of a town increases at a rate proportional to the population at that time. If the population increases from 26,000 to 39,000 in 50 years, then the population in another 25 years will be ______ `(sqrt(3/2) = 1.225)`

The solution of the differential equation `dy/dx - cos^2y = 0` is ______

The order of the differential equation of all circles of radius r, having centre on X-axis and passing through the origin is ______.

The area of the region bounded by the curve y = x IxI, X-axis and the ordinates x = 2, x = –2 is ______.

`int_0^9 1/(1 + sqrtx)` dx = ______

If f(x) = |x - 2|, then `int_-2^3 f(x) dx` is ______

`int_0^(pi4) sec^4x "d"x` = ______.

`int(((x^2 + 2)a^((x + tan^-1x)))/(x^2 + 1))dx` is equal to ______

General solution of `(x + y)^2 ("d"y)/("d"x) = "a"^2, "a" ≠ 0` is ______. (c is arbitrary constant)

`intcos^3x dx` = ______

A man of height 1.9 m walks directly away from a lamp of height 4.75m on a level road at 6m/s. The rate at which the length of his shadow is increasing is

If y = `x/"e"^(1 + x)`, then `("d"y)/("d"x)` = ______.

The point which provides the solution of the linear programming problem, Max.(45x + 55y) subject to constraints x, y ≥ 0, 6x + 4y ≤ 120, 3x + 10y ≤ 180, is ______

Determine the system of linear equation for which the solution set is the shaded region in the following figure ______.

The equation of the 1 plane passing through the points (1, –1, 1), (3, 2, 4) and parallel to Y-axis is ______.

A plane which passes through the point (3, 2, 0) and the line `(x - 3)/1 = (y - 6)/5, (z - 4)/4` is ______

The line passing through the points (5, 1, a) and (3, b, 1) crosses the YZ – plane at the point `(0, 17/2, (-13)/2)`, then ______.

Let A(4, 7, 8), B(2, 3, 4) and C(2, 5, 7) be the vertices of a triangle ABC. The length of the internal bisector of angle A is ______

If `overline(a),overline(b),overline(c)` are non-coplanar vectors and λ is a real number then `[lambda(overline(a)+overline(b))lambda^2overline(b) lambda overline(c)]=[overline(a) overline(b)+overline(c) overline(b)]` for ______.

lf `overlinea`, `overlineb` and `overlinec` are unit vectors such that `overlinea + overlineb + overlinec = overline0` and angle between `overlinea` and `overlineb` is `pi/3`, then `|overlinea xx overlineb| + |overlineb xx overlinec| + |overlinec xx overlinea|` = ______

The vector equation `overliner = hati - 2hatj - hatk + t(6hatj - hatk),` represents a line passing through points ______

The distance of the point (4, 3, 8) from the Y-axis is ______.

The joint equation of pair of lines having slopes 2 and 5 and passing through the origin is ______.

In ΔABC, if `"a" cos^2 "C"/2 + "c" cos^2 "A"/2 = (3"b")/2`, then a, b, c are in ______.

In ΔABC, if `cosA/a = cosB/b,` then triangle ABC is ______

The general solution of cosec x = `-sqrt2` is ______

The dual of '(~ q ∧ t) ∨ (~ p ∧ c)' where t is a tautology and c is a contradiction, is ______.

The Boolean expression ∼(p ∨ q) ∨ (∼p ∧ q) is equivalent to ______

Let f(x) = `{{:((tan pix)/(7x)";", x ≠ 0),("k"";", x = 0):}`. If f(x) is continuous at x = 0, then k = ______.

`lim_{n→∞}[1/(n^2 + 1) + 2/(n^2 + 1) + 3/(n^2 + 1) + .... + n/(n^2 + 1)]` = ______

Mapping f: R → R which is defined as f(x) = sin x, x ∈ R will be ______

In how many ways can a group of 5 boys and 6 girls be formed out of 10 boys and 11 girls?

If z ≠ 1 and `"z"^2/("z - 1")` is real, then the point represented by the complex number z lies ______.

Ram is visiting a friend. Ram knows that his friend has 2 children and 1 of them is a boy. Assuming that a child is equally likely to be a boy or a girl, then the probability that the other child is a girl, is ______.

If a r.v. X has p.d.f., f(x) = `1/(xlog3)`, for 1 < x < 3, then E(X) and Var(X) are respectively ______

If points (7, 6) and (-3, -4) lie on the locus ax + by = 6, then a and b are ______

In a ΔABC, A : B : C = 3 : 5 : 4. Then `a + b + csqrt2` is equal to ______