MHT - CET MCQ

A random variable X has the probability distribution:

X = x	–2	–1	0	1	2
P(X = x)	4b	5b	2b	b	2b

Then the value of P(X < 1) is ______.

A card is chosen from a well-shuffled pack of cards. The probability of getting an ace of spade or a jack of diamond is ______.

Let the population of rabbits surviving at a time t be governed by the differential equation `(dp(t))/dt = 1/2p(t) - 200`. If p(0) = 100, then p(t) equals ______

The solution of the differential equation `dy/dx=1+y/x+(y/x)^2` is ______.

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

`int_0^(pi/2) 1/(1 + cos^3x) "d"x` = ______.

`int_(pi/4)^(pi/2) sqrt(1-sin 2x) dx =` ______.

`int_3^9 x^3/((12 - x)^3 + x^3)` dx = ______

The value of `int "e"^(5x) (1/x - 1/(5x^2)) "d"x` is ______.

`int_1^3 ("d"x)/(x(1 + logx)^2)` = ______.

`int (cos x)/(1 - sin x) "dx" =` ______.

The sum of two non-zero numbers is 6. The minimum value of the sum of their reciprocals is ______.

The function `1/(1 + x^2)` is increasing in the interval ______

Let f (x) > 0 for all x and f '(x) exists for all x. If f is the inverse function of h and h'(x) = `1/(1 + logx)`. Then f'(x) will be ______

If 4x + 5y ≤ 20, x + y ≥ 3, x ≥ 0, y ≥ 0, maximum 2x + 3y is ______.

For the function z = 19x + 9y to be maximum under the constraints 2x + 3y ≤ 134, x + 5y ≤ 200, x ≥ 0, y ≥ 0; the values of x and y are ______.

If the plane passing through the points (1, 2, 3), (2, 3, 1) and (3, 1, 2) is ax + by + cz = d then a + 2b + 3c = ______.

A plane passes through (1, - 2, 1) and is perpendicular to two planes 2x - 2y + z = 0 and x - y + 2z = 4. The distance of the plane from the point (1, 2, 2) is ______.

Let `bar"a"` and `bar"b"` be two unit vectors. If the vectors `bar"c" = bar"a" + 2bar"b"` and `bar"d" = 5bar"a" - 4bar"b"` are perpendicular to each other, then the angle between `bar"a"` and `bar"b"` is ______.

Let `square`PQRS be a quadrilateral. If M and N are midpoints of the sides PQ and RS respectively then `bar"PS" + bar"OR"` = ______.

In a triangle ABC, if `1/(a + c) + 1/(b + c) = 3/(a + b + c)` then angle C is equal to ______

In a trapezium, if the vector `overline(BC) = lambda overline(AD)`, `overlinep = overline(AC) + overline(BD)` is collinear with `overline(AD)` and `overlinep = mu overline(AD)`, then ______

The joint equation of pair of lines through the origin, each of which makes an angle of 60° with Y-axis, is ______

If `tan^-1x + tan^-1y = (4pi)/5`, then `cot^-1x + cot^-1y` equals ______.

The value of cot `(tan^-1 2x + cot^-1 2x)` 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 ______.

If matrix A = `[(1, -1),(2, 3)]` such that AX = I, then X is equal to ______.

If A = `[(p/4, 0, 0), (0, q/5, 0), (0, 0, r/6)]` and `"A"^-1 = [(1/4, 0, 0), (0, 1/5, 0), (0, 0, 1/6)]`, then p + q + r = ______

If A = `[(1, 2, 1), (3, 2, 3), (2, 1, 2)]`, then `a_11A_11 + a_21A_21 + a_31A_31` = ______

The logically equivalent statement of (p ∨ q) ∧ (p ∨ r) is ______

Which of the following is not true for any two statements p and q?

The negation of ∼s ∨ (∼r ∧ s) is equivalent to ______

If f(x) is continuous over [- π, π], where f(x) is defined as

f(x) = `{(- 2 sin x "," - pi ≤ x ≤ (-pi)/2),(alpha sin x + beta"," - pi/2 < x < pi/2),(cos x "," pi/2 ≤ x ≤ pi):}` then α and β equals

`lim_(x -> 0) (15^x - 3^x - 5^x + 1)/(xtanx)` is equal to ______.

If `((11 - "n")!)/((10 - "n")!) = 9,`then n = ______.

The square roots of -18i are ______

Two dice are thrown. Find the probability that the sum of numbers appearing is more than 11, is ______.

For two data sets, each of size 5, the variances are given to be 4 and 5 and the corresponding means are given to be 2 and 4 respectively. The variance of the combined data set is ______

The centre of the circle x = 3 + 5 cos θ, y = - 4 + 5 sin θ, is ______

The lines `(x - 1)/2 = (y + 1)/2 = (z - 1)/4` and `(x - 3)/1 = (y - 6)/2 = z/1` intersect each other at point ______

`(tanA + secA - 1)/(tanA - secA + 1)` = ______