MHT - CET MCQ

If X follows a binomial distribution with parameters n = 10 and p. If 4P(X = 6) = P(X = 4), then p = ______

X is a continuous random variable with probability density function

f(x) = `x^3/16,` 0 ≤ x ≤ 1

= 0, otherwise

Then, the value of P(0.2 ≤ X ≤ 0.3) is

If X is a random variable with probability distribution as given below:

X	0	1	2	3
P(X)	2a	a	4a	3a

Then, the variance of X is ______

In tossing 8 coins, the probability of getting exactly 3 tails is ______

The general solution of the differential equation `y "d"x - (1 + x^2) cot^-1 x "d"y` = 0 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 ______.

The area of the region bounded by the X-axis and the curves defined by y = cot x, `(pi/6 ≤ x ≤ pi/4)` is ______.

`int_0^pi x*sin x*cos^4x "d"x` = ______.

`int_0^(pi"/"4)` log(1 + tanθ) dθ = ______

If `I_n = int_0^(pi/4) tan^n theta "d"theta " then " I_8 + I_6` equals ______.

If `int (sin2x)/(sin^4x + cos^4x) "d"x = tan^-1["f"(x)] + "c"`, then `"f"(pi/3)` = ______.

`int1/(sqrtx + sqrt(x^3))` dx is equal to ______

`int (sin4x)/(cos2x)` dx = ______

Let f(x) = `inte^x (x - 1)(x - 2)dx,` then f(x) decreases in the interval ______

The edge of a cube is increasing at the rate of 20 cm/sec. How fast is the volume of the cube increasing when the edge is 6 cm long?

The sum of intercepts on co-ordinate axes made by the tangent to the curve `sqrtx + sqrty = sqrta` is ______

If for x ∈ `(0, 1/4)`, the derivative of `tan^-1((6xsqrt(x))/(1 - 9x^3))` is `sqrt(x) * "g"(x)`, then g(x) equals ______.

The region XOY - plane which is represented by the inequalities -5 ≤ x ≤ 5, -5 ≤ y ≤ 5 is ______

The shaded region is represented by the in equations ______

The equation of the plane passing through the intersection of the planes x + 2y + 3z + 4 = 0 and 4x + 3y + 2z + 1 = 0 and the origin is ______.

The intercepts of the plane 3x - 4y + 6z = 48 on the co-ordinate axes are ______

The vector equation of the line passing through `4hati - hatj + 2hatk` and parallel to `-2hati - hatj + hatk` is ______

If θ is the angle between the unit vectors `bar"a"` and `bar"b"`, the `cos theta = theta/2` = ______.

The angle between the line `bar"r" = (hat"i" + 2hat"j" + hat"k") + lambda(hat"i" + hat"j" + hat"k")` and the plane `bar"r"*(2hat"i" - hat"j" + hat"k")` = 8 is ______.

If `3tan^-1x +cot^-1x = pi`, then xis equal to ______.

If `sin^-1x + cos^-1y = (3pi)/10,` then `cos^-1x + sin^-1y =` ______

If a = 13, b = 14, c = 15, then `cos("A"/2)` = ______.

If A = `[(a, 0, 0), (0, a, 0), (0, 0, a)]`, then the value of |A| |adj A| is ______

The negation of p → (~p ∨ q) is ______

The converse of 'If x is negative then we cannot find its square root' is ______.

Which of the following statement is a contingency?

The function `tanx/|x|` ______

If the value of `lim_(x -> 1) (1 - (1 - x))^"m"/x` is 99, then n = ______.

If f(x) =bx - 7 and f(-1) = 4, then b = ______.

Eight white chairs and four black chairs are randomly placed in a row. The probability that no two black chairs are placed adjacently equals.

In a simultaneous toss of five coins, the probability of getting exactly four tails is ______.

The means of two samples of sizes 60 and 120 respectively are 35.4 and 30.9 and the standard deviations are 4 and 5. Obtain the standard deviation of the sample of size 180 obtained by combining the two samples.

The abscissae of the points, where the tangent to curve `y = x^3 - 3/2x^2 - 6x + 7/5` is parallel to X-axis, are ______

The length of the perpendicular from the origin on the line `(xsinalpha)/"b" - (ycosalpha)/"a" - 1 = 0` is ______.

`(sec8A - 1)/(sec4A - 1)` = ______