MAH-MHT CET (PCM/PCB) entrance exam Question Bank Solutions

The number of ways in which 51 books can be distributed among three students, each receiving 17 books, is ______

The negation of "∀, n ∈ N, n + 7 > 6" is ______.

If `tan^-1x + tan^-1y = pi/4`, then ______

`d/dx[cot^-1(sqrtx)]` = ______ 

Derivative of `sin^-1 ("t"/sqrt(1 + "t"^2))` with respect to `cos^-1 (1/sqrt(1 + "t"^2))` is ______.

What is the mean of f(x) = 3x + 2 where x is a random variable with probability distribution

If `intsqrt((x - 7)/(x - 9)) dx = Asqrt(x^2 - 16x + 63) + log|x - 8 + sqrt(x^2 - 16x + 63)| + c`, then A = ______

If `y = sin^-1(1/x^3)`, then `dy/dx` = ______ 

The probability distribution of the random variable X is given by

Then, 4 var (X) - E (X²) is equal to ______ 

If y = `cot^-1(x/(sqrt(1 - x^2)))`, then `dy/dx` is equal to ______ 

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 ______ 

The probability distribution of X is 

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

The maximum value of P = 3x + 4y subject to the constraints x + y ≤ 40, x + 2y ≤ 60, x ≥ 0 and y ≥ 0 is ______ 

If the angle between the line x = `("y" - 1)/2 = ("z - 3")/lambda` and the plane x + 2y + 3z = 4 is `cos^-1 (sqrt(5/14))`, then λ equals.

In a box containing 100 eggs, 10 eggs are rotten. The probability that out of a sample of 5 eggs none are rotten, if the sampling is with replacement, 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 = ______ 

The probability distribution of a random variable X is 

Then the c.d.f. of X is

A company produces 10,000 items per day. On a particular day, 2500 items were produced on machine A, 3500 on machine B, and 4000 on machine C. The probability that an item is produced by the machines. A, B, C to be defective is respectively 2%, 3%, and 5%. If one item is selected at random from the output and is found to be defective, then the probability that it was produced by machine C, is ______ 

If x + y = k is normal to y² = 12x, then k is ______.

Point of the curve y² = 3(x – 2) at which the normal is parallel to the line 2y + 4x + 5 = 0 is ______.