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

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 ______.

A random variable X bas the following probability distribution: 

The value of P (X > 0) is 

A random variable X has the probability distribution:

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

In order to get a head at least once probability ~ 0.9, the minimum number of time a unbiased coin needs to be tossed is ______.

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

The p.m.f. of a r.v. X is as follows:
P(X = 1) = 5k³, P(X = 2) = 10k – 16k² – 1
P(X = 3) = 2k, P(X = 4) = k, P(X = x) = 0 for any other value of x. Then the value of k is ______.

The equation 3x² + 10xy + 8y² = 0 represents ______ 

The contrapositive of (p ∧ r) → q is ______.

Let A and B be two events such that P(A) ≠ 1 and P(B) ≠ 0, then `"P"(bar"B"/bar"A")` = ______.

The difference between the slopes of lines represented by 6x² – 5.xy + y² = 0 is ______.

If f(x) = `(sin^2x)/(1 + cotx) + (cos^2x)/(1 + tan x)`, then `"f'"(pi/4)` is ______.

The equation of tangent to the curve `(x/"a")^"n" + (y/"b")^"n"` = 2 at the point (a, b) is ______.

The point of contact of the tangent lo the circle x² + y² = 5 at the point (1, –2) which touches the circle, x² + y² – 8x + 6y + 20 = 0 is ______.

If x = a cos³θ, y = a sin³θ, then `1 + (("d"y)/("d"x))^2` is ______.

The equation of the tangent to the curve x = 2 cos³ θ and y = 3 sin³ θ at the point θ = `pi/4` is ______.