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

The line 3x - 2y = 0 coincides with one of the lines given by ax² + 2hxy + by² = 0, then ______

If `int(sin2x)/(sin5x  sin3x)dx = 1/3log|sin 3x| - 1/5log|f(x)| + c`, then f(x) = ______

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

Which of the following equation does not represent a pair of lines?

A group of 5 men and 4 women are arranged at random, one after the other. The probability that women and men occupy alternate seats is ______

The sum of the slopes of the lines represented by 5x² + 2xy - 3y² = 0 is ______ 

The angle between the lines represented by the equation ax² + xy + by² = 0 will be 45°, if ______ 

The plane 2x - 3y + 6z - 11 = 0 makes an angle sin^-1 (α) with X-axis. The value of α is equal to ______ 

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

"If two triangles are congruent, then their areas are equal'' is the given statement then the contrapositive of, the inverse of the given statement is ______.

If sum of the slopes of the lines given by x² - 4pxy + 8y² = 0 is three times their product then p = ______.

If sin y = x sin(a + y), then `dy/dx` = ______ 

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 cos y = x cos(a + y) with cos a ≠ ± 1, then `dy/dx` is equal to ______ 

The probability distribution of the random variable X is given by

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

The probability distribution of X is 

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

The line x - 2y = 0 is perpenrucular to one of the lines given by ax² + 2hxy + by² = 0, when ______.

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.

If the sum of the slopes of the lines represented by x² + kxy + y² = 0 is four times their product, the value of k is ______.