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

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

The ratio in which the area bounded by the curves y² = 8x and x² = 8y is divided by the line x = 2 is ______ 

In a ΔABC, `(sin  "C"/2)/(cos(("A" - "B")/2))` = ______ 

If the probability function of a random variable X is defined by P(X = k) = a`((k + 1)/2^k)` for k - 0, 1, 2, 3, 4, 5, then the probability that X takes a prime value is ______

All the letters of the word PADMAPRIYA are placed at random in a row. The probability that the word PRIY A occurs without getting split is ______

For a random variable X, if Var (X) = 5 and E (X²) = 21, the value of E (X) is ______

The order and degree of the differential equation `(dy/dx)^3 + ((d^3y)/dx^3) + xy = 0` are respectively ______

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

In a ΔABC, 2ab sin`((A + B - C)/2)` = ______

If one side of a triangle is double the other and the angles opposite to these sides differ by 60°, then the triangle is ______

If A = {x | x ∈ N, x is a prime number less than 12} and B = {x | x ∈ N, x is a factor of 10}, then A ∩ B = ______.

If `int1/(x + x^5)dx = f(x) + c`, then `intx^4/(x + x^5)dx` = ______

If `(- sqrt2, sqrt2)` are cartesian co-ordinates of the point, then its polar co-ordinates are ______.

`intlogx/(1 + logx)^2dx` = ______ 

If P(6, 10, 10), Q(1, 0, -5), R(6, -10, λ) are vertices of a triangle right angled at Q, then value of λ is ______.

A random variable X has the following probability distribution:

1hen, the mean of this distribution is ______ 

Which of the following can be considered as the objective function of a linear programming problem?

The third order differential equation is ______ 

In Δ ABC; with usual notations, `("b" sin "B" - "c" sin "C")/(sin ("B - C"))` = _______.

X is a continuous random variable with a probability density function

f(x) = `{{:(x^2/4 + k;     0 ≤ x ≤ 2),(0;              "otherwise"):}`

The value of k is equal to ______