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

The function `1/(1 + x^2)` is increasing in the interval ______ 

If `dy/dx = y + 3` and y(0) = 2, then y(log 2) is equal to ______ 

The value of `lim_{x→2} (e^{3x - 6} - 1)/(sin(2 - x))` is ______ 

Let L be the line joining the origin to the point of intersection of the lines represented by 2x² – 3xy – 2y² + 10x + 5y = 0. lf L is perpendicular to the line kx + y + 3 = 0, then k = ______.

Derivative of `log_6`x with respect 6^x to is ______

The only statement among the following i.e., a tautology is ______.

If f(x) = x³ – 15x² + 84x – 17, then ______.

If ax² + 2xy – 3y² + 4x + c = 0 represents a pair of perpendicular lines, then ______.

If f(x) = `x^(3/2) (3x - 10)`, x ≥ 0, then f(x) is increasing in ______.

The variance of α, β and ϒ is 8, then variance of 4α, 4β and 4ϒ is ______.

`lim_(x -> 0) (15^x - 3^x - 5^x + 1)/(xtanx)` is equal to ______.

The variance of first 50 even natural numbers is ______.

The interval in which the function f(x) = `(4x^2 + 1)/x` is decreasing is ______.

The value of `lim_(x rightarrow 0) (4^x - 1)^3/(sin  x^2/4 log(1 + 3x))`, is ______.

If y = `(1 + 1/x)^x` then `(2sqrt(y_2(2) + 1/8))/((log  3/2 - 1/3))` is equal to ______.

In an entrance test, there are multiple choice questions. There are four possible answers to each question, of which one is correct. The probability that a student knows the answer to a question is 90%. If he gets the correct answer to a question, then the probability that he was guessing is ______.

(p ∧∼ q) ∧ (∼ p ∧ q) is ______.

If y = `x^(x^2)`, then `dy/dx` is equal to ______.

If `log_10 ((x^3 - y^3)/(x^3 + y^3))` = 2 then `dy/dx` = ______.

The point of intersection of line represented by x² – y² + 3y – 2 = 0 is ______.