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

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 ______.

x^5x has a stationary point at ______.

The variance of first 50 even natural numbers is ______.

If f(x) = x sin x, then `f^'(π/2)` is equal to ______.

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 ______.

The contrapositive of (p v q) `implies` r is ______.

If y = `sqrt(log x + sqrt(log x + sqrt(log x + .... ∞)`, then `(dy)/(dx)` = ______.

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 ______.

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

If f(x) = `cos^-1[(1 - (logx)^2)/(1 + (logx)^2)]`, then f'(e) = ______.

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

The contrapositive of the statement : "If the weather is fine then my friends will come and we go for a picnic."

If f(x) = `x/(x^2 + 1)` is increasing function then the value of x lies in ______.

If a line makes angles 120° and 60° with the positive directions of X and Z axes respectively then the angle made by the line with positive Y-axis is ______.

If `int 1/sqrt(9 - 16x^2)dx` = α sin^–1 (βx) + c, then `α + 1/β` = ______.

`int 1/sqrt(8 + 2x - x^2) dx` is equal to ______.