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

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 ______.

Derivative of log (sec θ + tan θ) with respect to sec θ at θ = `π/4` is ______.

If `log_10 ((x^2 - y^2)/(x^2 + y^2))` = 2, then `dy/dx` is equal to ______.

The acute angle between the line `vecr = (hati + 2hatj + hatk) + λ(hati + hatj + hatk)` and the plane `vecr xx (2hati - hatj + hatk)` is ______.

The value of sin 50° – sin 70° + sin 10° is ______.

The value of `cos^2x + cos^2(x + π/3) + cos^2(π - (2π)/3)` is ______.

If A, B and C are the angles of a triangle, such that sec (A – B), sec A and sec (A + B) are in arithmetic progression, then ______.

If `cosx/(cos(x - 2y))` = λ, then tan (x – y) tan y is eqµal to ______.

sin 47° + sin 61° – sin 11° – sin 25° is equal to ______.

If sin (x + 3 α) = 3 sin (α – x), then ______.