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

The value of `lim_{x→0} (1 + sinx - cosx + log_e(1 - x))/x^3` is ______

The values of k for which the function f(x) = kx³ – 6x² + 12x + 11 may be increasing on R are ______.

`int dx/(sqrt(x + 3) - sqrt(x + 2))` = ______ 

The contrapositive of (p ∧ r) → q is ______.

`int (2x)/((2 + x^2)(3 + x^2)) dx` = ______ 

An integrating factor of the differential equation `x/y ("d"y)/("d"x) + log x = ("e"^x x^(-tanx))/y, (x > 0)`, is ______.

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 ______ 

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

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

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 ______.