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

`lim_(x -> 0) (log(1 + (5x)/2))/x` is equal to ______.

Let z be a complex number such that the imaginary part of z is non zero and a = z² + z + 1 is real. Then a cannot take the value ______ 

If y = `("e"^"2x" sin x)/(x cos x), "then" "dy"/"dx" = ?`

`lim_(x -> 0) (sin^4 3x)/x^4` = ________.

Let f(x) = x³ + 9x² + 33x + 13, then f(x) is ______.

If `y=sqrt(sinx+sqrt(sinx+sqrt(sinx+....oo))),` then `dy/dx` equals ______.

The converse of 'If x is negative then we cannot find its square root' is ______.

In which interval is the given function, f(x) = 2x³ - 21x² + 72x + 19 monotonically decreasing?

For every value of x, the function f(x) = `1/7^x` is ______ 

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 ______.