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

The function f(x) = sin x + 2x is ______ 

`d/dx(x^{sinx})` = ______ 

The variance of the data 3, 6, 9, 12, 15 is ______

`lim_{x→-5} (sin^-1(x + 5))/(x^2 + 5x)` is equal to ______ 

`int ("d"x)/(4x^2 + 11)` = ______.

`"d"/"dx" [(cos x)^(log x)]` = ______.

`int tan(sin^-1x)dx` = ______ 

If `("f"(x))/(log (sec x)) "dx"` = log(log sec x) + c, then f(x) = ______.

If `overline(a),overline(b),overline(c)` are non-coplanar vectors and λ is a real number then `[lambda(overline(a)+overline(b))lambda^2overline(b)  lambda overline(c)]=[overline(a)  overline(b)+overline(c)  overline(b)]` for ______.

`int 1/(2sin2x - 3)dx` = ______ 

For which interval the given function f(x) = 2x³ – 9x² + 12x + 7 is increasing?

`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 ______