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

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

9x² + hxy + y² = 0 represents pair of parallel straight lines, if h is ______.

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 ______.

Which of the following statement is contradiction?

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 ______.

Which of the following statement is a contingency?

Which of the following statements is a tautology?

The proposition (∼p → p) ∨ (p → ∼p) is a ______ 

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))` = ______ 

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