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

f(x) = `{{:(0","                 x = 0 ), (x - 3","   x > 0):}` The function f(x) is ______

If f: R → R is defined by f(x) = [x - 2] + |x - 5| for x ∈ R, then `lim_{x→2^-} f(x)` is equal to ______ 

`intx^x(1 + logx)dx` = ______ 

The sides of a square are increasing at the rate of 0.2 cm/sec. When the side is 25cm long, its area is increasing at the rate of ______

The variance and mean of distribution are 16 and 7 respectively. If every value is decreased by 3, then ______ 

Given P(x) = x⁴ + ax³ + bx² + cx + d such that x = 0 is the only real root of P'(x) = 0. If P(-1) < P(1), then in the interval [-1, 1] ______

Let y be an implicit function of x defined by `x^{2x} - 2x^x coty - 1 = 0`. Then, y'(1) equals ______ 

lf the function f(x) satisfies `lim_{x→1}(2f(x) - 5)/(2(x^2 - 1)) = e`, then `lim_{x→1}f(x)` is ______ 

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

In how many ways can the letters of the word 'IMAGE' be arranged so that the vowels should always occupy odd places?

`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?