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

If f(x) = [x], where [x] is the greatest integer not greater than x, then f'(1') = ______.

A ladder 20 ft Jong leans against a vertical wall. The top-end slides downwards at the rate of 2 ft per second. The rate at which the lower end moves on a horizontal floor when it is 12 ft from the wall is ______ 

`lim_{x→∞} ((3x + 3)^40(9x - 3)^5)/(3x + 1)^45` = ______ 

The function f(x) = x³ - 3x is ______.

If x^y = e^x-y, then `"dy"/"dx"` at x = 1 is ______.

"If two triangles are congruent, then their areas are equal'' is the given statement then the contrapositive of, the inverse of the given statement is ______.

`int tan^-1((2tanx)/(1 - tan^2x))`dx = ______

`int_0^1 1/(sqrt(3 + 2x - x^2))dx` = ______ 

`intx^2/sqrt(1 - x^6)dx` is equal to ______ 

If y = tan^-1 `((1 - cos 3x)/(sin 3x))`, then `"dy"/"dx"` = ______.

If `int1/((x^2 - 1)) log((x - 1)/(x + 1))dx = A[log((x - 1)/(x + 1))]^2 + c,` then ______

The value of `lim_{x→-∞} (sqrt(5x^2 + 4x + 7))/(5x + 4)` is ______ 

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 ______