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

The proposition ∼(p ∧ ∼q) → p is a ______ 

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] ______

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

If the slope of one of the lines given by ax² + 2hxy + by² = 0 is two times the other, then ______ 

If (a + 3b)(3a + b) = 4h², then the angle between the lines represented by ax² + 2hxy + by² = 0 is ______ 

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)]` = ______.

The dual of '(~ q ∧ t) ∨ (~ p ∧ c)' where t is a tautology and c is a contradiction, is ______.

If the equation `lambdax^2 + 2y^2 - 5xy + 5x - 7y + 3 = 0` represents two straight lines, then the value of λ will be ______.

`int tan(sin^-1x)dx` = ______ 

Which one of the following statements is not a tautology?