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

The logical statement [∼(q ∨ ∼r) ∨ (p ∧ r)] ∧ (q ∨ p) is equivalent to: ______ 

The minimum value of the function f(x) = 13 - 14x + 9x² is ______

If the S.D. of the data 1, 2, 4, 5, 6, 7, 9 is 2.59, then the S.D. of 3, 6, 12, 15, 18, 21, 27 is ______.

The two parts of 120 for which the sum of double of first and square of second part is minimum, are ______.

The sum of two non-zero numbers is 6. The minimum value of the sum of their reciprocals is ______.

If x = a(t – sin t) and y = a(1 – cos t), then `("d"y)/("d"x)` = ______.

The mean and standard deviation of random variable X are 10 and 5 respectively, then `"E"(("X" - 15)/5)^2` = ______.

If z = `5i ((-3)/5 i)`, then z is equal to 3 + bi. The value of ‘b’ is ______.

Negation of the Boolean expression `p Leftrightarrow (q \implies p)` is ______. 

If z = `π/4(1 + i)^4((1 - sqrt(π)i)/(sqrt(π) + i) + (sqrt(π) - i)/(1 + sqrt(π)i))`, then `(|z|/("amp"^((z))))` is equals to ______. 

A rectangle with one side lying along the x-axis is to be inscribed in the closed region of the xy plane bounded by the lines y = 0, y = 3x and y = 30 – 2x. The largest area of such a rectangle is ______.

∼ ((∼ p) ∧ q) is equal to ______.

The maximum value of z = 6x + 8y subject to constraints 2x + y ≤ 30, x + 2y ≤ 24 and x ≥ 0, y ≥ 0 is ______.

The volume of the greatest cylinder which can be inscribed in a cone of height 30 cm and semi-vertical angle 30° is ______.

If A, B, C are the angles of ΔABC then cotA.cotB + cotB. cotC + cotC + cotA = ______.

The minimum value of the function f(x) = xlogx is ______.

The maximum value of f(x) = `logx/x (x ≠ 0, x ≠ 1)` is ______.

If x = `a(t - 1/t)`, y = `a(t + 1/t)`, where t is the parameter, then `dy/dx` =?

If random variable waiting time in minutes for bus and probability density function of x is given by

f(x) = `{{:(1/5",", 0 ≤ x ≤ 5),(0",", "otherwise,"):}`

then probability of waiting time not more than 4 minutes is equal to ______.

If the probability density function of a random variable X is given as

then F(0) is equal to