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

`(sin20^circ +2sin40^circ)/sin70^circ=` ______.

The standard deviation of the data 8, 7, 1, 15, 14, 10, 12 is ______.

If P(α, β) be a point on the line 3x + y = 0 such that the point P and the point Q(1, 1) lie on either side of the line 3x = 4y + 8, then _______.

The statement pattern p ∧ (∼p ∧ q) is ______.

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

The odds against an event be 3 : 5. Find the probability of occurrence of the event.

The maximum and minimum values for the function f(x) = 4x³ - 6x² on [-1, 2] are ______

(p ∧ ∼q) ∧ (∼p ∧ q) is a ______.

For certain data, the following information is available. Obtain the combined standard deviation.

The negation of the Boolean expression (r ∧ ∼s) ∨ s is equivalent to: ______ 

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 ______.