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

Coefficients of variation of two distributions are 30 and 40 and their arithmetic means are 10 and 25 respectively. The difference of their standard deviations is ______ 

The value of `[(1 - cos  pi/6 + isin  pi/6)/(1 - cos  pi/6 - isin  pi/6)]^6` = ______

The logically equivalent statement of (p ∨ q) ∧ (p ∨ r) is ______ 

If `cos "A" = 3/4,`then 32 sin`"A"/2 cos  (5"A")/2` = ?

The function y = 1 + sin x is maximum, when x = ______ 

The negation of p → (~p ∨ q) is ______ 

The maximum value of function x³ - 15x² + 72x + 19 in the interval [1, 10] is ______.

For all complex numbers z₁, z₂ satisfying |z₁| = 12 and |z₂ - 3 - 4i| = 5, the minimum value of |z₁ - z₂| is ______.

If the probability density function continuous random variable X is

f(x) = k(1 - x₂); 0 < x < 1
      = 0  ;    otherwise

Then P`(0 < X < 1/2)` = ?

The S.D. of 20 items is 15 and if each item is decreased or increased by 1, then standard deviation will be ______.

`(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: ______