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

The modulus and amplitude of 4 + 3i are ______

The p.d.f of a random variable x is given by

f(x) = `1/"4a"`, 0 < x < 4a, (a > 0)

= 0, otherwise

and `"P"(x < "3a"/2) = "kp"(x > "5a"/2)` then k = ?

If R is the circum radius of Δ ABC, then A(Δ ABC) = ______.

If x + iy = `5/(3 + costheta + isintheta)`, then x² + y² is equal to ______ 

The mean and S.D. of the scores of 100 candidates were found to be 80 and 15 respectively. Later, it was discovered that a score of 50 was wrongly read as 40. The correct mean and S.D. respectively are ______ 

If z = ax + by; a, b > 0 subject to x ≤ 2, y ≤ 2, x + y ≥ 3, x ≥ 0, y ≥ 0 has minimum value at (2, 1) only, then ______.

The pdf of a random variable X is

f(x) = 3(1 - 2x²), 0 < x < 1

      = 0   otherwise

The P`(1/4 < "X" < 1/3)` = ?

If f(x) = `x + 1/x, x ne 0`, then local maximum and x minimum values of function f are respectively.

Twenty meters of wire is available for fencing off a flowerbed in the form of a circular sector. Then the maximum area (in sq. m) of the flower-bed, is ______

The S.D. and C.V. for the following frequency distribution is

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 ______.