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

If A = `[(1, -1, 3), (2, 5, 4)]`, then R₁ ↔ R₂ and C₃ → C₃ + 2C₂ gives ______

For any two statements p and q, the negation of the expression (p ∧ ∼q) ∧ ∼p is ______ 

If `[(1, -1, x), (1, x, 1), (x, -1, 1)]` has no inverse, then the real value of x is ______ 

A random variable X has following probability distribution

Then P(2 ≤ X < 5) = _____.

The square roots of -18i are ______

(p → q) ∨ p is logically equivalent to ______ 

Adjoint of ______

If the variance of x₁, x₂, x₃, ... , x_n is 49, then the S.D. of x₁ + 7, x₂ + 7, x₃ + 7, ... , x_n + 7, is ______ 

If the variance of x₁, x₂, x₃, ... , x_n is 49, then the S.D. of x₁ + 7, x₂ + 7, x₃ + 7, ... , x_n + 7, is ______ 

L and M are two points with position vectors `2veca - vecb` and `veca + 2vecb` respectively. The position vector of the point N which divides the line segment LM in the ratio 2 : 1 externally is ______ 

If A =`[(1, -1), (2, 3)]` and adj (A) = `[(a, b), (-2, 1)]`, then ______ 

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

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

Let `overlinep` and `overlineq` be the position vectors of P and Q respectively, with respect to O and `|overlinep|` = P, `|overlineq|` = q`. The points R and S divide PQ internally and externally in the ratio 2 : 3 respectively. If OR and OS are perpendicular, then ______

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

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

If the p.d.f. of a continuous random variable X is

f(x) = k (x - x²),    0 < x < 1

= 0,             otherwise

then the value of k is ______.

(p ∧ ∼q) ∧ (∼p ∧ q) is a ______.

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

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