GATE GNST|| Aptitude & Maths Quiz 2

The matrix satisfies which of the following equation__________?

Find the total Number of Prime Factors of 2¹⁷ × 6³¹ × 7⁵ × 10¹¹ × 11¹⁰ × 21¹²

Consider the following statements:

1) The rank of a matrix is the order of largest non-vanishing minor of A.

2) For any two matrices A & B, ρ(AB) ≥ min {ρ(A), ρ(B)}.

3) For any two matrices A and B, ρ(A+B) ≤ ρ(A)+ρ(B).

Which of the following statements is/are correct?

John has 30% more money than that of Johnson. Johnny has 60% more money than that of Johnson. How much % more money Johnny has than John?

If x = rcosθ , y = rsin θ then  is

In Taylor series expansion of f(x) = e^x + cos x about x = π the coefficient of (x – π)² is

If x increases at the rate of at the instant when x = 3 cm and y = 1 cm at what rate must y be changing in order that the function 2xy – 3x²y shall be neither increasing nor decreasing.

Consider matrix , then determinant of Adj (Adj A) is _________.