If $(24,92)=24m+92n$, then $(m,n)$ is

Q. If n is a natural number, then 9²ⁿ − 4²ⁿ is always divisible by

(a) 5
(b) 13
(c) both 5 and 13
(d) None of these

[Hint : 9²ⁿ − 4²ⁿ is of the form a²ⁿ − b²ⁿ which is divisible by both a − b and a + b. So, 9²ⁿ − 4²ⁿ is divisible by both 9 − 4 = 5 and 9 + 4 = 13.]

Q. If $m[-34]+n[4-3]=[10-11],$ then $3m+7n=$

Q. $f:R\to R,$ $f\left(x\right)=\frac{3x^2+mx+n}{x^2+1}.$ If the range of $f\left(x\right)$ is $[-4,3],$ then

Q.

If $I_{m,n}=\underset{0}{\overset{\pi /2}{\int }}{\cos }^{m}x\sin nxdx$, then $7I_{4,3}-4I_{3,2}$ is equal to

Q.

Two vertices of $△ABC$ are A(-1, 4) and B(5, 2) and its centroid is G(0, -3). Then, the coordinates of C are

(a) (4, 3) (b) (4, 15) (c) (-4, -15) (d) (-15, -4)