Symmetric Matrix

Q. $A$ is a $3\times 3$ diagonal matrix having integral entries such that $\text{det}\left(A\right)=120$, number of such matrices is $10n$, then $n$ is

1. $36$
2. $38$
3. $34$
4. $30$

Q. If A is a square matrix $A+A^T$ is symmetric matrix, then
$A-A^T=$

1. Unit matrix
2. Symmetric matrix
3. Skew symmetric matrix
4. Zero matrix

Q. Find the number of values of $t$ for which the system of equations
$(a+2t)x+by+cz=0$
$bx+(c+2t)y+az=0$
$cx+ay+(b+2t)z=0$
has non-trivial solutions.

Q. Solve${\int }_0^a\frac{x}{\sqrt{a^2+x^2}}dx$

Q. The factors of $(2a-b{)}^3+(b-2c{)}^3+8(c-a{)}^3$ are :

1. $2a\times b\times 2c$
2. $(2a-b)(b-2c)(c-a)$
3. $3(2a-b)(b-2c)(c-a)$
4. $6(2a-b)(b-2c)(c-a)$