24
MCQ (Single Correct Answer)
If $\left|\begin{array}{cc}2 x & 5 \\ 8 & x\end{array}\right|=\left|\begin{array}{cc}6 & -2 \\ 7 & 3\end{array}\right|$, then the value of $x$ is
A
3
B
$\pm$3
C
$\pm$6
D
6
25
MCQ (Single Correct Answer)
The value of $\left|\begin{array}{lll}a-b & b+c & a \\ b-a & c+a & b \\ c-a & a+b & c\end{array}\right|$ is
A
$a^3+b^3+c^3$
B
$3 b c$
C
$a^3+b^3+c^3-3 a b c$
D
None of these
26
MCQ (Single Correct Answer)
If the area of a triangle with vertices $(-3,0),(3,0)$ and $(0, k)$ is 9 sq units. Then, the value of $k$ will be
A
9
B
3
C
$-$9
D
6
27
MCQ (Single Correct Answer)
The determinant $\left|\begin{array}{lll}b^2-a b & b-c & b c-a c \\ a b-a^2 & a-b & b^2-a b \\ b c-a c & c-a & a b-a^2\end{array}\right|$ equals to
A
$a b c(b-c)(c-a)(a-b)$
B
$(b-c)(c-a)(a-b)$
C
$(a+b+c)(b-c)(c-a)(a-b)$
D
None of these
28
MCQ (Single Correct Answer)
The number of distinct real roots of $\left|\begin{array}{lll}\cos x & \sin x & \cos x \\ \cos x & \cos x & \sin x\end{array}\right|=0$ in the interval $-\frac{\pi}{4} \leq x \leq \frac{\pi}{4}$ is
A
0
B
2
C
1
D
3