30
MCQ (Single Correct Answer)
If $f(t)=\left[\begin{array}{ccc}\cos t & t & 1 \\ 2 \sin t & t & 2 t \\ \sin t & t & t\end{array}\right]$, then $\lim _\limits{t \rightarrow 0} \frac{f(t)}{t^2}$ is equal to
A
0
B
$-$1
C
2
D
3
31
MCQ (Single Correct Answer)
The maximum value of $\Delta=\left|\begin{array}{ccc}1 & 1 & 1 \\ 1 & 1+\sin \theta & 1 \\ 1+\cos \theta & 1 & 1\end{array}\right|$ is (where, $\theta$ is real number)
A
$\frac{1}{2}$
B
$\frac{\sqrt{3}}{2}$
C
$\sqrt{2}$
D
$\frac{2 \sqrt{3}}{4}$
32
MCQ (Single Correct Answer)
If $f(x)=\left|\begin{array}{ccc}0 & x-a & x-b \\ x+a & 0 & x-c \\ x+b & x+c & 0\end{array}\right|$, then
A
$f(a)=0$
B
$f(b)=0$
C
$f(0)=0$
D
$f(1)=0$
33
MCQ (Single Correct Answer)
If $A=\left|\begin{array}{rrr}2 & \lambda & -3 \\ 0 & 2 & 5 \\ 1 & 1 & 3\end{array}\right|$, then $A^{-1}$ exists, if
A
$\lambda=2$
B
$\lambda \neq 2$
C
$\lambda \neq-2$
D
None of these
34
MCQ (Single Correct Answer)
If $A$ and $B$ are invertible matrices, then which of the following is not correct?
A
$\operatorname{adj} A=|A| \cdot A^{-1}$
B
$\operatorname{det}(A)^{-1}=[\operatorname{det}(A)]^{-1}$
C
$(A B)^{-1}=B^{-1} A^{-1}$
D
$(A+B)^{-1}=B^{-1}+A^{-1}$