1
MHT CET 2023 13th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$A=\left[\begin{array}{cc}1 & \tan x \\ -\tan x & 1\end{array}\right]$$, then $$A^T \cdot A^{-1}=$$

A
$$\left[\begin{array}{ll}-\cos 2 x & \sin 2 x \\ -\sin 2 x & \cos 2 x\end{array}\right]$$
B
$$\left[\begin{array}{cc}\cos 2 x & -\sin 2 x \\ \sin 2 x & \cos 2 x\end{array}\right]$$
C
$$\left[\begin{array}{cc}\cos 2 x & \sin 2 x \\ -\sin 2 x & \cos 2 x\end{array}\right]$$
D
$$\left[\begin{array}{cc}\cos 2 x & -\sin 2 x \\ -\sin 2 x & \cos 2 x\end{array}\right]$$
2
MHT CET 2023 13th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$\mathbf{a}=2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{c}=\hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}$$ are three vectors. For a vector $$\mathbf{r}$$ with $$\mathbf{r} \times \mathbf{a}=\mathbf{b}$$ and $$\mathbf{r} \cdot \mathbf{c}=3,|\mathbf{r}|$$ is

A
$$\sqrt{55}$$
B
$$\sqrt{138}$$
C
$$\sqrt{155}$$
D
$$\sqrt{170}$$
3
MHT CET 2023 13th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

Let $$P Q R$$ be a right angled isosceles triangle, right angled at $$Q(2,1)$$. If the equation of the line $$P R$$ is $$2 x+y=3$$, then the combined equation representing the pair of lines $$P Q$$ and $$Q R$$ is

A
$$3 x^2+8 x y-3 y^2-20 x-10 y+25=0$$
B
$$3 x^2-8 x y-3 y^2-20 x-10 y-25=0$$
C
$$3 x^2+8 x y-3 y^2+20 x+10 y+25=0$$
D
$$3 x^2-8 x y-3 y^2+20 x+10 y-25=0$$
4
MHT CET 2023 13th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If a curve $$y=a \sqrt{x}+b x$$ passes through the point $$(1,2)$$ and the area bounded by the curve, line $$x=4$$ and $$X$$-axis is 8 sq units, then

A
$$a=3, b=-1$$
B
$$a=3, b=1$$
C
$$a=-3, b=1$$
D
$$a=-3, b=-1$$
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