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

Five students are selected from $$n$$ students such that the ratio of number of ways in which 2 particular students are selected to the number of ways 2 particular students not selected is $$2: 3$$. Then, the value of $$n$$ is

A
5
B
6
C
11
D
not possible
2
MHT CET 2023 13th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$\int \frac{\log \left(t+\sqrt{1+t^2}\right)}{\sqrt{1+t^2}} d t=\frac{1}{2}[g(t)]^2+c$$, (where $$c$$ is a constant of integration), then $$g(2)$$ is

A
$$\frac{1}{\sqrt{5}} \log (2+\sqrt{5})$$
B
$$\frac{1}{2} \log (2+\sqrt{5})$$
C
$$2 \log (2+\sqrt{5})$$
D
$$\log (2+\sqrt{5})$$
3
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
$$\left[\begin{array}{cc}\cos 2 x & -\sin 2 x \\ -\sin 2 x & \cos 2 x\end{array}\right]$$
4
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
$$\sqrt{170}$$
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