1
MHT CET 2021 23rd September Evening Shift
MCQ (Single Correct Answer)
+2
-0

The co-ordinates of the foot of the perpendicular drawn from the point $$2 \hat{i}-\hat{j}+5 \hat{k}$$ to the line $$\vec{r}=(11 \hat{i}-2 \hat{j}-8 \hat{k})+\lambda(10 \hat{i}-4 \hat{j}-11 \hat{k})$$ are

A
$$(1,-2,3)$$
B
$$(1,2,-3)$$
C
$$(-1,2,3)$$
D
$$(1,2,3)$$
2
MHT CET 2021 23rd September Evening Shift
MCQ (Single Correct Answer)
+2
-0

Which of the following matrices are invertible?

$$\begin{aligned} & \mathrm{A}=\left[\begin{array}{cc} 2 & 3 \\ 10 & 15 \end{array}\right], \mathrm{B}=\left[\begin{array}{ccc} 1 & 2 & 3 \\ 2 & -1 & 3 \\ 1 & 2 & 3 \end{array}\right], \mathrm{C}=\left[\begin{array}{lll} 1 & 2 & 3 \\ 3 & 4 & 5 \\ 4 & 6 & 8 \end{array}\right], \mathrm{D}=\left[\begin{array}{lll} 2 & 4 & 2 \\ 1 & 1 & 0 \\ 1 & 4 & 5 \end{array}\right] \end{aligned}$$

A
both A and B
B
only C
C
only A
D
only D
3
MHT CET 2021 23rd September Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $${ }^{11} \mathrm{C}_4+{ }^{11} \mathrm{C}_5+{ }^{12} \mathrm{C}_6+{ }^{13} \mathrm{C}_7={ }^{14} \mathrm{C}_5$$, then value of $$\mathrm{r}$$ is

A
11
B
14
C
7
D
3
4
MHT CET 2021 23rd September Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$\int \sec ^{-1} x d x=$$

A
$$x \sec ^{-1} x+\log \left|x+\sqrt{x^2-1}\right|+c$$
B
$$x \sec ^{-1} x-\log \left|x+\sqrt{x^2-1}\right|+c$$
C
$$x \sec ^{-1} x-\log \left|x+\sqrt{x^2+1}\right|+c$$
D
$$x \sec ^{-1} x+\log \left|x+\sqrt{x^2+1}\right|+c$$
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