1
MHT CET 2022 11th August Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$\matrix{ {f(x) = a{x^2} + bx + 1,} & {if} & {\left| {2x - 3} \right| \ge 2} \cr { = 3x + 2,} & {if} & {{1 \over 2} < x < {5 \over 2}} \cr } $$

is continuous on its domain, then $$a+b$$ has the value

A
$$\frac{13}{5}$$
B
$$\frac{31}{5}$$
C
$$\frac{23}{5}$$
D
$$\frac{1}{5}$$
2
MHT CET 2022 11th August Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$\bar{a}=\hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}}, \bar{b}=\hat{\boldsymbol{i}}-\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}}$$ and $$\bar{c}=\hat{\boldsymbol{i}}-\hat{\boldsymbol{j}}-\hat{\boldsymbol{k}}$$ are three vectors then vector $$\bar{r}$$ in the plane of $$\bar{a}$$ and $$\bar{b}$$, whose projection on $$\bar{c}$$ is $$\frac{1}{\sqrt{3}}$$, is given by

A
$\hat{i}-3 \hat{j}+3 \hat{k}$
B
$-3 \hat{i}-3 \hat{j}-\hat{k}$
C
$3 \hat{i}-\hat{j}+3 \hat{k}$
D
$\hat{i}+3 \hat{j}-3 \hat{k}$
3
MHT CET 2022 11th August Evening Shift
MCQ (Single Correct Answer)
+2
-0

A tetrahedron has verticles $$P(1,2,1), Q(2,1,3), R(-1,1,2)$$ and $$O(0,0,0)$$. Then the angle between the faces $$O P Q$$ and $$P Q R$$ is

A
$$\cos ^{-1}\left(\frac{17}{35}\right)$$
B
$$\cos ^{-1}\left(\frac{17}{31}\right)$$
C
$$\cos ^{-1}\left(\frac{19}{35}\right)$$
D
$$\cos ^{-1}\left(\frac{19}{31}\right)$$
4
MHT CET 2022 11th August Evening Shift
MCQ (Single Correct Answer)
+2
-0

The principal value of $$\sin ^{-1}\left(\sin \left(\frac{2 \pi}{3}\right)\right)$$ is

A
$$\left(\frac{\pi}{3}\right)$$
B
$$\left(\frac{2 \pi}{3}\right)$$
C
$$-\left(\frac{2 \pi}{3}\right)$$
D
$$\left(\frac{5 \pi}{3}\right)$$
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