1
MHT CET 2023 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$(\bar{a} \times \bar{b}) \times \bar{c}=-5 \bar{a}+4 \bar{b}$$ and $$\bar{a} \cdot \bar{b}=3$$, then the value of $$\bar{a} \times(\bar{b} \times \bar{c})$$ is

A
$$3 \bar{b}-4 \bar{c}$$
B
$$4 \overline{\mathrm{a}}-3 \overline{\mathrm{b}}$$
C
$$4 \bar{b}-3 \bar{c}$$
D
$$3 \overline{\mathrm{a}}-4 \overline{\mathrm{c}}$$
2
MHT CET 2023 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The plane through the intersection of planes $$x+y+z=1$$ and $$2 x+3 y-z+4=0$$ and parallel to $$\mathrm{Y}$$-axis also passes through the point

A
$$(3,3,-1)$$
B
$$(-3,0,1)$$
C
$$(3,2,1)$$
D
$$(-3,0,-1)$$
3
MHT CET 2023 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

Let $$\mathrm{f}(x)=\mathrm{e}^x-x$$ and $$\mathrm{g}(x)=x^2-x, \forall x \in \mathrm{R}$$, then the set of all $$x \in \mathrm{R}$$, where the function $$\mathrm{h}(x)=(\mathrm{fog})(x)$$ is increasing is

A
$$\left[0, \frac{1}{2}\right] \cup[1, \infty)$$
B
$$\left[-1,-\frac{1}{2}\right] \cup\left[\frac{1}{2}, \infty\right)$$
C
$$[0, \infty)$$
D
$$\left[-\frac{1}{2}, 0\right] \cup[1, \infty)$$
4
MHT CET 2023 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

Let $$f$$ be a differentiable function such that $$\mathrm{f}(1)=2$$ and $$\mathrm{f}^{\prime}(x)=\mathrm{f}(x)$$, for all $$x \in \mathrm{R}$$. If $$\mathrm{h}(x)=\mathrm{f}(\mathrm{f}(x))$$, then $$\mathrm{h}^{\prime}(1)$$ is equal to

A
$$4 \mathrm{e}^2$$
B
$$4 \mathrm{e}$$
C
$$2 \mathrm{e}$$
D
$$2 \mathrm{e}^2$$
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