1
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
$$2 \mathrm{e}^2$$
2
MHT CET 2023 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The joint equation of a pair of lines passing through the origin and making an angle of $$\frac{\pi}{4}$$ with the line $$3 x+2 y-8=0$$ is

A
$$5 x^2+24 x y-5 y^2=0$$
B
$$5 x^2-24 x y+5 y^2=0$$
C
$$5 x^2-24 x y-5 y^2=0$$
D
$$5 x^2+24 x y+5 y^2=0$$
3
MHT CET 2023 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

Two sides of a square are along the lines $$5 x-12 y+39=0$$ and $$5 x-12 y+78=0$$, then area of the square is

A
9 sq. units.
B
$$\frac{1}{3}$$ sq. units.
C
18 sq. units.
D
3 sq. units.
4
MHT CET 2023 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The value of $$\int \frac{\mathrm{d} x}{x^2\left(x^4+1\right)^{\frac{3}{4}}}$$ is

A
$$\left(\frac{x^4+1}{x^4}\right)^{\frac{1}{4}}+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.
B
$$\left(x^4+1\right)^{\frac{1}{4}}+c$$, where $$\mathrm{c}$$ is a constant of integration.
C
$$-\left(x^4+1\right)^{\frac{1}{4}}+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.
D
$$-\left(\frac{x^4+1}{x^4}\right)^{\frac{1}{4}}+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.
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