1
MHT CET 2021 20th September Evening Shift
MCQ (Single Correct Answer)
+2
-0

If area of the parallelogram with $$\bar{a}$$ and $$\bar{b}$$ as two adjacent sides is 20 square units, then the area of the parallelogram having $$3 \overline{\mathrm{a}}+\overline{\mathrm{b}}$$ and $$2 \overline{\mathrm{a}}+3 \overline{\mathrm{b}}$$ as two adjacent sides in square units is

A
105
B
120
C
75
D
140
2
MHT CET 2021 20th September Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$f(x) = {{{4^{x - \pi }} + {4^{x - \pi }} - 2} \over {{{(x - \pi )}^2}}}$$, for $$x \ne \pi $$, is continuous at $$x=\pi$$, then k =

A
$$2\log2$$
B
$$(\log2)^2$$
C
$$-(\log2)^2$$
D
$$8(\log2)^2$$
3
MHT CET 2021 20th September Evening Shift
MCQ (Single Correct Answer)
+2
-0

The equation of tangent to the circle $$x^2+y^2=64$$ at the point $$\mathrm{P\left(\frac{2\pi}{3}\right)}$$ is

A
$$x-\sqrt3 y-16=0$$
B
$$\sqrt3x+y-16=0$$
C
$$x+\sqrt3y+16=0$$
D
$$x-\sqrt3y+16=0$$
4
MHT CET 2021 20th September Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$2 f(x)-3 f\left(\frac{1}{x}\right)=x$$, then $$\int_\limits1^e f(x) d x=$$

A
$$-\left(\frac{2+\mathrm{e}^2}{5}\right)$$
B
$$\frac{2+e}{5}$$
C
$$\frac{2+e^2}{5}$$
D
$$\frac{2-e^2}{5}$$
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