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

The population of a city increases at a rate proportional to the population at that time. If the population of the city increase from 20 lakhs to 40 lakhs in 30 years, then after another 15 years the population is

A
$$10 \sqrt{2}$$ lakhs
B
$$40 \sqrt{2}$$ lakh
C
$$30 \sqrt{2}$$ lakhs
D
None of these
2
MHT CET 2021 20th September Evening Shift
MCQ (Single Correct Answer)
+2
-0

Let $$A=[a, b, c, d], B=[1,2,3]$$. Relation $$R_1, R_2, R_3, R_4$$ are as follows :

$$\begin{aligned} & R_1=[(\mathrm{a}, 1),(\mathrm{b}, 2),(\mathrm{c}, 1),(\mathrm{d}, 2)] \\ & \mathrm{R}_2=[(\mathrm{a}, 1),(\mathrm{b}, 1),(\mathrm{c}, 1),(\mathrm{d}, 1)] \\ & \mathrm{R}_3=[(\mathrm{a}, 2),(\mathrm{b}, 3),(\mathrm{c}, 2),(\mathrm{d}, 2)] \\ & \mathrm{R}_4=[(\mathrm{a}, 1),(\mathrm{b}, 2),(\mathrm{a}, 2),(\mathrm{d}, 3)] \text {, then } \end{aligned}$$

A
only $$R_3$$ and $$R_4$$ are not functions
B
only $$\mathrm{R}_1$$ and $$\mathrm{R}_2$$ are not functions.
C
only $$R_3$$ is not a function.
D
only $$R_4$$ is not a function.
3
MHT CET 2021 20th September Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$\cos x=\frac{25}{24}$$ and $$x$$ lięs in first quadrant, then $$\sin \frac{x}{2}+\cos \frac{x}{2}=$$

A
$$\frac{6}{5 \sqrt{2}}$$
B
$$\frac{8}{5 \sqrt{2}}$$
C
$$\frac{7}{5 \sqrt{2}}$$
D
$$\frac{1}{5 \sqrt{2}}$$
4
MHT CET 2021 20th September Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$\int_\limits2^e\left[\frac{1}{\log x}-\frac{1}{(\log x)^2}\right] d x=a+\frac{b}{\log 2}$$, then

A
$$a=-e, b=2$$
B
$$a=e, b=-2$$
C
$$a=e, b=2$$
D
$$a=-e, b=-2$$
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