1
COMEDK 2024 Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$ \text { If } I_n=\int_\limits0^{\frac{\pi}{4}} \tan ^n x d x \text {, for } n \geq 2 \text {, then } I_n+I_{n-2}= $$

A
$$\frac{1}{n-1}$$
B
$$\frac{1}{n+1}$$
C
$$\frac{1}{n}+\frac{1}{n-2}$$
D
$$\frac{1}{n}$$
2
COMEDK 2024 Evening Shift
MCQ (Single Correct Answer)
+1
-0

In the expansion $$\left(\frac{1}{x}+x \sin x\right)^{10}, \quad$$ the co - efficient of $$6^{\text {th }}$$ term is equal to $$7 \frac{7}{8}$$, then the principal value of $$x$$ is

A
$$45^{\circ}$$
B
$$60^{\circ}$$
C
$$25^{\circ}$$
D
$$30^{\circ}$$
3
COMEDK 2024 Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$ \text { If }(1-4 i)^3=a+i b \text { then the value of } \mathrm{a} \text { and } \mathrm{b} \text { is } $$

A
$$-47,52$$
B
$$49,-74$$
C
$$-74,49$$
D
$$-48,-52$$
4
COMEDK 2024 Evening Shift
MCQ (Single Correct Answer)
+1
-0

Two finite sets have '$$m$$' and '$$n$$' number of elements respectively. The total number of subsets of the first set is 112 more than the total number of subsets of the second set. Then the values of $$\mathrm{m}$$ and $$\mathrm{n}$$ are respectively.

A
7, 4
B
7, 7
C
4, 4
D
4, 7
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