1
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
$$30^{\circ}$$
2
COMEDK 2024 Afternoon Shift
MCQ (Single Correct Answer)
+1
-0

If the sum of the coefficients of the first three terms in the expansion of $$\left(x-\frac{a}{x^2}\right)^{12}, x \neq 0$$ is 559. Find the value of '$$a$$' if '$$a$$' belongs to positive integers

A
5
B
4
C
$$\frac{31}{11}$$
D
3
3
COMEDK 2024 Morning Shift
MCQ (Single Correct Answer)
+1
-0

The coefficient of the third term in the expansion of $$\left(x^2-\frac{1}{4}\right)^n$$, when expanded in the descending power of $$x$$ is 31, then $$n$$ is

A
31
B
16
C
30
D
32
4
COMEDK 2023 Morning Shift
MCQ (Single Correct Answer)
+1
-0

Using mathematical induction, the numbers $$a_n \delta$$ are defined by $$a_0=1, a_{n+1}=3 n^2+n+a_n, (n \geq 0)$$. Then, $$a_n$$ is equal to

A
$$n^3+n^2+1$$
B
$$n^3-n^2+1$$
C
$$n^3-n^2$$
D
$$n^3+n^2$$
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