1
TG EAPCET 2025 (Online) 2nd May Evening Shift
MCQ (Single Correct Answer)
+1
-0

The constant term in the expansion of $\left(1+\frac{1}{x}\right)^{20}\left(30 x(1+x)^{29}+(1+x)^{30}\right)$ is

A

${ }^{50} \mathrm{C}_{20}+30 \cdot{ }^{50} \mathrm{C}_{29}$

B

${ }^{50} \mathrm{C}_{19}+30 \cdot{ }^{49} \mathrm{C}_{19}$

C

${ }^{50} \mathrm{C}_{20}+30 \cdot{ }^{49} \mathrm{C}_{20}$

D

${ }^{50} \mathrm{C}_{20}+30 \cdot{ }^{49} \mathrm{C}_{19}$

2
TG EAPCET 2025 (Online) 2nd May Evening Shift
MCQ (Single Correct Answer)
+1
-0

When $|x|>3$, then coefficient of $\frac{1}{x^n}$ in the expansion of $x^{3 / 2}(3+x)^{1 / 2}$ is

A

$(-1)^n \frac{1 \cdot 3 \cdot 5 \ldots(2 n-1)}{2^n n!} 3^n$

B

$(-1)^{n+1} \frac{1 \cdot 3 \cdot 5 \ldots(2 n+1)}{2^{n+2}(n+2)!} 3^{n+2}$

C

$(-1)^{n+1} \frac{1 \cdot 3 \cdot 5 \ldots(2 n-1)}{2^n n!} 3^{n+1}$

D

$(-1)^{n+1} \frac{1 \cdot 3 \cdot 5 \ldots(2 n+1)}{2^{n+3}(n+2)!} 3^{n+1}$

3
TG EAPCET 2025 (Online) 2nd May Morning Shift
MCQ (Single Correct Answer)
+1
-0

If the coefficient of 3rd term from the beginning in the expansion of $\left(a x^2-\frac{8}{b x}\right)^9$ is equal to the coefficient of 3rd term from the end in the expansion of $\left(a x-\frac{2}{b x^2}\right)^9$, then the relation between $a$ and $b$ is

A

$a b=-1$

B

$a b=1$

C

$a^5 b^5=-2$

D

$a^5 b^5=2$

4
TG EAPCET 2025 (Online) 2nd May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If the expression $5^{2 n}-48 n+k$ is divisible by 24 for all $n \in N$, then the least positive integral value of $k$ is
A

47

B

48

C

24

D

23

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