1
IAT (IISER) 2025
MCQ (Single Correct Answer)
+4
-1

Let $n=\sum\limits_{r=0}^{10}(-1)^r{ }^{10} C_r\left(\frac{2}{3}\right)^{2 r} 3^{20}$. Which one of the following statements is TRUE?

A

$n$ is divisible by 5

B

$n$ is divisible by 6

C

$n$ is divisible by 8

D

$n$ is divisible by 9

2
IAT (IISER) 2024
MCQ (Single Correct Answer)
+4
-1
What is the value of ${ }^{23} C_0+{ }^{23} C_2+{ }^{23} C_4+\cdots+{ }^{23} C_{22}$ ?
A
$2^{23}$
B
$2^{22}-1$
C
$2^{23}+1$
D
$2^{22}$

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