Exams › JEE Main › Maths

Define S1 = \u2211(j=1 to 10) j(j-1) \u200a\u200a10Cj, S2 = \u2211(j=1 to 10) j \u200a\u200a10Cj, and S3 = \u2211(j=1 to 10) j^2 \u200a\u200a10Cj. Which of the following statements is correct? Statement 1: S3 = 55 \u00d7 2^9. Statement 2: S1 = 90 \u00d7 2^8 and S2 = 10 \u00d7 2^8.

1. Statement 1 is correct, and Statement 2 is correct; however, Statement 2 does not correctly explain Statement 1.
2. Statement 1 is correct, and Statement 2 is incorrect.
3. Statement 1 is incorrect, and Statement 2 is correct.
4. Statement 1 is correct, and Statement 2 is correct; moreover, Statement 2 correctly explains Statement 1.

Correct answer: Statement 1 is correct, and Statement 2 is incorrect.

Solution

Statement 1 is accurate because it correctly calculates S3 using combinatorial identities, while Statement 2 incorrectly computes S1 and S2, leading to the conclusion that Statement 1 stands alone as correct.

Related JEE Main Maths questions

• Let $P_n=\cos^n\theta+\sin^n\theta$. If $P_n-P_{n-2}=kP_{n-4}$, then the value of $k$ is:
• For any natural number $n$, the expression $x^{2n-1}+y^{2n-1}$ is divisible by which of the following?
• For a natural number $n$, which of the following always divides the expression $x^{n+1}+(x+1)^{2n-1}$?
• For a positive integer $n$, the expression $5^{2n+2}-24n-25$ is divisible by which of the following?
• For every natural number $n$, the expression $41^n-14^n$ is divisible by which of the following?
• Let \(C_0, C_1, C_2, \ldots, C_{15}\) denote the binomial coefficients in the expansion of \((1+x)^{15}\). Then the value of \(\frac{C_1}{C_0}+\frac{C_2}{C_1}+\frac{C_3}{C_2}+\cdots+\frac{C_{15}}{C_{14}}\) is:

⚔️ Practice JEE Main Maths free + battle 1v1 →