MHT-CET

11. Binomial Theorem & Mathematical Induction question bank (Mathematics)

Practice 7 free MHT-CET Mathematics - 11. Binomial Theorem & Mathematical Induction questions with answers and step-by-step solutions.

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Q1.

Consider the statement $P(n): n^2 - n + 37$ is prime. Which one of the following is true?

(A)

$P(3)$ is false,but $P(5)$ is true.

(B)

$P(5)$ is false,but $P(3)$ is true.

(C)

Both $P(3)$ and $P(5)$ are true.

(D)

Both $P(3)$ and $P(5)$ are false.

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Q2.

If $^nC_0 + \frac{1}{2} ^nC_1 + \frac{1}{3} ^nC_2 + \dots + \frac{1}{n+1} ^nC_n = \frac{1023}{10}$, then $n =$ ?

(A)

$7$

(B)

$8$

(C)

$9$

(D)

$10$

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