NDA Mathematics 21 April 2024 | Probability Question 2 | Mathematics

If a random variable $(x)$ follows binomial distribution with mean 5 and variance 4 , and $5^{23} P(X=3)=\lambda 4^\lambda$, then what is the value of $\lambda$ ?

NDA Mathematics 21 April 2024

MCQ (Single Correct Answer)

+2.5

-0.83

If the letters of the word 'TIRUPATI' are written down at random, then what is the probability that both Ts are always consecutive?

$\frac{1}{2}$

$\frac{1}{4}$

$\frac{1}{7}$

$\frac{1}{14}$

NDA Mathematics 21 April 2024

MCQ (Single Correct Answer)

+2.5

-0.83

Let $m = 77^n$. The index $n$ is given a positive integral value at random. What is the probability that the value of $m$ will have $1$ in the units place?

$\frac{1}{2}$

$\frac{1}{3}$

$\frac{1}{4}$

$\frac{1}{n}$

NDA Mathematics 21 April 2024

MCQ (Single Correct Answer)

+2.5

-0.83

Three different numbers are selected at random from the first 15 natural numbers. What is the probability that the product of two of the numbers is equal to third number?

$\frac{1}{91}$

$\frac{2}{455}$

$\frac{1}{65}$

$\frac{6}{455}$

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