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BITSAT Permutations and Combinations — practice questions

Explore 100 free Permutations and Combinations questions in BITSAT Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Permutations and Combinations questions and exercises with answers

Showing questions 1–30 of 100.

A fair coin is tossed twice. How many outcomes are there in the sample space?Read the answer and worked solution →A fair six-sided die is rolled once. What is the probability of getting an even number?Read the answer and worked solution →The value of $5!$ is:Read the answer and worked solution →The number of ways to arrange $n$ distinct objects in a row is:Read the answer and worked solution →How many different 4-digit numbers can be formed using the digits $1, 2, 3, 4, 5$ without repetition?Read the answer and worked solution →In how many ways can a committee of $3$ persons be chosen from a group of $10$ people?Read the answer and worked solution →$\sin(180° - \theta)$ equals:Read the answer and worked solution →$\sin^2\theta + \cos^2\theta$ equals:Read the answer and worked solution →$\sin(A + B) = $Read the answer and worked solution →If $\sin\theta + \cos\theta = 1$, then $\sin\theta \cdot \cos\theta$ equals:Read the answer and worked solution →$\cos 3\theta$ equals:Read the answer and worked solution →sin(0°) equals:Read the answer and worked solution →cos(90°) equals:Read the answer and worked solution →sin²θ + cos²θ equals:Read the answer and worked solution →tan(45°) equals:Read the answer and worked solution →In which quadrant is sin θ positive and cos θ negative?Read the answer and worked solution →sec θ is defined as:Read the answer and worked solution →sin(A + B) equals:Read the answer and worked solution →sin(2θ) equals:Read the answer and worked solution →If tan θ = 1/2 (acute), find sin 2θ:Read the answer and worked solution →In triangle ABC with sides a, b, c opposite to angles A, B, C: sine rule states:Read the answer and worked solution →General solution of cos θ = 0:Read the answer and worked solution →If sin θ = 12/13 (acute θ in Q1), find tan(θ/2):Read the answer and worked solution →The arithmetic mean of n values x1, x2, ..., xn is:Read the answer and worked solution →Median of an odd-length sorted data set is:Read the answer and worked solution →Probability of a certain event:Read the answer and worked solution →Probability of rolling a 6 on a fair die:Read the answer and worked solution →For independent events A and B, P(A and B) equals:Read the answer and worked solution →Sort each inverse function into its domainRead the answer and worked solution →Tap every function whose domain is [−1, 1]Read the answer and worked solution →

Worked practice questions

A fair coin is tossed twice. How many outcomes are there in the sample space?

  1. $2$
  2. $4$
  3. $6$
  4. $8$
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Correct answer: B. $4$

Each toss has 2 possible outcomes (H or T), and the tosses are independent. By the multiplication principle, the sample space has $2 \times 2 = 4$ outcomes: {HH, HT, TH, TT}.

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A fair six-sided die is rolled once. What is the probability of getting an even number?

  1. $\dfrac{1}{6}$
  2. $\dfrac{1}{2}$
  3. $\dfrac{1}{3}$
  4. $\dfrac{2}{3}$
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Correct answer: B. $\dfrac{1}{2}$

The even outcomes are {2, 4, 6}, so the number of favourable outcomes is 3. The total sample space has 6 outcomes. $P(\text{even}) = \dfrac{3}{6} = \dfrac{1}{2}$.

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The value of $5!$ is:

  1. $120$
  2. $60$
  3. $720$
  4. $25$
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Correct answer: A. $120$

Factorial definition: $n! = n \times (n-1) \times (n-2) \times \ldots \times 1$. $5! = 5 \times 4 \times 3 \times 2 \times 1 = 120$. Quick reference: $4! = 24$, $5! = 120$, $6! = 720$ (option D is $6!$, not $5!$). Factorials grow fast.

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More Mathematics topics

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