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BIHAR CET Permutations and Combinations — practice questions — page 2

Explore 121 free Permutations and Combinations questions in BIHAR CET 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 31–60 of 121.

A bag has balls marked 0–9. Four balls drawn with replacement. Probability that **none** is marked '0' is:Read the answer and worked solution →Probability of bomb hitting target = 0.8. Out of 10 bombs dropped, probability that **exactly 2 miss** equals (with $p = 0.2$ miss):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 →Match each inverse function to its domainRead the answer and worked solution →Match each inverse function to its principal value branchRead the answer and worked solution →Flip and pair: function with its principal rangeRead the answer and worked solution →Which principal ranges sit around zero, and which run 0 to π?Read the answer and worked solution →Tap every function whose principal range has a point removedRead the answer and worked solution →Name the principal value branchRead the answer and worked solution →Domain checkRead the answer and worked solution →Put the reasoning in order: why an inverse needs a restricted domainRead the answer and worked solution →True or false: existence of inversesRead the answer and worked solution →

Worked practice questions

A bag has balls marked 0–9. Four balls drawn with replacement. Probability that **none** is marked '0' is:

  1. $(1/10)^4$
  2. $(9/10)^4$
  3. $4(9/10)^4$
  4. $1 - (9/10)^4$
Show answer and solution

Correct answer: B. $(9/10)^4$

$p = 1/10$ for '0'; $q = 9/10$ for 'not 0'. $P(X = 0) = (9/10)^4 = 0.6561$.

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Probability of bomb hitting target = 0.8. Out of 10 bombs dropped, probability that **exactly 2 miss** equals (with $p = 0.2$ miss):

  1. ${}^{10}C_2 (0.2)^2 (0.8)^8$
  2. ${}^{10}C_2 (0.8)^2 (0.2)^8$
  3. $0.2 \times 10$
  4. $0.8 \times 10$
Show answer and solution

Correct answer: A. ${}^{10}C_2 (0.2)^2 (0.8)^8$

**Treat 'miss' as success:** $p = 0.2$. $P(2 \text{ misses out of 10}) = {}^{10}C_2 (0.2)^2 (0.8)^8 = 45 \times 0.04 \times 0.168 \approx 0.302$.

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sin(0°) equals:

  1. 1
  2. 1/2
  3. 0
  4. √3/2
Show answer and solution

Correct answer: C. 0

sin(0°) = 0. (Other key values: sin(30°) = 1/2, sin(45°) = 1/√2, sin(60°) = √3/2, sin(90°) = 1.)

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