Questions covered in Standard

Review the question prompts below before starting the timed test. Try each problem independently, then use the interactive test to record your answers and review the worked solutions.

1. If $^nC_8 = ^nC_2$, then the value of $^nC_2$ is
2. How many 3-digit even numbers can be formed from the digits 1, 2, 3, 4, 6, 7 if the digits can be repeated?
3. The number of diagonals in a polygon of $n$ sides is
4. Find the number of different signals that can be generated by arranging at least 2 flags in order (one below the other) on a vertical staff, if 5 different flags are available.
5. If $^nP_r = 840$ and $^nC_r = 35$, then $r$ is equal to
6. Find $n$ if $^{2n}C_3 : ^nC_3 = 12 : 1$.
7. In how many ways can the letters of the word PERMUTATIONS be arranged if the words start with P and end with S?
8. A bag contains 5 black and 6 red balls. Determine the number of ways in which 2 black and 3 red balls can be selected.
9. How many numbers greater than 1,000,000 can be formed by using the digits 1, 2, 0, 2, 4, 2, 4?
10. In an examination, a question paper consists of 12 questions divided into two parts i.e., Part I and Part II, containing 5 and 7 questions, respectively. A student is required to attempt 8 questions in all, selecting at least 3 from each part. In how many ways can a student select the questions?
11. What is the number of ways of choosing 4 cards from a pack of 52 playing cards? In how many of these:
    (i) four cards are of the same suit,
    (ii) four cards belong to four different suits,
    (iii) are face cards,
    (iv) two are red cards and two are black cards,
    (v) cards are of the same colour?
12. Case Study: A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of:
    (i) exactly 3 girls?
    (ii) at least 3 girls?
    (iii) at most 3 girls?