Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.

Permutations and Combinations

Short Answer Type

1. Given 5 flags of different colours, how many different signals can be generated if each signal requires use of 2 flags, one below the other?

991 Views

Long Answer Type

A class has 30 students. In how many ways can three prizes be awarded so that:

(a) no students get more than one prize?

(b) a student may get any number of prizes?

745 Views

Short Answer Type

3. A coin is tossed 3 times and the outcomes are recorded. How many possible outcomes are there?

Event 1: A coin is tossed and the outcomes recorded.

Number of outcomes $open curly brackets straight H. space straight T close curly brackets space equals space 2$

$rightwards double arrow$ m = 2

Event 2: The coin is tossed again and the outcomes recorded.

Number of outcomes $open curly brackets straight H comma space straight T close curly brackets space equals space 2$

$rightwards double arrow$ n = 2

Event 3: The coin is tossed third time and the outcomes recorded.

Number of outcomes $open curly brackets straight H comma space straight T close curly brackets space equals space 2$

$rightwards double arrow$ p = 2

∴ By fundamental principle of counting, the total number of outcomes recorded

= $straight m cross times straight n cross times straight p space equals space 2 cross times 2 cross times 2 equals 8$

548 Views

How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that repetition of the digits is allowed.

458 Views

How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that repetition of the digits is not allowed.

526 Views

Long Answer Type

6. How many 3-digit odd numbers can be formed from the digits 1,2,3,4,5,6 if:

(a) the digits can be repeated (b) the digits cannot be repeated?

231 Views

Short Answer Type

7. How many 5-digit telephone numbers can be constructed, using the digits 0 to 9 if each number starts with 67 and no digit appears more than once ?

138 Views

8. 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 five different flags are available.

358 Views

9. How many 3 digit numbers are there without repetition?

204 Views

10. 3 men board a bus in which there are 5 vacant seats. In how many ways can they occupy the seats?

237 Views