Categories \(\Rightarrow\) Class IX Class X Class XI Mathematics Physics Chemistry Biology
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1.
The number of ways of arranging 3 different objects taken all at a time is
(Basic Concept – Counting)
2.
The value of \(5!\) is
(Basic Factorial)
3.
The number of permutations of 4 objects taken 2 at a time is
(Formula Application)
4.
The value of \(^{6}P_{6}\) is
(Basic Permutations)
5.
The number of combinations of 5 objects taken 2 at a time is
(Basic Combination)
6.
If \(^{n}C_{1} = 15\), then \(n\) is
(Simple Combination Property)
7.
The number of ways of arranging the letters of the word “CAT” is
(Simple Word Problem)
8.
The number of ways of selecting 3 students from 7 students is
(Basic Selection)
9.
The value of \(^{n}P_{1}\) is
(Permutation Property)
10.
The number of ways of arranging 4 different books on a shelf is
(Simple Arrangement)
11.
The number of permutations of the letters of the word “BOOK” is
(Repetition of Letters)
12.
The value of \(^{8}C_{0}\) is
(Combination Property)
13.
The number of ways of choosing a president and a vice-president from 6 people is
(Permutation in Selection)
14.
The number of combinations of 6 objects taken 4 at a time is
(Combination Formula)
15.
The number of ways of arranging the letters of “LEVEL” is
(Repetition-Based Arrangement)
16.
If \(^{n}C_{2} = 45\), then \(n\) is
(Algebraic Combination)
17.
The number of ways of selecting 5 cards from a deck of 52 cards is
(Standard Combination)
18.
The number of permutations of 5 objects taken 3 at a time is
(Intermediate Permutation)
19.
The number of ways of forming a committee of 3 members from 8 members is
(Committee Formation)
20.
The value of \(^{n}C_{n}\) is
(Combination Identity)
21.
The number of ways of arranging 6 people in a row is
(Linear Arrangement)
22.
The number of combinations of 10 objects taken 1 at a time is
(Simple Combination)
23.
The number of ways of arranging the letters of “MATH” is
(Simple Word Arrangement)
24.
If \(^{n}P_{2} = 56\), then \(n\) is
(Intermediate Algebraic Permutation)
25.
The number of ways of selecting at least one object from 3 distinct objects is
(Conceptual Counting)
26.
The number of permutations of the letters of the word “MISS” is
(Repetition with Multiple Letters)
27.
The number of ways of choosing 2 boys and 1 girl from 4 boys and 3 girls is
(Mixed Selection)
28.
The value of \(^{9}C_{7}\) is
(Combination Symmetry)
29.
The number of ways of arranging 5 people around a round table is
(Circular Permutation)
30.
The number of combinations of 7 objects taken 3 at a time is
(Intermediate Combination)
31.
The number of ways of arranging 7 different books if 2 particular books are always together is
(Constraint-Based Arrangement)
32.
The number of ways of selecting a team of 4 from 6 men and 5 women consisting of 2 men and 2 women is
(Mixed Combination)
33.
The value of \(^{10}P_{0}\) is
(Permutation Property)
34.
The number of ways of arranging the letters of “INDIA” is
(Repetition and Distinct Letters)
35.
The number of subsets of a set containing 5 elements is
(Power Set Concept)
36.
If \(^{n}C_{3} = 35\), then \(n\) is
(Advanced Combination)
37.
The number of ways of arranging 4 boys and 3 girls in a row such that all boys are together is
(Advanced Arrangement)
38.
The number of ways of choosing at most 2 objects from 5 distinct objects is
(Conceptual Combination)
39.
The number of permutations of the digits 1, 2, 3, 4 taken all at a time is
(Digit Arrangement)
40.
The number of ways of forming a 3-digit number from the digits 1, 2, 3, 4 without repetition is
(Permutation of Digits)
41.
The number of combinations of 8 objects taken 5 at a time is
(Intermediate Combination)
42.
The number of ways of arranging the letters of “BANANA” is
(Advanced Repetition)
43.
The number of ways of choosing 4 balls from a box containing 6 red and 5 blue balls is
(Color-Based Selection)
44.
The number of ways of selecting exactly 3 red balls from 6 red and 5 blue balls is
(Restricted Combination)
45.
The number of permutations of 10 objects taken all at a time is
(High-Level Permutation)
46.
The number of ways of choosing a chairman, vice-chairman, and secretary from 7 persons is
(Advanced Permutation)
47.
The number of ways of arranging 5 men and 5 women alternately in a row is
(Advanced Arrangement)
48.
The number of combinations of 12 objects taken 10 at a time is
(Combination Symmetry)
49.
The number of ways of arranging the letters of “STATISTICS” is
(High-Level Repetition)
50.
The number of ways of selecting a committee of 5 from 10 people if 2 particular people are always included is
(Advanced Selection Constraint)

Frequently Asked Questions

A permutation is an arrangement of objects in a definite order. If the order of selection changes, the permutation changes.

A combination is a selection of objects where order is not important. Different orders of the same objects represent the same combination.

In permutation, order matters; in combination, order does not matter.

The number of permutations is \(^{n}P_{r} = \dfrac{n!}{(n-r)!}\).

The number of combinations is \(^{n}C_{r} = \dfrac{n!}{r!(n-r)!}\).

The factorial of \(n\), written as \(n!\), means the product \(n \times (n-1) \times (n-2) \times \cdots \times 1\).

By definition, \(0! = 1\).

This definition ensures the validity of formulas such as \(^{n}P_{n} = n!\) and \(^{n}C_{0} = 1\).

The value of \(^{n}P_{n}\) is \(n!\), which represents all possible arrangements of \(n\) objects.

Both \(^{n}C_{0}\) and \(^{n}C_{n}\) are equal to 1.

For all integers \(n\) and \(r\), \(^{n}C_{r} = {}^{n}C_{n-r}\).

They are related by \(^{n}P_{r} = {}^{n}C_{r} \times r!\).

A linear permutation is an arrangement of objects in a straight line.

A circular permutation is an arrangement of objects around a circle, where relative positions matter.

The number of circular permutations is \((n-1)!\).

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