Work, Energy and Power
Motion of System of Particles and Rigid Body
Gravitation
Behaviour of Perfect Gas and Kinetic Theory
Current Electricity
Magnetic Effects of Current and Magnetism
Electromagnetic Induction and Alternating Currents
Electromagnetic Waves
Optics
Uncategorized
Physical World and Measurement
Kinematics
Vectors
Laws of Motion
Properties of Bulk Matter
Thermodynamics
Oscillations and Waves
Electrostatics
Dual Nature of Matter and Radiation
Atoms and Nuclei
Electronic Devices & Semiconductor
Communication System

Solutions
Electrochemistry
Chemical Kinetics
Surface Chemistry
General Principles and Processes of Isolation of Elements
Some Basic Concepts of Chemistry
Structure of Atom
Classification of Elements and Periodicity in Properties
Chemical Bonding and Molecular Structure
States of Matter: Gases and Liquids
Equilibrium
Redox Reactions
Hydrogen
s-Block Element (Alkali and Alkaline earth metals)
Some p-Block Elements
Organic Chemistry- Some Basic Principles and Techniques
Hydrocarbons
Environmental Chemistry
Solid State
p-Block Elements
d and f Block Elements
Coordination Compounds
Haloalkanes and Haloarenes
Alcohols, Phenols and Ethers
Aldehydes, Ketones and Carboxylic Acids
Organic Compounds Containing Nitrogen
Amines
Biomolecules
Polymers
Chemistry in Everyday Life
Thermodynamics
Uncategorized
Nuclear Chemistry

Coordinate Geometry (2D)
Mathematical Reasoning
Statistics and Probability
Vectors and Three-Dimensional Geometry
Uncategorized
Sets, Relations and Functions
Permutations and Combinations
Linear Programming
Matrices and Determinants
Logarithm, Indices, Surds and Partial Fraction
Correlation and Regression
Trigonometry
Principle of Mathematical Induction
Complex Numbers and Quadratic Equations
Linear Inequalities
Binomial Theorem
Sequence and Series
Conic Sections
Differential Calculus
Limits, Continuity and Differentiability
Integral Calculus
Differential Equations
Coordinate Geometry
Straight Lines

Permutations and Combinations

**Correct Marks**
4

**Incorrectly Marks**
-1

Q 1. In a shop there are five types of ice creams available. A child buys six ice creams.

Statement 1: The number of different ways the child can buy the six ice creams is {tex} ^ { 10 } \mathrm { C } _ { 5 } {/tex}.

Statement 2: The number of different ways the child can buy the six ice creams is equal to the number of different ways of arranging {tex}6 A ^ { \prime } s {/tex} and {tex}4 B ^ { \prime }s {/tex} in a row.

Statement 1 is false, Statement 2 is true

Statement 1 is true, Statement 2 is true; Statement 2 is a correct explanation for Statement 1

Statement 1 is true, Statement 2 is true; Statement 2 is not a correct explanation for Statement 1

Statement 1 is true, Statement 2 is false

**Correct Marks**
4

**Incorrectly Marks**
-1

Q 2. From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. Then the number of such arrangements is

less than 500 .

at least 500 but less than 750 .

at least 750 but less than 1000 .

at least 1000

**Correct Marks**
4

**Incorrectly Marks**
-1

Q 3. There are two urns. Urn A has 3 distinct red balls and urn B has 9 distinct blue balls. From each urn two balls are taken out at random and then transferred to the other. The number of ways in which this can be done is

36

66

108

3

**Correct Marks**
4

**Incorrectly Marks**
-1

Q 4. Statement {tex} 1 : {/tex} The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is empty is {tex} ^ { 9 } \mathrm { C } _ { 3 } {/tex}.
Statement 2: The number of ways of choosing any 3 places from 9 different places is {tex} ^ { 9 } \mathrm { C } _ { 3 } {/tex} .

Statement 1 is true, Statement 2 is true; Statement 2 is not a correct explanation for Statement 1

Statement 1 is true, Statement 2 is false

Statement 1 is false, Statement 2 is true

Statement 1 is true, Statement 2 is true; Statement 2 is a correct explanation for Statement 1

**Correct Marks**
4

**Incorrectly Marks**
-1

Q 5. Let {tex} T _ { n } {/tex} be the number of all possible triangles formed by joining vertices of an {tex} n {/tex} -sided regular polygon. If {tex} T _ { n + 1 } - T _ { n } = 10 {/tex} , then the value of {tex} n {/tex} is

5

10

8

7

**Correct Marks**
4

**Incorrectly Marks**
-1

Q 6. Let {tex} A {/tex} and {tex} B {/tex} be two sets containing 2 elements and 4 elements, respectively. The number of subsets of {tex} A \times B {/tex} having 3 or more elements is

220

219

211

256

**Correct Marks**
4

**Incorrectly Marks**
-1

Q 7. The sum of the digits in the unit's place of all the {tex}4{/tex} -digit numbers formed by using the numbers {tex} 3,4,5 {/tex} and {tex} 6 , {/tex} without repetition is

432

108

36

18

**Correct Marks**
4

**Incorrectly Marks**
-1

Q 8. The number of integers greater than {tex}6000{/tex} that can be formed using the digits {tex} 3,5,6,7 {/tex} and {tex}8{/tex} without repetition is

192

120

72

216

**Correct Marks**
4

**Incorrectly Marks**
-1

Q 9. The value of {tex} \underset {r=1}{ \overset {15} \sum} r ^ { 2 } \left( \frac { ^ { 15 } C _ { r } } { ^ { 15 } C _ { r - 1 } } \right) {/tex} is equal to

1240

560

1085

680

**Correct Marks**
4

**Incorrectly Marks**
-1

Q 10. If the four letter words (need not be meaningful) are to be formed using the letters from the word 'MEDITERRANEAN' such that the first letter is {tex} R {/tex} and the fourth letter is {tex} E {/tex} , then the total number of all such words is

{tex}\small 110{/tex}

{tex}\small 59{/tex}

{tex}\large \frac { 11 ! } { ( 2 ! ) ^ { 3 } } {/tex}

{tex}\small 56{/tex}

**Correct Marks**
4

**Incorrectly Marks**
-1

Q 11. If {tex} \frac { ^{n + 2}C_6 } { ^{n - 2}P_2 } = 11 , {/tex} then {tex} n {/tex} satisfies the equation:

{tex} n ^ { 2 } + n - 110 = 0 {/tex}

{tex} n ^ { 2 } + 2 n - 80 = 0 {/tex}

{tex} n ^ { 2 } + 3 n - 108 = 0 {/tex}

{tex} n ^ { 2 } + 5 n - 84 = 0 {/tex}

**Correct Marks**
4

**Incorrectly Marks**
-1

Q 12. Everybody in a room shakes hand with everybody else. The total number of handshakes is equal to {tex} 153 . {/tex} The total number of persons in the room is equal to

18

19

17

16

**Correct Marks**
4

**Incorrectly Marks**
-1

Q 13. Number of triangles that can be formed joining the angular points of decagon is

30

20

90

120

**Correct Marks**
4

**Incorrectly Marks**
-1

Q 14. A class contains three girls and four boys. Every Saturday, five students go on a picnic, a different group of students is being sent each week. During the picnic, each girl in the group is given a doll by the accompanying teacher. All possible groups of five have gone once. The total number of dolls the girls have got is

21

45

27

24

**Correct Marks**
4

**Incorrectly Marks**
-1

Q 15. The number of all the odd divisors of 3600 is

45

4

18

9

**Correct Marks**
4

**Incorrectly Marks**
-1

Q 16. There are 'n' numbered seats around a round table. Total number of ways in which {tex} n _ { 1 } \left( n _ { 1 } < n \right) {/tex} persons can sit around the round table is equal to

{tex} ^ { n } C _ { n _ { 1 } } {/tex}

{tex} ^ { n } P _ { n_1} {/tex}

{tex} ^ { n } \mathrm { C } _ { n _ { 1 } - 1 } {/tex}

{tex} ^ { n } P _ { n _ { 1 } - 1 } {/tex}

**Correct Marks**
4

**Incorrectly Marks**
-1

Q 17. The total number of three-digit numbers, the sum of whose digits is even, is equal to

450

350

250

325

**Correct Marks**
4

**Incorrectly Marks**
-1

Q 18. A teacher takes three children from her class to the zoo at a time as often as she can, but she doesn't take the same set of three children more than once. She finds out that she goes to the zoo 84 times more than a particular child goes to the zoo. Total number of students in her class is equal to

12

14

10

11

**Correct Marks**
4

**Incorrectly Marks**
-1

Q 19. Five balls of different colours are to be placed in three boxes of different sizes. Each box can hold all five balls. The number of ways in which we can place the balls in the boxes (order is not considered in the box) so that no box remains empty is

150

300

200

None of these

**Correct Marks**
4

**Incorrectly Marks**
-1

Q 20. Total number of ways of selecting two numbers from the set {tex} \{ 1,2,3,4 , \ldots , 3 n \} , {/tex} so that their sum is divisible by {tex}3{/tex} is equal to

{tex}\large \frac { 2 n ^ { 2 } - n } { 2 } {/tex}

{tex}\large \frac { 3 n ^ { 2 } - n } { 2 } {/tex}

{tex} 2 n ^ { 2 } - n {/tex}

{tex} 3 n ^ { 2 } - n {/tex}

**Correct Marks**

**Incorrectly Marks**

Q 21. The total number of selections of fruit which can be made from 3 bananas, 4 apples and 2 oranges, is

39

315

512

None of these

We have,

Required number of ways = (2+1)(3+1)(4+10−1) = 59

**Correct Marks**

**Incorrectly Marks**

Q 22. If m = ^{n}C_{2}, then ^{m}C_{2} is equal to

3 ^{n}C_{4}

^{n + 1}C_{4}

3^{.n + 1}C_{4}

3. ^{n + 1}C_{3}

Given, $m = {\ ^{n}C}_{2} = \frac{n!}{2!(n - 2)!} = \frac{n(n - 1)}{2}$

Now, ${\ ^{n}C}_{2} = \frac{m!}{2!(m - 2)!} = \frac{m(m - 1)}{2}$

$= \frac{\frac{n(n - 1)}{2}.\left( \frac{n^{2} - n - 2}{2} \right)}{2}$

$= \frac{\left( n + 1 \right)n\left( n - 1 \right)(n - 2)}{8}$

= 3. ^{n + 1}C_{4}

**Correct Marks**

**Incorrectly Marks**

Q 23. Five balls of different colours are to be placed in three boxes of different sizes. Each box can hold all five balls. In how many ways can we place the balls so that no box remains empty?

50

100

150

200

Let the boxes be marked as A, B, C. We have to ensure that no box remains empty and all five balls have to put in. There will be two possibilities.

(i) Any two box containing one ball each and 3^{rd} box containing 3 balls. Number of ways

= A(1)B(1)C(3)

= ^{5}C_{1}.^{4}C_{1}.^{3}C_{3} = 5.4.1 = 20

Since, the box containing 3 balls could be any of the three aboxes A, B, C. Hence, the required number of ways 20 × 3 = 60

(ii) Any two box containing 2 balls each and 3rd containing 1 ball, the number of ways

= A(2)B(2)C(1) = ^{5}C_{2}. ^{3}C_{2}. ^{1}C_{1}

= 10 × 3 × 1 = 30

Since, the box containing 1 ball could be any of the three boxes A, B, C. Hence, The required number of ways

= 30 × 3 = 90

Hence, total number of ways = 60 + 90 = 150

**Correct Marks**

**Incorrectly Marks**

Q 24. The interior angles of a regular polygon measure 160^{∘} each. The number of diagonals of the polygon are

97

105

135

146

Let n be the number of sides of the polygon

n.160^{∘} = (n−2).180^{∘}

⇒ 20^{∘}.n = 360^{∘}

∴ n = 18

Then number of diagonals = ^{18}C_{2} − 18 = 153 − 18 = 135

**Correct Marks**

**Incorrectly Marks**

Q 25. There are n number of sets and m number of people have to be seated, then how many ways are possible to do this (m<n)?

^{n}P_{m}

^{n}C_{m}

^{n}C_{n} × (m−1)!

^{n − 1}P_{m − 1}

Required number of ways = ^{n}C_{m} × m! = ^{n}P_{m}

Your request has been placed successfully.