Physics

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

Chemistry

Hydrocarbons
Chemistry
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
Environmental Chemistry
Solid State
Solutions
Thermodynamics
Electrochemistry
Chemical Kinetics
Surface Chemistry
General Principles and Processes of Isolation of Elements
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

Mathematics

Sets, Relations and Functions
Mathematical Reasoning
Statistics and Probability
Properties of Triangle
Vectors and Three-Dimensional Geometry
Linear Programming
Matrices and Determinants
Mathematics
Trigonometric Ratios & Identities
Algebra
Permutations and Combinations
Coordinate Geometry
Circle and System of Circles
Calculus
Logarithm, Indices, Surds and Partial Fraction
Progressions
Correlation and Regression

Q 1.

Correct4

Incorrect-1

{tex} ^ n C _ { r - 1 } = 36 , ^ { n } C _ { r } = 84 {/tex} and {tex} ^ { n } C _ { r + 1 } = 126 , {/tex} then {tex} r {/tex} is

1

2

3

None of these

Q 2.

Correct4

Incorrect-1

Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have at least one letter repeated are

69760

30240

99748

none of these

Q 3.

Correct4

Incorrect-1

The value of the expression {tex} ^ { 47 } C _ { 4 } + \sum _ { j = 1 } ^ { 5 }{^{ 52 - j }C _ { 3 }} {/tex} is equal to

{tex} ^ { 47 } C _ { 5 } {/tex}

{tex} ^ { 52 } C _ { 5 } {/tex}

{tex} ^ { 52 } C _ { 4 } {/tex}

none of these

Q 4.

Correct4

Incorrect-1

Eight chairs are numbered 1 to 8. Two women and three men wish to occupy one chair each. First the women choose the chairs from amongst the chairs marked 1 to 4 ; and then the men select the chairs from amongst the remaining. The number of possible arrangements is

{tex}\mathrm { ^ { 6 } C _ { 3 } \times ^ { 4 } C _ { 2 }} {/tex}

{tex}\mathrm { ^ { 4 } P _ { 2 } \times ^ { 4 } P _ { 3 }} {/tex}

{tex}\mathrm { ^ { 4 } C _ { 2 } + ^ { 4 } P _ { 3 } }{/tex}

none of these

Q 5.

Correct4

Incorrect-1

A five-digit numbers divisible by {tex}3{/tex} is to be formed using the numerals {tex} 0,1,2,3,4 {/tex} and {tex} 5 , {/tex} without repetition. The total number of ways this can be done is

216

240

600

3125

Q 6.

Correct4

Incorrect-1

How many different nine digit numbers can be formed from the number 223355888 by rearranging its digits so that the odd digits occupy even positions?

16

36

60

180

Q 7.

Correct4

Incorrect-1

Let {tex} T _ { n } {/tex} denote the number of triangles which can be formed using the vertices of a regular polygon of {tex} n {/tex} sides. If {tex} T _ { n + 1 } - T _ { n } = 21 , {/tex} then {tex} n {/tex} equals

5

7

6

4

Q 8.

Correct4

Incorrect-1

The number of arrangements of the letters of the word BANANA in which the two N's do not appear adjacently is

40

60

80

100

Q 9.

Correct4

Incorrect-1

A rectangle with sides of length {tex} ( 2 m - 1 ) {/tex} and {tex} ( 2 n - 1 ) {/tex} units is divided into squares of unit length by drawing parallel lines as shown in the diagram, then the number of rectangles possible with odd side lengths is

{tex} ( m + n - 1 ) ^ { 2 } {/tex}

{tex} 4 ^ { m + n - 1 } {/tex}

{tex} m ^ { 2 } n ^ { 2 } {/tex}

{tex} m ( m + 1 ) n ( n + 1 ) {/tex}

Q 10.

Correct4

Incorrect-1

If the LCM of {tex} p , q {/tex} is {tex} r ^ { 2 } t ^ { 4 } s ^ { 2 } , {/tex} where {tex} r , s , t {/tex} are prime numbers and {tex} p , q {/tex} are the positive integers then the number of ordered pair {tex} ( p , q ) {/tex} is

252

254

225

224

Q 11.

Correct4

Incorrect-1

The letters of the word {tex} \mathrm {COCHIN}{/tex} are permuted and all the permutations are arranged in an alphabetical order as in an English dictionary. The number of words that appear before the word {tex} \mathrm {COCHIN}{/tex} is

360

192

96

48

Q 12.

Correct4

Incorrect-1

The number of seven digit integers, with sum of the digits equal to {tex}10{/tex} and formed by using the digits {tex} 1,2 {/tex} and {tex}3{/tex} only, is

55

66

77

88

Q 13.

Correct4

Incorrect-1

The total number of ways in which 5 balls of different colours can be distributed among 3 persons so that each person gets at least one ball is

75

150

210

243

Q 14.

Correct4

Incorrect-1

Six cards and six envelopes are numbered {tex} 1,2,3,4,5,6 {/tex} and cards are to be placed in envelopes so that each envelope contains exactly one card and no card is placed in the envelope bearing the same number and moreover the card numbered {tex}1{/tex} is always placed in envelope numbered {tex} 2 . {/tex} Then the number of ways it can be done is

264

265

53

67

Q 15.

Correct4

Incorrect-1

A debate club consists of 6 girls and 4 boys. A team of 4 members is to be selected from this club including the selection of a captain (from among these 4 memoers) for the team. If the team has to include at most one boy, then the number of ways of selecting the team is

380

320

260

95

Q 16.

Correct4

Incorrect-1

The number of 4-digit natural numbers in which digit at {tex} 1000 ^ { \text {th } } {/tex} places are 1 and exactly one of the digit comes twice are

108

216

432

864

Q 17.

Correct4

Incorrect-1

Consider 26 tangent lines to an ellipse. The lines separate the plane into several regions, some enclosed and others unbounded. Then the number of unbounded regions is

50

52

{tex} ^ { 26 } C _ { 2 } {/tex}

None of these

Q 18.

Correct4

Incorrect-1

Given 6 different toys of green colour, 5 different toys of blue colour and 4 different toys of red colour. Combination of toys that can be chosen taking at least one green and one blue toys are

31258

31248

31

63

Q 19.

Correct4

Incorrect-1

Given distinct lines {tex} L _ { 1 } , L _ { 2 } , \ldots , L _ { 1000 } {/tex} in which all lines of the form {tex} L _ { 4 n ^ { \prime } } {/tex} where {tex} n {/tex} is a positive integer, are parallel to each other. All lines {tex} L _ { 4 n - 3 ^ { \prime } } {/tex} are concurrent at a point. The maximum number of the points of intersection of pairs of line from the complete set {tex} \left( L _ { 1 } , L _ { 2 } , \cdots , L _ { 1000 } \right) {/tex} is

437251

437250

437252

437200

Q 20.

Correct4

Incorrect-1

The number of integral points on the hyperbola {tex} x ^ { 2 } - y ^ { 2 } = ( 2000 ) ^ { 2 } {/tex} is (an integral point is a point both of whose co-ordinates are integer)

98

96

48

24

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