Physics

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
Physics
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

Chemistry

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
Chemistry
Nuclear Chemistry

Mathematics

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

Q 1.

Correct4

Incorrect-1

In a certain A.P., 5 times the 5^{th} term is equal to 8 times the 8^{th} term, then its 13^{th} term is

0

-1

-12

-13

We have

Let a and d be the first term and common difference respectively

⇒ ⇒ , i.e. .

Hence 13^{th} term = 0

Q 2.

Correct4

Incorrect-1

If 7^{th} and 13^{th} term of an A.P. be 34 and 64 respectively, then its 18^{th} term is

87

88

89

90

Let a be the first term and d be the common difference of the given A.P., then

⇒

⇒

From

(i) and

(ii), d = 5, a = 4

Trick: ⇒

⇒ ⇒

Q 3.

Correct4

Incorrect-1

If is an arithmetic sequence, then equals

1

-1

0`

None of these

Let a be the first term and d the common difference. Then

Q 4.

Correct4

Incorrect-1

The n^{th} term of the series 3 + 10 + 17 + .. and 63 + 65 + 67 +...... are equal, then the value of n is

11

12

13

15

n^{th} term of 1^{st} series

n^{th} term of 2^{nd} series

we have, ⇒ n = 13

Q 5.

Correct4

Incorrect-1

7^{th} term of an A.P. is 40, then the sum of first 13 terms is

53

520

1040

2080

Q 6.

Correct4

Incorrect-1

The first term of an A.P. is 2 and common difference is 4. The sum of its 40 terms will be

3200

1600

200

2800

Q 7.

Correct4

Incorrect-1

The sum of the first and third term of an A.P. is 12 and the product of first and second term is 24, the first term is

1

8

4

6

Let be an A.P.

. Also,

⇒ ⇒

First term

Q 8.

Correct4

Incorrect-1

If denotes the sum of the first r terms of an A.P., then is equal to

2r - 1

2r + 1

4r + 1

2r + 3

Q 9.

Correct4

Incorrect-1

If the sum of the first 2n terms of 2, 5, 8...... is equal to the sum of the first n terms of 57, 59, 61., then n is equal to

10

12

11

13

We have,

⇒ ⇒

Q 10.

Correct4

Incorrect-1

If the sum of the 10 terms of an A.P. is 4 times to the sum of its 5 terms, then the ratio of first term and common difference is

1 : 2

2 : 1

2 : 3

3 : 2

Let a be the first term and d the common difference

Then,

⇒ ⇒ ⇒ , a : d = 1 : 2`

Q 11.

Correct4

Incorrect-1

150 workers were engaged to finish a piece of work in a certain number of days. 4 workers dropped the second day, 4 more workers dropped the third day and so on. It takes eight more days to finish the work now. The number of days in which the work was completed is

15

20

25

30

Let the work was to be finished in x days.

Work of 1 worker in a day

Now the work will be finished in (x + 8) days.

Work done = Sum of the fraction of work done

to

(x + 8) terms

⇒

⇒ ⇒

⇒ ,

Hence work completed in 25 days.

Q 12.

Correct4

Incorrect-1

If the sum of first p terms, first q terms and first r terms of an A.P. be x, y and z respectively, then is

0

2

pqr

We have a, the first term and d, the common difference, ⇒

Similarly, and

Q 13.

Correct4

Incorrect-1

The sum of all odd numbers of two digits is

2475

2530

4905

5049

Required sum,

Let the number of odd terms be n, then

⇒

Q 14.

Correct4

Incorrect-1

If sum of n terms of an A.P. is and , then m =

26

27

28

None of these

⇒

⇒ ⇒

Q 15.

Correct4

Incorrect-1

The sum of n terms of the series is

Q 16.

Correct4

Incorrect-1

If are in A.P., then is

As are in A.P., i.e.

(say)

Q 17.

Correct4

Incorrect-1

If the p^{th}, q^{th} and r^{th} term of a G.P. are a, b, c respectively, then is equal to

0

1

abc

pqr

Let be a G.P.

Now,

Q 18.

Correct4

Incorrect-1

Let be the n^{th} term of the G.P. of positive numbers. Let and , such that α≠β, then the common ratio is

Let x be the first term and y, the common ratio of the G.P.

Then,and

⇒. Thus, common ratio

Q 19.

Correct4

Incorrect-1

The sum of first two terms of a G.P. is 1 and every term of this series is twice of its previous term, then the first term will be

We have, common ratio r = 2;

Let a be the first term, then

⇒ ⇒

Q 20.

Correct4

Incorrect-1

The first term of an infinite geometric progression is x and its sum is 5. Then

According to the given conditions, , r being the

common ratio ⇒

Now, |r|< 1 i.e. ⇒ ⇒ ⇒ i.e. ,

Q 21.

Correct4

Incorrect-1

is

e + 1

e - 1

1 - e

e

.

Q 22.

Correct4

Incorrect-1

The value of .234 is

Q 23.

Correct4

Incorrect-1

If a, b, c are in A.P. and |a|, |b|, |c| < 1, and , , Then x, y, z shall be in

A.P.

G.P.

H.P.

None of these

Now, a, b, c are in A.P.

⇒ 1 - a, 1 - b, 1 - c are in A.P.

⇒ are in H.P.

Therefore x, y, z are in H.P.

Q 24.

Correct4

Incorrect-1

The G.M. of the numbers is

G.M. of

Q 25.

Correct4

Incorrect-1

If a, b, care in A.P. b - a, c - b and a are in G.P., then a : b : c is

1 : 2 : 3

1 : 3 : 5

2 : 3 : 4

1 : 2 : 4

Given, a, b, c are in A.P. ⇒ 2b = a + c

b - a, c - b, a are in G.P. So

⇒

⇒ [∵ b ≠ a]

Put in 2b = a + c, we get c = 3a. Therefore a : b : c = 1 : 2 : 3

Your request has been placed successfully.