NCERT Solutions for Class 11 Maths

Q: Question 1. an=n(n+2)

Answer: Given, an=n(n+2) Substituting n=1,2,3,4,5, we obtain a1=1(1+2)=3, a2=2(2+2)=8, a3=3(3+2)=15, a4=4(4+2)=24, a5=5(5+2)=35.

Q: Question 2. an=2n

Answer: Given, an =2n Substituting n=1,2,3,4,5 we obtain a1=21=2, a2=22=4, a3=23=8, a4=24=16, a5=25=32

Q: Question 3. Find the sum of odd integers from 1 to 2001.

Answer: The odd integers from1 to 2001 are 1,3,5,...1999,2001. This sequence form an A.P. Here, first term is, a=1 and common difference, d=2 Here a+(n−1)d=2001 ⇒1+(n−1)(2)=2001 ⇒2n−2=2000 ⇒n=1001 Hence the required sum is, Sn=$\frac{n}{2}$ [2a+(n−1)d] = $\frac{1001}{2}$ [2×1+(1001−1)×2] =$\frac{1001}{2}$ [2+1000×2] =$\frac{1001}{2}$ ×2002 =1001×1001 =1002001

Q: Question 4. Find the sum of all natural numbers lying between 100 and 1000, which are multiples of 5.

Answer: First and last natural number lying between 100 and 1000 (excluding these two) are 105 and 995 respectively ⇒a=105,d=5,a+(n−1)d=995 ⇒105+(n−1)5=995 ⇒(n−1)5=995−105=890 ⇒n−1=178 ⇒n=179 ∴Sn=$\frac{179}{2}$ [2(105)+(179−1)(5)] =$\frac{179}{2}$ [2(105)+(178)(5)] =179[105+(89)5] =(179)(105+445) =(179)(550) =98450 Thus the sum of all natural numbers lying between 100 and 1000, which are multiples of 5, is 98450.

NCERT Solutions for Class 11 Maths

The NCERT solutions for Class 11 Maths cover the solutions for all the exercise problems of the textbook. NCERT Solutions for Class 11 are as per the NCERT guidelines and syllabus and are prepared by experts. NCERT solutions for Class 11 Maths covers all the concept of the subject help you in scoring higher marks. While solving the problems from NCERT solutions for Class 11 Maths if you have doubts, we have a team of teachers who solve your doubts any time.

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NCERT Solutions for Class 11 Maths Chapterwise

CBSE Class 11 Maths Chapter 1 – Sets

CBSE Class 11 Maths Chapter 2 – Relations and Functions

CBSE Class 11 Maths Chapter 3 – Trigonometric Functions

CBSE Class 11 Maths Chapter 4 – Principle of Mathematical Induction

CBSE Class 11 Maths Chapter 5 – Complex Numbers and Quadratic Equations

CBSE Class 11 Maths Chapter 6 – Linear Inequalities

CBSE Class 11 Maths Chapter 7 – Permutations and Combinations

CBSE Class 11 Maths Chapter 8 – Binomial Theorem

CBSE Class 11 Maths Chapter 9 – Sequences and Series

CBSE Class 11 Maths Chapter 10 – Straight Lines

CBSE Class 11 Maths Chapter 11 – Conic Sections

CBSE Class 11 Maths Chapter 12 – Introduction to Three Dimensional Geometry

CBSE Class 11 Maths Chapter 13 – Limits and Derivatives

CBSE Class 11 Maths Chapter 14 – Mathematical Reasoning

CBSE Class 11 Maths Chapter 15 – Statistics

CBSE Class 11 Maths Chapter 16 – Probability

NCERT Solutions for class 11 maths

CBSE Class 11 Maths Chapterwise NCERT Solutions

NCERT Solutions for Class 11 Maths Chapter 1 – Sets

In this chapter Sets and their representations, Types of Sets, Subsets, Venn diagrams, Union and Intersection of sets, Complement of a set and Properties.

NCERT Solutions for Class 11 Maths Chapter 2 – Relations and Functions

In this Ordered pairs, Cartesian product of sets, relation, pictorial diagrams, domain, co-domain and range, Function and its representation, domain, and range of functions, constant, identity, polynomial, rational, modulus, exponential, logarithmic and greatest integer functions, with their graphs.

NCERT Solutions for Class 11 Maths Chapter 3 – Trigonometric Functions

In this chapter, you will study the concepts of trigonometric ratios, their properties, and functions.

NCERT Solutions for Class 11 Maths Chapter 4 – Principle of Mathematical Induction

Here, you will study the process of the proof by induction, and its application, the principle of mathematical induction and simple applications.

NCERT Solutions for Class 11 Maths Chapter 5 – Complex Numbers and Quadratic Equations

In this chapter, you will study Algebraic properties, Square root, Argand plane and polar representation, solution of quadratic equations of complex numbers, Statement of Fundamental Theorem of Algebra.

NCERT Solutions for Class 11 Maths Chapter 6 – Linear Inequalities

In this chapter, you will study Linear inequalities, their Algebraic solutions, and representation on the number line, Graphical representation, and method of finding a solution in two variables.

NCERT Solutions for Class 11 Maths Chapter 7 – Permutations and Combinations

Here, you will learn the fundamental principle of counting, Permutations and combinations, derivation of formulae and their connections, applications.

NCERT Solutions for Class 11 Maths Chapter 8 – Binomial Theorem

In this you will know about the statement and proof of the binomial theorem, Pascal’s triangle, General and middle term in binomial expansion, applications.

NCERT Solutions for Class 11 Maths Chapter 9 – Sequences and Series

Here, you will get to know about Arithmetic Progression and Mean Geometric Progression and mean, the general term, the sum of first, n terms of a G.P., infinite G.P. and its sum, the relation between Arithmetic Mean and Geometric mean.

NCERT Solutions for Class 11 Maths Chapter 10 – Straight Lines

In this you will study about Shifting of origin , Slope of a line and angle between two lines, parallel to axis, point-slope form, slope-intercept form, two-point form, intercept form and normal form, General equation of a line, lines passing through the point of intersection of two lines, Distance of a point from a line..

NCERT Solutions for Class 11 Maths Chapter 11 – Conic Sections

Here, you will study sections of a cone, circle, ellipse, parabola, hyperbola, a point, a straight line and a pair of intersecting lines, Standard equations and simple properties of parabola, ellipse and hyperbola, circle.

NCERT Solutions for Class 11 Maths Chapter 12 – Introduction to Three Dimensional Geometry

This chapter explains about Coordinate axes and coordinate planes in three dimensions, Coordinates of a point, Distance between two points and section formula

NCERT Solutions for Class 11 Maths Chapter 13 – Limits and Derivatives

In this chapter, you will learn the Limits and Derivatives of polynomials and rational functions, trigonometric, exponential and logarithmic functions. derivative, the scope of the tangent of the curve, Derivative of sum, difference, product and quotient of functions.

NCERT Solutions for Class 11 Maths Chapter 14 – Mathematical Reasoning

In this explanation of Mathematically acceptable statements, connecting words/phrases such as if, implied by, etc. , Difference between contradiction, converse, and contrapositive.

NCERT Solutions for Class 11 Maths Chapter 15 – Statistics

This chapter explains measures of dispersion, Range, mean deviation, variance and standard deviation, Analysis of frequency distributions.

NCERT Solutions for Class 11 Maths Chapter 16 – Probability

In this chapter Probability of an event, outcomes, sample spaces, Axiomatic probability, exhaustive events.

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Solved Questions For You:

Question 1. a_n=n(n+2)

Answer:

Given, $a_{n} = n (n + 2)$

Substituting

n = 1, 2, 3, 4, 5,

we obtain

a_{1} = 1 (1 + 2) = 3,

a_{2} = 2 (2 + 2) = 8,

a_{3} = 3 (3 + 2) = 15,

a_{4} = 4 (4 + 2) = 24,

a_{5} = 5 (5 + 2) = 35 .

Question 2. $a_{n} = 2^{n}$

Answer:

Given, $a_{n} = 2^{n}$
Substituting $n = 1, 2, 3, 4, 5$ we obtain
$a_{1} = 2^{1} = 2,$

$a_{2} = 2^{2} = 4,$

$a_{3} = 2^{3} = 8,$

$a_{4} = 2^{4} = 16,$

$a_{5} = 2^{5} = 32$

Question 3. Find the sum of odd integers from $1$ to $2001$ .

Answer:

The odd integers from $1$ to $2001$ are $1, 3, 5, . . . 1999, 2001$ .

This sequence form an A.P.

Here, first term is,

a = 1

and common difference,

d = 2

Here

a + (n - 1) d = 2001

\Rightarrow 1 + (n - 1) (2) = 2001

\Rightarrow 2 n - 2 = 2000

\Rightarrow n = 1001

Hence the required sum is,

S_{n} =\(\frac{n}{2}\) [2 a + (n - 1) d]

= \(\frac{1001}{2}\) [2 \times 1 + (1001 - 1) \times 2]

=\(\frac{1001}{2}\) [2 + 1000 \times 2]

=\(\frac{1001}{2}\) \times 2002

$= 1001 \times 1001$ $= 1002001$

Question 4. Find the sum of all natural numbers lying between $100$ and $1000$ , which are multiples of $5$ .

Answer:

First and last natural number lying between

100

and

1000

(excluding these two) are

105

and

995

respectively

\Rightarrow a = 105, d = 5, a + (n - 1) d = 995

\Rightarrow 105 + (n - 1) 5 = 995

\Rightarrow (n - 1) 5 = 995 - 105 = 890

\Rightarrow n - 1 = 178

\Rightarrow n = 179

∴ S_{n} =\(\frac{179}{2}\) [2 (105) + (179 - 1) (5)]

= [2 (105) + (178) (5)]

= 179 [105 + (89) 5]

= (179) (105 + 445)

= (179) (550)

= 98450

Thus the sum of all natural numbers lying between

100

and

1000

, which are multiples of

5

, is

98450

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NCERT Solutions for Class 11 Maths Free PDF Download

NCERT Solutions for Class 11 Maths

NCERT Solutions for Class 11 Maths Chapterwise

CBSE Class 11 Maths Chapterwise NCERT Solutions

NCERT Solutions for Class 11 Maths Chapter 1 – Sets

NCERT Solutions for Class 11 Maths Chapter 2 – Relations and Functions

NCERT Solutions for Class 11 Maths Chapter 3 – Trigonometric Functions

NCERT Solutions for Class 11 Maths Chapter 4 – Principle of Mathematical Induction

NCERT Solutions for Class 11 Maths Chapter 5 – Complex Numbers and Quadratic Equations

NCERT Solutions for Class 11 Maths Chapter 6 – Linear Inequalities

NCERT Solutions for Class 11 Maths Chapter 7 – Permutations and Combinations

NCERT Solutions for Class 11 Maths Chapter 8 – Binomial Theorem

NCERT Solutions for Class 11 Maths Chapter 9 – Sequences and Series

NCERT Solutions for Class 11 Maths Chapter 10 – Straight Lines

NCERT Solutions for Class 11 Maths Chapter 11 – Conic Sections

NCERT Solutions for Class 11 Maths Chapter 12 – Introduction to Three Dimensional Geometry

NCERT Solutions for Class 11 Maths Chapter 13 – Limits and Derivatives

NCERT Solutions for Class 11 Maths Chapter 14 – Mathematical Reasoning

NCERT Solutions for Class 11 Maths Chapter 15 – Statistics

NCERT Solutions for Class 11 Maths Chapter 16 – Probability

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