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In this article, we have provided step by step Chapter 5 Ex 5.2 Class 10 Maths NCERT Solutions.

NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions Ex 5.2 are part of
NCERT Solutions for Class 10 Maths. Here are we have given Chapter 5 Arithmetic Progressions Class 10 NCERT Solutions Ex 5.2. 

• Arithmetic Progressions Class 10 Ex 5.1
• Arithmetic Progressions Class 10 Ex 5.3
• Arithmetic Progressions Class 10 Ex 5.4

NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions Ex 5.2

You can also Read Latest NCERT Solutions for Class 10 Maths Chapter-wise to help you to revise the complete Syllabus and score more marks in your examinations.

Page No: 105

Question 1. Fill in the blanks in the following table, given that a is the first term, d the common difference and a_n the n^th term of the A.P.

Solution :

Question 2. Choose the correct choice in the following and justify
(i) 30^th term of the A.P: 10, 7, 4, …, is
(A) 97 (B) 77 (C) −77 (D.) −87

(ii) 11^th term of the A.P. -3, -1/2, ,2 …. is
(A) 28 (B) 22 (C) – 38 (D) -48×1/2

Solution :

Question 3. In the following APs find the missing term in the boxes.

Solution :

Question 4. Which term of the A.P. 3, 8, 13, 18, … is 78?

Solution :

Question 5. Find the number of terms in each of the following A.P.

Solution :

Question 6. Check whether -150 is a term of the A.P. 11, 8, 5, 2, …

Solution :

Question 7. Find the 31^st term of an A.P. whose 11^th term is 38 and the 16^thterm is 73.

Solution :

Question 8. An A.P. consists of 50 terms of which 3^rd term is 12 and the last term is 106. Find the 29^th term.

Solution :

Question 9. If the 3^rd and the 9^th terms of an A.P. are 4 and − 8 respectively. Which term of this A.P. is zero.

Solution :

Question 10. If 17^th term of an A.P. exceeds its 10^th term by 7. Find the common difference.

Solution :

Question 11. Which term of the A.P. 3, 15, 27, 39, … will be 132 more than its 54^th term?

Solution :

Question 12. Two APs have the same common difference. The difference between their 100^th term is 100, what is the difference between their 1000^th terms?

Solution :

Question 13. How many three digit numbers are divisible by 7?

Solution :

Question 14. How many multiples of 4 lie between 10 and 250?

Solution :

Question 15. For what value of n, are the n^th terms of two APs 63, 65, 67, and 3, 10, 17, … equal?

Solution :

Question 16. Determine the A.P. whose third term is 16 and the 7^th term exceeds the 5^th term by 12.

Solution :

Page No: 107

Question 17. Find the 20^th term from the last term of the A.P. 3, 8, 13, …, 253.

Solution :

Question 18. The sum of 4^th and 8^th terms of an A.P. is 24 and the sum of the 6^th and 10^th terms is 44. Find the first three terms of the A.P.

Solution :

Question 19. Subba Rao started work in 1995 at an annual salary of Rs 5000 and received an increment of Rs 200 each year. In which year did his income reach Rs 7000?

Solution :

Question 20. Ramkali saved Rs 5 in the first week of a year and then increased her weekly saving by Rs 1.75. If in the n^th week, her week, her weekly savings become Rs 20.75, find n.

Solution :

We hope the NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions Ex 5.2 help you. If you have any query regarding NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions Ex 5.2, drop a comment below and we will get back to you at the earliest.

Get the comprehensive Chapter 14 Ex 14.4 Class 10 Maths NCERT Solutions from here and score good marks in CBSE Class 10 Board Examinations.

NCERT Solutions for Class 10 Maths Chapter 14 Statistics Ex 14.4 are part of NCERT Solutions for Class 10 Maths. Here are we have given Chapter 14 Statistics Class 10 NCERT Solutions Ex 14.4.

• Statistics Class 10 Ex 14.1
• Statistics Class 10 Ex 14.2
• Statistics Class 10 Ex 14.3

NCERT Solutions for Class 10 Maths Chapter 14 Statistics Ex 14.4

NCERT Solutions for Class 10 Maths

Question 1.
The following distribution gives the daily income of 50 workers of a factory.

We hope the NCERT Solutions for Class 10 Maths Chapter 14 Statistics Ex 14.4 help you. If you have any query regarding NCERT Solutions for Class 10 Maths Chapter 14 Statistics Ex 14.4, drop a comment below and we will get back to you at the earliest.

NCERT Maths Solutions for Ex 1.4 Class 10 Real Numbers is the perfect guide to boost up your preparation during CBSE 10th Class Maths Examination.

NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Ex 1.4 are part of NCERT Solutions for Class 10 Maths. Here are we have given Chapter 1 Real Numbers Class 10 NCERT Solutions Ex 1.4. 

• Real Numbers Class 10 Ex 1.1
• Real Numbers Class 10 Ex 1.2
• Real Numbers Class 10 Ex 1.3
• Real Numbers Class 10 Ex 1.4

NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Ex 1.4

Page No: 17

Question 1
Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion:
(i) 13/3125
(ii) 17/8
(iii) 64/455
(iv) 15/1600
(v) 29/343
(vi) 23/2³ × 5²
(vii) 129/2² × 5⁷ × 7⁵
(viii) 6/15
(ix) 35/50
(x) 77/210

Solution:

Question 3
The following real numbers have decimal expansions as given below. In each case, decide whether they are rational or not. If they are rational, and of the form p, q you say about the prime factors of q?
(i) 43.123456789
(ii) 0.120120012000120000…
(iii) 43.123456789

We hope the NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Ex 1.4 help you. If you have any query regarding NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Ex 1.4, drop a comment below and we will get back to you at the earliest.

Get the comprehensive Chapter 8 Ex 8.2 Class 10 Maths NCERT Solutions from here and score good marks in CBSE Class 10 Board Examinations

NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.2 are part of NCERT Solutions for Class 10 Maths. Here are we have given Chapter 8 Introduction to Trigonometry Class 10 NCERT Solutions Ex 8.2.

• Introduction to Trigonometry Class 10 Ex 8.1
• Introduction to Trigonometry Class 10 Ex 8.3
• Introduction to Trigonometry Class 10 Ex 8.4

NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.2

NCERT Solutions for Class 10 Maths

Page No: 187

Question 1. Evaluate the following :
(i) sin 60° cos 30° + sin 30° cos 60°
(ii) 2 tan²45° + cos²30° – sin²60°
(iii) \(\frac { cos45^{ 0 } }{ sec{ 30 }^{ 0 }+cosec{ 30 }^{ 0 } } \)
(iv) \(\frac { sin{ 30 }^{ 0 }+tan45^{ 0 }-cosec{ 60 }^{ 0 } }{ sec{ 30 }^{ 0 }+cosec{ 60^{ 0 } }+cot{ 45 }^{ 0 } } \)
(v) \(\frac { 5cos^{ 2 }{ 60 }^{ 0 }+4sec^{ 2 }{ 30 }^{ 0 }-tan^{ 2 }{ 45 }^{ 0 } }{ sin^{ 2 }{ 30 }^{ 0 }+cos^{ 2 }{ 30 }^{ 0 } } \)

Solution:

Question 2. Choose the correct option and justify your choice :
(i) \(\frac { 2tan{ 30 }^{ 0 } }{ 1+tan^{ 2 }{ 30 }^{ 0 } } =\)
(A) sin 60° (B) cos 60° (C) tan 60° (D) sin 30°

(ii) \(\frac { 1-tan{ ^{ 2 }45 }^{ 0 } }{ 1+tan{ ^{ 2 }45 }^{ 0 } } =\)
(A) tan 90° (B) 1 (C) sin 45° (D) 0

(iii) sin 2A = 2 sin A is true when A =
(A) 0° (B) 30° (C) 45° (D) 60°

(iv) \(\frac { 2tan{ 30 }^{ 0 } }{ 1-tan{ ^{ 2 }30 }^{ 0 } } =\)
(A) cos 60° (B) sin 60° (C) tan 60° (D) sin 30°

Solution:

Question 3. If tan (A + B) = √3 and tan (A – B) = 1/√3; 0° < A + B ≤ 90°; A > B, find A and B.

Solution:

Question 4. State whether the following are true or false. Justify your answer.
(i) sin (A + B) = sin A + sin B.
(ii) The value of sin θ increases as θ increases.
(iii) The value of cos θ increases as θ increases.
(iv) sin θ = cos θ for all values of θ.
(v) cot A is not defined for A = 0°.

Solution:

We hope the NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.2 help you. If you have any query regarding NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.2, drop a comment below and we will get back to you at the earliest.

NCERT Maths Solutions for Ex 2.3 class 10 Polynomials is the perfect guide to boost up your preparation during CBSE 10th Class Maths Examination.

NCERT Solutions for Class 10 Maths Chapter 2 Polynomials Ex 2.3 are part of NCERT Solutions for Class 10 Maths. Here are we have given Chapter 2 Polynomials Class 10 NCERT Solutions Ex 2.3. 

• Polynomials Class 10 Ex 2.1
• Polynomials Class 10 Ex 2.2
• Polynomials Class 10 Ex 2.4

NCERT Solutions for Class 10 Maths Chapter 2 Polynomials Ex 2.3

Page No: 36

Question 1. Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following:

Question 2. Check whether the first polynomial is a factor of the second polynomial by dividing the
second polynomial by the first polynomial:

Solution:
The polynomial 2t⁴ + 3t³ – 2t² – 9t – 12  can be divided by the polynomial t² – 3 = t² + 0.t – 3 as follows:

Question 3. Obtain all other zeroes of 3x⁴ + 6x³ – 2x² – 10x – 5, if two of its zeroes are √(5/3) and – √(5/3).

Solution:
Let p(x) = 3x⁴ + 6x³ – 2x² – 10x -5

Now, x² + 2x + 1 = (x + 1)²
So, the two zeroes of  x² + 2x + 1 are -1 and -1.

Concept Insight:  Remember that if (x – a) and (x – b) are factors of a polynomial, then (x – a)(x – b) will also be a factor of that polynomial. Also, if a is a zero of a polynomial p(x), where degree of p(x) is greater than 1, then (x – a) will be a factor of p(x), that is when p(x) is divided by (x – a), then the remainder obtained will be 0 and the quotient will be a factor of the polynomial p(x). To cross check your answer number of zeroes of the polynomial will be less than or equal to the degree of the polynomial.

Question 4. On dividing x³ – 3x² + x + 2 by a polynomial g(x), the quotient and remainder were x – 2 and
-2x + 4, respectively. Find g(x).

Solution:
Divided, p(x) = x³ – 3x² + x + 2
Quotient = (x – 2)
Remainder = (-2x + 4)
Let g(x) be the divisor.
According to the division algorithm,
Dividend = Divisor x Quotient + Remainder

Concept Insight: When a polynomial is divided by any other non-zero polynomial, then it satisfies the division algorithm which is as below:
Dividend = Divisor x Quotient + Remainder
Divisor x Quotient = Dividend – Remainder
So, from this relation, the divisor can be obtained by dividing the result of (Dividend – Remainder) by the quotient.

Question 5. Give examples of polynomial p(x), g(x), q(x) and r(x), which satisfy the division algorithm and
(i) deg p(x) = deg q(x)
(ii) deg q(x) = deg r(x)
(iii) deg r(x) = 0

Solution:
According to the division algorithm, if p(x) and g(x) are two polynomials with g(x) ≠ 0, then we can find polynomials q(x) and r(x) such that
p(x) = g(x) x q(x) + r(x), where r(x) = 0 or degree of r(x) < degree of g(x).

(i)  Degree of quotient will be equal to degree of dividend when divisor is constant.
Let us consider the division of 18x² + 3x + 9  by 3.
Here, p(x) = 18x² + 3x + 9  and g(x) = 3
q(x) = 6x² + x + 3  and r(x) = 0
Here, degree of p(x) and q(x) is the same which is 2.
Checking:
p(x) = g(x) x q(x) + r(x)

Thus, the division algorithm is satisfied.

(ii)  Let us consider the division of 2x⁴ + 2x by 2x³,
Here, p(x) = 2x⁴ + 2x and g(x) = 2x³
q(x) = x and r(x) = 2x
Clearly, the degree of q(x) and r(x) is the same which is 1.
Checking,
p(x) = g(x) x q(x) + r(x)
2x⁴ + 2x =  (2x³ ) x x  + 2x
2x⁴ + 2x = 2x⁴ + 2x
Thus, the division algorithm is satisfied.

(iii)    Degree of remainder will be 0 when remainder obtained on division is a constant.
Let us consider the division of 10x³ + 3 by 5x².
Here, p(x) = 10x³ + 3 and g(x) = 5x²
q(x) = 2x and r(x) = 3
Clearly, the degree of r(x) is 0.
Checking:
p(x) = g(x) x q(x) + r(x)
10x³ + 3 = (5x² ) x 2x  +  3
10x³ + 3 = 10x³ + 3
Thus, the division algorithm is satisfied.

Concept Insight: In order to answer such type of questions, one should remember the division algorithm. Also, remember the condition on the remainder polynomial r(x). The polynomial r(x) is either 0 or its degree is strictly less than g(x). The answer may not be unique in all the cases because there can be multiple polynomials which satisfy the given conditions.

We hope the NCERT Solutions for Class 10 Maths Chapter 2 Polynomials Ex 2.3 help you. If you have any query regarding NCERT Solutions for Class 10 Maths Chapter 2 Polynomials Ex 2.3, drop a comment below and we will get back to you at the earliest.