NCERT Solutions For Class 7 Maths Chapter 12

NCERT Solutions Class 7 Maths Algebraic Expressions

Ncert Solutions For Class 7 Maths Chapter 12 PDF Download

NCERT Solutions For Class 7 Maths Chapter 12 are given here in a simple and detailed way. These NCERT Solutions for algebraic expressions of class 7 maths can be extremely helpful for the students to clear all their doubts easily and understand the basics of this chapter in a better and detailed way.

NCERT class 7 maths chapter 12 Algebraic Expressions solutions given here are very easily understandable so that students does not face any difficulties regarding any of the solutions. The class 7 maths chapter 12 NCERT solutions PDF is also available here that the students can download and study.

NCERT Solutions For Class 7 Maths Chapter 12 Exercises

Exercise 12.1

Q1: Using arithmetic operations, constants and variables find the algebraic expressions of the cases given below:

(i) Numbers a and b both squared and added.

(ii) Number 5 added to three times the product of s and t.

(iii) One-fourth of the product of numbers m and n.

(iv) One-half of the sum of numbers a and b.

(v) Product of numbers e and f subtracted from 10.

(vi) Subtraction of v from u.

(vii) Sum of numbers s and t subtracted from their product

(viii) The number x multiplied by itself.

 

Sol:

(i) \(a^{2}+b^{2}\)

(ii) \(3st+5\)

(iii) \(\frac{mn}{4}\)

(iv) \(\frac{a+b}{2}\)

(v) \(10- ef\)

(vi) u-v

(vii) \(st-(s+t)\)

(viii) \(x^{2}\)

 

Q2:  

(a) Figure out the terms and their factors in the expression given below and show them by the help of tree diagram

(i) \(a-3\)

(ii) \(1+a+a^{2}\)

(iii) \(y-y^{3}\)  

(iv)\(5ab^{2}+7x^{2}y\)  

(v) \(-xy+2y^{2}-3x^{2}\)

 

(b) Figure out the terms and factors in the expressions below:

(i)  \(-4a+5\)

(ii) \(-4a+5b\)

(iii) \(5a+3a^{2}\)  

(iv) \(ab+2a^{2}b^{2}\)

(v) \(ab+b\)  

(vi) \(1.2xy-2.4y+3.6x\)  

(vii) \(\frac{3}{4}x+\frac{1}{4}\)

(viii) \(0.1a^{2}+0.2b^{2}\)

Also show the terms and factors by tree diagram.

 

Sol:

(a)

(i) \(a-3\)

(ii)   \(1+a+a^{2}\)

(iii) \(y-y^{3}\)

(iv)  \(5ab^{2}+7x^{2}y\)

(v)   \(-xy+2y^{2}-3x^{2}\)

 

(b)-

(i)   \(-4a+5\)

Terms:  \(-4a,5\)

Factors:  \( -4,\; a;\; 5\)

 

(ii) \(-4a+5b\)

Terms:  \(-4a,5b\)

Factors:   \(-4,\;a;\;5,\;b\)

 

(iii) \(5a+3a^{2}\)

Terms:  \(5a,3a^{2}\)

Factors:   \(5,\;a;\;3,\;a\;a\)

 

(iv) \(ab+2a^{2}b^{2}\)

Terms:  \(ab,2a^{2}b^{2}\)

Factors:   \(a,\;b;\;2,\;a,\;a;\;b,\;b\)

 

(v) \(ab+b\)

Terms:  \(ab,b\)

Factors:   \(a,\;b;\;b\)

 

(vi) \(1.2xy-2.4y+3.6x\)

Terms:  \(1.2xy,-2.4y,3.6x\)

Factors:   \(1.2,\;x,\;y;\;-2.4,\;y;\;3.6\; x\)

 

(vii) \(\frac{3}{4}x+\frac{1}{4}\)

Terms:  \(\frac{3}{4}x,\frac{1}{4}\)

Factors:   \(\frac{3}{4},\;x;\; \frac{1}{4}\)

 

(viii) \(0.1a^{2}+0.2b^{2}\)

Terms:  \(0.1a^{2},0.2b^{2}\)

Factors:   \(0.1,\;a,\;a;\;0.2,\;b\;b\)

 

Q3: Other than the constants figure out the numerical coefficients of the given expressions:

(i) \(5-3a^{2}\)

(ii)  \(1=a+a^{2}+a^{3}\)

(iii) \(a+2ab+3b\)

(iv) \(100x+100y\)

(v) \(-x^{2}y^{2}+7xy\)

(vi) \(1.2x+0.8y\)

(vii) \(3.14x^{2}\)

(viii) \(2(a+b)\)

(ix) \(0.1x+0.01x^{2}\)

 

S.no Expression Terms Numerical Coefficient
(i) \(5-3a^{2}\) \(-3a^{2}\)
(ii) \(1=a+a^{2}+a^{3}\)  

a
\(a^{2}\)
\(a^{3}\)
 

1
1
1
(iii) \(a+2ab+3b\)  

a
2ab
3b
 

1
2
3
(iv) \(100x+100y\)  

100m
100n
 

100
100
(v) \(-x^{2}y^{2}+7xy\)  

\(-x^{2}y^{2}\)
\(7xy\)
 

-1
7
(vi) \(1.2x+0.8y\)  

\(1.2x\)
\(0.8y\)
 

1.2
0.8
(vii) \(3.14x^{2}\) \(3.14x^{2}\) 3.14
(viii) \(2(a+b)\)  

2a
2b
 

2
2
(ix) \(0.1x+0.01x^{2}\)  

\(0.1x\)
\(0.01x^{2}\)
 

0.1
0.01

 

Q4:

(a) Identify the terms which contain ‘a’ and give the coefficient of a.

 

(i) \(b^{2}a+b\)

(ii) \(13b^{2}-8ab\)

(iii) \(a+b+15\)

(iv) \(5+m+ma\)

(v) \(1+a+ab\)

(vi) \(12ab^{2}+10\)

(vii) \(7a+am^{2}\)

 

(b) Figure out the terms which contain \(b^{2}\) and also give the coefficient of the same term.

(i) \(8-ab^{2}\)

(ii) \(5b^{2}+10a\)

(iii) \(2a^{2}b-5ab^{2}+15b^{2}\)

 

Sol:

 

S.no Expression Terms with factor a Coefficient of a
(i) \(b^{2}a+b\) \(b^{2}a\) \(b^{2}\)
(ii) \(13b^{2}-8ab\) \(-8ab\) \(-8b\)
(iii) \(a+b+15\) a 1
(iv) \(5+m+ma\) ma m
(v) \(1+a+ab\)  

a
ab
 

1
b
(vi) \(12ab^{2}+10\) \(12ab^{2}\) \(12b^{2}\)
(vii) \(7a+am^{2}\)  

\(am^{2}\)
7a
 

\(m^{2}\)
7

 

(b)

 

S.no Expression Terms containing \(b^{2}\) Coefficient of \(b^{2}\)
(i) \(8-ab^{2}\) \(-ab^{2}\) \(-a\)
(ii) \(5b^{2}+10a\) \(5b^{2}\) 5
(iii) \(2a^{2}b-5ab^{2}+15b^{2}\)  

\(-5ab^{2}\)
\(15b^{2}\)
 

\(-5a\)
15

 

Q5: Classify into monomials, binomials and trinomials:

(i) \(4b-7a\)

(ii) \(b^{2}\)

(iii) \(a+b-ab\)

(iv) \(50\)

(v) \(ab+b+a\)

(vi) \(5+10x\)

(vii) \(15a^{2}b-10ab^{2}\)

(viii) \(10yz\)

(ix) \(x^{2}+10x-5\)

(x) \(x^{2}+y^{2}\)

(xi) \(x^{2}+y\)

(xii) \(a^{2}+a+50\)

 

Sol:

 

S.no Expression Type of Polynomial
(i) \(4b-7a\) Binomial
(ii) \(b^{2}\) Monomial
(iii) \(a+b-ab\) Trinomial
(iv) \(50\) Monomial
(v) \(ab+b+a\) Trinomial
(vi) \(5+10x\) Binomial
(vii) \(15a^{2}b-10ab^{2}\) Binomial
(viii) \(10yz\) Monomial
(ix) \(x^{2}+10x-5\) Trinomial
(x) \(x^{2}+y^{2}\) Binomial
(xi) \(x^{2}+y\) Binomial
(xii) \(a^{2}+a+50\) Trinomial

 

Q6: State whether a given pair of term is of like or unlike terms:

(i) 1,100

(ii) \(-20x, \frac{1}{2}x\)

(iii) \(-10x, -10 y\)

(iv) \(50ab,30ba\)

(v) \(2 a^{2}b,8ab^{2}\)

(vi) \(10ab, 20 a^{2}b\)

 

Sol:

 

S.no Pair of terms Like/Unlike terms
(i) 1,100 Like terms
(ii) \(-20x, \frac{1}{2}x\) Like terms
(iii) \(-10x, -10 y\) Unlike terms
(iv) \(50ab,30ba\) Like terms
(v) \(2 a^{2}b,8ab^{2}\) Unlike terms
(vi) \(10ab, 20 a^{2}b\) Unlike terms

 

Q7: Identify the like terms in the following:

(a) \(-a^{2}b,-4ab^{2},9a^{2},2ab^{2},10a,-20a^{2},-30a, -5a^{2}b,-2ab,35a\)

(b) \(10pq,10p,5q,2p^{2}q^{2},-5pq,-50q,-30,18p^{2}q^{2},55,100p,-30pq, 105p^{2}q,-200\)

 

Sol:

(a) Like terms are:

(i) \(-a^{2}b, -5a^{2}b\)

(ii) \(-4ab^{2}, 2ab^{2}\)

(iii) \(9a^{2},-20a^{2}  \)

(iv) \(10a,-30a,35a\)

(v) \(-2ab \)

 

(b) Like terms are:

(i)  \(10pq,-5pq,-30pq \)

(ii)  \( 10p,100p,\)

(iii) \(5q, -50q \)

(iv) \(2p^{2}q^{2}, 18p^{2}q^{2}\)

(v) \(-30, 55,-200\)

(vi) \(105p^{2}q \)

 

Exercise 12.2 

 

Q1: Simplify the terms:

(i) \(21a-32+7a-20a\)

(ii) \(-x^{2}+13x^{2}-5x+7x^{3}-15x\)

(iii) \(a-(a-b)-b-(b-a)\)

(iv) \(3x-2y-xy-(x-y+xy)+3xy+y-x\)

(v) \(5a^{2}b-5a^{2}+3a^{2}b-3b^{2}+a^{2}-b^{2}+8ab^{2}-3b^{2}\)

(vi) \((3b^{2}+5b-4)-(8b-b^{2}-4)\)

Sol:

(i) \(21a-32+7a-20a=21a+7a-20b-32\)

\(\Rightarrow 8b-32\)

 

(ii) \(-x^{2}+13x^{2}-5x+7x^{3}-15x=7x^{3}+13x^{2}-x^{2}-5x-15x\)

\(=7x^{3}+12x^{2}-20x\)

 

(iii) \(a-(a-b)-b-(b-a)=a-a+b-b-b+a\)

\(=a-b\)

 

(iv) \(3x-2y-xy-(x-y+xy)+3xy+y-x=3x-2y-xy-x+y-xy+3xy+y-x\)

\(=3x-x-x+y+y-2y-xy-xy+3xy\)

\(=x-2xy+3xy\)

 

(v)  \(5a^{2}b-5a^{2}+3a^{2}b-3b^{2}+a^{2}-b^{2}+8ab^{2}-3b^{2}\)

\(5a^{2}b+3a^{2}b+8ab^{2}-5a^{2}+a^{2}-3b^{2}-b^{2}-3b^{2}=8a^{2}b+8ab^{2}-4a^{2}-7b^{2}\)

 

(vi) \((3b^{2}+5b-4)-(8b-b^{2}-4)\)

\(3b^{2}+5b-4-8b+b^{2}+4=3b^{2}+b^{2}+5b-8b+4-4\)

\(=4b^{2}-3b\)

 

Q2: Add:

(i) \(3mn,-5mn,8mn,-4mn\)

(ii) \(a-8ab,3ab-b,b-a\)

(iii) \(-7mn+5,12mn+2, 9mn-8, 2mn-3\)

(iv) \(a+b-3,b-a+3,a-b+3\)

(v) \(14x+10y-12xy-13,18-7x-10y+8xy,4xy\)

(vi) \(5m-7n,3n-4m+2,2m-3mn-5\)

(vii) \(4x^{2}y,-3xy^{2},-5xy^{2},5x^{2}y\)

(viii) \(3p^{2}q^{2}-4pq+5,-10p^{2}q^{2},15+9pq+7p^{2}q^{2}\)

(ix) \(ab-4a,4b-ab,4a-4b\)

(x) \(x^{2}-y^{2}-1,y^{2}-1-x^{2},1-x^{2}-y^{2}\)

Sol:

(i) \(3mn,-5mn,8mn,-4mn\)

\(3mn+(-5mn)+8mn(-4mn)=(3-5+8-4)mn\)

\(=(2)mn\)

 

(ii) \(a-8ab,3ab-b,b-a\)

\(a-8ab+3ab-b+b-a=a-a+b-b-8ab+3ab\)

\(=-5ab\)

 

(iii) \(-7mn+5,12mn+2, 9mn-8, 2mn-3\)

\(-7mn+5+12mn+2+9mn-8+2mn-3=-7mn+12mn+9mn+5+2-8-3\)

\(=(-7+12+9)mn+(5+2-8-3)=14mn+2\)

 

(iv) \(a+b-3,b-a+3,a-b+3\)

\(a+b-3+b-a+3+a-b+3=a+a-a+b+b-b+3+3-3\)

\(=(1+1-1)a+(1+1-1)b+(3+3-3)=a+b+3\)

 

(v) \(14x+10y-12xy-13,18-7x-10y+8xy,4xy\)

\(=14x-7x+10y-10y+8xy+4xy-12xy+18-13=7x+18\)

\(=7x+18\)

 

(vi) \(5m-7n,3n-4m+2,2m-3mn-5\)

\(5m-4m+2m-7n+3n+2-5-3mn=3m-4n-3mn-3\)

 

(vii) \(4x^{2}y,-3xy^{2},-5xy^{2},5x^{2}y\)

\(4x^{2}y+(-3xy^{2})+(-5xy^{2})+5x^{2}y=4x^{2}y+5x^{2}y-3xy^{2}-5xy^{2}\)

\(=9x^{2}y-8xy^{2}\)

 

(viii) \(3p^{2}q^{2}-4pq+5,-10p^{2}q^{2},15+9pq+7p^{2}q^{2}\)

\(3p^{2}q^{2}-4pq+5+(-10p^{2}q^{2})+15+9pq+7p^{2}q^{2}=3p^{2}q^{2}+7p^{2}q^{2}-10p^{2}q^{2}+9pq-4pq+15-5\)

\(=5pq+10\)

 

(ix) \(ab-4a,4b-ab,4a-4b\)

\(ab-4a+4b-ab+4a-4b=4a-4a+4b-4b+ab-ab\)

\(=0\)

 

(x) \(x^{2}-y^{2}-1,y^{2}-1-x^{2},1-x^{2}-y^{2}\)

\(x^{2}-y^{2}-1+y^{2}-1-x^{2}+1-x^{2}-y^{2}=x^{2}-x^{2}-x^{2}+y^{2}-y^{2}-y^{2}+1-1-1\)

\(=-x^{2}-y^{2}-1\)

 

Q3: Subtract:

(i)  \(-5y^{2}\) from \(y^{2}\)

(ii) \(6xy\) from \(-12xy\)

(iii) \((a-b)\) from \((a+b)\)

(iv) \(a(b-5)\) from \(b(5-a)\)

(v) \(-m^{2}+5mn\) from \(4m^{2}-3mn+8\)

(vi) \(-x^{2}+10x-5\) from \(5x-10\)

(vii) \(5a^{2}-7ab+5b^{2}\) from \(3ab-2a^{2}-2b^{2}\)

(viii) \(4pq-5q^{2}-3p^{2}\) from \(5p^{2}+3q^{2}-pq\)

 

Sol:

(i) \(y^{2}-(-5y^{2})\)

    \(=y^{2}+5y^{2}\)

\(=6y^{2}\)

 

(ii) \(-12xy-6xy\)

\(=-18xy\)

 

(iii) \((a+b)-(a-b)\)

\(=a+b-a+b\)

\(=2b\)

 

(iv) \(b(5-a)-a(b-5)\)

\(=5b-ab-ab+5a\)

\(=5a+5b-2ab\)

 

(v)  \(4m^{2}-3mn+8-(-m^{2}+5mn)\)

\(=4m^{2}-3mn+8+m^{2}-5mn\)

\(=5m^{2}-8mn+8\)

 

(vi) \(5x-10-(-x^{2}+10x-5)\)

\(=5x-10+x^{2}-10x+5\)

\(=x^{2}-5x-5\)

 

(vii) \(3ab-2a^{2}-2b^{2}-(5a^{2}-7ab+5b^{2})\)

\(=3ab-2a^{2}-2b^{2}-5a^{2}+7ab-5b^{2}\)

\(=3ab+7ab-2a^{2}-5a^{2}-2b^{2}-5b^{2}\)

\(=10ab-7a^{2}-7b^{2}\)

 

(viii) \(5p^{2}+3q^{2}-pq-(4pq-5q^{2}-3p^{2})\)

\(=5p^{2}+3q^{2}-pq-4pq+5q^{2}+3p^{2}\)

\(=5p^{2}+3p^{2}+3q^{2}+5q^{2}-pq-4pq\)

\(=8p^{2}+8q^{2}-5pq\)

 

Q4: (a) What should be added to \(x^{2}+xy+y^{2}\) to obtain \(2x^{2}+3xy\) ?

(b) What should be subtracted from \(2a+8b+10\) to get \(-3a+7b+16\)?

 

Sol:

(a) Let a should be added

Then according to the question

\(x^{2}+xy+y^{2}+a=2x^{2}+3xy\)

 

\(\Rightarrow a=2x^{2}+3xy-(x^{2}+xy+y^{2})\)

 

\(\Rightarrow a=2x^{2}+3xy-x^{2}-xy-y^{2}\)

 

\(\Rightarrow a=2x^{2}-x^{2}-y^{2}+3xy-xy\)

 

\(\Rightarrow a=x^{2}-y^{2}+2xy\)

Hence the value of a comes out to be \(x^{2}-y^{2}+2xy\).

Hence  \(x^{2}-y^{2}+2xy\) should be added.

 

(b) Let b should be subtracted

Then according to the question,

\(2a+8b+10-q= -3a+7b+16\)

 

\(2a+8b+10-q= -3a+7b+16\)

 

\( q = 2a+8b+10-( -3a+7b+16)\)

 

\( q = 2a+8b+10+3a-7b-16\)

 

\( q = 2a+3a+8b-7b+10-16\)

 

\( q = 5a+b-6\)

 

Q5: What should be taken from 3x2-4y2+5xy+20 to obtain –x2-y2+6xy+20 ?

Sol:

Let a be subtracted

Then according to the question,

3x-4y2+5xy+20 – q= –x2-y2+6xy+20

q=  3x-4y2+5xy+20 -(–x2-y2+6xy+20)

q= 3x2-4y2+5xy+20+x2+y2-6xy-20

q=3x2+x2-4y2+y2+5xy-6xy +20 -20

q=4x2-3y2-xy

Hence, 4x2-3y2-xy should be subtracted in the given equation.

 

Q6:

(a) From the sum of 3x – y + 11 and – y – 11, subtract 3x – y – 11.

(b) From the sum of 4 + 3x and 5 – 4x + 2x, subtract the sum of 3x2 – 5x and –x2 + 2x + 5.

Sol:

(a)According to the question

(3x – y + 11)+( – y – 11)-( 3x – y – 11)= 3x – y + 11 – y – 11- 3x + y + 11

= 3x-3x+y-y+11+11-11

=11

(b) According to question,

(4 + 3x)+( 5 – 4x + 2x2)-( 3x2 – 5x)-( –x2 + 2x + 5)

= 4 + 3x+ 5 – 4x + 2x2– 3x2 + 5x +x2 – 2x – 5

= 3x-4x+5x-2x +2x2– 3x2+x2+4+5-5

= 2x+4

 

Exercise 12.3

 

Q1: If a=2, find the values of:

(i) a-2

(ii) 3a-5

(iii) 9-5a

(iv) \(3a^{2}-2a-7\)

(v) \(\frac{5m}{2}-4\)

 

Sol:

(i) a-2 =2-2  (Putting a=2)

=0

 

(ii)  3a-5= \(3\times 2-5\)   (Putting a=2)

=1

 

(iii)   9-5a=\(9-5\times 2\) (Putting a=2)

= -1

 

(iv)  \(3a^{2}-2a-7=3\times 2^{2}-2\times 2-7\)  (Putting a=2)

=12-4-7

=1

 

(v)  \(\frac{5m}{2}-4 =\frac{5\times 2}{2}-4 =5-4\)   (Putting a=2)

=1

 

Q2: If x=-2, find

(i)  4x+7

(ii)  \(-3x^{2}+4x+7\)

(iii) \(-2x^{3}-3x^{2}+4x+7\)

 

Sol:

(i)  4x+7=4(-2)+7   (Putting x= -2)

= -8+7=-1

 

(ii)  \(-3x^{2}+4x+7=-3(-2)^{2}+4(-2)+7\)

= -3(4)-8+7=-12-8+7

= -13

 

(iii) \(-2x^{3}-3x^{2}+4x+7=-2(-2)^{3}-3(-2)^{2}+4(-2)+7\)  (Putting x= -2)

= -2(-8)-3(4)+4(-2)+7

=  16-12-8+7

=3

 

Q3: Find the value of the following expressions, when x= -1:

(i) 5x-35

(ii) -2x+4

(iii) \(3x^{2}+6x+3\)

(iv) \(6x^{2}-3x-6\)  

Sol:

(i) 5x-35 = 5(-1)-35 =-5-35              [Putting x= -1 ]

= -40

(ii)  -2x+4  = -2(-1)+4            [Putting x= -1 ]

= 2 + 4 = 6

(iii) \(3x^{2}+6x+3\) = \(3(-1)^{2}+6(-1)+3\)      [Putting x= -1 ]

= 3-6+3 =0

(iv) \(6x^{2}-3x-6\)  = \(6(-1)^{2}-3(-1)-6\)        [Putting x= -1 ]

= 6+1-6 =1

 

Q 4: If x=2, y= -2, find the value of:

(i) \(x^{2}+y^{2}\)  

(ii) \(x^{2}+xy+y^{2}\)  

(iii) \(x^{2}-y^{2}\)

 

Sol:

(i) \(x^{2}+y^{2}\) = \(2^{2}+(-2)^{2}\)                        [Putting a=2,  b= -2 ]

= 4 + 4 = 8

(ii) \(x^{2}+xy+y^{2}\)  = \(2^{2}+2(-2)+(-2)^{2}\)        [Putting a=2,b= -2 ]

= 4 – 4 + 4 = 4

(iii) \(x^{2}-y^{2}\) = \((2)^{2}-(-2)^{2}\)                        [Putting a=2, b= -2]

= 4 – 4 = 0

 

Q5: When x=0,y= -1, find the value of the given expressions:

(i) 2x+2y

(ii) \(2x^{2}+y^{2}+1\)  

(iii) \(2x^{2}y+2xy^{2}+xy\)

(iv) \(x^{2}+xy+2\)

Sol:

(i) 2x+2y = 2(0)+2(-1)     [Putting x=0,y= -1 ]

= 0 – 2 = -2

(ii) \(2x^{2}+y^{2}+1\) = \(2(0)^{2}+(-1)^{2}+1\)   [Putting x=0, y=-1 ]

= 0 + 1 + 1 = 2

(iii) \(2x^{2}y+2xy^{2}+xy\) =  \(2(0)^{2}(-1)+2(0)(-1)^{2}+0(-1)\)      [Putting x=0, y= -1]

= 0 + 0 + 0 = 0

(iv) \(x^{2}+xy+2\) = \((0)^{2}+(0)(-1)+2\)    [Putting x=0, y= -1 ]

= 0 + 0 + 2 = 2

 

Q6: Simplify the following expressions and find the value at a= 2:

(i) a+7+4(a-5)

 (ii) 3(a+2)+5a-7  

(iii) 10a+4(a-2)

(iv) 5(3a-2)+4a+8    

 

Sol:

(i) a+7+4(a-5) = a+7+4a-20

=4a+a+7-20 =5a-13

= 5(2)-13 =10-13                                                                                   [Putting a=2 ]

= -3

 

(ii) 3(a+2)+5a-7 = 3a+6+5a-7

= 3a+5a+6-7  = 8a-1

= 8( 2) – 1                                                                                               [Putting a=2 ]

= 16 – 1 = 15

 

(iii) 10a+4(a-2) = 10a+4a-8

= 14a-8

= 14( 2) – 8                                                                                            [Putting a= 2 ]

= 28 – 8 = 20

 

(iv) 5(3a-2)+4a+8 = 15a-10+4a+8

=15a+4a-10+8 = 19a-2                                                                           [Putting =2  ]

= 19(2)-2 = 38-2

= 36

 

Q7: Simplify the expression given below and find the value at x=3, y= -1, z= -2  :

(i) 8x-10-3x+5

(ii) 10-5x+3x+6

(iii) 5y+3-2y+6

(iv) 5-8z-12-4z

(v) 3y-5z-6x+15

Sol:

(i) 8x-10-3x+5 = 8x-3x-10+5

=5x-5 = 5(3)-5                                                                                                [Putting x=3 ]

= 15-5 = 0

(ii) 10-5x+3x+6 = 10+6-5x+3x

= 16-2x = 16-2(3)                                                                                           [Putting x= 3 ]

=  16-6 =10

(iii) 5y+3-2y+6 = 5y-2y+3+6

= 3y+9 = 3(-1)+9                                                                                             [Putting y= -1 ]

= -3 + 9 = 6

(iv) 5-8z-12-4z = 5-12-8z-4z

= -7-12 z                                                                                                         [Putting z= -2 ]

= -7 -12(-2) = -7+24

= 17

(v) 3y-5z-6x+15

= 3(-1)-5(-2)-6(3)+15                                                                       [Putting x=3, y=-1, z=-2]

= -3+10-18+15

= 25-21

= 4

 

Q8:

(i) If x= 10, find the value of \(x^{3}-3x^{2}-5x+15\) .

(ii) If y= -10, find the value of \(2y^{2}-3y+50\)

 

Sol:

(i) \(x^{3}-3x^{2}-5x+15\)

= \(10^{3}-3(10)^{2}-5(10)+15\)                                                   [Putting x=10 ]

=1000-300-50+15

= 665

 

(ii) \(2y^{2}-3y+50\)

=\(2(-10)^{2}-3(-10)+50\)                                                            [Putting y= -10 ]

=200+30+50

=280

 

Q9: What should be the value of p if the value of \(2a^{2}+a-p=5\) equals to 5, when a=0 ?

Sol:

\(2a^{2}+a-p=5\)

\(2(0)^{2}+0-p=5\)                                                                         [ Putting x= 0 ]

\(-p=5\)

Hence, the value of p is -5.

 

Q10: Simplify the expression and find its value when x= 5 and y= -3:   

\(2(x^{2}+xy)+3-xy\).

Sol:

 

Given:

\(2(x^{2}+xy)+3-xy\)

 

\(\Rightarrow 2x^{2}+2xy+3-xy\)

 

\(\Rightarrow 2x^{2}+2xy-xy+3\)

 

\(\Rightarrow 2x^{2}+xy+3\)

 

\(\Rightarrow 2(5)^{2}+(5)(-3)+3\)             [Putting x=5, y= -3 ]

 

\(\Rightarrow 2(25)+(-15)+3\)

 

\(\Rightarrow 50-15+3\)

\(\Rightarrow 38\)

 

Exercise 12.4

Q1: Observe the pattern made from the line segment, which are of equal length which are found in display of calculators and digital speedometer: If n is the number of digits, and the number of required segments to form the digit n is given by the algebraic expression on the right of the digit. So how many segments are required to form 5,10,100 digits of the kind .

Sol:

 

S.no Symbols Digit’s number Pattern Formulae No. of segments
(i)  

5
10
100
\(5n+1\)  

26
51
501
(ii)  

5
10
100
\(3n+1\)  

16
31
301
(iii)  

5
10
100
\(5n+2\)  

27
52
502

 

(i) \(5n+1\)

Putting n=5,          \(5\times 5+1=25+1=26\)

Putting n=10,        \(5\times 10+1=50+1=51\)

Putting n=100,       \(5\times 100+1=500+1=501\)

 

(ii) \(3n+1\)

Putting n=5,          \(3\times 5+1=15+1=16\)

Putting n=10,        \(3\times 10+1=30+1=31\)

Putting n=100,        \(3\times 100+1=300+1=301\)

 

(iii) \(5n+2\)

Putting n=5,          \(5\times 5+2=25+2=27\)

Putting n=10,        \(5\times 10+2=50+1=52\)

Putting n=100,       \(5\times 100+2=500+1=502\)

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