# NCERT Solutions For Class 7 Maths Chapter 12

## NCERT Solutions Class 7 Maths Algebraic Expressions

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

$3b^{2}+5b-4-8b+b^{2}+4=3b^{2}+b^{2}+5b-8b+4-4$

$=4b^{2}-3b$

(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,       $5\times 100+2=500+1=502$