Ncert Solutions For Class 7 Maths Ex 12.1

Ncert Solutions For Class 7 Maths Chapter 12 Ex 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) a2+b2

(ii) 3st+5

(iii) mn4

(iv) a+b2

(v) 10ef

(vi) u-v

(vii) st(s+t)

(viii) x2

 

Q2:  

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

(i) a3

(ii) 1+a+a2

(iii) yy3  

(iv)5ab2+7x2y  

(v) xy+2y23x2

 

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

(i)  4a+5

(ii) 4a+5b

(iii) 5a+3a2  

(iv) ab+2a2b2

(v) ab+b  

(vi) 1.2xy2.4y+3.6x  

(vii) 34x+14

(viii) 0.1a2+0.2b2

Also show the terms and factors by tree diagram.

 

Sol:

(a)

(i) a3

(ii)   1+a+a2

(iii) yy3

(iv)  5ab2+7x2y

(v)   xy+2y23x2

 

(b)-

(i)   4a+5

Terms:  4a,5

Factors:  4,a;5

 

(ii) 4a+5b

Terms:  4a,5b

Factors:   4,a;5,b

 

(iii) 5a+3a2

Terms:  5a,3a2

Factors:   5,a;3,aa

 

(iv) ab+2a2b2

Terms:  ab,2a2b2

Factors:   a,b;2,a,a;b,b

 

(v) ab+b

Terms:  ab,b

Factors:   a,b;b

 

(vi) 1.2xy2.4y+3.6x

Terms:  1.2xy,2.4y,3.6x

Factors:   1.2,x,y;2.4,y;3.6x

 

(vii) 34x+14

Terms:  34x,14

Factors:   34,x;14

 

(viii) 0.1a2+0.2b2

Terms:  0.1a2,0.2b2

Factors:   0.1,a,a;0.2,bb

 

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

(i) 53a2

(ii)  1=a+a2+a3

(iii) a+2ab+3b

(iv) 100x+100y

(v) x2y2+7xy

(vi) 1.2x+0.8y

(vii) 3.14x2

(viii) 2(a+b)

(ix) 0.1x+0.01x2

 

S.no Expression Terms Numerical Coefficient
(i) 53a2 3a2
(ii) 1=a+a2+a3  

a
a2
a3
 

1
1
1
(iii) a+2ab+3b  

a
2ab
3b
 

1
2
3
(iv) 100x+100y  

100m
100n
 

100
100
(v) x2y2+7xy  

x2y2
7xy
 

-1
7
(vi) 1.2x+0.8y  

1.2x
0.8y
 

1.2
0.8
(vii) 3.14x2 3.14x2 3.14
(viii) 2(a+b)  

2a
2b
 

2
2
(ix) 0.1x+0.01x2  

0.1x
0.01x2
 

0.1
0.01

 

Q4:

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

 

(i) b2a+b

(ii) 13b28ab

(iii) a+b+15

(iv) 5+m+ma

(v) 1+a+ab

(vi) 12ab2+10

(vii) 7a+am2

 

(b) Figure out the terms which contain b2 and also give the coefficient of the same term.

(i) 8ab2

(ii) 5b2+10a

(iii) 2a2b5ab2+15b2

 

Sol:

 

S.no Expression Terms with factor a Coefficient of a
(i) b2a+b b2a b2
(ii) 13b28ab 8ab 8b
(iii) a+b+15 a 1
(iv) 5+m+ma ma m
(v) 1+a+ab  

a
ab
 

1
b
(vi) 12ab2+10 12ab2 12b2
(vii) 7a+am2  

am2
7a
 

m2
7

 

(b)

 

S.no Expression Terms containing b2 Coefficient of b2
(i) 8ab2 ab2 a
(ii) 5b2+10a 5b2 5
(iii) 2a2b5ab2+15b2  

5ab2
15b2
 

5a
15

 

Q5: Classify into monomials, binomials and trinomials:

(i) 4b7a

(ii) b2

(iii) a+bab

(iv) 50

(v) ab+b+a

(vi) 5+10x

(vii) 15a2b10ab2

(viii) 10yz

(ix) x2+10x5

(x) x2+y2

(xi) x2+y

(xii) a2+a+50

 

Sol:

 

S.no Expression Type of Polynomial
(i) 4b7a Binomial
(ii) b2 Monomial
(iii) a+bab Trinomial
(iv) 50 Monomial
(v) ab+b+a Trinomial
(vi) 5+10x Binomial
(vii) 15a2b10ab2 Binomial
(viii) 10yz Monomial
(ix) x2+10x5 Trinomial
(x) x2+y2 Binomial
(xi) x2+y Binomial
(xii) a2+a+50 Trinomial

 

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

(i) 1,100

(ii) 20x,12x

(iii) 10x,10y

(iv) 50ab,30ba

(v) 2a2b,8ab2

(vi) 10ab,20a2b

 

Sol:

 

S.no Pair of terms Like/Unlike terms
(i) 1,100 Like terms
(ii) 20x,12x Like terms
(iii) 10x,10y Unlike terms
(iv) 50ab,30ba Like terms
(v) 2a2b,8ab2 Unlike terms
(vi) 10ab,20a2b Unlike terms

 

Q7: Identify the like terms in the following:

(a) a2b,4ab2,9a2,2ab2,10a,20a2,30a,5a2b,2ab,35a

(b) 10pq,10p,5q,2p2q2,5pq,50q,30,18p2q2,55,100p,30pq,105p2q,200

 

Sol:

(a) Like terms are:

(i) a2b,5a2b

(ii) 4ab2,2ab2

(iii) 9a2,20a2

(iv) 10a,30a,35a

(v) 2ab

 

(b) Like terms are:

(i)  10pq,5pq,30pq

(ii)  10p,100p,

(iii) 5q,50q

(iv) 2p2q2,18p2q2

(v) 30,55,200

(vi) 105p2q