Exercise 10.1 (Revised) - Chapter 12 - Algebraic Expressions - Ncert Solutions class 7 - Maths

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Chapter 10 - Algebraic Expressions | NCERT Solutions for Class 7 Maths

Ex 10.1 Question 1.

Get the algebraic expressions in the following cases using variables, constants and arithmetic operations:
1. Subtraction of $z$ from $y$.
2. One-half of the sum of numbers $x$ and $y$.
3. The number $z$ multiplied by itself.
4. One-fourth of the product of numbers $p$ and $q$.
5. Numbers $x$ and $y$ both squared and added.
6. Number 5 added to three times the product of $m$ and $n$.
7. Product of numbers $y$ and $z$ subtracted from 10 .
8. Sum of numbers $a$ and $b$ subtracted from their product.

Answer:

(i) $y-z$
(ii) $\frac{x+y}{2}$
(iii) $z^2$
(iv) $\frac{p q}{4}$
(v) $x^2+y^2$
(vi) $3 m n+5$
(vii) $10-y z$
(viii) $a b-(a+b)$
Ex 10.1 Question 2.

(i) Identify the terms and their factors in the following expressions, show the terms and factors by tree diagram:
(a) $x-3$

(b) $1+x+x^2$
(c) $y-y^3$
(d) $5 x y^2+7 x^2 y$
(e) $-a b+2 b^2-3 a^2$
(ii) Identify the terms and factors in the expressions given below:
(a) $-4 x+5$
(b) $-4 x+5 y$
(c) $5 y+3 y^2$
(d) $x y+2 x^2 y^2$
(e) $p q+q$
(f) $1.2 a b-2.4 b+3.6 a$
(g) $\frac{3}{4} x+\frac{1}{4}$
(h) $0.1 p^2+0.2 q^2$

Answer:

(i) (a) $x-3$

(b) $1+x+x^2$

Expression

(c) $y-y^3$

Expression

(d) $5 x y^2+7 x^2 y$

Expression

(e) $-a b+2 b^2-3 a^2$

Expression

(ii) (a) $-4 x+5$

Terms: $-4 x, 5$
Factors: $-4, x ; 5$
(b) $-4 x+5 y$

Terms: $-4 x, 5 y$
Factors: $-4, x ; 5, y$
(c) $5 y+3 y^2$

Terms: $5 y, 3 y^2$
Factors: $5, y ; 3, y, y$
(d) $x y+2 x^2 y^2$

Terms: $x y, 2 x^2 y^2$
Factors: $x, y ; 2 x, x, y, y$
(e) $p q+q$

Terms: $p q, q$

Factors: $p, q ; q$
(f) $1.2 a b-2.4 b+3.6 a$

Terms: $1.2 a b,-2.4 b, 3.6 a$
Factors: $1.2, a, b ;-2.4, b ; 3.6, a$
(g) $\frac{3}{4} x+\frac{1}{4}$

Terms: $\frac{3}{4} x, \frac{1}{4}$
Factors: $\frac{3}{4}, x ; \frac{1}{4}$

(h) $0.1 p^2+0.2 q^2$

Terms: $0.1 p^2, 0.2 q^2$
Factors: $0.1, p, p ; 0.2, q, q$

Ex 10.1 Question 3.

Identify the numerical coefficients of terms (other than constants) in the following expressions:
(i) $5-3 t^2$
(ii) $1+t+t^2+t^3$
(iii) $x+2 x y+3 y$
(iv) $100 m+1000 n$
(v) $-p^2 q^2+7 p q$
(vi) $1.2 a+0.8 b$
(vii) $3.14 r^2$
(viii) $2(l+b)$
(ix) $0.1 y+0.01 y^2$

Answer:

Ex 10.1 Question 4.

(a) Identify terms which contain $x$ and give the coefficient of $x$.
(i) $y^2 x+y$
(ii) $13 y^2-8 y x$
(iii) $x+y+2$
(iv) $5+z+z x$
(v) $1+x+x y$
(vi) $12 x y^2+25$
(vii) $7 x+x y^2$
(b) Identify terms which contain $y^2$ and give the coefficient of $y^2$.
(i) $8-x y^2$
(ii) $5 y^2+7 x$

(iii) $2 x^2 y-15 x y^2+7 y^2$

Answer:

(a)

(b)

Ex 10.1 Question 5.

Classify into monomials, binomials and trinomials:
(i) $4 y-7 x$
(ii) $y^2$
(iii) $x+y-x y$
(iv) 100

(v) $a b-a-b$
(vi) $5-3 t$
(vii) $4 p^2 q-4 p q^2$
(viii) $7 m n$
(ix) $z^2-3 z+8$
(x) $a^2+b^2$
(xi) $z^2+z$
(xii) $1+x+x^2$

Answer:

Ex 10.1 Question 6.

State whether a given pair of terms is of like or unlike terms:
(i) 1,100
(ii) $-7 x, \frac{5}{2} x$
(iii) $-29 x,-29 y$

(iv) $14 x y, 42 y x$
(v) $4 m^2 p, 4 m p^2$
(vi) $12 x z, 12 x^2 z^2$

Answer:

Ex 10.1 Question 7.

Identify like terms in the following:
(a) - $x y^2,-4 y x^2, 8 x^2, 2 x y^2, 7 y,-11 x^2-100 x,-11 y x, 20 x^2 y,-6 x^2, y, 2 x y, 3 x$
(b) 10pq, 7p, 8q, $-p^2 q^2,-7 q p,-100 q,-23,12 q^2 p^2,-5 p^2, 41,2405 p, 78 q p, 13 p^2 q, q^2, 701 p^2$

Answer:

(a) Like terms are:
(i) $-x y^2, 2 x y^2$
(ii) $-4 y x^2, 20 x^2 y$
(iii) $8 x^2,-11 x^2,-6 x^2$
(iv) $7 y, y$
(v) $-100 x, 3 x$
(vi) $-11 y x, 2 x y$
(b) Like terms are:
(i) $10 p q,-7 p q, 78 p q$
(ii) $7 p, 2405 p$
(iii) $8 q,-100 q$
(iv) $-p^2 q^2, 12 p^2 q^2$
(v) $-12,41$
(vi) $-5 p^2, 701 p^2$
(vii) $13 p^2 q, q p^2$