Exercise 10.2 (Revised) - Chapter 12 - Algebraic Expressions - Ncert Solutions class 7 - Maths
Updated On 26-08-2025 By Lithanya
You can Download the Exercise 10.2 (Revised) - Chapter 12 - Algebraic Expressions - Ncert Solutions class 7 - Maths with expert answers for all chapters. Perfect for Tamil & English Medium students to revise the syllabus and score more marks in board exams. Download and share it with your friends
Share this to Friend on WhatsApp
Chapter 10 - Algebraic Expressions | NCERT Solutions for Class 7 Maths
Ex 10.2 Question 1.
If $m=2$, find the value of:
(i) $m-2$
(ii) $3 m-5$
(iii) $9-5 m$
(iv) $3 m^2-2 m-7$
(v) $\frac{5 m}{2}-4$
Answer:
(i) $m-2=2-2$ [Putting $m=2$ ]
$
=0
$
(ii) $3 m-5=3 \times 2-5$ [Putting $m=2$ ]
$
=6-5=1
$
(iii) $9-5 m=9-5 \times 2$ [Putting $m=2$ ]
$
=9-10=-1
$
(iv) $3 m^2-2 m-7=3(2)^2-2(2)-7$ [Putting $m=2$ ]
$
\begin{aligned}
& =3 \times 4-2 \times 2-7=12-4-7 \\
& =12-11=1
\end{aligned}
$
(v) $\frac{5 m}{2}-4=\frac{5 \times 2}{2}-4$
[Putting $m=2$ ]
$
=5-4=1
$
Ex 10.2 Question 2
If $p=-2$, find the value of:
(i) $4 p+7$
(ii) $-3 p^2+4 p+7$
(iii) $-2 p^3-3 p^2+4 p+7$
Answer:
(i) $4 p+7=4(-2)+7$
[Putting $p=-2$ ]
$
=-8+7=-1
$
$
\begin{aligned}
& \text { (ii) }-3 p^2+4 p+7=-3(-2)^2+4(-2)+7 \text { [Putting } p=-2 \text { ] } \\
& =-3 \times 4-8+7=-12-8+7 \\
& =-20+7=-13
\end{aligned}
$
$
\begin{aligned}
& \text { (iii) }-2 p^3-3 p^2+4 p+7=-2(-2)^3-3(-2)^2+4(-2)+7 \text { [Putting } p=-2 \text { ] } \\
& ==-2 \times(-8)-3 \times 4-8+7=16-12-8+7 \\
& =-20+23=3
\end{aligned}
$
Question 3.
Find the value of the following expressions, when $x=-1$ :
(i) $2 x-7$
(ii) $-x+2$
(iii) $x^2+2 x+1$
(iv) $2 x^2-x-2$
Answer:
(i) $2 x-7=2(-1)-7$
[Putting $x=-1$ ]
$
=-2-7=-9
$
(ii) $-x+2=-(-1)+2$
[Putting $x=-1$ ]
$
=1+2=3
$
(iii) $x^2+2 x+1=(-1)^2+2(-1)+1$ [Putting $x=-1$ ]
$
=1-2+1=2-2=0
$
(iv) $2 x^2-x-2=2(-1)^2-(-1)-2$ [Putting $x=-1$ ]
$
\begin{aligned}
& =2 \times 1+1-2=2+1-2 \\
& =3-2 \\
& =1
\end{aligned}
$
Ex 10.2 Question 4.
If $a=2, b=-2$, find the value of:
(i) $a^2+b^2$
(ii) $a^2+a b+b^2$
(iii) $a^2-b^2$
Answer:
(i) $a^2+b^2=(2)^2+(-2)^2$ [Putting $\left.a=2, b=-2\right]$
$
=4+4=8
$
(ii) $a^2+a b+b^2=(2)^2+(2)(-2)+(-2)^2$ [Putting $\left.a=2, b=-2\right]$
$
=4-4+4=4
$
(iii) $a^2-b^2=(2)^2-(-2)^2$ [Putting $a=2, b=-2$ ]
$
=4-4=0
$
Ex 10.2 Question 5.
When $a=0, b=-1$, find the value of the given expressions:
(i) $2 a+2 b$
(ii) $2 a^2+b^2+1$
(iii) $2 a^2 b+2 a b^2+a b$
(iv) $a^2+a b+2$
Answer:
(i) $2 a+2 b=2(0)+2(-1)$
[Putting $a=0, b=-1$ ]
$
=0-2=-2
$
(ii) $2 a^2+b^2+1=2(0)^2+(-1)^2+1$ [Putting $\left.a=0, b=-1\right]$
$
=2 \times 0+1+1=0+2=2
$
(iii) $2 a^2 b+2 a b^2+a b=2(0)^2(-1)+2(0)(-1)^2+(0)(-1)$ [Putting $a=0, b=-1$ ]
$
=0+0+0=0
$
(iv) $a^2+a b+2=(0)^2+(0)(-1)+2[$ Putting $a=0, b=-1]$
$
=0+0+2=2
$
Ex 10.2 Question 6.
Simplify the expressions and find the value if $x=2$ :
(i) $x+7+4(x-5)$
(ii) $3(x+2)+5 x-7$
(iii) $6 x+5(x-2)$
(iv) $4(2 x-1)+3 x+11$
Answer:
(i) $x+7+4(x-5)=x+7+4 x-20=x+4 x+7-20$
$
\begin{aligned}
& =5 x-13=5 \times 2-13 \text { [Putting } x=2 \text { ] } \\
& =10-13=-3
\end{aligned}
$
(ii) $3(x+2)+5 x-7=3 x+6+5 x-7=3 x+5 x+6-7$
$
=8 x-1=8 \times 2-1 \text { [Putting } x=2]
$
$
=16-1=15
$
$
\begin{aligned}
& \text { (iii) } 6 x+5(x-2)=6 x+5 x-10=11 x-10 \\
& =11 \times 2-10 \text { [Putting } x=2 \text { ] } \\
& =22-10=12
\end{aligned}
$
(iv) $4(2 x-1)+3 x+11=8 x-4+3 x+11=8 x+3 x-4+11$ $=11 x+7=11 \times 2+7$ [Putting $x=-1]$
$
=22+7=29
$
Ex 10.2 Question 7.
Simplify these expressions and find their values if $x=3, a=-1, b=-2$ :
(i) $3 x-5-x+9$
(ii) $2-8 x+4 x+4$
(iii) $3 a+5-8 a+1$
(iv) $10-3 b-4-5 b$
(v) $2 a-2 b-4-5+a$
Answer:
(i) $3 x-5-x+9=3 x-x-5+9=2 x+4$
$
\begin{aligned}
& =2 \times 3+4 \text { [Putting } x=3 \text { ] } \\
& =6+4=10
\end{aligned}
$
$
\begin{aligned}
& \text { (ii) } 2-8 x+4 x+4=-8 x+4 x+2+4=-4 x+6 \\
& =-4 \times 3+6 \text { [Putting } x=3 \text { ] } \\
& =-12+6=-6 \\
& \text { (iii) } 3 a+5-8 a+1=3 a-8 a+5+1=-5 a+6 \\
& =-5(-1)+6 \text { [Putting } a=-1 \text { ] } \\
& =5+6=11
\end{aligned}
$
$
\begin{aligned}
& \text { (iii) } 3 a+5-8 a+1=3 a-8 a+5+1=-5 a+6 \\
& =-5(-1)+6 \text { [Putting } a=-1 \text { ] } \\
& =5+6=11
\end{aligned}
$
(iv) $10-3 b-4-5 b=-3 b-5 b+10-4=-8 b+6$
$\begin{aligned}
&\begin{aligned}
& =-8(-2)+6 \text { [Putting } b=-2] \\
& =16+6=22
\end{aligned}\\
&\begin{aligned}
& \text { (v) } 2 a-2 b-4-5+a=2 a+a-2 b-4-5 \\
& \text { = } 3 a-2 b-9=3(-1)-2(-2)-9 \text { [Putting } a=-1, b=-2 \text { ] } \\
& =-3+4-9=-8
\end{aligned}
\end{aligned}$
Ex 10.2 Question 8.
(i) If $z=10$, find the value of $z^3-3(z-10)$.
(ii) If $p=-10$, find the value of $p^2-2 p-100$.
Answer:
(i) $z^3-3(z-10)=(10)^3-3(10-10)$ [Putting $z=10$ ]
$
=1000-3 \times 0=1000-0=1000
$
(ii) $p^2-2 p-100=(-10)^2-2(-10)-100$ [Putting $p=-10$ ]
$
=100+20-100=20
$
Ex 10.2 Question 9.
What should be the value of $a$ if the value of $2 x^2+x-a$ equals to 5, when $x=0$ ?
Answer:
Given: $2 x^2+x-a=5$
$
\begin{aligned}
& \Rightarrow 2(0)^2+0-a=5 \text { [Putting } x=0 \text { ] } \\
& \Rightarrow 0+0-a=5 \Rightarrow a=-5
\end{aligned}
$
Hence, the value of $a$ is -5 .
Ex 10.2 Question 10.
Simplify the expression and find its value when $a=5$ and $b=-3$ :
$
2\left(a^2+a b\right)+3-a b
$
Answer:
Given: $2\left(a^2+a b\right)+3-a b$
$\begin{aligned}
& \Rightarrow 2 a^2+2 a b+3-a b \Rightarrow 2 a^2+2 a b-a b+3 \\
& \Rightarrow 2 a^2+a b+3 \\
& \Rightarrow 2(5)^2+(5)(-3)+3 \text { [Putting } a=5, b=-3 \text { ] } \\
& \Rightarrow 2 \times 25-15+3 \\
& \Rightarrow 50-15+3 \\
& \Rightarrow 38
\end{aligned}$
