Exercise 5 F
Q1 | Ex-5F | Class 8 | SChand Composite Maths | Algebraic Expressions and Special Products | myhelper
Question 1
Write down the squares of :
(i) p+5
Sol :
(ii) 2t+9
Sol :
(iii) 5c+2d
Sol :
(iv) $9 m+\frac{1}{4}$
Sol :
(v) $3 x+\frac{1}{3 x}$
Sol :
(vi) $\left(2 y^{2}+5 z^{2}\right)$
Sol :
(vii) $\left(7 x^{3}+\frac{1}{7} y^{3}\right)$
Sol :
(viii) $\left(\frac{1}{2} a^{4}+\frac{1}{3} b^{7}\right)$
Sol :
(ix) t-3
Sol :
(x) 7p-8q
Sol :
(xi) $8 m-\frac{1}{2}$
Sol :
(xii) $3 m^{3}-7 n^{4}$
Sol :
(xiii) $x^{3}-\frac{1}{x^{3}}$
Sol :
(xiv) $\frac{1}{5} p^{5}-\frac{1}{2} q^{6}$
Sol :
Q2 | Ex-5F | Class 8 | SChand Composite Maths | Algebraic Expressions and Special Products | myhelper
Question 2
Simplify:
(i) $\left(a^{3} b-x y^{3}\right)^{2}$
Sol :
(ii) $\left(\frac{3}{5} a-10 b\right)^{2}$
Sol :
(iii) $\left(2 x^{2}+\frac{1}{3 x^{2}}\right)^{2}$
Sol :
(iv) $\left(5 m^{3}-\frac{1}{5 m^{3}}\right)^{2}$
Sol :
Q3 | Ex-5F | Class 8 | SChand Composite Maths | Algebraic Expressions and Special Products | myhelper
Question 3
Using the identity for square of a binomial, evaluate the following:
(i) $(102)^{2}$
Sol :
(ii) $(501)^{2}$
Sol :
(iii) $(709)^{2}$
Sol :
(iv) $(59)^{2}$
Sol :
(v) $(199)^{2}$
Sol :
(vi) $(999)^{2}$
Sol :
Q4 | Ex-5F | Class 8 | SChand Composite Maths | Algebraic Expressions and Special Products | myhelper
Question 4
Find the value of the expression : $25 x^{2}+70 x+49$ if $x=-1$
Sol :
Q5 | Ex-5F | Class 8 | SChand Composite Maths | Algebraic Expressions and Special Products | myhelper
Question 5
If $\left(x+\frac{1}{x}\right)=12$, find the value of $\left(x^{2}+\frac{1}{x^{2}}\right)$
Sol :
Q6 | Ex-5F | Class 8 | SChand Composite Maths | Algebraic Expressions and Special Products | myhelper
Question 6
If $\left(x+\frac{1}{x}\right)=5$, find the values of $\left(x^{2}+\frac{1}{x^{2}}\right)$ and $\left(x^{4}+\frac{1}{x^{4}}\right)$.
Sol :
Q7 | Ex-5F | Class 8 | SChand Composite Maths | Algebraic Expressions and Special Products | myhelper
Question 7
If $x-\frac{1}{x}=7$, find the value of $\left(x^{2}+\frac{1}{x^{2}}\right)$
Sol :
Q8 | Ex-5F | Class 8 | SChand Composite Maths | Algebraic Expressions and Special Products | myhelper
Question 8
If $x-\frac{1}{x}=8$, find the values of $\left(x^{2}+\frac{1}{x^{2}}\right)$ and $\left(x^{4}+\frac{1}{x^{4}}\right)$.
Sol :
Q9 | Ex-5F | Class 8 | SChand Composite Maths | Algebraic Expressions and Special Products | myhelper
Question 9
If $x+y=9$ and $x y=16$, find the value of $\left(x^{2}+y^{2}\right)$.
Sol :
Multiple Choice Questions (MCQs)
Q10 | Ex-5F | Class 8 | SChand Composite Maths | Algebraic Expressions and Special Products | myhelper
Question 10
$(t-3)^{2}-(t+3)^{2}$ equals
(a) $2 t^{2}+18$
(b) $-12 t$
(c) $12 t$
(d) 18
Sol :
Q11 | Ex-5F | Class 8 | SChand Composite Maths | Algebraic Expressions and Special Products | myhelper
Question 11
If $x^{2}+\frac{1}{x^{2}}=27$, find the value of $x-\frac{1}{x}$
(a) 5
(b) 29
(c) $\sqrt{29}$
(d) 57
Sol :
Q12 | Ex-5F | Class 8 | SChand Composite Maths | Algebraic Expressions and Special Products | myhelper
Question 12
If $x-y=9$ and $x y=16$, find the value of $x^{2}+y^{2}$
(a) 113
(b) 49
(c) 65
(d) 97
Sol :
High Order Thinking Skills (HOTS)
Q13 | Ex-5F | Class 8 | SChand Composite Maths | Algebraic Expressions and Special Products | myhelper
Question 13
If $\left(a x^{3}+2\right)^{2}=a^{2} x^{6}+x^{3}+4$, then find $a$.
Sol :
Q14 | Ex-5F | Class 8 | SChand Composite Maths | Algebraic Expressions and Special Products | myhelper
Question 14
If $\sqrt{\frac{x}{y}}+\sqrt{\frac{y}{x}}=\frac{10}{3}$ and x+y=10 ,then find $x y$.
Sol :
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