S.chand Class 8 Maths Solution Chapter 5 Algebraic Expressions and Special Products Exercise 5 F

  Exercise 5 F

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Q1 | Ex-5F | Class 8 | SChand Composite Maths | Algebraic Expressions and Special Products | myhelper

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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 :

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Q2 | Ex-5F | Class 8 | SChand Composite Maths | Algebraic Expressions and Special Products | myhelper

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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 :

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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 :

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Question 4

Find the value of the expression : $25 x^{2}+70 x+49$ if $x=-1$

Sol :

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Q5 | Ex-5F | Class 8 | SChand Composite Maths | Algebraic Expressions and Special Products | myhelper

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Question 5

If $\left(x+\frac{1}{x}\right)=12$, find the value of $\left(x^{2}+\frac{1}{x^{2}}\right)$

Sol :

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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 :

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Question 7

If $x-\frac{1}{x}=7$, find the value of $\left(x^{2}+\frac{1}{x^{2}}\right)$

Sol :

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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 :

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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)

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Question 10

$(t-3)^{2}-(t+3)^{2}$ equals

(a) $2 t^{2}+18$

(b) $-12 t$

(c) $12 t$

(d) 18

Sol :

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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 :

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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)

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Question 13

 If $\left(a x^{3}+2\right)^{2}=a^{2} x^{6}+x^{3}+4$, then find $a$.

Sol :

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Question 14

If $\sqrt{\frac{x}{y}}+\sqrt{\frac{y}{x}}=\frac{10}{3}$ and x+y=10 ,then find $x y$.

Sol :