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MATHS [1 Mark Question Answer]

Identities · ICSE STD 8 (ICSE - English Medium). 24 questions.

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[1 Mark Question Answer]

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24 questions · timed · auto-graded

Question 11 Mark
Find the square of $\frac{5 a}{6 b}-\frac{6 b}{5 a}$
Answer
$\left(\frac{5 a}{6 b}-\frac{6 b}{5 a}\right)^2=\left(\frac{5 a}{6 b}\right)^2+\left(\frac{6 b}{5 a}\right)^2-2 \times \frac{5 a}{6 b} \times \frac{6 b}{5 a} $
$ =\frac{25 a^2}{36 a^2}-2+\frac{36 b^3}{25 a^2}$
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Question 21 Mark
Find the square of  $3a − 2b − 5c$
Answer
$(3a − 2b − 5c)^2$
$= (3a)^2 + (−2b)^2+ (−5c)^2 + 2 \times 3a \times −2b + 2 \times (−2b)(−5c) + 2 \times −5c \times 3a$
$= 9a^2 + 4b^2 + 25c^2− 12ab + 20bc − 30ca$
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Question 31 Mark
Find the square of $x − 2y +1$
Answer
$(x − 2y +1)^2$
$= (x)^2 + (−2y)^2+ (1)^2 + 2 \times x \times −2y + 2 \times (−2y) \times 1 + 2 \times 1 \times x$
$= x^2 + 4y^2 + 1 − 4xy − 4y + 2x$
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Question 41 Mark
Find the square of $2 a-\frac{1}{a}$
Answer
$\left(2 a-\frac{1}{a}\right)^2=(2 a)^2+\left(\frac{1}{a}\right)^2-2 \times 2 a \times \frac{1}{a} $
$ =4 a^2+\frac{1}{a^2}-4$
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Question 51 Mark
Find the square of $a+\frac{1}{5 a}$
Answer
$\left(a+\frac{1}{5 a}\right)^2=(a)^2+\left(\frac{1}{5 a}\right)^2+2 \times a \times \frac{1}{5 a} $
$=a^2+\frac{1}{25 a^2}+\frac{2}{5}$
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Question 61 Mark
Find the square of $2x − 5y$
Answer
$(2x − 5y)^2$
$= (2x)^2 + (5y)^2 − 2 \times 2x \times 5y$
$= 4x^2 + 25y^2 − 20xy$
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Question 71 Mark
Find the square of $x+ 3y$
Answer
$(x + 3y)^2$
$= (x)^2 + (3y)^2+ 2\times x \times 3y$
$= x^2 + 9y^2+ 6xy$
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Question 81 Mark
Expand : $\left(2 \mathrm{x}-\frac{1}{2 \mathrm{x}}\right)^2$
Answer
$\left(2 x-\frac{1}{2 x}\right)^2=(2 x)^2+\left(\frac{1}{2 x}\right)^2-2 \times 2 x \times \frac{1}{2 x} $
$ =4 x^2+\frac{1}{4 x^2}-2$
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Question 91 Mark
Expand : $\left(3 \mathrm{x}+\frac{1}{3 \mathrm{x}}\right)^2$
Answer
$ \left(3 \mathrm{x}+\frac{1}{3 \mathrm{x}}\right)^2=(3 \mathrm{x})^2+\left(\frac{1}{3 \mathrm{x}}\right)^2+2 \times 3 \mathrm{x} \times \frac{1}{3 \mathrm{x}}$
$ =9 \mathrm{x}^2+\frac{1}{9 \mathrm{x}^2}+2$
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Question 101 Mark
Expand : $(a+b−c)^2$
Answer
$(a+b−c)^2$
$= (a)^2 + (b)^2 +(−c)^2 + 2 \times a \times b + 2 \times b \times (−c) + 2 \times (−c) \times (a)$
$= a^2 + b^2 + c^2 + 2ab − 2bc − 2ca$
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Question 111 Mark
Expand : $\left(2 a-\frac{1}{a}\right)^2$
Answer
$ \left(2 \mathrm{a}-\frac{1}{\mathrm{a}}\right)^2=(2 \mathrm{a})^2+\left(\frac{1}{\mathrm{a}}\right)^2-2 \times 2 \mathrm{a} \times \frac{1}{\mathrm{a}}$
$ =4 \mathrm{a}^2+\frac{1}{\mathrm{a}^2}-4$
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Question 121 Mark
Expand :$(a – 2b)^2$
Answer
$(a – 2b)^2$
$= (a)^2 + (2b)^2− 2 \times a \times 2b ........[(a−b)^2$
$= a^2 + b^2− 2ab]$
$= a^2+ 4b^2− 4ab$
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Question 131 Mark
Expand : $(2a + b)^2$
Answer
$(2a + b)^{2}$
$= (2a)^2 + (b)^2 + 2 \times 2a \times b ......[(a+b)^2$
$= a^2 + b^2+ 2ab]$
$= 4a^2 + b^2 + 4ab$
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Question 151 Mark
Use the direct method to evaluate : $(3x^2+5y^2) (3x^2−5y^2)$
Answer
Note: $(a+b) (a−b)$
$= a^2 − b^2(3x^2+5y^2) (3x^2−5y^2)$
$= (3x^2)^2 − (5y^2)^2$
$= 9x^4 − 25y^4$
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Question 161 Mark
Use the direct method to evaluate : $(ab+x^2) (ab−x^2)$
Answer
Note: $(a+b) (a−b)$
$= a^2 − b^2(ab+x^2) (ab−x^2)$
$= (ab)^2 − (x^2)^2$
$= a^2b^2 − x^4$
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Question 171 Mark
Use the direct method to evaluate : $(xy+4) (xy−4)$
Answer
Note: $(a+b) (a−b)$
$= a^2 − b^2(xy+4) (xy−4)$
$= (xy)^2 − (4)^2$
$= x^2y^2 − 16$
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Question 181 Mark
Use the direct method to evaluate : $(2a+3) (2a−3)$
Answer
Note : $(a+b) (a−b)$
$= a^2 − b^2(2a+3) (2a−3)$
$= (2a)^2 − (3)^2$
$= 4a^2− 9$
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Question 191 Mark
Use the direct method to evaluate : $(2+a) (2−a)$
Answer
Note: $(a+b) (a−b)$
$= a^2 − b^2(2+a) (2−a)$
$= (2)^2 − (a)^2$
$= 4 − a^2$
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Question 201 Mark
Use the direct method to evaluate : $(x+1) (x−1)$
Answer
Note: $(a+b) (a−b)$
$= a^2 − b^2(x+1) (x−1)$
$= (x)^2 − (1)^2$
$= x^2− 1$
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Question 211 Mark
Use the direct method to evaluate the following products : $(8 – b) (3 + b)$
Answer
$(8 – b) (3 + b)$
$= (8 \times 3) + (8 \times b) + (−b \times 3) + (−b \times b)$
$= 24 + 8b − 3b − b^2$
$= 24 + 5b − b^2$
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Question 221 Mark
Use the direct method to evaluate the following products : $(3x – 2y) (2x + y)$
Answer
$(3x – 2y) (2x + y)$
$= (3x \times 2x) + (3x \times y) + (−2y \times 2x) + (−2y \times y)$
$= 6x^2 + 3xy − 4xy − 2y^2$
$= 6x^2 − xy − 2y^2$
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Question 231 Mark
Use the direct method to evaluate the following products : $(b – 3) (b – 5)$
Answer
$(b – 3) (b – 5)$
$= (b \times b) + (b \times −5) + (−3) \times b + (−3) (−5)$
$= b^2 − 5b − 3b + 15$
$= b^2− 8b + 15$
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Question 241 Mark
Use the direct method to evaluate the following products : $(a – 8) (a + 2)$
Answer
$(a – 8) (a + 2)$
$= (a \times a) + (a \times 2) + (−8)\times a + (−8)(2)$
$= a^2+ 2a − 8a − 16$
$= a^2 − 6a − 16$
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[1 Mark Question Answer] - MATHS STD 8 Questions - Vidyadip