MCQ

MCQ 11 Mark

Factors of $x^2-4 x y+4 y^2$ are

A
$(x-2 y)(x+2 y)$
✓
$(x-2 y)(x-2 y)$
C
$(x+2 y)(x+2 y)$
D
none of these

Answer

Correct option: B.

$(x-2 y)(x-2 y)$

$x^2-4 x y+4 y^2$
$=(x)^2-2 \times x \times 2 y+(2 y)^2=(x-2 y)^2$
$=(x-2 y)(x-2 y) $

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MCQ 21 Mark

Factors of $16 x^2+40 x+25$ are

✓
$(4 x+5)(4 x+5)$
B
$(4 x+5)(4 x-5)$
C
$(4 x+5)(4 x+8)$
D
none of these

Answer

Correct option: A.

$(4 x+5)(4 x+5)$

$16 x^2+40 x+25$
$=(4 x)^2+2 \times 4 x \times 5+(5)^2$
$=(4 x+5)^2$
$=(4 x+5)(4 x+5)$

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MCQ 31 Mark

Factors of $3 x+7 x-6$ are

✓
$(3 x-2)(x+3)$
B
$(3 x+2)(x-3)$
C
$(3 x-2)(x-3)$
D
$(3 x+2)(x+3)$

Answer

Correct option: A.

$(3 x-2)(x+3)$

$3 x^2+7 x-6$
$=3 x^2+9 x-2 x-6$
$=3 x(x+3)-2(x+3)$
$=(3 x-2)(x+3)$

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MCQ 41 Mark

Factors of $p^4-81$ are

A
$\left(p^2-9\right)\left(p^2+9\right)$
B
$(p+3)^2(p-3)^2$
✓
$(p+3)(p-3)\left(p^2+9\right)$
D
none of these

Answer

Correct option: C.

$(p+3)(p-3)\left(p^2+9\right)$

$p^4-81=\left(p^2\right)^2-(9)^2$
$=\left(p^2+9\right)\left(p^2-9\right)$
$=\left(p^2+9\right)\left\{(p)^2-(3)^2\right\}$
$=\left(p^2+9\right)(p+3)(p-3)$

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MCQ 51 Mark

Factors of $63 a^2-112 b^2$ are

A
$63(a-2 b)(a+2 b)$
B
$7(3 a+2 b)(3 a-2 b)$
✓
$7(3 a+4 b)(3 a-4 b)$
D
none of these

Answer

Correct option: C.

$7(3 a+4 b)(3 a-4 b)$

Factors of $63 a^2-112 b^2$ are
$=7\left(9 a^2-16 b^2\right)$
$=7\left[(3 a)^2-(4 b)^2\right]$
$=7(3 a+4 b)(3 a-4 b)$

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MCQ 61 Mark

Factors of $(l\ m + l) + m + 1$ are

A
$(lm + l )(m + l)$
B
$(lm + m)(l + 1)$
C
$l(m + 1)$
✓
$(l + 1)(m + 1)$

Answer

Correct option: D.

$(l + 1)(m + 1)$

Factors of $lm + l + m + 1$ are $l(m + 1) + l (m + 1) = (m + 1)(l + 1) $

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MCQ 71 Mark

Factors of $y\ (y – z) + 9\ (z – y)$ are

A
$(y – z) (y + 9)$
B
$(z – y) (y + 9)$
✓
$(y – z) (y – 9)$
D
none of these

Answer

Correct option: C.

$(y – z) (y – 9)$

$y\ (y – z) + 9(z – y)$
$= y\ (y – z) – 9\ (y – z)$
$= (y – z) (y – 9) $

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MCQ 81 Mark

Factors of $49 p^3 q-36 p q$ are

A
$p(7 p+6 q)(7 p-6 q)$
B
$q(7 p-6)(7 p+6)$
✓
$p q(7 p+6)(7 p-6)$
D
none of these

Answer

Correct option: C.

$p q(7 p+6)(7 p-6)$

$49 p^2 q-36 p q$
$=p q\left(49 p^2-36\right)$
$=p q\left[(7 p)^2-(6)^2\right]$
$=p q(7 p+6)(7 p-6)$

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MCQ 91 Mark

Factors of $6xy – 4y + 6 – 9x$ are

A
$(3y – 2) (2x – 3)$
B
$(3x – 2) (2y – 3)$
C
$(2y – 3) (2 – 3x)$
D
none of these

Answer

$6\ xy – 4y + 6 – 9x$
$= 6\ xy – 9x – 4y + 6$
$= 3x\ (2y – 3) -2(2y – 3)$
$= (2y – 3) (3x – 2)$

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MCQ 101 Mark

Factors of $12 a^2 b+15 a b^2$ are

A
$3 a(4 a b+5 b 2)$
✓
$3 a b(4 a+5 b)$
C
$3 b\left(4 a^2+5 a b\right)$
D
none of these

Answer

Correct option: B.

$3 a b(4 a+5 b)$

$12 a^2 b+15 a b^2=3 a b(4 a+5 b)$

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MCQ 111 Mark

$\text{H.C.F.}$ of $6 a b c, 24 a b^2, 12 a^2 b$ is

✓
$6 ab$
B
$6 a b^2$
C
$6 a^2 b$
D
$6 a b c$

Answer

Correct option: A.

$6 ab$

$\text{H.C.F}$. of babe, $24 a b^2, 12 a^2 b$
$= \text{H.C.F}$. of $6,24,12 \times \text{H.C.F}$. of $a b c, a b^2, a^2 b$
$=6 \times a \times b=6 a b$

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