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MATHEMATICS MCQ

Factorisation · ICSE STD 9 (ICSE - English Medium). 28 questions.

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28 questions · timed · auto-graded

MCQ 11 Mark
An expression is factorised as $\left(2 x^3+2 x^2+x\right)\left(x^2-2 x+2\right)$. Which of the following terms will appear in the simplest form of the above expression?
  • A
    $-2 x^3$
  • B
    $3 x^3$
  • C
    $6 x^3$
  • ✓
    $x^3$
Answer
Correct option: D.
$x^3$
D
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MCQ 21 Mark
If $x=\frac{a+b+c}{3}$, then $(x-a)^3+(x-b)^3+(x-c)^3$ can be factorised as :
  • A
    $(x-a)(x-b)(x-c)$
  • B
    $\frac{(x-a)(x-b)(x-c)}{3}$
  • ✓
    $3(x-a)(x-b)(x-c)$
  • D
    none of these
Answer
Correct option: C.
$3(x-a)(x-b)(x-c)$
C
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MCQ 31 Mark
$x^4+7 x^2+16$ can be factorised as :
  • ✓
    $\left(x^2+x+4\right)\left(x^2-x+4\right)$
  • B
    $\left(x^2+x-4\right)\left(x^2-x+4\right)$
  • C
    $\left(x^2-x-4\right)\left(x^2+x+4\right)$
  • D
    none of these
Answer
Correct option: A.
$\left(x^2+x+4\right)\left(x^2-x+4\right)$
A
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MCQ 41 Mark
One of the factors of $\left(x^2-4 x\right)\left(x^2-4 x-1\right)-20$ is :
  • A
    $x-1$
  • ✓
    $x-2$
  • C
    $x-4$
  • D
    $x+5$
Answer
Correct option: B.
$x-2$
B
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MCQ 51 Mark
Assertion (A) : $a^3-2 \sqrt{2} b^3$ can be factorised as $(a-2 \sqrt{2})\left(a^2+\sqrt{2} a b+2 b^2\right)$
Reason (R) : $x^3-y^3=(x-y)\left(x^2+x y+y^2\right)$.
  • A
    A is true, R is false
  • ✓
    A is false, R is true
  • C
    Both A and R are true
  • D
    Both A and R are false.
Answer
Correct option: B.
A is false, R is true
B
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MCQ 61 Mark
Assertion (A) : One of the factors of $(5 x+1)^2+\left(25 x^2-1\right)$ is $2 x$.
Reason (R) : $(a+b)^2=(a+b)(a+b)$
$a^2-b^2=(a+b)(a-b)$
  • A
    A is true, R is false
  • B
    A is false, R is true
  • ✓
    Both A and R are true
  • D
    Both A and R are false.
Answer
Correct option: C.
Both A and R are true
C
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MCQ 71 Mark
Factorization of $p^2-2 p-(q+1)(q-1)$ is :
  • A
    $(p+q-1)(p-q+1)$
  • B
    $(p-q+1)(p-q-1)$
  • ✓
    $(p+q-1)(p-q-1)$
  • D
    $(p+q+1)(p-q)$
Answer
Correct option: C.
$(p+q-1)(p-q-1)$
C
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MCQ 81 Mark
$7-12 m-4 m^2=$
  • ✓
    $(1-2 m)(7+2 m)$
  • B
    $(1+2 m)(7-2 m)$
  • C
    $(1+2 m)(7+2 m)$
  • D
    $(2 m-1)(7+2 m)$
Answer
Correct option: A.
$(1-2 m)(7+2 m)$
A
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MCQ 91 Mark
$1-x^9=(1-x)\left(1+x+x^2\right)$ __________
  • A
    $\left(1-x^3+x^6\right)$
  • ✓
    $\left(1+x^3+x^6\right)$
  • C
    $\left(1-x^3-x^6\right)$
  • D
    $\left(1+x^3-x^6\right)$
Answer
Correct option: B.
$\left(1+x^3+x^6\right)$
B
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MCQ 101 Mark
$\sqrt{3} x^2+11 x+6 \sqrt{3}=$
  • A
    $(\sqrt{3} x+2)(x-3 \sqrt{3})$
  • ✓
    $(\sqrt{3} x+2)(x+3 \sqrt{3})$
  • C
    $(\sqrt{3} x-2)(x-3 \sqrt{3})$
  • D
    $(x-2)(x+3 \sqrt{3})$
Answer
Correct option: B.
$(\sqrt{3} x+2)(x+3 \sqrt{3})$
B
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MCQ 111 Mark
$12 a^2-27 b^4=$
  • A
    $3\left(2 a+3 b^2\right)\left(2 a-b^2\right)$
  • B
    $\left(2 a+3 b^2\right)\left(2 a-3 b^2\right)$
  • C
    $3\left(2 a+3 b^2\right)\left(a-3 b^2\right)$
  • ✓
    $3\left(2 a+3 b^2\right)\left(2 a-3 b^2\right)$
Answer
Correct option: D.
$3\left(2 a+3 b^2\right)\left(2 a-3 b^2\right)$
D
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MCQ 121 Mark
Factorization of $3 a(3 a+2 c)-4 b(b+c)$ is :
  • A
    $(3 a+2 b)(3 a+2 b+2 c )$
  • B
    $(3 a-2 b)(3 a-2 b+2 c )$
  • ✓
    $(3 a-2 b)(3 a+2 b+2 c)$
  • D
    $(3 a-2 b)(3 a+2 b-2 c )$
Answer
Correct option: C.
$(3 a-2 b)(3 a+2 b+2 c)$
C
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MCQ 131 Mark
$16(2 a-b)^2-9(a+b)^2=$
  • ✓
    $(5 a-7 b)(11 a-b)$
  • B
    $(5 a+7 b)(11 a-b)$
  • C
    $(5 a-7 b)(11 a+b)$
  • D
    $(5 a+7 b)(11 a+b)$
Answer
Correct option: A.
$(5 a-7 b)(11 a-b)$
A
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MCQ 151 Mark
The value of $(1+x)^2\left(1+y^2\right)-\left(1+x^2\right)(1+y)^2$ is :
  • A
    $2(x-y)(1+x y)$
  • B
    $(x-y)(1-x y)$
  • ✓
    $2(x-y)(1-x y)$
  • D
    $2(x+y)(1-x y)$
Answer
Correct option: C.
$2(x-y)(1-x y)$
C
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MCQ 161 Mark
$b^2-a c-b c+a b=$
  • ✓
    $(a+b)(b-c)$
  • B
    $(b-a)(b-c)$
  • C
    $(a-b)(b+c)$
  • D
    $(a-b)(b-c)$
Answer
Correct option: A.
$(a+b)(b-c)$
A
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MCQ 171 Mark
Factorization of $p^2-2 p-(q+1)(q-1)$ is :
  • A
    (p + q - 1)(p - q + 1)
  • B
    (p - q + 1)(p - q - 1)
  • ✓
    (p + q - 1)(p - q - 1)
  • D
    (p + q + 1)(p - q)
Answer
Correct option: C.
(p + q - 1)(p - q - 1)
C
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MCQ 181 Mark
$7-12 m-4 m^2=$
  • ✓
    (1 - 2m)(7 + 2m)
  • B
    (1 + 2m)(7 - 2m)
  • C
    (1 + 2m)(7 + 2m)
  • D
    (2m - 1)(7 + 2m)
Answer
Correct option: A.
(1 - 2m)(7 + 2m)
A
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MCQ 191 Mark
$1-x^9=(1-x)\left(1+x+x^2\right)$ _________
  • A
    $\left(1-x^3+x^6\right)$
  • ✓
    $\left(1+x^3+x^6\right)$
  • C
    $\left(1-x^3-x^6\right)$
  • D
    $\left(1+x^3-x^6\right)$
Answer
Correct option: B.
$\left(1+x^3+x^6\right)$
B
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MCQ 201 Mark
$\sqrt{3} x^2+11 x+6 \sqrt{3}=$
  • A
    $(\sqrt{3} x+2)(x-3 \sqrt{3})$
  • ✓
    $(\sqrt{3} x+2)(x+3 \sqrt{3})$
  • C
    $(\sqrt{3} x-2)(x-3 \sqrt{3})$
  • D
    $(x-2)(x+3 \sqrt{3})$
Answer
Correct option: B.
$(\sqrt{3} x+2)(x+3 \sqrt{3})$
B
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MCQ 211 Mark
$12 a^2-27 b^4=$
  • A
    $3\left(2 a+3 b^2\right)\left(2 a-b^2\right)$
  • B
    $\left(2 a+3 b^2\right)\left(2 a-3 b^2\right)$
  • C
    $3\left(2 a+3 b^2\right)\left(a-3 b^2\right)$
  • ✓
    $3\left(2 a+3 b^2\right)\left(2 a-3 b^2\right)$
Answer
Correct option: D.
$3\left(2 a+3 b^2\right)\left(2 a-3 b^2\right)$
D
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MCQ 221 Mark
Factorization of 3a(3a + 2c) - 4b(b + c) is :
  • A
    (3a + 2b)(3a + 2b + 2c)
  • B
    (3a - 2b)(3a - 2b + 2c)
  • ✓
    (3a - 2b)(3a + 2b + 2c)
  • D
    (3a - 2b)(3a + 2b - 2c)
Answer
Correct option: C.
(3a - 2b)(3a + 2b + 2c)
C
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MCQ 231 Mark
$16(2 a-b)^2-9(a+b)^2=$
  • ✓
    (5a - 7b)(11a - b)
  • B
    (5a + 7b)(11a - b)
  • C
    (5a - 7b)(11a + b)
  • D
    (5a + 7b)(11a + b)
Answer
Correct option: A.
(5a - 7b)(11a - b)
A
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MCQ 251 Mark
The value of $(1+x)^2\left(1+y^2\right)-\left(1+x^2\right)(1+y)^2$ is :
  • A
    2(x - y)(1 + xy)
  • B
    (x - y)(1 - xy)
  • ✓
    2(x - y)(1 - xy)
  • D
    2(x + y)(1 - xy)
Answer
Correct option: C.
2(x - y)(1 - xy)
C
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MCQ 261 Mark
$b^2-a c-b c+a b=$
  • ✓
    (a + b)(b - c)
  • B
    (b - a)(b - c)
  • C
    (a - b)(b + c)
  • D
    (a - b)(b - c)
Answer
Correct option: A.
(a + b)(b - c)
A
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MCQ 271 Mark
Assertion (A) : $a^3-2 \sqrt{2} b^3$ can be factorised as $(a-2 \sqrt{2})\left(a^2+\sqrt{2} a b+2 b^2\right)$
Reason (R) : $x^3-y^3=(x-y)\left(x^2+x y+y^2\right)$.
  • A
    A is true, R is false
  • ✓
    A is false, R is true
  • C
    Both A and R are true
  • D
    Both A and R are false.
Answer
Correct option: B.
A is false, R is true
B
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MCQ 281 Mark
Assertion (A) : One of the factors of $(5 x+1)^2+\left(25 x^2-1\right)$ is $2 x$.
Reason (R):
$\begin{aligned}(a+b)^2 & =(a+b)(a+b) \\ a^2-b^2 & =(a+b)(a-b)\end{aligned}$
  • A
    A is true, R is false
  • B
    A is false, R is true
  • ✓
    Both A and R are true
  • D
    Both A and R are false.
Answer
Correct option: C.
Both A and R are true
C
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