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Maths M.C.Q. [1 Marks Each]

Factorisation · Jharkhand Board (JAC) STD 8 (Jharkhand - English Medium). 39 questions.

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M.C.Q. [1 Marks Each]

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39 questions · auto-graded multiple-choice test.

MCQ 11 Mark
Tick $(\checkmark)$ the correct answer: $x^3- 144x = ?$
  • A
    $ x(x-12)^2 $
  • B
    $ x(x+12)^2 $
  • ✓
    $ x(x-12)(x+12)$
  • D
    None of these
Answer
Correct option: C.
$ x(x-12)(x+12)$
$ x^3-144 x $
$ =x\left(x^2-144\right) $
$ =x\left\{(x)^2-(12)^2\right\} $
$ =x(x-12)(x+12) $
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MCQ 21 Mark
Tick $(\checkmark)$ the correct answer: $x^2-x z+x y-y z = ?$
  • A
    $(x - y)(x + z)$
  • B
    $(x - y)(x - z)$
  • ✓
    $(x + y)(x - z)$
  • D
    $(x - y)(z - x)$
Answer
Correct option: C.
$(x + y)(x - z)$
 $x^2-x z+x y-y z$
$= x(x - z) + y(x - z)$
$= (x + y) (x - z)$
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MCQ 31 Mark
Tick $(\checkmark)$ the correct answer: $ 2 x^2+5 x+3 = ?$
  • A
    $(x + 3)(2x + 1)$
  • B
    $(x + 1)(2x + 3)$
  • C
    $(2x + 5)(x − 3)$
  • ✓
    None of these
Answer
Correct option: D.
None of these
$ 2 x^2+5 x+3 $
$ =2 x^2+2 x+3 x+3 $
$= 2x(x + 1) + 3(x + 1)$
$= (2x + 3) (x + 1)$
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MCQ 41 Mark
Tick $(\checkmark)$ the correct answer: $ x^3-x = ?$
  • A
    $x(x^2- x)$
  • B
    $x(x - x^2)$
  • C
    $x(1 + x)(1 - x)$
  • ✓
    $x(x + 1)(x - 1)$
Answer
Correct option: D.
$x(x + 1)(x - 1)$
$ x^3-x $
$ =x\left(x^2-1\right) $
$= x(x - 1)(x + 1)$
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MCQ 51 Mark
Tick $(\checkmark)$ the correct answer: $(2x - 32x^3) = ?$
  • A
    $2(x - 4)(x + 4)$
  • B
    $2x(1 - 2x)^2$
  • C
    $2x(1 + 2x)^2$
  • ✓
    $2x(1 - 4x)(1 + 4x)$
Answer
Correct option: D.
$2x(1 - 4x)(1 + 4x)$
 $ 2 x-32 x^3=2 x\left(1-16 x^2\right)$
$=2 x\left\{(1)^2-(4 x)^2\right\} $
$= 2x(1 - 4x)(1 + 4x)$
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MCQ 61 Mark
Tick $(\checkmark)$ the correct answer: $ab - mn + an - bm = ?$
  • A
    $(a - b)(m - n)$
  • ✓
    $(a - m)(b + n)$
  • C
    $(a - n)(m + b)$
  • D
    $(m - a)(n - b)$
Answer
Correct option: B.
$(a - m)(b + n)$
$ab - mn + an - bm$
$= ab + an - bm - mn$
$= a(b + n) - m(b + n)$
$= (a - m)(b + n)$
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MCQ 71 Mark
Tick $(\checkmark)$ the correct answer: $ x^2+4 x-21 = ?$
  • A
    $(x - 7)(x + 3)$
  • ✓
    $(x + 7)(x - 3)$
  • C
    $(x - 7)(x - 3)$
  • D
    $(x + 7)(x + 3)$
Answer
Correct option: B.
$(x + 7)(x - 3)$
 $ x^2+4 x-21 $
$ =x^2+7 x-3 x-21 $
$= x(x + 7) - 2(x + 7)$
$= (x - 3)(x + 7)$
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MCQ 81 Mark
Tick $(\checkmark)$ the correct answer: $ 4 z^2-8 z+3 = ?$
  • ✓
    $(2z - 1)(2z - 3)$
  • B
    $(2z + 1)(3 - 2z)$
  • C
    $(2z + 3)(3z - 1)$
  • D
    $(z - 1)(4z - 3)$
Answer
Correct option: A.
$(2z - 1)(2z - 3)$
 $ 4 z^2-8 z+3 $
$ =4 z^2-6 z-2 z+3 $
$\{4 × 3 = 12, 12 = (-6) × (-2), -8 = -6 - 2\}$
$= 2z(2z - 3) - 1(2z - 3)$
$= (2z - 1)(2z - 3)$
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MCQ 91 Mark
Tick $(\checkmark)$ the correct answer: $12 m^2-27= ?$
  • A
    $(2m - 3)(3m - 9)$
  • B
    $3(2m - 9)(3m - 1)$
  • ✓
    $3(2m - 3)(2m + 3)$
  • D
    None of these
Answer
Correct option: C.
$3(2m - 3)(2m + 3)$
 $12 m^2-27$
$= 3(4m^2- 9)$
$= 3(2m - 3)(2m + 3)$
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MCQ 101 Mark
Tick $(\checkmark)$ the correct answer: $ x^2+6 x+8 = ?$
  • A
    $(x + 3)(x + 5)$
  • B
    $(x + 3)(x + 4)$
  • ✓
    $(x + 2)(x + 4)$
  • D
    $(x + 1)(x + 8)$
Answer
Correct option: C.
$(x + 2)(x + 4)$
 $ x^2+6 x+8 $
$ =x^2+4 x+2 x+8 $
$\{8 = 4 × 2, 6 = 4 + 2\}$
$= x(x + 4) + 2(x + 4)$
$= (x + 2)(x + 4)$
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MCQ 111 Mark
Tick $(\checkmark)$ the correct answer: $ab - a - b + 1 = ?$
  • ✓
    $(a - 1)(b - 1)$
  • B
    $(1 - a)(1 - b)$
  • C
    $(a - 1)(1 - b)$
  • D
    $(1 - a)(b - 1)$
Answer
Correct option: A.
$(a - 1)(b - 1)$
$ab - a - b + 1$
$= a(b - 1) - 1(b - 1)$
$= (a - 1)(b - 1)$
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MCQ 121 Mark
Tick $(\checkmark)$ the correct answer: $ 40+3 x-x^2 = ?$
  • A
    $(x + 5)(x - 8)$
  • B
    $(5 - x)(8 + x)$
  • ✓
    $(5 + x)(8 - x)$
  • D
    $(5 - x)(8 - x)$
Answer
Correct option: C.
$(5 + x)(8 - x)$
 $ 40+3 x-x^2 $
$ =40+8 x-5 x-x^2 $
$\{40 = 8x(-5), 3 = 8 - 5\}$
$= 8(5 + x) - x(5 + x)$
$= (8 - x)(x + 5)$
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MCQ 131 Mark
Tick $(\checkmark)$ the correct answer: $ 3+23 y-8 y^2 = ?$
  • A
    $(1 - 8y)(3 + y)$
  • ✓
    $(1 + 8y)(3 - y)$
  • C
    $(1 - 8y)(y - 3)$
  • D
    $(8y - 1)(y + 3)$
Answer
Correct option: B.
$(1 + 8y)(3 - y)$
 $ 3+23 y-8 y^2 $
$ =3+24 y-y-8 y^2 $
$\{3 × (-8) = -24, -24 = 24 × (-1), 23 = 24 - 1\}$
$= 3(1 + 8y) - y(1 + 8y)$
$= (1 + 8y)(3 - y)$
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MCQ 141 Mark
Tick $(\checkmark)$ the correct answer of the following:$ 7 a^2-63 b^2=7\left(a^2-9 b^2\right)= ?$
  • A
    $(7a - 9b)(9a + 7b)$
  • B
    $(7a - 9b)(7a + 9b)$
  • C
    $9(a - 3b)(a + 3b)$
  • ✓
    $7(a - 3b)(a + 3b)$
Answer
Correct option: D.
$7(a - 3b)(a + 3b)$
 $ 7 a^2-63 b^2=7\left(a^2-9 b^2\right)$
$ =7\left\{(a)^2-(3 b)^2\right\} $
$= 7(a - 3b)(a + 3b)$
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MCQ 151 Mark
Tick $(\checkmark)$ the correct answer: $(2 - 50x^2 Z) = ?$
  • A
    $ 2(1-5 x)^2 $
  • B
    $ 2(1+5 x)^2 $
  • C
    $ (2-5 x)(2+5 x) $
  • ✓
    $ 2(1-5 x)(1+5 x) $
Answer
Correct option: D.
$ 2(1-5 x)(1+5 x) $
 $ 2-50 x^2=2\left(1-25 x^2\right) $
$ =2\left\{(1)^2-(5 x)^2\right\} $
$= 2(1 - 5x)(1 + 5x)$
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MCQ 161 Mark
Tick $(\checkmark)$ the correct answer: $ p q^2+q(p-1)-1 = ?$
  • A
    $(pq + 1)(q − 1)$
  • B
    $p(q + 1)(q − 1)$
  • C
    $q(p − 1)(q + 1)$
  • ✓
    $(pq − 1) (q + 1)$
Answer
Correct option: D.
$(pq − 1) (q + 1)$
 $ p q^2+q(p-1)-1 $
$ =p q^2+p q-q-1 $
$= pq(q + 1) + -1(q + 1)$
$= (q + 1)(pq - 1)$
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MCQ 171 Mark
Tick $(\checkmark)$ the correct answer: $ a^2+b c+a b+a c= ?$
  • ✓
    $(a + b)(a + c)$
  • B
    $(a + b)(b + c)$
  • C
    $(b + c)(c + a)$
  • D
    $a(a + b + c)$
Answer
Correct option: A.
$(a + b)(a + c)$
 $ a^2+b c+a b+a c$
$=a^2+a b+a c+b c $
$= a(a + b) + c(a + b)$
$= (a + b)(a + c)$
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MCQ 181 Mark
Tick $(\checkmark)$ the correct answer: $1 - 2ab - (a^2+ b^2) = ?$
  • A
    $(1 + a - b)(1 + a + b)$
  • B
    $(1 + a + b)(1 - a + b)$
  • ✓
    $(1 + a + b)(1 - a - b)$
  • D
    $(1 + a - b)(1 - a + b)$
Answer
Correct option: C.
$(1 + a + b)(1 - a - b)$
 $ 1-2 a b-\left(a^2+b^2\right) $
$ =1-2 a b-a^2-b^2 $
$ =1-\left(a^2+b^2+2 a b\right) $
$ =1-(a+b)^2 $
$= (1 + a + b)(1 - a - b)$
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MCQ 191 Mark
Tick $(\checkmark)$ the correct answer: $ y^2+2 y-3 = ?$
  • ✓
    $(y - 1)(y + 3)$
  • B
    $(y + 1)(y - 3)$
  • C
    $(y - 1)(y - 3)$
  • D
    $(y + 2)(y - 3)$
Answer
Correct option: A.
$(y - 1)(y + 3)$
 $ y^2+2 y-3 $
$ \{-3=3 \times(-1), 2=3-1\} $
$ =y^2+3 y-y-3 $
$= y(y + 3) - 1(y + 3)$
$= (y - 1)(y + 3)$
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MCQ 201 Mark
$3+23 y-8 y^2=?$
  • A
    $(1-8 y)(3+y)$
  • ✓
    $(1+8 y)(3-y)$
  • C
    $(1-8 y)(3-y)$
  • D
    $(8 y-1)(y+3)$
Answer
Correct option: B.
$(1+8 y)(3-y)$
B
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MCQ 211 Mark
$4 z^2-8 z+3=?$
  • ✓
    $(2 z-1)(2 z-3)$
  • B
    $(2 z+1)(3-2 z)$
  • C
    $(2 z+3)(3 z-1)$
  • D
    $(z-1)(4 z-3)$
Answer
Correct option: A.
$(2 z-1)(2 z-3)$
A
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MCQ 221 Mark
$6 a^2-13 a+6=?$
  • A
    $(2 a+3)(3 a-2)$
  • B
    $(2 a-3)(3 a+2)$
  • ✓
    $(3 a-2)(2 a-3)$
  • D
    $(3 a+1)(2 a-3)$
Answer
Correct option: C.
$(3 a-2)(2 a-3)$
C
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MCQ 231 Mark
$2 x^2+5 x+3=?$
  • A
    $(x+3)(2 x+1)$
  • ✓
    $(x+1)(2 x+3)$
  • C
    $(2 x+5)(x-3)$
  • D
    none of these
Answer
Correct option: B.
$(x+1)(2 x+3)$
B
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MCQ 281 Mark
$1-2 a b-\left(a^2+b^2\right)=?$
  • A
    $(1+a-b)(1+a+b)$
  • B
    $(1+a+b)(1-a+b)$
  • ✓
    $(1+a+b)(1-a-b)$
  • D
    $(1+a-b)(1-a+b)$
Answer
Correct option: C.
$(1+a+b)(1-a-b)$
C
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MCQ 291 Mark
$x^3-x=?$
  • A
    $x\left(x^2-x\right)$
  • B
    $x\left(x-x^2\right)$
  • C
    $x(1+x)(1-x)$
  • ✓
    $x(x+1)(x-1)$
Answer
Correct option: D.
$x(x+1)(x-1)$
D
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MCQ 301 Mark
$\left(12 m^2-27\right)=?$
  • A
    $(2 m-3)(3 m-9)$
  • B
    $3(2 m-9)(3 m-1)$
  • ✓
    $3(2 m-3)(2 m+3)$
  • D
    none of these
Answer
Correct option: C.
$3(2 m-3)(2 m+3)$
C
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MCQ 311 Mark
$x^2-x z+x y-y z=?$
  • A
    $(x-y)(x+z)$
  • B
    $(x-y)(x-z)$
  • ✓
    $(x+y)(x-z)$
  • D
    $(x-y)(z-x)$
Answer
Correct option: C.
$(x+y)(x-z)$
C
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MCQ 331 Mark
$a b-m n+a n-b m=?$
  • A
    $(a-b)(m-n)$
  • ✓
    $(a-m)(b+n)$
  • C
    $(a-n)(m+b)$
  • D
    $(m-a)(n-b)$
Answer
Correct option: B.
$(a-m)(b+n)$
B
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MCQ 341 Mark
$p q^2+q(p-1)-1=?$
  • A
    $(p q+1)(q-1)$
  • B
    $p(q+1)(q-1)$
  • C
    $q(p-1)(q+1)$
  • ✓
    $(p q-1)(q+1)$
Answer
Correct option: D.
$(p q-1)(q+1)$
D
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MCQ 351 Mark
$a^2+b c+a b+a c=?$
  • ✓
    $(a+b)(a+c)$
  • B
    $(a+b)(b+c)$
  • C
    $(b+c)(c+a)$
  • D
    $a(a+b+c)$
Answer
Correct option: A.
$(a+b)(a+c)$
A
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MCQ 361 Mark
$\left(2-50 x^2\right)=?$
  • A
    $2(1-5 x)^2$
  • B
    $2(1+5 x)^2$
  • C
    $(2-5 x)(2+5 x)$
  • ✓
    $2(1-5 x)(1+5 x)$
Answer
Correct option: D.
$2(1-5 x)(1+5 x)$
D
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MCQ 371 Mark
$x^3-144 x=?$
  • A
    $x(x-12)^2$
  • B
    $x(x+12)^2$
  • ✓
    $x(x-12)(x+12)$
  • D
    none of these
Answer
Correct option: C.
$x(x-12)(x+12)$
C
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MCQ 381 Mark
$\left(2 x-32 x^3\right)=?$
  • A
    $2(x-4)(x+4)$
  • B
    $2 x(1-2 x)^2$
  • C
    $2 x(1+2 x)^2$
  • ✓
    $2 x(1-4 x)(1+4 x)$
Answer
Correct option: D.
$2 x(1-4 x)(1+4 x)$
D
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MCQ 391 Mark
$\left(7 a^2-63 b^2\right)=?$
  • A
    $(7 a-9 b)(9 a+7 b)$
  • B
    $(7 a-9 b)(7 a+9 b)$
  • C
    $9(a-3 b)(a+3 b)$
  • ✓
    $7(a-3 b)(a+3 b)$
Answer
Correct option: D.
$7(a-3 b)(a+3 b)$
D
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