MCQ

MCQ 11 Mark

$a^2-a c+a b-b c=$ ?

A
$(a-b)(c-a)$
✓
$(a+b)(a-c)$
C
$(a-b)(a-c)$
D
$(a-b)(a+c)$

Answer

Correct option: B.

$(a+b)(a-c)$

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MCQ 21 Mark

$m n-m-n+1=$ ?

A
$(1-m)(n-1)$
B
$(m-1)(1-n)$
C
$(1-m)(1-n)$
✓
$(m-1)(n-1)$

Answer

Correct option: D.

$(m-1)(n-1)$

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MCQ 31 Mark

$x y-p q+x q-y p=$ ?

A
$(p-x)(q-y)$
B
$(x-q)(a+c)$
✓
$(x-p)(y+q)$
D
$(x-y)(a+c)$

Answer

Correct option: C.

$(x-p)(y+q)$

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MCQ 41 Mark

$a b^2+b(a-1)-1=$ ?

✓
$(a b-1)(b+1)$
B
$b(a-1)(b+1)$
C
$a(b+1)(b-1)$
D
$(a b+1)(b-1)$

Answer

Correct option: A.

$(a b-1)(b+1)$

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MCQ 51 Mark

$x^2+y z+x y+x z=$ ?

A
$x(x+y+z)$
B
$(y+z)(z+x)$
C
$(x+y)(y+z)$
✓
$(x+y)(x+z)$

Answer

Correct option: D.

$(x+y)(x+z)$

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MCQ 61 Mark

$\left(2-50 z^2\right)=$ ?

A
$2(1+5 z)^2$
B
$2(1-5 z)^2$
✓
$2(1-5 z)(1+5 z)$
D
$(2-5 z)(2+5 z)$

Answer

Correct option: C.

$2(1-5 z)(1+5 z)$

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MCQ 71 Mark

$a^3-144 a=$ ?

A
$a(a+12)^2$
✓
$a(a-12)(a+12)$
C
$a(a-12)^2$
D
none of these

Answer

Correct option: B.

$a(a-12)(a+12)$

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MCQ 81 Mark

$3+23 x-8 x^2=$ ?

A
$(8 x-1)(x+3)$
B
$(1-8 x)(x-3)$
✓
$(1+8 x)(3-x)$
D
$(1-8 x)(3+x)$

Answer

Correct option: C.

$(1+8 x)(3-x)$

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MCQ 91 Mark

$\left(2 p-32 x^3\right)=$ ?

A
$2 p(1+2 p)^2$
B
$2 p(1-2 p)^2$
✓
$2 p(1-4 p)(1+4 p)$
D
$2(p-4)(p+4)$

Answer

Correct option: C.

$2 p(1-4 p)(1+4 p)$

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MCQ 101 Mark

$4 p^2-8 p+3=$ ?

A
$(p-1)(4 p-3)$
B
$(2 p+3)(3 p-1)$
C
$(2 p+1)(3-2 p)$
✓
$(2 p-1)(2 p-3)$

Answer

Correct option: D.

$(2 p-1)(2 p-3)$

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MCQ 111 Mark

$6 x^2-13 x+6=$ ?

A
$(6 x+3)(3 x-2)$
B
$(6 x+1)(2 x-3)$
C
$(6 x-3)(6 x+2)$
✓
$(3 x-2)(2 x-3)$

Answer

Correct option: D.

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

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MCQ 121 Mark

$2 a^2+5 a+3=$ ?

A
$(2 a+5)(a-3)$
B
$(a+3)(2 a+1)$
✓
$(a+1)(2 a+3)$
D
None of these

Answer

Correct option: C.

$(a+1)(2 a+3)$

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MCQ 131 Mark

$40+3 y-y^2=$ ?

A
$(5-y)(8-y)$
✓
$(5+y)(8-y)$
C
$(5-y)(8+y)$
D
$(y+5)(y-8)$

Answer

Correct option: B.

$(5+y)(8-y)$

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MCQ 141 Mark

$x^2+2 x-3=$ ?

A
$(x+2)(x-3)$
B
$(x-1)(x-3)$
C
$(x+1)(x-3)$
✓
$(x-1)(x+3)$

Answer

Correct option: D.

$(x-1)(x+3)$

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MCQ 151 Mark

$p^2+4 p-21=$ ?

A
$(p+7)(p+3)$
B
$(p-7)(p-3)$
✓
$(p+7)(p-3)$
D
$(p-7)(p+3)$

Answer

Correct option: C.

$(p+7)(p-3)$

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MCQ 161 Mark

$a^2+6 a+8=$ ?

A
$(a+1)(a+8)$
✓
$(a+2)(a+4)$
C
$(a+3)(a+4)$
D
$(a+3)(a+5)$

Answer

Correct option: B.

$(a+2)(a+4)$

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MCQ 171 Mark

$a^2+6 a+8=$ ?

A
$(a+1)(a+8)$
✓
$(a+2)(a+4)$
C
$(a+3)(a+4)$
D
$(a+3)(a+5)$

Answer

Correct option: B.

$(a+2)(a+4)$

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MCQ 181 Mark

$1-2 x y-\left(x^2+y^2\right)=$ ?

A
$(1+x-y)(1-x+y)$
B
$(1+x+y)(1-x-y)$
C
$(1+x+y)(1-x+y)$
✓
$(1+x-y)(1+x+y)$

Answer

Correct option: D.

$(1+x-y)(1+x+y)$

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MCQ 191 Mark

$\left(12 a^2-27\right)=$ ?

✓
$3(2 a-3)(2 a+3)$
B
$(2 a-3)(3 a-9)$
C
$3(2 a-9)(3 a-1)$
D
None of these

Answer

Correct option: A.

$3(2 a-3)(2 a+3)$

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MCQ 201 Mark

$7 x^2-63 y^2=?$

A
$(7 x-9 y)(9 x+7 y)$
B
$(7 x-9 y)(7 x+9 y)$
C
$9(x-3 y)(x+3 y)$
✓
$7(x-3 y)(x+3 y)$

Answer

Correct option: D.

$7(x-3 y)(x+3 y)$

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MCQ 211 Mark

Area of floor of a hall is given by the expression $\left(a^2+9 a+20\right) m ^2$. If $a=2 m$, which of the following can be the dimensions of the hall?

A
length $=14 m$, breadth $=3 m$
✓
length $=7 m$, breadth $=6 m$
C
length $=21 m$, breadth $=2 m$
D
all the above

Answer

Correct option: B.

length $=7 m$, breadth $=6 m$

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MCQ 221 Mark

Which of the following is true for the expression $a^2-8 a-16 b^2+16$ ?

A
It can be factorised into three terms
✓
Its one factor is $(a-4-4 b)$
C
Its one factor is $(a+4+4 b)$
D
none of these

Answer

Correct option: B.

Its one factor is $(a-4-4 b)$

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MCQ 231 Mark

The expression $3 x^2-11 x+6$ is factorised into two terms. The sum of these two factors is:

A
$4 x+1$
B
$3 x^2-11 x+6$
✓
$4 x-5$
D
$2 x+1$

Answer

Correct option: C.

$4 x-5$

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MCQ 241 Mark

We can regroup the terms of $3 x+4 y+4 x y+3$, so that it can be factorised, as:

A
$(4 x y+3 x)+(4 y+3)$
B
$(4 x y+4 y)+(3 x+3)$
✓
both (a) and (b) are correct
D
none of these

Answer

Correct option: C.

both (a) and (b) are correct

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MCQ 251 Mark

While factorising the algebraic expression $20 x^2+5 x y^2-25 x y z$, a student followed the steps given below:
In which step did he make his first mistake?
Step I: $5 \times 2 \times 2 \times x \times x+5 \times x \times y \times y-5 \times 5 \times x \times y \times z$
Step II: $5 \times x(2 \times 2+y \times y+5 \times y \times z)$
Step III: $5 x\left(4+y^2+5 y z\right)$

A
Step I
✓
Step II
C
Step III
D
no mistake

Answer

Correct option: B.

Step II

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MCQ 261 Mark

Which among the following expressions is not in factorised form?

A
$(2 a b+5)(a+2)$
B
$5 a+2 a b+14$
C
$5(a+3)$
✓
$2 a^2+9(a-2)$

Answer

Correct option: D.

$2 a^2+9(a-2)$

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MCQ 271 Mark

$x^2+\frac{1}{x^2}-\frac{3}{x}+2-3 x$ can be factorised as:

A
$\left(x-\frac{1}{x}\right)\left(x+\frac{1}{x}-3\right)$
B
$\left(x+\frac{1}{x}\right)\left(x+\frac{1}{x}+3\right)$
C
$\left(x+\frac{1}{x}\right)\left(3+x-\frac{1}{x}\right)$
✓
$\left(x+\frac{1}{x}\right)\left(x+\frac{1}{x}-3\right)$

Answer

Correct option: D.

$\left(x+\frac{1}{x}\right)\left(x+\frac{1}{x}-3\right)$

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MCQ 281 Mark

$a^2 b+a^2 c+a b+a c+b^2 c+c^2 b$ is same as:

✓
$\left(a^2+a+b c\right)(b+c)$
B
$\left(a^2+b c\right)(b+c)$
C
$\left(a^2+a b+b c\right)(a+c)$
D
none of these

Answer

Correct option: A.

$\left(a^2+a+b c\right)(b+c)$

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