MCQ

MCQ 11 Mark

Tick $(\checkmark)$ the correct answer: $(x+5)(x-3)=?$

A
$x^2+5 x-15$
B
$x^2-3 x-15$
C
$x^2+2 x+15$
✓
$x^2+2 x-15$

Answer

Correct option: D.

$x^2+2 x-15$

$(x+5)(x-3)$
$(x)^2+(5-3) x+5 \times(-3)$
$=x^2+2 x-15$

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MCQ 21 Mark

Tick $(\checkmark)$ the correct answer: If $\Big(\text{x}+\frac{1}{\text{x}}\Big)=5,$ then $\Big(\text{x}^2+\frac{1}{\text{x}^2}\Big)=?$

A
$25$
B
$27$
✓
$23$
D
$25\frac{1}{25}$

Answer

Correct option: C.

$23$

$\Big(\text{x}+\frac{1}{\text{x}}\Big)=5,$
$\Big(\text{x}+\frac{1}{\text{x}}\Big)^2=(5)^2$
$\Rightarrow\text{x}^2+\frac{1}{\text{x}^2}+2=25$
$\Rightarrow\text{x}^2+\frac{1}{\text{x}^2}+25-2=23$

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MCQ 31 Mark

Tick $(\checkmark)$ the correct answer: $\left(2 x^2+3 x+1\right) \div(x+1)=?$

A
$(x+1)$
✓
$(2 x+1)$
C
$(x+3)$
D
$(2 x+3)$

Answer

Correct option: B.

$(2 x+1)$

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MCQ 41 Mark

Tick $(\checkmark)$ the correct answer: $\left(2 x^2+3 x+1\right) \div(x+1)=?$

A
$(x+1)$
✓
$(2 x+1)$
C
$(x+3)$
D
$(2 x+3)$

Answer

Correct option: B.

$(2 x+1)$

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MCQ 51 Mark

Tick $(\checkmark)$ the correct answer: $8 a^2 b^3 \div(-2 a b)=?$

A
$4 a b^2$
B
$4 a^2 b$
✓
$-4 a b^2$
D
$-4 a^2 b$

Answer

Correct option: C.

$-4 a b^2$

$8 a^2 b^3 \div(-2 a b)$
$\Rightarrow \frac{8 a^2 b^3}{-2 a b}$
$\Rightarrow-4 a^{2-1} b^{3-1}$

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MCQ 61 Mark

Tick $(\checkmark)$ the correct answer:
If $(a-b)=7$ and $a b=9$, then $\left(a^2+b^2\right)= ?$

✓
$67$
B
$31$
C
$40$
D
$58$

Answer

Correct option: A.

$67$

$a-b=7$
$a b=9$
$a^2+b^2=(a-b)^2+2 a b$
$=(7)^2+2 \times 9$
$=49+18$
$=67$

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MCQ 71 Mark

Tick $(\checkmark)$ the correct answer:
$(82)^2-(18)^2=$ ?

A
$8218$
B
$6418$
✓
$6400$
D
$7204$

Answer

Correct option: C.

$6400$

$(82)^2-(18)^2$
$=(82+18)(82-18)$
$=100 \times 64$
$=6400$

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MCQ 81 Mark

Tick $(\checkmark)$ the correct answer: If $\Big(\text{x}-\frac{1}{\text{x}}\Big)=6,$ then $\Big(\text{x}^2+\frac{1}{\text{x}^2}\Big)=?$

A
$36$
✓
$38$
C
$32$
D
$36\frac{1}{36}$

Answer

Correct option: B.

$38$

$\Big(\text{x}-\frac{1}{\text{x}}\Big)=6,$
Squaring on both sides
$\Big(\text{x}-\frac{1}{\text{x}}\Big)^2=(6)^2$
$\Rightarrow\text{x}^2+\frac{1}{\text{x}^2}-2=36$
$\Rightarrow\text{x}^2+\frac{1}{\text{x}^2}=36+2=38$

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MCQ 91 Mark

Tick $(\checkmark)$ the correct answer:
$\left(3 q+7 p^2-2 r^3+4\right)-\left(4 p^2-2 q+7 r^3-3\right)=?$

A
$\left(p^2+2 q+5 r^3+1\right)$
B
$\left(11 p^2+q+5 r^3+1\right)$
C
$\left(-3 p^2-5 q+9 r^3-7\right)$
✓
$\left(3 p^2+5 q-9 r^3+7\right)$

Answer

Correct option: D.

$\left(3 p^2+5 q-9 r^3+7\right)$

$\left(3 q+7 p^2-2 r^3+4\right)-\left(4 p^2-2 q+7 r^3-3\right)$
$=3 q+7 p^2-2 r^3+4-4 p^2+2 q-7 r^3+3$
$=5 q+3 p^2-9 r^3+7$
$=3 p^2+5 q-9 r^3+7$

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MCQ 101 Mark

Tick $(\checkmark)$ the correct answer:
$(a+1)(a-1)\left(a^2+1\right)=?$

A
$\left(a^4-2 a^2-1\right)$
B
$\left(a^4-a^2-1\right)$
✓
$\left(a^4-1\right)$
D
$\left(a^4+1\right)$

Answer

Correct option: C.

$\left(a^4-1\right)$

$(a+1)(a-1)\left(a^2+1\right)$
$=\left(a^2-1\right)\left(a^2+1\right)$
$=a^4-1$

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MCQ 111 Mark

Tick $(\checkmark)$ the correct answer: $(2 x+5)(2 x-5)=?$

A
$\left(4 x ^2+25\right)$
✓
$\left(4 x^2-25\right)$
C
$\left(4 x^2-10 x+25\right)$
D
$\left(4 x^2+10 x-25\right)$

Answer

Correct option: B.

$\left(4 x^2-25\right)$

$(2 x+5)(2 x-5)$
$=(2 x)^2-(5)^2$
$=4 x^2-25$

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MCQ 121 Mark

Tick $(\checkmark)$ the correct answer:
If $x=10$, then the value of $\left(4 x^2+20 x+25\right)=$ ?

A
$256$
B
$425$
✓
$625$
D
$575$

Answer

Correct option: C.

$625$

$x=10$
$=\left(4 x^2+20 x+25\right)$
$=(2 x)^2+2 \times 2 x \times 5+(5)^2$
$=(2 x+5)^2$
$=(2 \times 10+5)^2$
$=(20+5)^2$
$=(25)^2$
$=625$

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MCQ 131 Mark

Tick $(\checkmark)$ the correct answer:
$(2 x+3)(3 x-1)=?$

A
$\left(6 x^2+8 x-3\right)$
✓
$\left(6 x^2+7 x-3\right)$
C
$6 x^2-7 x-3$
D
$\left(6 x^2-7 x+3\right)$

Answer

Correct option: B.

$\left(6 x^2+7 x-3\right)$

$(2 x+3)(3 x-1)$
$=6 x^2-2 x+9 x-3$
$=6 x^2+7 x-3$

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MCQ 141 Mark

Tick $(\checkmark)$ the correct answer:
$(197 \times 203)=\text { ? }$

✓
$39991$
B
$39999$
C
$40009$
D
$40001$

Answer

Correct option: A.

$39991$

$(197 \times 203)$
$=(200-3)(200+3)$
$=(200)^2-(3)^2$
$=40000-9$
$=39991$

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MCQ 151 Mark

Tick $(\checkmark)$ the correct answer: $\Big(\frac{1}{\text{x}}+\frac{1}{\text{y}}\Big)\Big(\frac{1}{\text{x}}-\frac{1}{\text{y}}\Big)=?$

A
$\Big(\frac{1}{\text{x}^2}-\frac{1}{\text{y}2}\Big)$
✓
$\Big(\frac{1}{\text{x}^2}+\frac{1}{\text{y}2}\Big)$
C
$\Big(\frac{1}{\text{x}^2}+\frac{1}{\text{y}^2}-\frac{1}{\text{xy}}\Big)$
D
$\Big(\frac{1}{\text{x}^2}-\frac{1}{\text{y}^2}+\frac{1}{\text{xy}}\Big)$

Answer

Correct option: B.

$\Big(\frac{1}{\text{x}^2}+\frac{1}{\text{y}2}\Big)$

$\Big(\frac{1}{\text{x}}+\frac{1}{\text{y}}\Big)\Big(\frac{1}{\text{x}}-\frac{1}{\text{y}}\Big)$
$=\Big(\frac{1}{\text{x}}\Big)^2-\Big(\frac{1}{\text{y}}\Big)^2$
$=\frac{1}{\text{x}^2}-\frac{1}{\text{y}^2}$

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