MCQ 11 Mark
Tick $(\checkmark)$ the correct answer: If $\frac{\text{n}}{2}-\frac{3\text{n}}{4}+\frac{5\text{n}}{6}=21,$ then $\text{n}=?$
Answer$\frac{\text{n}}{2}-\frac{\text{3n}}{4}+\frac{5\text{n}}{6}=21$
$\Rightarrow\frac{ 6\text{n} - 9\text{n} + 10\text{n}}{12}= 21$
$\Rightarrow7\text{n}=21\times12$
$\Rightarrow7\text{n}=252$
$\Rightarrow\text{n}=\frac{252}{7}$
$\text{n}=36$
View full question & answer→MCQ 21 Mark
Tick $(\checkmark)$ the correct answer: If $5\text{x}+\frac{7}{1}=\frac{3}{2}\text{x}-14,$ then $\text{x} = ?$
Answer$\text{5x}+\frac{7}{2}=\frac{3}{2}\text{x}-14$
$\Rightarrow\frac{10\text{x}+7}{2}=\frac{3\text{x}-28}{2}$
$\Rightarrow10\text{x}+7=3\text{x}-28$
$\Rightarrow10\text{x}-3\text{x}=-28-7$
$\Rightarrow7\text{x}=-35$
$\Rightarrow\text{x}=\frac{-35}{7}=-5$
View full question & answer→MCQ 31 Mark
Tick $(\checkmark)$ the correct answer: Sum of three consecutive integers is $51.$ The middle one is:
AnswerLet the three consecutive integers be $x, x + 1$ and $x + 2.$
Equation $= \text{x} + \text{x} + 1 + \text{x} + 2 = 51$
$\Rightarrow3\text{x} + 3 = 51$
$\Rightarrow3\text{x} = 51 - 3$
$\Rightarrow3\text{x} = 48$
$\Rightarrow\text{x} = \frac{48}{3}= 16$
Middle integer $= \text{x}+1 = 16 + 1 = 17$
View full question & answer→MCQ 41 Mark
Tick $(\checkmark)$ the correct answer: The base of an isosceles triangle is $6\ cm$ and its perimeter is $16\ cm.$ Length of each of the equal sides is:
- A
$4\ cm$
- ✓
$5\ cm$
- C
$3\ cm$
- D
$6\ cm$
AnswerCorrect option: B. $5\ cm$
Let the equal side of the isosceles triangle be $x.$
Then, the perimeter of the triangle would be $(x + x + 6).$
$\therefore2\text{x} + 6 = 16 $
$\Rightarrow2\text{x} = 16 - 6$
$\Rightarrow2\text{x} = 10$
$\Rightarrow\text{x} = \frac{10}{2}= 5$
$\therefore$ Length of each equal side $= 5\ cm$
View full question & answer→MCQ 51 Mark
Tick $(\checkmark)$ the correct answer: Four$-$fifths of a number is greater than three$-$fourths of the number by $4.$ The number is:
AnswerLet the number be $x.$
$\therefore\frac{4}{5}\text{x}=\frac{3}{4}\text{x}+4$
$\Rightarrow\frac{4}{5}\text{x}=\frac{3\text{x}+16}{4}$
$\Rightarrow16\text{x} = 15\text{x} + 80$
$\Rightarrow16\text{x} - 15\text{x} = 80$
$\Rightarrow \text{x} = 80$
View full question & answer→MCQ 61 Mark
Tick $(\checkmark)$ the correct answer: If $\frac{\text{4x}+8}{2\text{5x}+8}=\frac{5}{6},$ then $\text{x}=?$
Answer$\frac{\text{4x}+8}{2\text{5x}+8}=\frac{5}{6}$
$\Rightarrow6(\text{4x}+8)=5(5\text{x}+8)$
$\Rightarrow24\text{x}+48=25\text{x}+40$
$\Rightarrow24\text{x}-25\text{x}=-48\text{x}+40$
$\Rightarrow-\text{x}=-8$
$\Rightarrow\text{x}=8$
View full question & answer→MCQ 71 Mark
Tick $(\checkmark)$ the correct answer: Number of boys and girls in a class are in the ratio $7 : 5.$ The number of boys is $8$ more than the number of girls. The total class strength is:
AnswerLet the number of boys in the class be $x.$
Then, the number of girls will be $(x - 8).$
The equation becomes:
$\Rightarrow\frac{\text{x}}{\text{x}-8}=\frac{7}{5}$
$\Rightarrow5\text{x} = 7\text{x} - 56$
$\Rightarrow5\text{x} -7\text{x} = -56$
$\Rightarrow -2\text{x} = -56$
$\Rightarrow \text{x} = \frac{-56} {-2} = 28$
Therefore, the number of boys is $28.$
Number of girls $= ( \text{x}- 8) = 28 -8 =20$
Total strength of the class $= 28 + 20 = 48$
View full question & answer→MCQ 81 Mark
Tick $(\checkmark)$ the correct answer: The sum of two numbers is $95.$ If one exceeds the other by $15,$ then the smaller of the two is:
AnswerLet the numbers be $x$ and $x + 15.$
$\therefore x + x + 15 = 95$
$\Rightarrow 2x + 15 = 95$
$\Rightarrow 2x = 95 - 15$
$\Rightarrow 2x = 80$
$\Rightarrow x = 40$
The smaller number is $40.$
View full question & answer→MCQ 91 Mark
Tick $(\checkmark)$ the correct answer: If $2\text{y}+\frac{5}{3}=\frac{26}{3}-\text{y},$ then $\text{y}=?$
- A
$1$
- B
$\frac{2}{3}$
- C
$\frac{6}{5}$
- ✓
$\frac{7}{3}$
AnswerCorrect option: D. $\frac{7}{3}$
$2\text{y}+\frac{5}{3}=\frac{26}{3}-\text{y}$
$\Rightarrow\frac{6\text{y}+5}{3}=\frac{26-3\text{y}}{3}$
$\Rightarrow6\text{y}+5=26-3\text{y}$
$\Rightarrow6\text{y}+3\text{y}=26-5$
$\Rightarrow9\text{y}=21$
$\Rightarrow\text{y}=\frac{21}{9}=\frac{7}{3}$
View full question & answer→MCQ 101 Mark
Tick $(\checkmark)$ the correct answer: If $2x - 3 = x + 2,$ then $x = ?$
Answer$\text{2x}-3=\text{x}+2$
$\Rightarrow2\text{x}-\text{x}=3+2$
$\Rightarrow\text{x}=5$
View full question & answer→MCQ 111 Mark
Tick $(\checkmark)$ the correct answer: If $\frac{\text{x}+1}{2\text{x}+3}=\frac{3}{8},$ then $\text{x}=?$
- A
$\frac{1}{4}$
- B
$\frac{1}{3}$
- C
$\frac{1}{6}$
- ✓
$\frac{1}{2}$
AnswerCorrect option: D. $\frac{1}{2}$
$\frac{\text{x}+1}{2\text{x}+3}=\frac{3}{8}$
$\Rightarrow8(\text{x}+1)=3(2\text{x}+3)$
$\Rightarrow8\text{x}+8=6\text{x}+9$
$\Rightarrow8\text{x}-6\text{x}=9-8$
$\Rightarrow2\text{x}=1$
$\Rightarrow\text{x}=\frac{1}{2}$
View full question & answer→MCQ 121 Mark
Mark $(\checkmark)$ against the correct answer: $7 x^2-19 x-6=?$
- ✓
$(x-3)(7 x+2)$
- B
$(x+3)(7 x-2)$
- C
$(x-3)(7 x-2)$
- D
$(7 x-3)(x+2)$
AnswerCorrect option: A. $(x-3)(7 x+2)$
$7 x^2-19 x-6$
$=7 x^2-21 x+2 x-6$
$=7 x(x-3)+2(x-3)$
$=(x-3)(7 x+2)$
View full question & answer→MCQ 131 Mark
Tick $(\checkmark)$ the correct answer: If $3(t - 3) = 5(2t + 1),$ then $t = ?$
Answer$3 ( \text{t} - 3 ) = 5 ( 2\text{t} + 1 )$
$\Rightarrow3\text{t} - 9 = 10\text{t} + 5$
$\Rightarrow3\text{t} - 10\text{t} = 9 + 5$
$\Rightarrow-7\text{t} = 14$
$\Rightarrow -\text{t} = \frac{14}{7}=2$
$\Rightarrow \text{t} = -2$
View full question & answer→MCQ 141 Mark
Mark $(\checkmark)$ against the correct answer: $12 x^2+60 x+75=?$
- A
$(2 x+5)(6 x+5)$
- B
$(3 x+5)^2$
- ✓
$3(2 x+5)^2$
- D
AnswerCorrect option: C. $3(2 x+5)^2$
$12 x^2+60 x+75$
$=3\left(4 x^2+20 x+25\right)$
$=3\left((2 x)^2+2 \times 2 x \times 5+5^2\right)$
$=3(2 x+5)^2$
View full question & answer→MCQ 151 Mark
Mark $(\checkmark)$ against the correct answer: $ab - a - b + 1 = ?$
- A
$(1 - a)(1 - b)$
- B
$(1 - a)(b - 1)$
- ✓
$(a - 1)(b - 1)$
- D
$(a - 1)(1 - b)$
AnswerCorrect option: C. $(a - 1)(b - 1)$
$(a - 1)(b - 1)$
$ab - a - b + 1$
$= a(b - 1)-1(b - 1)$
$= (a - 1)(b - 1)$
View full question & answer→MCQ 161 Mark
Tick $(\checkmark)$ the correct answer: If $\frac{6\text{x}+1}{3}=\frac{\text{x}-3}{6}$ then $\text{x}=?$
Answer$\Rightarrow\frac{6\text{x} +1 }{3} = \frac{\text{x}{ - 3}}{{6}}$
$\Rightarrow \frac{6\text{x} + 1 + 3}{3} =\frac{\text{ x} − 3}{6}$
$\Rightarrow 6 ( 6\text{x} + 4) = 3 ( \text{x} - 3 )$
$\Rightarrow 36\text{x} + 24 = 3\text{x} - 9$
$\Rightarrow 36\text{x} - 3\text{x} = -24 -9$
$\Rightarrow 33\text{x} = -33$
$\Rightarrow \text{x} =\frac{-33}{33}= -1$
View full question & answer→MCQ 171 Mark
Mark $(\checkmark)$ against the correct answer: $10 p^2+11 p+3=?$
- A
$(2 p+3)(5 p+1)$
- ✓
$(5 p+3)(2 p+1)$
- C
$(5 p-3)(2 p-1)$
- D
AnswerCorrect option: B. $(5 p+3)(2 p+1)$
$10 p^2+11 p+3$
$=10 p^2+5 p+6 p+3$
$=5 p(2 p+1)+3(2 p+1)$
$=(5 p+3)(2 p+1)$
View full question & answer→MCQ 181 Mark
Tick $(\checkmark)$ the correct answer: If $3\text{m}=5\text{m}-\frac{8}{5},$ then, $\text{m} = ?$
- A
$\frac{2}{5}$
- B
$\frac{3}{5}$
- ✓
$\frac{4}{5}$
- D
$\frac{1}{5}$
AnswerCorrect option: C. $\frac{4}{5}$
$3\text{m}=5\text{m}-\frac{8}{5}$
$\Rightarrow3\text{m} = 25\text{m} - \frac{8}{5}$
$\Rightarrow15\text{m} = 25\text{m} - 8$
$15\text{m} - 25\text{m} =-8$
$⇒ -10\text{m} = -8$
$\Rightarrow\text{m} = \frac{-8}{-10}= \frac{4}{5}$
View full question & answer→MCQ 191 Mark
Tick $(\checkmark)$ the correct answer: If $\text{z}=\frac{4}{5}(\text{z}+10),$ then $\text{z} = ?$
Answer$\text{z}=\frac{4}{5}(\text{z}+10)$
$\Rightarrow5\text{z}=4(\text{z}+10)$
$\Rightarrow5\text{z}=4\text{z}+40$
$\Rightarrow5\text{z}-4\text{z}=40$
$\Rightarrow\text{z}=40$
View full question & answer→MCQ 201 Mark
Mark $(\checkmark)$ against the correct answer: $3+23 x-8 x^2=?$
- A
$(1-8 x)(3+x)$
- ✓
$(1+8 x)(3-x)$
- C
$(1-8 x)(3-x)$
- D
AnswerCorrect option: B. $(1+8 x)(3-x)$
$3+23 x-8 x^2$
$=3+24 x-x-8 x^2$
$=3(1+8 x)-x(1+8 x)$
$=(1+8 x)(3-x)$
View full question & answer→MCQ 211 Mark
Tick $(\checkmark)$ the correct answer: If $\frac{\text{n}}{\text{n}+15}=\frac{4}{9},$ then $\text{n}=?$
Answer$\frac{\text{n}}{\text{n}+15}=\frac{4}{9}$
$\Rightarrow\text{9n}=4(\text{n}+15)$
$\Rightarrow9\text{n}=4\text{n}+60$
$\Rightarrow9\text{n}-4\text{n}=60$
$\Rightarrow5\text{n}=60$
$\Rightarrow\text{n}=\frac{60}{5}=12$
View full question & answer→MCQ 221 Mark
Tick $(\checkmark)$ the correct answer: If $5t - 3 = 3t - 5,$ then $t = ?$
Answer$5\text{t}-3=3\text{t}-5$
$\Rightarrow5\text{t}-3\text{t}=3-5$
$\Rightarrow2\text{t}=-2$
$\Rightarrow\text{t}=\frac{-2}{2}=-1$
View full question & answer→MCQ 231 Mark
Tick $(\checkmark)$ the correct answer: The ages of $A$ and $B$ are in the ratio $5 : 7.$ Four years from now the ratio of their ages will be $3 : 4.$ The present age of $B$ is:
- A
$20$ years
- ✓
$28$ years
- C
$15$ years
- D
$21$ years
AnswerCorrect option: B. $28$ years
Let the number be $x.$
Let $x $ be the common multiple of the ages of $A$ and $B.$
Then. the ages of $A$ and $B$ would be $5x$ and $7x,$ respectively.
$\therefore\frac{5\text{x}+4}{7\text{x}-4}=\frac{3}{4}$
$\Rightarrow4( 5\text{x} +4 ) = 3 ( 7\text{x} + 4 )$
$\Rightarrow20\text{x} + 16 = 21\text{x} + 12$
$\Rightarrow16 - 12 = 21\text{x} - 20\text{x}$
$\Rightarrow4 = \text{x}$
$\Rightarrow\text{x} = 4 $
$\therefore$ Age of $\text{B} = 7(\text{x}) = 7\times4 $
$= 28 \text{ years}$
View full question & answer→