MCQ 1011 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 1021 Mark
If $a$ and $b$ are positive integers, then the solution of the equation $ax = b$ has to be always:
AnswerIf $ax = b,$ then $\text{x}=\frac{\text{b}}{\text{a}}$
Since, $a$ and $b$ are positive integers. So, $\frac{\text{b}}{\text{a}}$ is also positive integer.
Hence, the solution of the given equation has to be always positive.
View full question & answer→MCQ 1031 Mark
The digit in the tens place of a two-digit number is $4$ more than the digit in the units place. Let the digit in the units place be $'a'.$ Find the number in the tens place.
- A
$40a + 11$
- ✓
$11a + 40$
- C
$50a + a$
- D
$41a + 10$
AnswerCorrect option: B. $11a + 40$
As given, digit in the units place $= a$
So, the digit in the tens place $= (4 + a)$
Using the values of the numbers,
$⇒ 10(4 + a) + a$
$⇒ 40 + 10a + a$
$⇒ 11a + 40$
View full question & answer→MCQ 1041 Mark
The solution of the equation $ax + b = 0$ is:
- A
$\text{x}=\frac{\text{a}}{\text{b}}$
- B
$\text{x}=-\text{b}$
- ✓
$\text{x}=-\frac{\text{b}}{\text{a}}$
- D
$\text{x}=\frac{\text{b}}{\text{a}}$
AnswerCorrect option: C. $\text{x}=-\frac{\text{b}}{\text{a}}$
Given equation is
$ax + b = 0$
$ax = -b$
$\frac{\text{ax}}{\text{a}}=-\frac{\text{b}}{\text{a}}$
$\text{x}=-\frac{\text{b}}{\text{a}}$
Hence, the solution of the equation $ax + b = 0$ is $\text{x}=-\frac{\text{b}}{\text{a}}$
View full question & answer→MCQ 1051 Mark
The degree of the equation $x^2 - 2x + 1 = x^2 - 3$ is:
AnswerA. $1$
Solution:
$x^2 - 2x + 1 = x^2 - 3 \Rightarrow 2x = 4$
View full question & answer→MCQ 1061 Mark
The root of the equation $9z - 15 = 9 - 3z$ is:
Answer $9\text{z} - 15 = 9 - 3\text{z}$
$\Rightarrow9\text{z}+ 3\text{z} = 9 + 15$
$\Rightarrow\text{3x = 24 }\Rightarrow\text{z}= \frac{24}{12}= 2$
View full question & answer→MCQ 1071 Mark
What do we get when we transpose $\frac{5}{2}$ to $\text{RHS}$ in the equation $\frac{\text{x}}{4} + \frac{5}{2} = - \frac{3}{3}$?
- A
$\frac{\text{x}}{4} = - \frac{3}{4} + \frac{5}{2}$
- B
$\frac{\text{x}}{4} = - \frac{5}{2} + \frac{3}{4}$
- C
$\frac{\text{x}}{4} = - \frac{3}{4} + \big(\frac{-5}{2}\big)$
- ✓
$\text{None of these}$
AnswerCorrect option: D. $\text{None of these}$
$\frac{\text{x}}{4} + \frac{5}{2} = - \frac{3}{3}$
$\frac{\text{x}}{4} = - \frac{3}{3} - \frac{5}{2}$
$\frac{\text{x}}{4} = - \frac{5}{2}$
$\text{x} = - \frac{5}{2} \times 4$
$\text{x} = - 20$
View full question & answer→MCQ 1081 Mark
If $\Big(\frac{2}{3}\Big)$rd of a number is $20$ less than the original number, then the number is ________.
View full question & answer→MCQ 1091 Mark
A number when subtracted from $40$ results into $15.$ This statement in the form of an equation is:
- ✓
$ 40- x = 15$
- B
$x - 40 = 15$
- C
$40 + x = 15$
- D
$40x = 15$
AnswerCorrect option: A. $ 40- x = 15$
$40 - x = 15$
View full question & answer→MCQ 1101 Mark
The degree of $x^2 - 5x + 2 = x^3$ is:
AnswerC. $3$
Solution:
Degree is the highest power of the variable in an equation. Therefore, in the given equation, the highest degree is $3.$
View full question & answer→MCQ 1111 Mark
The shifting of a number from one side of an equation to other is called:
AnswerThe shifting of a number from one side of an equation to other side is called transposition.
e. g. $x + a = 0$ is the equation, $x = -a$
Here, number $'a'$ shifts from left hand side to right hand side.
View full question & answer→MCQ 1121 Mark
Which of the following is a linear expression:
- A
$x^2 + 1$
- B
$y + y^2$
- C
$4$
- ✓
$1 + z$
AnswerCorrect option: D. $1 + z$
D. $1 + z$
Solution:
We know that, the algebraic expression in one variable having the highest power of the variable as $1,$ is known as the linear expression.
Here, $1 + z$ is the only linear expression, as the power of the variable $z$ is $1.$
View full question & answer→MCQ 1131 Mark
The prices of a scooter and cycle are in the ratio $9 : 5.$ If a scooter costs $Rs. 4200$ more than a cycle. The price of cycle is:
- ✓
$Rs. 5250$
- B
$Rs.5000$
- C
$Rs. 5200$
- D
$Rs.4800$
AnswerCorrect option: A. $Rs. 5250$
Let cost of scooter $= 9x$
and Let cost of cycle $= 5x$
We have, $9x - 5x = 4200$
$x = 1050$
$\therefore$ cost price of cycle $= 5 × 1,050 = Rs. 5250$
View full question & answer→MCQ 1141 Mark
The root of the equation $z + 4 = -8$ is:
View full question & answer→MCQ 1151 Mark
If the digit $1$ is placed after a two digit number whose tens digit is $‘t’$ and units digit is $‘u’,$ the new number is:
- A
- B
$10t + u + 1$
- C
$t + u + 1$
- ✓
$100t + 10u + 1$
AnswerCorrect option: D. $100t + 10u + 1$
If any digit $q$ is appended to any number $x,$ it's value becomes $10x + q.$
So at first we have a number with tens' digit t and unit's digit $u.$
The number is $10t + u.$
After placing one more digit $1,$
it becomes $10(10t + u) + 1$
That is, $100t + 10u + 1.$
View full question & answer→MCQ 1161 Mark
The difference between the two numbers is 30. If the bigger number is $x,$ then what is the smaller number$?$
- A
$30 - x$
- B
$30x$
- ✓
$x - 30$
- D
AnswerCorrect option: C. $x - 30$
$x -$ Small number $= 30$
Small number $= x - 30$
View full question & answer→MCQ 1171 Mark
Find the solution of $\frac{\text{x}}{2}+30=19.$
Answer$\frac{\text{x}}{2}+30=19.$
$\Rightarrow x + 60 = 38$
$\Rightarrow x = 38 - 60$
$\Rightarrow x = -22$
View full question & answer→MCQ 1181 Mark
In which of the following, the solution is not an integer$?$
- A
$3x - 4 = x + 2$
- B
$2x - 18 = 2$
- ✓
$4x + 7 = x + 12$
- D
$5x + 3 = x - 7$
AnswerCorrect option: C. $4x + 7 = x + 12$
$4x + 7 = x + 12$
$⇒ 4x - x = 12 - 7$
$⇒ 3x = 5$
$\Rightarrow\text{x}=\frac{5}{3}$
$\frac{5}{3}$ is not an integer.
View full question & answer→MCQ 1191 Mark
The sum of three consecutive even natural numbers is $54.$ Find the greatest of these numbers.
AnswerLet three consecutive even natural numbers be $x, x + 2,$ and $x + 4,$
As per the question,
$x - x + 2 + x + 4 = 54$
$⇒ 3x + 6 = 54$
$⇒ 3x = 54 - 6$
$⇒ 3x = 48$
$⇒ x = 16$
Therefore, the three consecutive even natural numbers are $16, 18$ and $20.$ The highest of these numbers is $20.$
View full question & answer→MCQ 1201 Mark
The ratio of number of males to number of females in a club are $7 : 4.$ If there are $84$ males in the club, the total number of members in the club are:
Answer Let the number of males $7x$ and number of females $= 4x$
Given that,
$7x = 84 ⇒ x = 12$
Total number of members $7x + 4x = 11x = 11 × 12 = 132.$
View full question & answer→MCQ 1211 Mark
The numerator of a fraction is $4$ less than the denominator. If the numerator is decreased by $2$ and denominator is increased by $1,$ then the denominator is eight times the numerator. Find the fraction.
- A
$\frac{4}{12}$
- B
$\frac{3}{13}$
- ✓
$\frac{3}{7}$
- D
$\frac{11}{7}$
AnswerCorrect option: C. $\frac{3}{7}$
$\frac{3}{7}$
View full question & answer→MCQ 1221 Mark
If 9 is added to a number, it becomes $25.$ This statement in the from of an equation is:
- ✓
$x + 9 = 25$
- B
$x - 9 = 25$
- C
$9x = 25$
- D
$\frac{\text{x}}{9}=25$
AnswerCorrect option: A. $x + 9 = 25$
Let the number be $x.$
View full question & answer→MCQ 1231 Mark
The difference between two whole numbers is $66. $ The ratio of the two numbers is $2 : 5.$ The two numbers are:
- ✓
$110$ and $44$
- B
$99$ and $33$
- C
$60$ and $6$
- D
$100$ and $33$
AnswerCorrect option: A. $110$ and $44$
Let the two numbers be $2x$ and $5x$ since they are in the ratio of $2 : 5.$
The difference between $5x$ and $2x = 66$
$5x - 2x = 66$
$3x = 66$
$x = 22$
Hence, $2x = 2(22) = 44$ and $5x = 5(22) = 110.$
View full question & answer→MCQ 1241 Mark
$\frac{3}{4}$ part of a number is $5$ more than its $\frac{2}{3}$ part. This statement in the form of an equation is:
- A
$\frac{2}{3}\text{x} -\frac{3}{4}\text{x = 5}$
- B
$\frac{2}{3}\text{x} - 5=\frac{3}{4}\text{ x}$
- ✓
$\frac{3}{4}\text{ x }=\frac{2}{3}\text{ x + 5}$
- D
$\frac{3}{4}\text{x} - 5=-\frac{2}{3}\text{ x}$
AnswerCorrect option: C. $\frac{3}{4}\text{ x }=\frac{2}{3}\text{ x + 5}$
C. $\frac{3}{4}\text{ x }=\frac{2}{3}\text{ x + 5}$
Solution:
Let the number be $x^2$
View full question & answer→MCQ 1251 Mark
Twice a number is as much greater than $30$ as the three times of the number less than $60.$ The number is:
Answer$ 2x - 30 = 60 - 3x $
$\Rightarrow 5x = 90$
$\Rightarrow x = 18.$
View full question & answer→MCQ 1261 Mark
The number $299$ is divided into two parts in the ratio $5 : 8.$ The product of the numbers is ________.
- A
$21140$
- B
$21294$
- ✓
$21160$
- D
$31294$
AnswerCorrect option: C. $21160$
$21160$
View full question & answer→MCQ 1271 Mark
Which of the following is not a linear equation in one variable$?$
- A
$33y + 5 = 0$
- B
$33z + 5 = 0$
- C
$33x + 5 = 0$
- ✓
$33(x + y) = 0$
AnswerCorrect option: D. $33(x + y) = 0$
In $33(x + y) = 0, x$ and $y$ are two variables.
View full question & answer→MCQ 1281 Mark
Find the value of $x$ if $2x + 10 = 76.$
Answer$2x + 10 = 76$
$2x = 76 - 10$
$2x = 66$
$\text{x} = \frac{66}{2}$
$x = 33$
View full question & answer→MCQ 1291 Mark
After $21$ years, Manish will be $4$ times as old is he is now, What is his present age$?$
AnswerLet Manish's present age be $y$ years
So, after $21$ years, his age will be $= (y + 21)$ years.
As per the question,
$\Rightarrow y + 21 = 4y$
$\Rightarrow 21 = 4y - y$
$\Rightarrow 3y = 21$
$\Rightarrow y = 21$
Therefore, his present age is $7$ years.
View full question & answer→MCQ 1301 Mark
Solve the following: $\frac{1}{4}(\text{x}-2)+\frac{2}{3}(\text{2x}-1)=\frac{5}{6}\text{x}+2$
- A
$\frac{3}{2}$
- B
$-\frac{2}{3}$
- ✓
$\frac{2}{3}$
- D
$-\frac{3}{2}$
AnswerCorrect option: C. $\frac{2}{3}$
$\frac{1}{4}(\text{x}-2)+\frac{2}{3}(\text{2x}-1)=\frac{5}{6}\text{x}+2$
$\Rightarrow\frac{\text{x}}{4}+\frac{\text{2}}{4}+\frac{\text{4x}}{4}+\frac{\text{2}}{3}=\frac{\text{5x}}{6}+\frac{\text{10}}{6}$
$\Rightarrow\frac{\text{x}}{4}+\frac{\text{4x}}{3}-\frac{\text{5x}}{6}=\frac{\text{10}}{6}-\frac{\text{2}}{4}-\frac{\text{2}}{4}$
$\Rightarrow\frac{\text{4x+16x-10x}}{12}=\frac{\text{20-6-8}}{12}$
$\Rightarrow\frac{\text{9x}}{12}=\frac{\text{6}}{12}$
$\Rightarrow\text{9x}=6$
$\Rightarrow\text{x}=\frac{\text{6}}{9}$
$\Rightarrow\text{x}=\frac{\text{2}}{3}$
View full question & answer→MCQ 1311 Mark
If $\Big(\frac{\text{x}}{3}\Big) + 1 =\Big(\frac{7}{15}\Big)$ then the value of $'x\ ’$ is:
- A
$\frac{22}{5}$
- ✓
$-\frac{8}{5}$
- C
$\frac{7}{5}$
- D
$\text{3}$
AnswerCorrect option: B. $-\frac{8}{5}$
$\frac{\text{x}}{3} +1=\frac{7}{15}$
$\frac{\text{x}}{3}=\frac{7}{15}-1$
$\frac{\text{x}}{3}=\frac{7-15}{15}$
$\frac{\text{x}}{3}=\frac{-8}{15}$
${\text{x}}=\frac{-8}{5}$
View full question & answer→MCQ 1321 Mark
The value of x in $\frac{3}{4}\text{x} = 7 - \text{x}$ is:
- ✓
$4$
- B
$3$
- C
$\frac{7}{3}$
- D
$7$
Answer$\frac{3}{4}\text{x} = 7 - \text{x} \Rightarrow\frac{3}{4}\text{ x + x = 7}$
$\Rightarrow\frac{3}{4}\text{ x = 7 } \Rightarrow\text{x = 4}$
View full question & answer→MCQ 1331 Mark
Of the following, the linear equation in one variable $x,$ is:
- A
$\frac{4}{\text{x}}=\frac{\text{x}}{4}$
- B
$\frac{1}{\text{x}}+\frac{1}{\text{x - 1}}=1$
- ✓
$\frac{\text{x}}{2}+\frac{\text{x}}{3}+\frac{1}{4}$
- D
$\text{x}^2 + \text{2x}+ 3=0 $
AnswerCorrect option: C. $\frac{\text{x}}{2}+\frac{\text{x}}{3}+\frac{1}{4}$
$\frac{\text{x}}{2}+\frac{\text{x}}{3}+\frac{1}{4}$
View full question & answer→MCQ 1341 Mark
The consecutive multiples of $3$ whose sum is $51$ are:
- ✓
$24, 27$
- B
$40, 11$
- C
$20, 31$
- D
$25, 26$
AnswerCorrect option: A. $24, 27$
Lets say $x$ is the multiple of $3$
Next consecutive multiple of $3$ will be $(x + 3)$
Given sum is $= 51$
$⇒ x + x + 3 = 51$
$⇒ 2x = 48$
$⇒ x = 24$
Two consecutive multiples of $3$ are $24, 27.$
View full question & answer→MCQ 1351 Mark
The solution of $2y + 9 = 4$ is:
- A
$-\frac{2}{5}$
- ✓
$-\frac{5}{2}$
- C
$\frac{9}{2}$
- D
$\frac{4}{9}$
AnswerCorrect option: B. $-\frac{5}{2}$
$2y + 9 = 4$
$2y = 4 - 9 = -5$
$\text{y}=-\frac{5}{2}$
View full question & answer→MCQ 1361 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 1371 Mark
The digit in the tens place of a two digit number is $3$ more than the digit in the units place. Let the digit at units place be $b.$ Then the number is:
- ✓
$11b + 30$
- B
$10b + 30$
- C
$11b + 3$
- D
$10b + 3$
AnswerCorrect option: A. $11b + 30$
Let digit at ten's be $b.$
Then, digit at ten’s place $= (3 + b)$
Number $= 10(3 + b) + b - 30 + 10b + b = 11b + 30$
View full question & answer→MCQ 1381 Mark
If $x$ is an even number then the consecutive even number is:
- A
$x + 1$
- ✓
$x + 2$
- C
$2x$
- D
$x - 1$
AnswerCorrect option: B. $x + 2$
$x + 2$
View full question & answer→MCQ 1391 Mark
In a two digit number, the unit’s digit is $x$ and the ten’s digit is $y.$ Then, the number is:
- ✓
$10y + x$
- B
$10x + y$
- C
$10y - x$
- D
$10x - y$
AnswerCorrect option: A. $10y + x$
Required number
$= 10 × y + 1 × x = 10y + x.$
View full question & answer→MCQ 1401 Mark
If $10$ is added to four times a certain number, the result is $5$ less than five times the number. The number is:
Answer Let the number be $x.$
According to given condition, we have
$4x + 10 = 5x - 5$
Putting $x$ terms to one side and constants to another side, we have
$10 + 5 = 5x - 4x$
$\therefore x = 15$
Therefore, the number is $15.$
View full question & answer→MCQ 1411 Mark
What is the solution of $ax - b = 0.$
- A
$\text{x}=\frac{\text{a}}{\text{b}}$
- ✓
$\text{x}=\frac{\text{b}}{\text{a}}$
- C
$\text{x}=-\frac{\text{b}}{\text{a}}$
- D
$\text{x}=\text{b}$
AnswerCorrect option: B. $\text{x}=\frac{\text{b}}{\text{a}}$
$ ax - b = 0.$
$\Rightarrow\text{ax}=\text{b}$
$\Rightarrow\text{x}=\frac{\text{b}}{\text{a}}$
Therefore, $\text{x}=\frac{\text{b}}{\text{a}}$
View full question & answer→MCQ 1421 Mark
Solve, $4y = 20$
View full question & answer→MCQ 1431 Mark
An $MNC$ company employed $25$ men to do the official work in $32$ days. After 16 days, it employed $5$ more men and work was finished one day earlier. If it had not employed additional men, it would have been behind by how many days$?$
- A
$1$ Day
- ✓
$2$ Days
- C
$3$ Days
- D
$2.5$ Days
AnswerCorrect option: B. $2$ Days
$2$ Days
View full question & answer→MCQ 1441 Mark
Mark $(\checkmark)$ against the correct answer: $10p^2 + 11p + 3 =\ ?$
- A
$(2p + 3)(5p + 1)$
- ✓
$(5p + 3)(2p + 1)$
- C
$(5p - 3)(2p - 1)$
- D
AnswerCorrect option: B. $(5p + 3)(2p + 1)$
B. $(5p + 3)(2p + 1)$
Solution:
$10p^2+ 11p + 3$
$= 10p^2+ 5p + 6p + 3$
$= 5p(2p + 1) + 3(2p + 1)$
$= (5p + 3)(2p + 1)$
View full question & answer→MCQ 1451 Mark
If $\frac{2\text{x}}{5} = 4$ the value of $x$ is:
- ✓
$10$
- B
$- 10$
- C
$-\frac{8}{5}$
- D
$\frac{8}{5}$
Answer$x = 10$ then
$2 \times 10 = \frac{20}{5} = 4$
View full question & answer→MCQ 1461 Mark
The root of the equation $14 - x = 8$ is:
Answer$14 - x = 8 $
$⇒ x = 14 - 8 = 6$
View full question & answer→MCQ 1471 Mark
If $6$ is added to $3$ times of a number, it becomes $15.$ This statement in the from of an eqution is:
AnswerCorrect option: A. $3x + 6 = 15$
$3x + 6 = 15$
View full question & answer→MCQ 1481 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. $\frac{4}{5}$
$3\text{m}=5\text{m}-\frac{8}{5}$
$\Rightarrow3\text{m} = 25\text{m} - \frac{8}{5}$
$\Rightarrow15\text{m} = 25\text{m} - 8$
$15\text{m} - 25\text{m} =-8$
$\Rightarrow -10\text{m} = -8$
$\Rightarrow\text{m} = \frac{-8}{-10}= \frac{4}{5}$
View full question & answer→MCQ 1491 Mark
If the sum of three consecutive even numbers is $234,$ then the smallest among them is:
Answer Let the three consecutive even number be $2x - 2, 2x, 2x + 2.$
We have,
$(2x - 2) + 2x + (2x + 2) = 234$
$⇒ 6x = 234$
$⇒ x = 39$
$\therefore$ Least even number is $2x - 2 = 2(39) - 2 = 76.$
View full question & answer→MCQ 1501 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→