MCQ 11 Mark
Mark $(\checkmark)$ against the correct answer in the following:Which of the following are co$-$primes?
- ✓
$91$ and $72$
- B
$34$ and $51$
- C
$21$ and $36$
- D
$15$ and $ 20$
AnswerCorrect option: A. $91$ and $72$
$91$ and $72$
View full question & answer→MCQ 21 Mark
Mark $(\checkmark)$ against the correct answer in the following: Which of the following is a prime number?
Answer$(A). 323$ is not a prime number because $323$ can be written as $17 \times 19.$
$(B). 361$ is not a prime number because $361$ can be written as $19 \times 19.$
$(C). 263$ is a prime number.
View full question & answer→MCQ 31 Mark
Mark $(\checkmark)$ against the correct answer in the following: The greatest number which divides $134$ and $167$ leaving $2$ as remainder in each case is:
AnswerSince we need $2$ as the remainder, we will subtract $2$ from each of the numbers.
$167 - 2 = 165$
$134 - 2 = 132$
Now, any of the common factors of $165$ and $132$ will be the required divisor.
On factorising:
$165 = 3 \times 5 \times 11$
$132 = 2 \times 2 \times 3 \times 11$
Their common factors are $11$ and $3.$
So, $3 \times 11 = 33$ is the required divisor.
View full question & answer→MCQ 41 Mark
Mark $(\checkmark)$ against the correct answer in the following: Which of the following is a composite number?
View full question & answer→MCQ 51 Mark
Mark $(\checkmark)$ against the correct answer in the following: Which of the following are co$-$primes?
- A
$39, 91$
- ✓
$161, 192$
- C
$385, 462$
- D
AnswerCorrect option: B. $161, 192$
$161$ and $192$
View full question & answer→MCQ 61 Mark
Mark $(\checkmark)$ against the correct answer in the following: Which of the following numbers is divisible by $11?$
- A
$3333333$
- B
$1111111$
- ✓
$22222222$
- D
AnswerCorrect option: C. $22222222$
Consider the number $22222222.$
Sum of its digits in odd places $(2 + 2 + 2 + 2)= 8$
Sum of its digits in even places $(2 + 2 + 2 + 2) = 8$
Difference of the two sums $= 8 - 8 = 0$
Since this number $(0)$ is divisible by $11, 22222222$ is also divisible by $11.$
View full question & answer→MCQ 71 Mark
Mark $(\checkmark)$ against the correct answer in the following:The number which is neither prime nor composite is:
View full question & answer→MCQ 81 Mark
Mark $(\checkmark)$ against the correct answer in the following:Which of the following is a prime number?
AnswerTo find a prime number between $100$ and $200,$ we have to check whether the given number is divisible by any prime number less than $15.$ If yes, it is not prime, otherwise it is.
By examining, we find that $131$ is a prime number.
View full question & answer→MCQ 91 Mark
Mark $(\checkmark)$ against the correct answer in the following:Which of the following numbers is divisible by $9?$
- ✓
$8576901$
- B
$96345210$
- C
$67594310$
- D
AnswerCorrect option: A. $8576901$
$8576901$
View full question & answer→MCQ 101 Mark
Mark $(\checkmark)$ against the correct answer in the following: If $a$ and $b$ are co$-$primes, then their $\ce{LCM}$ is:
AnswerCorrect option: B. $\frac{\text{a}}{\text{b}}$
If $a$ and $b$ are co$-$primes then their $\ce{LCM}$ will be $ab.$
For example, $4$ and $9$ are co$-$primes.
$\ce{LCM}$ of $4$ and $9$ is $4 \times 9.$
View full question & answer→MCQ 111 Mark
Mark $(\checkmark)$ against the correct answer in the following: Which of the following are co$-$primes?
- A
$8, 12$
- ✓
$9, 10$
- C
$6, 8$
- D
$15, 18$
AnswerCorrect option: B. $9, 10$
$9, 10$
View full question & answer→MCQ 121 Mark
Mark $(\checkmark)$ against the correct answer in the following:The $\ce{LCM}$ of two co$-$prime numbers is their:
AnswerThe $\ce{LCM}$ of two co$-$prime numbers is their product.
View full question & answer→MCQ 131 Mark
Mark $(\checkmark)$ against the correct answer in the following:
The $\text{HCF}$ of $144, 180$ and $192$ is:
AnswerWe will first factorise the two numbers:
$\begin{array}{c|c}2&144\\\hline2&72\\\hline2&36\\\hline2&18\\\hline3&9\\\hline3&3\\\hline&1\end{array}$
$\begin{array}{c|c}2&8188\\\hline2&90\\\hline3&45\\\hline3&15\\\hline5&5\\\hline&1\end{array}$
$\begin{array}{c|c}2&192\\\hline2&96\\\hline2&48\\\hline2&24\\\hline2&12\\\hline2&6\\\hline3&3\\\hline&1\end{array}$
$144=2\times2\times2\times2\times3\times3=2^4\times3^2$
$180=2\times2\times3\times3\times5=2^2\times3^2\times5$
$192=2\times2\times2\times2\times2\times3=2^6\times3$
Here, $12(i.e. 2^2 \times 3 = 12)$ is the highest common factor of the three numbers.
View full question & answer→MCQ 141 Mark
Mark $(\checkmark)$ against the correct answer in the following: Which of the following is a prime number?
View full question & answer→MCQ 151 Mark
Mark $(\checkmark)$ against the correct answer in the following: The product of two numbers is $2160$ and their $\ce{HCF}$ is $12.$ The $\ce{LCM}$ of these numbers is:
AnswerHere, $\ce{HCF} = 12$
Product of two number $= 2160$
We know:
$\ce{LCM} \times \ce{HCF} =$ Product of the two numbers
$\ce{LCM}=\frac{2160}{\text{HCF}}$
$=\frac{2160}{12}$
$= 180$
$\ce{LCM} = 180$
View full question & answer→MCQ 161 Mark
Mark $(\checkmark)$ against the correct answer in the following:What least number should be replaced for $^*$ so that the number $67301^*2$ is exactly divisible by $9?$
Answer$6 + 7 + 3 + 0 + 1 + ^* + 2 = 19 + ^*$
$8$ is the least number that should be added to $19$ such that number will be divisible by $9.$
Sum of the digits:
$6 + 7 + 3 + 0 + 1 + 8 + 2 = 27$
$27$ is divisible by $9.$
View full question & answer→MCQ 171 Mark
Mark $(\checkmark)$ against the correct answer in the following:Which of the following numbers is divisible by $6?$
- A
$67821$
- B
$78134$
- ✓
$87432$
- D
AnswerCorrect option: C. $87432$
$87432$
View full question & answer→MCQ 181 Mark
Find which of the following numbers are prime:
Answer$89$ is a prime number.
View full question & answer→MCQ 191 Mark
Mark $(\checkmark)$ against the correct answer in the following: Which of the following numbers is divisible by $3?$
- A
$24357806$
- B
$35769812$
- ✓
$83479560$
- D
$3336433$
AnswerCorrect option: C. $83479560$
$83479560$
View full question & answer→MCQ 201 Mark
Mark $(\checkmark)$ against the correct answer in the following:$\frac{289}{391}$ when reduced to lowest term is:
- A
$\frac{13}{17}$
- B
$\frac{17}{19}$
- ✓
$\frac{17}{23}$
- D
$\frac{17}{21}$
AnswerCorrect option: C. $\frac{17}{23}$
$\begin{array}{c|c}17&289\\\hline17&17\\\hline&1\end{array}$
$\begin{array}{c|c}17&391\\\hline23&23\\\hline&1\end{array}$
$289 = 17 \times 17$
$391 = 17 \times 23$
The $\ce{HCF}$ of $289$ and $391$ is $17.$
Dividing both the numerator and the denominator by $17:$
$\frac{289\div17}{391\div17}=\frac{17}{23}$
View full question & answer→MCQ 211 Mark
Mark $(\checkmark)$ against the correct answer in the following:
The least number divisible by each of the numbers $15, 20, 24, 32$ and $36$ is:
AnswerCorrect option: C. $1440$
The least number divisible by each of the numbers $15, 20, 24, 32$ and $36$ is their $\text{LCM.}$
$\begin{array}{c|c}2&15,20,24,32,36\\\hline2&15,10,12,16,18\\\hline2&15,5,6,8,9\\\hline2&15,5,3,4,9\\\hline2&15,5,3,2,9\\\hline3&15,5,3,1,9\\\hline3&5,5,1,1,3\\\hline5&5,5,1,1,1\\\hline&1,1,1,1,1\end{array}$
$\text{LCM} =2^5 \times 3^2 \times 5$
$=1440$
View full question & answer→MCQ 221 Mark
Mark $(\checkmark)$ against the correct answer in the following: $\frac{289}{391}$ When reduced to the lowest terms is:
- A
$\frac{11}{23}$
- B
$\frac{13}{31}$
- C
$\frac{17}{31}$
- ✓
$\frac{17}{23}$
AnswerCorrect option: D. $\frac{17}{23}$
$\ce{HCF} = 17$
Dividing both the numerator and the denominator by the $\ce{HCF}$ of $289$ and $391:$
$\begin{array}{c|c}17&289\\\hline17&17\\\hline&1\end{array}$
$\begin{array}{c|c}17&391\\\hline23&23\\\hline&1\end{array}$
$\frac{289\div17}{391\div17}=\frac{17}{23}$
View full question & answer→MCQ 231 Mark
Mark $(\checkmark)$ against the correct answer in the following:Every counting number has an infinite number of:
AnswerEvery counting number has an infinite number of multiples.
If $p$ is a counting number, its multiples are $1p, 2p, 3p....$
View full question & answer→MCQ 241 Mark
Mark $(\checkmark)$ against the correct answer in the following:
The $\text{LCM}$ of $12, 15, 20, 27$ is:
Answer$\begin{array}{c|c}2&12,15,20,27\\\hline2&6,15,10,27\\\hline3&3,15,5,27\\\hline3&1,5,5,9\\\hline3&1,5,5,3\\\hline5&1,5,5,1\\\hline&1,1,1,1\end{array}$
$\text{LCM}\ 2^2 \times 3^3 \times 5 = 540$
View full question & answer→MCQ 251 Mark
Mark $(\checkmark)$ against the correct answer in the following:
The LCM of $24, 36, 40$ is:
Answer$360$
$\begin{array}{c|c}2&24,36,40\\\hline2&12,18,20\\\hline2&6,9,10\\\hline3&3,9,5\\\hline3&1,3,5\\\hline5&1,1,5\\\hline&1,1,1\end{array}$
LCM =$ 2^3 \times 3^2 \times 5$
$= 360$
View full question & answer→MCQ 261 Mark
Mark $(\checkmark)$ against the correct answer in the following: Which of the following numbers is divisible by $4?$
- A
$78653234$
- B
$98765042$
- C
$24689602$
- ✓
$87941032$
AnswerCorrect option: D. $87941032$
$87941032$
View full question & answer→MCQ 271 Mark
Mark $(\checkmark)$ against the correct answer in the following: Which of the following is a prime number?
View full question & answer→MCQ 281 Mark
Mark $(\checkmark)$ against the correct answer in the following: The $\text{HCF}$ of $144$ and $198$ is:
AnswerWe first factorise the two numkbers:
$\begin{array}{c|c}2&144\\\hline2&72\\\hline2&36\\\hline2&18\\\hline3&9\\\hline3&3\\\hline&1\end{array}$
$\begin{array}{c|c}2&198\\\hline3&99\\\hline3&33\\\hline11&11\\\hline&1\end{array}$
$144=2\times2\times2\times2\times3\times3=2^4\times3^2$
$198=2\times3\times3\times11=2\times3^2\times11$
Here, $18(2 \times 3^2 = 18)$ is the highest common factor of the two numbers.
View full question & answer→MCQ 291 Mark
Mark $(\checkmark)$ against the correct answer in the following: The $\ce{HCF}$ of two co$-$primes is:
Answer$\ce{HCF}$ of two co$-$primes is $1.$
This is because two co$-$prime numbers do not have any common factor.
For example, $15$ and $16$ are co$-$primes.Their.
$\ce{HCF}$ is $1.$
View full question & answer→MCQ 301 Mark
Mark $(\checkmark)$ against the correct answer in the following: Which of the following numbers is divisible by $8?$
- A
$96354142$
- ✓
$37450176$
- C
$57064214$
- D
AnswerCorrect option: B. $37450176$
$37450176$
View full question & answer→MCQ 311 Mark
Mark $(\checkmark)$ against the correct answer in the following: Which of the following numbers is divisible by $6?$
- A
$8790432$
- B
$98671402$
- C
$85492014$
- ✓
View full question & answer→MCQ 321 Mark
Mark $(\checkmark)$ against the correct answer in the following: Three bells toll together at intervals of $9, 12, 15$ minutes. If they start tolling together, after what time will they next toll together?
- A
$1\text{ hour}$
- B
$1\frac12\text{ hours}$
- C
$2\frac12\text{hours}$
- ✓
$3\text{ hours}$
AnswerCorrect option: D. $3\text{ hours}$
The $\text{L.C.M}.$ of $9, 12$ and $15$ will give us the minutes after which the bells will next toll together.
$\begin{array}{c|c}2&9,12,15\\\hline2&9,6,15\\\hline3&9,6,15\\\hline3&3,1,5\\\hline5&1,1,5\\\hline&1,1,1\end{array}$
$\text{LCM} = 2^2 \times 3^2 \times 5$
$= 180$
So,the bells will toll together after $180 \min$.
On converting into hours:
$180/60 = 3 \text{hours}$
View full question & answer→MCQ 331 Mark
Mark $(\checkmark)$ against the correct answer in the following: The $\ce{HCF}$ of two numbers is $145$ and their $\ce{LCM}$ is $2175.$ If one of the numbers is $725,$ the other number is:
AnswerOne of the numbers is $725.$
$\ce{HCF} = 145$
$\ce{LCM }= 2175$
We know:
$\ce{LCM} \times \ce{HCF} =$ Product of the two numbers
$\therefore$ Product of the two numbers $= 145 \times 2175$
$= 315375$
$\therefore$ Other number $=\frac{315375}{725}$
$=435$
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