### Multiplication and division

 Description: multiplication and division Number of Questions: 80 Created by: Naresh Verma Tags: history of mathematics vedic mathematics maths
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Which of the following numbers are not divisible by 2, by 3 and by 6?

1. 321729

2. 197232

3. 972132

4. 312792

Correct Option: A
Explanation:

$321729$not divisible by $2,3,6$

$197232$ divisible by $2,3,6$
$972132$ divisible by $2,3,6$
$312792$ divisible by $2,3,6$

Evaluate :
$60\times 8$

1. 480

2. 58

3. 25

4. 420

Correct Option: A
Explanation:

We have,

$60\times 8$$=480$

Somya caught twice as many fishes as her dad. If her dad caught F fishes, how many fishes did Somya catch ?

1. $F + 2$

2. $F - 2$

3. $F \times 2$

4. $F \div 2$

Correct Option: C
Explanation:

Given that:

Somya caught twice as many fishes as her dad.
$\because$ Somya's dad caught $=F\$ Fishes
$\therefore$ Somya caught $=2\times F\$ Fishes

$587\times 999=$?

1. $586413$

2. $587523$

3. $614823$

4. $615173$

Correct Option: A
Explanation:

$587\times 999=587\times (1000-1)$
$=587\times 1000-587\times 1$
$=587000-587$
$=586413$

$(935421\times 625)=$?

1. $575648125$

2. $584638125$

3. $584649125$

4. $585628125$

Correct Option: B
Explanation:

$93521\times 625=935421\times {5}^{4}=935421\times {(\cfrac{10}{2})}^{4}$
$\cfrac{935421\times{10}^{4}}{{2}^{4}}=\cfrac{9354210000}{16}$
$=584638125$

$2056\times 987=$?

1. $1936372$

2. $2029272$

3. $1896172$

4. $1926172$

5. None of these

Correct Option: B
Explanation:

$2056\times 987=2056\times (1000-13)$
$=2056\times 1000-2056\times 13$
$=2056000-26728$
$=2029272$.

$72519\times 9999=$?

1. $725117481$

2. $674217481$

3. $685126481$

4. $696217481$

5. None of these

Correct Option: A
Explanation:

$72519\times 9999=72519\times(10000-1)$
$=72519\times 10000-72519\times1$
$=725190000-72519$
$=725117481$

$(123456789\times 72)=$?

1. $88888888$

2. $888888888$

3. $898989898$

4. $9999999998$

Correct Option: B
Explanation:

$12345679\times 72=123456789\times (70+2)$
$=12345679\times 70+123445679\times 2$
$=864197530+24691358$
$=888888888$

On multiplying a number by $7$, the product is a number each of whose digits is $3$. The smallest such number is:

1. $47619$

2. $47719$

3. $48619$

4. $47649$

Correct Option: A
Explanation:

By hit and trial , we find that
$47619\times=333333$.

$(112\times {5}^{4})=$?

1. $67000$

2. $70000$

3. $76500$

4. $77200$

Correct Option: B
Explanation:

$(112\times {5}^{4})=112\times { \left( \cfrac { 10 }{ 2 } \right) }^{ 4 }=\cfrac { 112\times { 10 }^{ 4 } }{ { 2 }^{ 4 } } =\cfrac { 1120000 }{ 16 } =70000$

The sum of all two digit numbers divisible by $5$ is:

1. $1035$

2. $1245$

3. $1230$

4. $945$

5. None of these

Correct Option: D
Explanation:

Required numbers are $10,15,20,25,......96$
This is an A.P. in which $a=10,d=5$ and $l=95$
${t} _{n}=95$ $\Rightarrow$ $a+(n-1)d=95$
$\Rightarrow$ $10+(n-1)\times 5=95$
$\Rightarrow$ $(n-1)\times 5=85$
$\Rightarrow$ $(n-1)=17$
$\Rightarrow$ $n=18$
$\therefore$ Required Sum $=\cfrac { n }{ 2 } (a+l)=\cfrac { 18 }{ 2 } \times (10+95)=(95\times 105)=945$

$5358\times 51=$?

1. $273258$

2. $273268$

3. $273348$

4. $273358$

Correct Option: A
Explanation:

$5358\times 51=5358\times (50+1)$
$=5358\times 50+5358\times 1$
$=267900+5358$
$=273258$

$1397\times 1397=$?

1. $1951609$

2. $1981709$

3. $18362619$

4. $2031719$

5. None of these

Correct Option: A
Explanation:

.

Multiply $78, 76$ using NIkhilam formula (sub-base) of vedic mathematics.

1. $5248$

2. $5758$

3. $59756$

4. $5928$

Correct Option: D

Multiply $132, 124$ by Urdhwtirgbhyaam method of vedic mathematics.

1. $15348$

2. $17548$

3. $16368$

4. None of these

Correct Option: C

Multiply $57, 68$ by Urdhwtirgbhyaam method of vedic mathematics.

1. $3846$

2. $3676$

3. $3876$

4. None of these

Correct Option: C

Multiply $349, 986$ by Urdhwtirgbhyaam method of vedic mathematics.

1. $355114$

2. $353514$

3. $344114$

4. None of these

Correct Option: C

Multiply $41, 41$ by Urdhwtirgbhyaam method of vedic mathematics.

1. $1681$

2. $1461$

3. $1535$

4. None of these

Correct Option: A

Multiply $12, 14$ by Urdhwtirgbhyaam method of vedic mathematics.

1. $156$

2. $148$

3. $188$

4. $168$

Correct Option: D

Multiply $19, 17$ using NIkhilam formula (sub-base) of vedic mathematics.

1. $303$

2. $343$

3. $373$

4. None of these

Correct Option: D

Multiply $234, 316$ by Urdhwtirgbhyaam method of vedic mathematics.

1. $73944$

2. $73454$

3. $76464$

4. None of these

Correct Option: A

Multiply $123, 45$ by Urdhwtirgbhyaam method of vedic mathematics.

1. $5535$

2. $5675$

3. $5435$

4. None of these

Correct Option: A

Multiply $32, 24$ by Urdhwtirgbhyaam method of vedic mathematics.

1. $758$

2. $768$

3. $724$

4. None of these

Correct Option: B

Multiply $390$ by $11$ using vedic mathematics.

1. $4350$

2. $4290$

3. $4560$

4. None of these

Correct Option: B

Multiply $9999$ by $9$ using vedic mathematics.

1. $89991$

2. $88991$

3. $89891$

4. None of these

Correct Option: A
Explanation:

9999  × 9
= (100000 - 1) 9
= 99999 - 9
= 89991

Multiply $987$ by $11$ using vedic mathematics.

1. $10857$

2. $12457$

3. $12337$

4. None of these

Correct Option: A

Multiply $111$ by $11$ using vedic mathematics.

1. $1221$

2. $1231$

3. $12321$

4. None of these

Correct Option: A

Multiply $28, 22$ using NIkhilam formula (sub-base) of vedic mathematics.

1. $616$

2. $626$

3. $656$

4. None of these

Correct Option: A

Multiply $432$ by $9$ using vedic mathematics.

1. $3788$

2. $3888$

3. $3988$

4. $3778$

Correct Option: B
Explanation:

432  × 9
= 432  × (10 - 1)
= 4320 - 432
= 3888

Multiply $386$ by $11$ using vedic mathematics.

1. $4246$

2. $4348$

3. $4366$

4. $4896$

Correct Option: A

Multiply $86$ by $11$ using vedic mathematics.

1. $936$

2. $946$

3. $956$

4. $966$

Correct Option: B
Explanation:
To multiply any number by 11 do the following:
Working from right to left
Write the rightmost digit of the starting number down.
Add each pair of digits and write the results down, (carrying digits where necessary right to left).
Finally write down the left most digit (adding any final carry if necessary).
For 8 6
8 (8+6) 6
8 (14) 6
(8+1) 4 6
86×11= 946
So option B is the correct answer.

Multiply $999$ by $11$ using vedic mathematics.

1. $10889$

2. $12489$

3. $10989$

4. None of these

Correct Option: C
Explanation:

999 ×  11 = 999 (10 + 1)
= 9990 + 999
= 10989

Multiply $99, 96$ using Nikhilam formula (sub-base) of vedic mathematics.

1. $9504$

2. $9254$

3. $9974$

4. None of these

Correct Option: A

Multiply $10001$ by $99$ using vedic mathematics.

1. $990009$

2. $990999$

3. $909999$

4. None of these

Correct Option: D
Explanation:

10001  × 99 = 10001 (100 - 1)
= 1000100 - 10001
= 990099

Multiply $90098$ by $99$ using vedic mathematics.

1. $8919702$

2. $8917702$

3. $8919902$

4. None of these

Correct Option: A
Explanation:

90098  × 99 = 90098 (100 - 1)
= 9009800 - 90098
= 8919702

Multiply $5555$ by $9$ using vedic mathematics.

1. $49985$

2. $49995$

3. $495955$

4. None of these

Correct Option: B
Explanation:

5555  × 9 = 5555 (10 - 1)
= 55550 - 5555
= 49995

Multiply $1111$ by $9$ using vedic mathematics.

1. $9990$

2. $9999$

3. $9119$

4. None of these

Correct Option: B
Explanation:

1111  × 9 = 1111 (10 - 1)
= 11110 - 1111
= 9999

Identify the correct representation of the multiplication of $9999$ by $99$ using vedic mathematics.

1. $999900-9900$

2. $999999-9999$

3. $999900-9999$

4. None of these

Correct Option: C
Explanation:

9999  × 99 = 9999 (100 - 1)
= 999900 - 9999

identify the correct representation of the multiplication of $1111$ by $9$ using vedic mathematics.

1. $11110-9999$

2. $11111-1110$

3. $11110-1111$

4. None of these

Correct Option: C
Explanation:

1111  × 9 = 1111 (10 - 1) = 11110 - 1111

Multiply $9999$ by $99$ using vedic mathematics.

1. $988801$

2. $988901$

3. $989801$

4. $989901$

Correct Option: D
Explanation:

9999  × 99 = 9999 (100 - 1)
= 999900 - 9999
= 989901

Identify the correct representation of the multiplication of $12345$ by $99$ using vedic mathematics.

1. $1234567-12345$

2. $1234500-12345$

3. $12345000-99$

4. None of these

Correct Option: B
Explanation:

12345  × 99 = 12345 (100 - 1)
= 1234500 - 12345

Multiply $12345$ by $99$ using vedic mathematics.

1. $1222455$

2. $1223155$

3. $1222155$

4. $1233155$

Correct Option: C
Explanation:

12345  × 99 = 12345  × (100  - 1)
= 1234500 - 12345
= 1222155

Identify the correct representation of the multiplication of $9999$ by $9$ using vedic mathematics.

1. $99990-9999$

2. $99980-9999$

3. $99990-9990$

4. $99999-9990$

Correct Option: A
Explanation:

9999  × 9 = 9999 (10 - 1) = 99990 - 9999

Find the cube of $103$ by Nikhilam formula of Vedic Mathematics.

1. $1092727$

2. $1093727$

3. $1092997$

4. None of these

Correct Option: A

Multiply $98, 97, 99$ by Nikhilam formula of vedic maths.

1. $941194$

2. $941094$

3. $941294$

4. None of these

Correct Option: B

Multiply $98, 99, 99$ by Nikhilam formula of vedic maths.

1. $966498$

2. $964498$

3. $969498$

4. None of these

Correct Option: D

Identify the representation of two rightmost digits in the multiplication $98, 97, 99$ by Nikhilam formula of vedic maths.

1. $100-6$

2. $100-(2)(3)(1)$

3. $06$

4. None of these

Correct Option: A,B
Explanation:

The two rightmost digits in the multiplication 98,97, 99 = 100 - (2 + 3 + 1) = 100 - (2)(3)(1)

Multiply $51, 52, 53$ by Nikhilam formula of vedic maths.

1. $140556$

2. $140456$

3. $1445566$

4. None of these

Correct Option: A

Identify the two rightmost digits in the multiplication $98, 97, 99$ by Nikhilam formula of vedic maths.

1. $106$

2. $94$

3. $98$

4. None of these

Correct Option: B
Explanation:

The two rightmost digits in the multiplication 98,97, 99 = 100 - (2 + 3 + 1) = 100 - 6 = 94

Multiply $99$ by $99$ using vedic mathematics.

1. $9001$

2. $9881$

3. $9801$

4. None of these

Correct Option: C
Explanation:

99  × 99 = 99 (100 - 1)
= 9900 - 99
= 9801

Find the correct representation of deviations from the base in the multiplication of $101, 102, 103$ by Nikhilam formula of vedic maths.

1. $1, 2, 3$

2. $01, 02, 03$

3. $10, 20, 30$

4. None of these

Correct Option: B
Explanation:

The correct representation of deviations from the base in the multiplication of 101,102,103 by Nikhilam formula of vedic maths is 01, 02 and 03.

Perform $12\div 9$ using Nikhilam Sutra Method on base $10$. Also, find the quotient$(Q)$ and remainder$(R)$.

1. $Q=1$ and $R=3$

2. $Q=1$ and $R=2$

3. $Q=1$ and $R=0$

4. $Q=1$ and $R=1$

Correct Option: A

Find the cube of $96$ by Nikhilam formula of Vedic Mathematics.

1. $877736$

2. $884736$

3. $844736$

4. None of these

Correct Option: B

$21,35,680$ voters are to be equally distributed among $235$ polling booths. How many voters will be there in each polling booth?

1. $9080$

2. $9800$

3. $9088$

4. $8800$

Correct Option: C
Explanation:

Total number of voters $= 21,35,680$
Number of polling booth $= 235$
So, number of voters at each polling booth $= 21,35,680 \div 235 = 9088$.

Dividing using 'Dhwajanka' Sutra.
(i) $3987\div 28$
(ii) $5786 \div 78$
(iii) $7396 \div 82$

1. $i) Q=140, R=14, ii)Q=74, R=14, iii)Q=90, R=16$

2. $i) Q=142, R=11, ii)Q=74, R=14, iii)Q=90, R=16$

3. $i) Q=142, R=11, ii)Q=74, R=0, iii)Q=90, R=16$

4. $i) Q=142, R=11, ii)Q=74, R=14, iii)Q=90, R=12$

Correct Option: B

Find the cube of $99$ by Nikhilam formula of Vedic Mathematics.

1. $97299$

2. $972299$

3. $973299$

4. None of these

Correct Option: D

Write multiplication table of $46$ by using Vinculum method and identify fourth term in the table.

1. $184$

2. $230$

3. $143$

4. $138$

Correct Option: A

If $31z5$ is a multiple of $9$, where $z$ is a digit, what is the value of $z$?

1. 0

2. 4

3. 7

4. 9

Correct Option: A,D
Explanation:

Given that $31z5$ is a multiple of $9$.

According to the divisibility rule of $9$, the sum of all the digits should be a multiple of $9$.
Therefore,
$3 + 1 + z + 5 = 9\ OR\ 18$
$\Rightarrow z = 9 - 9 = 0$
$\Rightarrow z = 18 - 9 = 9$

Multiply $54, 57$ using NIkhilam formula (sub-base) of vedic mathematics.

1. $3278$

2. $3768$

3. $3078$

4. None of these

Correct Option: C

Multiply $63, 58$ using NIkhilam formula (sub-base) of vedic mathematics.

1. $3454$

2. $3654$

3. $3754$

4. None of these

Correct Option: B

Multiply $524$ by $11$ using vedic mathematics.

1. $5854$

2. $5354$

3. $5774$

4. None of these

Correct Option: D
Explanation:
To multiply any number by 11 do the following:

Working from right to left

Write the rightmost digit of the starting number down.

Add each pair of digits and write the results down, (carrying digits where necessary right to left).

Finally write down the left most digit (adding any final carry if necessary).

For  5 2 4

5 (5+2) (2+4) 4

5764

There are no options with this.
So, option D is the correct answer.

Multiply $11, 15$ using NIkhilam formula (sub-base) of vedic mathematics.

1. $145$

2. $165$

3. $185$

4. None of these

Correct Option: B

Multiply $12, 13, 17$ by Nikhilam formula of vedic maths.

1. $2662$

2. $2652$

3. $2552$

4. None of these

Correct Option: B

$(102\times 98)-(9.5\times 10.5)=$

1. 9896.25

2. 10095.75

3. 21

4. 9897.75

Correct Option: A
Explanation:

$(102 \times 98) -(9.5 \times 10.5)=(100 + 2) (100 -2) -[(10 -0.5) (10 + 0.5)]$
$=(100^2-2^2) -(10^2 -0.5^2)$
$=10000 -4 -(100 -0.25)$
$=10000 -104 + 0.25$
$=9896 + 0.25=9896.25$

Identify groups to be made in the multiplication $349, 986$ by Urdhwtirgbhyaam method of vedic mathematics.

1. $3\times 9\ / \ 3\times 8+4 \times 9 \ / \ 3\times 6 \ + 4 \times 8 / \ 4\times 6 \ + 9 \times 8 \ / \ 9\times 6\$

2. $3\times 9\ / \ 3\times 8+4 \times 9 \ / \ 3\times 6\ +9 \times 9+ 4 \times 8 / \ 4\times 6 \ + 9 \times 8 \ / \ 9\times 6\$

3. $3\times 9\ / \ 4 \times 9 \ / \ 3\times 6\ +9 \times 9+ 4 \times 8 / \ 4\times 6 \ + 9 \times 8 \ / \ 9\times 6\$

4. None of these

Correct Option: B

Multiply $12, 18$ using NIkhilam formula (sub-base) of vedic mathematics.

1. $246$

2. $236$

3. $216$

4. None of these

Correct Option: C

Find the cubage of $65$ by Nikhilam formula of Vedic Mathematics.

1. $27005$

2. $235625$

3. $274625$

4. None of these

Correct Option: C

Find the deviation in the cubage of $96$ by Nikhilam formula of Vedic Mathematics.

1. $04$

2. $-04$

3. $6$

4. None of these

Correct Option: B

Find the representation of the rightmost two digits in the cubage of $96$ by Nikhilam formula of Vedic Mathematics.

1. $100-64$

2. $-64$

3. $64$

4. None of these

Correct Option: A

Perform division of $422\div 11$ using Nikhilam Sutra Method on base $10$. Also, find the quotient$(Q)$ and remainder$(R)$.

1. $Q=40$ and $R=3$

2. $Q=39$ and $R=5$

3. $Q=33$ and $R=3$

4. $Q=38$ and $R=4$

Correct Option: D

Multiply $9, 8, 15$ by Nikhilam formula of vedic maths.

1. $1060$

2. $1070$

3. $1080$

4. None of these

Correct Option: C

Multiply $101, 102, 103$ by Nikhilam formula of vedic maths.

1. $1061166$

2. $1061106$

3. $1661106$

4. None of these

Correct Option: B

Find the cubage of $80$ by Nikhilam formula of Vedic Mathematics.

1. $512000$

2. $512200$

3. $514000$

4. $516000$

Correct Option: A

Multiply $32, 38$ using Nikhilam formula (sub-base) of vedic mathematics____________.

1. $1216$

2. $1261$

3. $1621$

4. $1612$

Correct Option: A

Which of the following statements is CORRECT?

1. The product of $\dfrac{231}{119}$ and $\dfrac{117}{118}$ is greater than $\dfrac{231}{119}$

2. The product of $\dfrac{17}{25}$ and $\dfrac{117}{225}$ is greater than $\dfrac{17}{25}$

3. The product of $\dfrac{1735}{2001}$ and $\dfrac{2734}{2724}$ is greater than $\dfrac{1735}{2001}$

4. $\dfrac{1}{3}$ of $\dfrac{4}{5}$ is greater than $\dfrac{3}{4}$ of $\dfrac{8}{7}$

Correct Option: C
Explanation:

Option $[A]$  :  $\dfrac{117}{118}<1$.
The product of any number with a number less than $1$ is less than that number.
So,  $\dfrac{231}{119}\times\dfrac{117}{118}<\dfrac{231}{119}$.

$\Rightarrow[A]$ is not correct.

Option $[B]$  :  $\dfrac{117}{225}<1$
The product of any number with a number less than $1$ is less than that number.
So,  $\dfrac{17}{25}\times\dfrac{117}{225}<\dfrac{17}{25}$.
$\Rightarrow[B]$ is not correct.

Option $[C]$  :  $\dfrac{2734}{2724}>1$
The product of any number with a number greater than $1$ is greater than that number.
So,  $\dfrac{1735}{2001}\times\dfrac{2734}{2724}>\dfrac{1735}{2001}$.
$\Rightarrow[C]$ is correct.

Option $[D]$  :
$\dfrac{1}{3}\times\dfrac{4}{5}=\dfrac{4}{15}\approx0.267$   and   $\dfrac{3}{4}\times\dfrac{8}{7}=\dfrac{6}{7}\approx0.857$.
But  $0.857>>0.267$.
So, $[D]$ is not correct.

$\therefore$  The correct answer is  $[C]$.

A milkman sells $42$ litres of milk at Rs. $19.75$ per litre to a hostel. How much money should be get from the hostel?

1. Rs. $1892$

2. Rs. $829.50$

3. Rs. $165.85$

4. Rs. $122.50$

Correct Option: B
Explanation:

Cost of $1$ liter milk = $Rs.19.75$

$\Rightarrow$   Cost of $42$ liters milk = $Rs(19.75\times 42)=Rs.829.50$

Multiply $51, 55$ using Nikhilam formula (sub-base) of vedic mathematics.

1. $2850$

2. $2805$

3. $2508$

4. $2580$

Correct Option: B

A board 7 feet 9 inches long is divided into 3 equal parts. What is the length of each part?

1. 2 feet 9 inches

2. 2 feet 7 inches

3. 2 feet 12 inches

4. 2 feet 3 inches

Correct Option: B
Explanation:

Length of board $=\text{7 feet 9 inches}$

$=(7\times 12+9)$ inches       $[\because \text{1 feet = 12 inches}]$
$=93 inches$
Number of parts to be cut $3$
$\therefore$ Length of each part $=(93+3) \text{inches}$
$=\text{31 inches}$
$=\text{2feet 7 inches}$

Find the cubage of $71$ by Nikhilam formula of Vedic Mathematics.

1. $359911$

2. $357911$

3. $351911$

4. $385911$

Correct Option: B
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