### Operations - class-VI

 Description: operations Number of Questions: 91 Created by: Niharika Sharma Tags: real numbers (rational and irrational numbers) playing with numbers operations natural numbers mental skills whole numbers and operations with whole numbers the fish tale four operations number world maths numbers : revision calculations and mental strategies 2
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The given table shows the average temperature of some cities of India in a particular month.

City Average maximum temperature Average minimum temperature
New Delhi $39^oC$ $27^o$
Mumbai $36^oC$ $19^oC$
Ahemdabad $37^oC$ $19^oC$
Chennai $42^oC$ $26^oC$
Kolkata $38^oC$ $24^oC$

Which city has the highest difference its average maximum temperature and average minimum temperature?

1. Kolkata

2. Mumbai

3. Chennai

Correct Option: D
Explanation:
Highest difference of arg maximum temperature & arg minimum temperature.

New Delhi = $39^{\circ}-27^{\circ}=12^{\circ}C$

Mumbai = $36^{\circ}-19^{\circ}=17^{\circ}C$

Ahmadabad = $37^{\circ}-19^{\circ}=18^{\circ}C$

Chennai = $42^{\circ}-26^{\circ}=16^{\circ}C$

Kolkata = $38^{\circ}-24^{\circ}=14^{\circ}C$

$\therefore$ Highest difference = $18^{\circ}C$ in city Ahmadabad.

Jenny has $4$ red roses and $5$ yellow roses. How many roses does Jenny have in all

1. $7$

2. $4$

3. $5$

4. $9$

Correct Option: D
Explanation:

$Total &gt;roses =4+5=9$

Shraddha needs $6$ containers which can hold $15600$ oil. Find the capacity of each container.

1. $2500$

2. $2600$

3. $3200$

4. $152100$

Correct Option: B
Explanation:

$6$ containers can hold $15600$ amount of oil

capacity of each container is $\dfrac{15600}{6}=2600$

If average of $6$ consecutive numbers is $48$what is the difference between the smallest and the largest numbers ?

1. $5$

2. $10$

3. $9$

Correct Option: A
Explanation:

Let the $6$ numbers are $x, x+1, x+2, x+3, x+4, x+5$.

Since,
$average=48$
$\dfrac{x+x+1+x+2+x+3+x+4+x+5}{6}=48$
$6x+15=288$
$6x=273$
$x=45.5$
So,
The smallest number $=45.5$
The largest number $=x+5=45.5+5=50.5$
Difference $=50.5-45.5=5$

The additive inverse of $\sqrt { 3 } -2\quad is$_____________

1. $\sqrt { 3 } +2$

2. $-\sqrt { 3 } +2$

3. $-\sqrt { 3 } -2$

4. $\sqrt { 3 } +\sqrt { 2 }$

Correct Option: B
Explanation:
The additive inverse of a number a is the number that, when added to a, yields zero.
This number is also known as the opposite (number), sign change, and negation.

$Additive \ Inverse \ of (\sqrt {3}-2 )\ is$
$\rightarrow -(\sqrt{3}-2)$
$\rightarrow -\sqrt{3}+2$
$\rightarrow B \ is \ correct \ answer$

which is the number formed by $34 TL,2TL, 4TH, 5H, 2T$ and $5U$

1. $54,04,525$

2. $3, 40, 24, 525$

3. $24, 34, 255$

4. $52, 34, 245$

Correct Option: A
Explanation:
34 Ten lakhs =      34,00,000
2 Ten lakhs =        20,00,000
4 Ten thousands = 4,000
5 hundreds =          500
2 tens =                   20
5 units =                  5
____________
54,04,425

State whether the following statement is True or False.
$600$ is the successor of $599$.

1. True

2. False

Correct Option: A
Explanation:

True,  we can find the successor of $599$ as follows:

$=599+1$
$=600$

State whether the following statement is True or False.
$400$ is the predecessor.

1. True

2. False

Correct Option: B
Explanation:

False, as predecessor of  $399$ is $398 (399-1=398)$

State whether the following statement is True or False.
The predecessor of a two digit number is never a single digit number.

1. True

2. False

Correct Option: B
Explanation:

False, since we can clearly analyse that predecessor of $10$ is

$10-1=9$
And $9$ is a single digit number.
Hence predecessor of two digit number is single digit number.

State whether the following statement is True or False.
The successor of a two digit number is always a two digit number.

1. True

2. False

Correct Option: B
Explanation:

False, as successor of $99$ is $100$.

$99$ is a two digit number whereas $100$ is a three digit number.

Find : $50342135 -46380651 = .............$

1. $3961484$

2. $3942384$

3. $3969484$

4. $3989284$

Correct Option: A
Explanation:

$50342135 - 46380651 = 3961484$.

So, correct answer is option A.

Find the value of $7895432-1689654$.

1. $6105778$

2. $6205778$

3. $6205788$

4. $6205888$

Correct Option: B
Explanation:
$7895432-1629654=6205778$
so correct answer will be option B

What is $1 + 2-3 + 4-5 + 6-7 + 8$ ?

1. $2$

2. $3$

3. $4$

4. $6$

Correct Option: D
Explanation:

$1 + 2 - 3 + 4 - 5 + 6 - 7 + 8$

$=3 - 3 + 4 - 5 + 6 - 7 + 8$
$=0 + 4 - 5 + 6 - 7 + 8$
$=4 + 1 - 7 + 8$
$=5+1$

$=6$
Thus, the correct answer is $6$.

Sum of 10 and 40 is

1. $20$

2. $0$

3. $50$

4. $400$

Correct Option: C
Explanation:

1 0

+ 4 0
-----------
5 0
So correct answer will be option C

Difference of $500$ and $200$ is

1. $100$

2. $300$

3. $0$

4. $1000$

Correct Option: B
Explanation:

5 0 0

- 2 0 0
-----------
3 0 0
So the correct answer will be option B

The difference between the largest 5-digit number and smallest 5-digit number is

1. 90,000

2. 89,999

3. 109,999

4. None

Correct Option: B
Explanation:

$99999$
$-10000$
______
$89999$

Two pipes X and Y can fill a cistern in 24 min. and 32 min. respectively. If both the pipes are opened together, then after how much time Y should be closed so that the tank is full in 18 minutes?

1. 6 min

2. 8 min

3. 10 min

4. None of these

Correct Option: B
Explanation:

Let Y closed pipe after a min .
Then part filled by (X+Y) in a min +Part filled by X in (18-x)
So $a(\frac{1}{24}+\frac{1}{32})+(18-a)\frac{1}{24}= 1$
Multy by 96
Or 4a+3a+72-4a=96
Or 3x=24
Or x=8 min

If $\displaystyle x=\frac{4\sqrt{2}}{\sqrt{2}+1}$ then find the value of $\displaystyle \frac{1}{\sqrt{2}}\left ( \frac{x+2}{x-2}+\frac{x+2\sqrt{2}}{x-2\sqrt{2}} \right )$

1. $\displaystyle \sqrt{2}$

2. $12+8\displaystyle \sqrt{2}/5$

3. $12-8\displaystyle \sqrt{2}$

4. $\displaystyle \frac{16\sqrt{2}+24}{5}$

Correct Option: A
Explanation:

$x=\frac{4\sqrt{2}}{\sqrt{2+1}}$
$\frac{1}{\sqrt{2}}\left ( \frac{x+2}{x-2}+\frac{x+2\sqrt{2}}{x-2\sqrt{2}} \right )$
Put the value of x
$\frac{1}{\sqrt{2}}\left ( \frac{\frac{4\sqrt{2}}{\sqrt{2+1}}+2}{\frac{4\sqrt{2}}{\sqrt{2+1}}-2}+\frac{\frac{4\sqrt{2}}{\sqrt{2+1}}+2\sqrt{2}}{\frac{4\sqrt{2}}{\sqrt{2+1}}-2\sqrt{2}} \right )$
=$\frac{1}{\sqrt{2}}\left ( \frac{4\sqrt{2}+2\sqrt{2}+2}{4\sqrt{2}-2\sqrt{2}-2} \right )+\left ( \frac{4\sqrt{2}+4+2\sqrt{2}}{4\sqrt{2}-4-2\sqrt{2}} \right )$
=$\frac{6\sqrt{2}+2}{2\sqrt{2-2}}+\frac{6\sqrt{2}+4}{2\sqrt{2}-4}$
=$\frac{1}{\sqrt{2}}\left ( \frac{32-24\sqrt{2}}{16-12\sqrt{2}} \right )$
=$\sqrt{2}$

If P : Q : R = 6 : 5 : 4 and $\displaystyle P^{2}+Q^{2}+R^{2}=192500$ then find $\displaystyle \frac{(P+Q-R)}{2}$

1. 175

2. 165

3. 185

4. 200

Correct Option: A
Explanation:

$:Q:R\quad =\quad 6:5:4\ Let\quad P\quad \quad =\quad 6x\ Q=\quad 5x\ R\quad =\quad 4x\ { P }^{ 2 }+{ Q }^{ 2 }{ +\quad R }^{ 2 }\quad =\quad 192500\ { (6x) }^{ 2 }+{ (5x) }^{ 2 }+(4x)^{ 2 }\quad =\quad 192500\ 77{ x }^{ 2 }\quad =\quad 192500\ { x }^{ 2 }\quad =\quad 2500\ x\quad =\quad 50\ \ \frac { P+Q-R }{ 2 } \quad =\quad \frac { 6x+5x-4x }{ 2 } \quad =\quad \frac { 7x }{ 2 } \quad =\quad \frac { 7\times 50 }{ 2 } \quad =\quad 175$

Given $5A9+3B7+2C8=1114$, then the maximum value of $C$ is

1. $5$

2. $7$

3. $9$

4. $none\ of\ these$

Correct Option: C
Explanation:

1  2
5  A  9
3  B  7
2  C  8
1 1  1  4
$2+A+B+C=11$
$A+B+C=9$
Clearly max value of $C=9$

A 3-digit number 4a3 is added to another 3-digit number 984 to give the four-digit number 13b7 which is divisible by 11 Then (a + b) is

1. 10

2. 11

3. 12

4. 15

Correct Option: A
Explanation:

According to the question
$4 a 3 + 9 8 4 = 1 3 b 7$
$a + 8 = b$
Then$b - a = 8$
According to the question  13b7 is divisible by 11
$(7 + 3) - (b + 1) = (9 - b)$
$(9 - b) = 0$
$b = 9$
$b = 9 and a = 1$
Then $a+b=9+1=10$

In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. If she attempts in all 50 questions and scores 120 marks, the number of questions she attempts correct is........

1. 62

2. 44

3. 42

4. 34

Correct Option: D
Explanation:

Let student get x correct answer then 50-x student get wrong answer
Then 4(x)+(50-x)(-1)=120
Or 4x-50+x=120
Or 5x=120+50=170
Or x=34

What is the value of $(\sqrt 7+\sqrt 5)(\sqrt 7-\sqrt 5)$?

1. 1

2. 2

3. 5

4. 3

Correct Option: B
Explanation:

$(\sqrt 7+\sqrt 5)(\sqrt 7-\sqrt 5)$
$\Rightarrow \left(\sqrt {7}\right)^2-\left(\sqrt{5}\right)^2$
$\Rightarrow 7-5 =2$

If the sum of two consecutive odd numbers is 2004, then the smaller of the two numbers could be

1. 2001

2. 1001

3. 1003

4. 1

Correct Option: B
Explanation:

Let the two consecutive odd numbers are x and x+2
$x+x+2 = 2004$
$x+x+2-2 = 2004 -2$ (Subtract 2 from both the sides)
$2x = 2002$
$\frac{2x}{2} = \frac{2002}{2}$ (Divide 2 from both the sides)
$x = 1001$
Hence two numbers are 1001 and 1003

How many times does the sum of 375 and 125 contain their difference?

1. $5$

2. $4$

3. $3$

4. $2$

Correct Option: D
Explanation:

The sum of  375 and 125 $=375+125 = 500$
The difference of 375 and 125 $= 375-125 = 250$
Hence Sum contains $500 \div 250 = 2$ times their differences.

A man can row 16 km downstream in one hour but upstream he takes twice the time then the speed of the current is

1. 8 km/h

2. 12 km/h

3. 4 km/h

4. 2 km/h

Correct Option: C
Explanation:

The man down stream is 16 km in one hour and he take twice time in upstream

Then he take time 2 hour in 16 km
So speed in upstream =$\frac{16}{2}=8 km /hr$
Then current spread =$\frac{16-8}{2}=4$ km/hr

If a=2, b=3, c=4, then the difference between $\displaystyle 2\frac{3}{4}$ and $\displaystyle b\frac{a}{c}$ is

1. $-1/4$

2. $1/4$

3. $-3/4$

4. $5/4$

Correct Option: C
Explanation:

If a=2 ,b=3 and c=4

Then $b\tfrac{a}{c}=3\tfrac{2}{4}=3\tfrac{1}{2}$
Then difference between=$2\tfrac{3}{4}-3\tfrac{1}{2}=\frac{11}{4}-\frac{7}{2}=\frac{11-14}{4}=\frac{-3}{4}$

If 125 x centimetre per second = (x+7) km/hour then the value of x is

1. 4

2. 3

3. 2

4. 1

Correct Option: C
Explanation:

Given 125 x cm \second=(x+7)x km\hr

WE know that 125 cm \ sec =4.5 km \ hr
$\therefore 125x cm\ sec =4.5 x km/hr$
Then $4.5 x=(x+7)\Rightarrow 4.5x-x=7\Rightarrow 3.5 x=7 \Rightarrow x=2$

If 5 labourers can make 5 mats in 5 hours then the number of mats that 10 labourers can make in 10 hours are

1. 10

2. 20

3. 15

4. 100

Correct Option: B
Explanation:

Given 5 mates in 5 hours makes 5 laborers

Then 10  laborers can make in 10 hours =$\frac{5\times 10\times 10}{5\times 5}=20$

The average weight of 7 men is diminished by 3 kg when one of them who weighs 73 kg is replaced by a new man then the weight of the new man is

1. 50 kg

2. 52 kg

3. 53 kg

4. 54 kg

Correct Option: B
Explanation:

The averages weight of seven man diminished by 3 kg .Then total weight diminished by $3\times 7=21 kg$

If one of them whose weight is 73 kg is replased by anew man
Then weight of new man =72-21=52 kg

What number should be subtracted from each of the numbers 54, 71, 75 and 99, so that the remainders may be in proportion?

1. 5

2. 4

3. 3

4. 2

Correct Option: C
Explanation:

Let the number to be subtracted is $x$

$(54-x), (71-x), (75-x)$  and $(99-x)$ are in proportion

$\Rightarrow \dfrac{54-x}{71-x}=\dfrac{75-x}{94-x}$ Which is true if $x=3$

$\Rightarrow \dfrac{54-3}{71-3}=\dfrac{75-3}{94-3}$

$\Rightarrow \dfrac{51}{68}=\dfrac{72}{91}$

i.e $\Rightarrow \dfrac{3}{4}=\dfrac{3}{4}$

Then subtracted $3$ in these number may be in proportion

Sum of the greatest 8 digit number and the smallest 9 digit number is

1. 1,99,99,999

2. 19,99,99,999

3. 99,99,99,999

4. 1,00,00,999

Correct Option: B
Explanation:

Greatest - 8 digit no. 99999999
Smallest - 9 digit no. $\underline {100000000}$
$=\underline {199999999}$

A student was asked to multiply a certain number by 3 and to add 2 to it, but he divided the number by 3 and subtracted 2 from it and got the number 1. The correct answer is

1. 9

2. 25

3. 29

4. none of these

Correct Option: C
Explanation:

Let the certain number be x
As per problem,
$\Rightarrow \frac { x }{ 3 } -2=1$
$\Rightarrow \frac { x-6 }{ 3 } =1$
$\Rightarrow x-6=3$
$\Rightarrow x=9$
The correct answer will be $9\times 3+2=27+2=29$

A shopkeeper had a stock of 23,898 kg of wheat out of which 1,795 kg is sold in the morning and 2,348 kg of wheat is sold in the evening. Quantity of wheat left in the shop is

1. 1,97,555 kg

2. 197 kg

3. 19,755 kg

4. 1,975 kg

Correct Option: C
Explanation:

Stock $=23,898 kg$.
Stock sold in morning $=1,795$
Stock sold in evening $=\underline {2,348}$
$\underline {4,143}$
Stock left $=23,898-4143$
$=19,755 kg$.

The population of a city is 5,12,10,913. Out of which 23,05,218 were males, 18,47,525 were females and remaining are children. The number of children in the city is

1. 4,70,58,170

2. 5,53,63,656

3. 5,07,53,220

4. 5,16,68,606

Correct Option: A
Explanation:

$18,47,525$
$+\underline {23,05,218}$
$\underline { 41,52,743}$
$\therefore$ Number of children
$=5,12,10,913-41,52,743$
$=4,70,58,170$

Is it possible to make 1000 with eight 8's in any way by using any operation?

1. Yes

2. No

3. Impossible

4. None of these

Correct Option: A
Explanation:

888
088
008
008
$\underline {+8}$
$\underline {1000}$

The maximum temperature on a day is 35$^o$C and the minimum temperature is 25$^o$C. The difference of these temperatures, on Fahrenheit scale is

1. 25$^o$F

2. 75$^o$F

3. 50$^o$F

4. 100$^o$F

Correct Option: C
Explanation:

$35^oC- 25^o C = 10^oC$
$10^o C = \displaystyle \left( 10 \times \frac{9}{5} \right ) + 32$
$= 18 + 32 = 50^o F$.

Sum of $2.8, 26.3$ and $62.874$ is ______

1. $91.974$

2. $9.1974$

3. $919.74$

4. $9197.4$

Correct Option: A
Explanation:

To add Various numbers with different decimal points we pick the number with the largest decimal point and extend the others to the same decimal point.

In our question,

$2.800+26.300+62.874= 91.974$

So option A is the correct answer.

A shopkeeper sold$\ 12.750\ kg$ of sugar on a day. On the next day he sold$\ 38.250\ kg$ of sugar. On the third day he sold $\ 50.50\ kg$ of sugar. How much of sugar in all did the shopkeeper sell?

1. 100 kg

2. 101.5 kg

3. 102.5 kg

4. 101 kg

Correct Option: B
Explanation:

The amount of sugar sold on first day = 12.75 Kg

The amount of sugar sold on second day = 38.25 Kg
The amount of sugar sold on third day = 50.50 Kg

We have to calculate the total sugar sold by the shopkeeper. Thus, we have to take the sum of sugar sold on all three days.

$\therefore$ The total sugar sold by the shopkeeper is $12.75 + 38.25 + 50.50 = 101.5$

In a movie hall, 363 seats are vacant and 1560 seats are occupied. What is the seating capacity of the hall ?

1. 1923

2. 2000

3. 1900

4. 2393

Correct Option: A
Explanation:

In a movie hall, the vacant seats are $=363$

And occupied seats are $=1560$

Therefore, the capacity of the hall will be
$=1560+363$
$=1923$

2530 soldiers were sent out on a mission. Each army truck could carry a maximum of 55 soldiers. How many army trucks were needed to carry all 2530 soldiers ?

1. 44

2. 45

3. 46

4. 47

Correct Option: C
Explanation:

Each army truck could carry a maximum soldiers $=55$

Therefore, the number of trucks are required for $2530$ soldiers
$=\dfrac{2530}{55}$
$=46$ trucks

A balloon seller sold 236 red balloons, 23 white balloons and 749 blue balloons. How many balloons were sold in all ?

1. 186

2. 654

3. 1,005

4. 1,008

Correct Option: D
Explanation:

A balloon seller sold $=236$ red balloons

$=23$ white balloons
$=749$ blue balloons

Therefore, the total numbers of balloons will be sold
$=236+23+749$
$=1008$

$\displaystyle \Uparrow \, \Uparrow\, \Uparrow\, \Uparrow$  Number represented by figures is ,if each symbol represents 5 houses

1. 4

2. 20

3. 5

4. 40

Correct Option: B
Explanation:

There are 4 symbols used in the question to depict houses.

Each symbol = 5 houses.
So total number of houses= 4×5 = 20 houses.
Hence option B is the correct answer.

The sum of all even natural numbers between $1$ and $31$ is:

1. $16$

2. $128$

3. $240$

4. $512$

Correct Option: C
Explanation:

Required sum $=(2+4+6+......+30)$
This is an A.P in which $a=2,d=(4-2)=2$ and $l=30$.
Let the number of terms be $n$. Then,
${t} _{n}=30$ $\Rightarrow$ $a+(n-1)d=30$
$\Rightarrow$ $2+(n-1)\times 2=30$
$\Rightarrow$ $n-1=14$
$\Rightarrow$ $n=15$
$\therefore$ ${S} _{n}=\cfrac{n}{2}(a+l)=\cfrac{15}{2}\times (2+30)=240$

If Seema and Reema has $10$ and $6$ chocolates respectively. Find the total number of chocolates.

1. $10$

2. $6$

3. $16$

4. $4$

Correct Option: C
Explanation:

Number of chocolates with Seema $=10$

Number of chocolates with Reema $=6$
$\therefore$ total number of chocolates $=10+6=16$
Option $C$ is correct

A box contains $25$ packets of pencils. Sachin takes $7$ packets, Ajay takes $8$ packet. How many packets are left in the box?

1. $25$

2. $10$

3. $18$

4. $17$

Correct Option: B
Explanation:

Total number of packets  pencils $=25$

Number of packets pencils taken by Sachin $=7$
Number of packets of pencils taken by Ajay $=8$
Number of packets left $=25-7-8=10$
Thus, the correct answer is $10$.

Ravi has $15$ magic pens. If he gives $4$ magic pens to Suraj, then the number of pens Ravi left with is :

1. $19$

2. $11$

3. $4$

4. $15$

Correct Option: B
Explanation:

Number of magic pens with Ravi $=15$

Number of pens he given to Suraj $=4$
So number of pens left with Ravi $=15-4=11$
Thus, the correct answer is $11$.

Negative integers are at ___________ side of $0$ on numberline.

1. Left

2. Right

3. Middle

4. None of the above

Correct Option: A
Explanation:

Negative numbers lie left side of Zero.

Positive integers are at ______________ side of $0$ on numberline.

1. Left

2. Right

3. Middle

4. None of the above

Correct Option: B
Explanation:

Positive Numbers lie right side of Zero on numberline.

Richa walks $4km$ in the direction of sun on sunset time. Then she turns a right and walks $1km$. She turns left and walks $1km$ then she turns left and walks $1km$. Find displacement of her walk in km?

1. $3$

2. $4$

3. $5$

4. $6$

Correct Option: C
Explanation:
So it will be simple displacement.
First she walks $4$ km and then turn right and walk $1$ km
Then she turn left and walk $1$ km and finally turn left and walk $1$ km .
If you draw this in paper then you will clearly that she is $4$+$1$=$5$ km away form the origin.

What will we get if we subtract $1$ from smallest $6$-digit number?

1. $99999$

2. $100009$

3. $19999$

4. $999999$

Correct Option: A
Explanation:

The smallest 6 digit number $=1,00,000$

therefore,
$100000-1=99999$

Raghu is $21$ years old and Kavita is $72$ years old. The sum of their ages is

1. $83$

2. $85$

3. $93$

4. $103$

Correct Option: C
Explanation:

Age of Raghu $= 21$ years
Age of Kavita $= 72$ years
Therefore, sum of their ages $= 21+72 =93$ years

The sum of the digit of a two digit number is $15$ and the difference between the digits is $3$. What the two digit number?

1. $69$

2. $78$

3. $90$

4. $86$

Correct Option: A
Explanation:

Sum of digit of $2$ digit number $10x+y$ is $15$

$x+y=15$
is $3, x-y=3\x+y=15\x-y=3\----\2x=18\x=9$
So, $y=15-x\15-9\y=6$
solution can be $96$ or $69$
Answer $A$

Neha, Joy and Karan are helping Uncle Shyam in picking apples. Uncle Shyam gives each of them $230$ apples. How many apples do Neha, Joy and Karan have in all?

1. $580$

2. $690$

3. $740$

4. $870$

Correct Option: B
Explanation:

$\Rightarrow$  Uncle shyam gives $230$ each apples to Neha, Joy and Karan.

$\Rightarrow$  Total apples Neha, Joy and Karan have in all$=230+230+230=690\,apples.$

If $a+b=30$ and $ab=176$, find $a^{3}+b^{3}$

1. $10160$

2. $11060$

3. $11160$

4. $None\ of\ these$

Correct Option: C
Explanation:

$a+b=30,ab=176 \ a+b=30 \ \Rightarrow { \left( { a+b } \right) ^{ 2 } }={ \left( { 30 } \right) ^{ 2 } }$

$\Rightarrow { a^{ 2 } }+{ b^{ 2 } }+2ab=900 \ \Rightarrow { a^{ 2 } }+{ b^{ 2 } }+2\times 176=900 \ \Rightarrow { a^{ 2 } }+{ b^{ 2 } }=900-352 \ \Rightarrow { a^{ 2 } }+{ b^{ 2 } }=548$

$Now \ { a^{ 3 } }+{ b^{ 3 } }=\left( { a+b } \right) \left( { { a^{ 2 } }+{ b^{ 2 } }-ab } \right) \ =30\left( { 548-176 } \right) \ =30\times 372 \ =11160$

$(308+264)cm^{2}=572cm^{2}$

1. True

2. False

Correct Option: A
Explanation:

$\begin{matrix} \left( { 308+264 } \right) c{ m^{ 2 } }=572c{ m^{ 2 } } \ It\, \, is\, \, true.\, \, \, \, Ans. \ \end{matrix}$

Find the sum of $-59,\ -41,\ 73,\ -92,\ 81,\ -(-41)$ and $-3$.

1. $3$

2. $0$

3. $1$

4. $-2$

Correct Option: B
Explanation:

$-59, -41, 73, -92, 81, -(-41), -3$.

$=-59+(-41)+73+(-92)+81+[-(-41)]+(-3)$.

$=-59-41+73-92+81+41-3$.

$=73+81+41-59-92-41-3$

$=195-195$

$=0$.

Subtract the second term form first term.
$5p , 11p$

1. $-6p$

2. $1p$

3. $5p$

4. $12p$

Correct Option: A
Explanation:

$5p-11p=-6p$

Hence, the answer is $-6p.$

Subtract : $3x^{2}+2yx$ from $2x^{2}+3yx$

1. $x^{2}-4xy$

2. $5x^{2}y$

3. $xy-x^{2}$

4. $x^{2}+4xy$

Correct Option: C
Explanation:
$(2x^{2}+3yx)-(3x^{2}+2yx)$

$=2x^{2}+3xy-3x^{2}-2xy$

$=-x^{2}+xy\Rightarrow (C)$

State whether true or false
There is a natural number which when added to a natural number, gives that number.

1. True

2. False

Correct Option: B
Explanation:

We know that $0$ is the only number which, when added to some other number then it gives the same number.

Since $0$ is not a natural number then the given statement is false.

State whether the following statement is true or false
There is a whole number which when added to a whole number, gives that number

1. True

2. False

Correct Option: A
Explanation:

Assume the whole numbers

$p,q$
According to question
$p+q=p$
$q=p-p$
$\boxed{q=0}$
Zero is the whole number which satisfies the condition mentioned in question
So statement is true.

When the signs are changed as shown below which one of the following equation is correct?
$- to + , + to \times , \times to \div , \div to =$

1. $40 +5 \div 45\times 15-25$

2. $40 \div 5 \times 15- 25$

3. $40\times 5-45\div 15+ 25$

4. $40 + 5-45\times 15\div 25$

Correct Option: B
Explanation:

For option A
$40+5\div45\times15-25$
if we change sign according to the question then
$40\times5=45\div15+25$
$200\neq28$
For option B
$40\div5+45\times15-25$
If we change the sign according to the question then
$40=5\times45\div15+25$
$40=5\times3+25$
$40=40$
Hence, option 'B' is correct.

Difference of the greatest 7 digit number and the smallest 5 digit number is

1. 998999

2. 9989999

3. 99899

4. 998099

Correct Option: B
Explanation:

the greatest $7$ digit number is $9999999$

the smallest $5$ digit number is $10000$

we have to find the difference between these two numbers

$9999999-10000=9989999$

So option $B$ is the answer

The two numbers formed by subtracting one from $5$ and $10$ are:

1. 11 and 12

2. 4 and 10

3. 4 and 9

4. 5 and 6

Correct Option: C
Explanation:

Let us first subtract one from $5$ as shown below:

$5-1=4$

Similarly, subtract one from $10$ as follows:

$10-1=9$

Hence, the two numbers formed by subtracting one from $5$ and $10$ are $4$ and $9$.

If a and b are two whole numbers, then commutative law is applicable to subtraction if and only if

1. $a = b$

2. a $\neq$ b

3. $a > b$

4. $a < b$

Correct Option: A
Explanation:
Commutative property : The subtraction of whole numbers is not commutative, that is, if $a$ and $b$ are two whole numbers, then in general $a – b$ is not equal to $(b – a)$.

Verification:

We know that $9 – 5 = 4$ but $5 – 9=-4$ which is not a whole number. Thus, for two whole numbers $a$ and $b$ if $a > b$, then $a – b$ is a whole number but $b – a$ is not possible and if $b > a$, then $b – a$ is a whole number but $a – b$ is not possible.

Now, if $a=b=3$ then, $a-b=3-3=0$ which is also a whole number.

Hence, whole numbers are commutative under subtraction if and only if $a=b$.

Which of the following properties are not applicable to the subtraction of whole numbers?

1. Closure property

2. Commutative property

3. Associative proptery

4. All the above

Correct Option: D
Explanation:

Let us have a look at the properties of whole numbers under subtraction:

(i) Closure property : If $a$ and $b$ are two whole numbers such that $a > b$ or $a = b$, then $a – b$ is a whole number. If $a < b$, then subtraction $a – b$ is not possible in whole numbers. For example: If $a=3$ and $b=5$ then,

$3-5=-2$ which is not a whole number.

Therefore, whole numbers are not closed under subtraction.

(ii) Commutative property : The subtraction of whole numbers is not commutative, that is, if $a$ and $b$ are two whole numbers, then in general $a – b$ is not equal to $(b – a)$.

Verification:

We know that $9 – 5 = 4$ but $5 – 9=-4$ which is not a whole number. Thus, for two whole numbers $a$ and $b$ if $a > b$, then $a – b$ is a whole number but $b – a$ is not possible and if $b > a$, then $b – a$ is a whole number but $a – b$ is not possible.

Therefore, whole numbers are not commutative under subtraction.

(iii) Associative of addition : The subtraction of whole numbers is not associative. That is, if $a, b, c$ are three whole numbers, then in general $a – (b – c)$ is not equal to $(a – b) – c$.

Verification:

We have,

$20 – (15 – 3) = 20 – 12 = 8$,

and, $(20 – 15) – 3 = 5 – 3 = 2$

So, $20 – (15 – 3) ≠ (20 – 15) – 3$.

Therefore, whole numbers are not associative under subtraction.

Hence, all of the properties are not applicable to subtraction of whole numbers.

If $\displaystyle a^{2}-b^{2}=13$ where a and b are natural numbers then value of a is

1. $6$

2. $7$

3. $8$

4. $9$

Correct Option: B
Explanation:

$a^2 - b^2 = 13$
$(a-b)(a +b) = 1 \times 13$
By comparing, $a - b = 1, a + b = 13$
$2a = 14$
$a = 7$

Find the value of A and B in the following sum:
$6 A 3$
$\underline {+2 2 B}$
$\underline {B B 1}$

1. $A=5,B=8$

2. $A=6,B=8$

3. $A=5,B=7$

4. $A=5,B=9$

Correct Option: A
Explanation:

Since 3 + B given us 1 in the answer, so B has to be 8 as $3+8=11$.
Now 1 is carried over so, $A+1+2=B$
i.e. $A+1+2=8$. So, A is 5.
Also $6+2=B$ in hundred's place to confirm that B is 8.
The value of A is 5 and B is 8.

If x stands for addition, < for substraction, + stands for division, > for multiplication, - stands for equal to, + for greater than and = stands for less than, state which of the following is true?

1. $3 \times 2 < 4 \div 16 > 2 + 4$

2. $5 > 2 + 2 = 10 < 4 \times 2$

3. $3 \times 4 > 2 - 9 + 3 < 3$

4. $5 \times 3 < 7 \div 8 + 4 \times 1$

Correct Option: B

Two rows of numbers are given The resultant number in each row is to be worked out separately based on the following rules and the question below the rows of numbers is to be answered The operations of numbers progress from left to right
Rules
I. If an odd number is followed by a two-digit even number then they are to be added.
II. If an odd number is followed by a two-digit odd number then the second number is to be subtracted from the first number
III. If an even number is followed by a number which is a perfect square of a number then the second number is to be divided by the first number
IV. If an even number is followed by a two-digit even number then the first number is to be multiplied by the second number
8  16  16  14
13  11  12  144
What is the difference between the resultant of the first set of numbers and the second set of numbers ?

1. 106

2. 118

3. 210

4. 222

Correct Option: A

Savita has Rs. 27 in the form of fifty paise and twenty-five paise coins. She has twice as many twenty-five paise coins as she has 50 paise coins. How many coins of each kind does she have?

1. 27, 54

2. 30, 60

3. 25, 50

4. 40, 80

Correct Option: A
Explanation:

Let the number of 50 paise coins =x
So the number of 25 paise coins=2x
Amount with 50 paise coines=0.5x
Amount with 25 paise coines=0.5x
According to question
0.5x+0.5x=27
Or x=27
So the number of 50 paise coins=x=27
Or the number of 25 paise coines=2x=54

$1+5+9+\cdots\cdots+(4n-3)$ is equal to

1. $n(4n-3)$

2. $(2n-1)$

3. $n(2n-1)$

4. $(4n-3)^2$

Correct Option: C
Explanation:

In the given Arithmetic Progression,
First term $= a = 1$
Common difference $= 5 - 1 = 4$

Let $4n - 3$ be the $k$ th term.

Then ${x} _{n} = a + (n-1)d$
$=> 4n- 3 = 1 + (k-1)4$
$=> 4n -1 = 1 +4k-4$
$=> k = n$

So,  $4n - 3$ is the $n$ th term.

Now, Sum to 'n' terms of an AP $= \frac {n}{2} (2a+(n-1)d) = \frac {n}{2} (2+(n-1)4) = \frac {n}{2} (4n-2) =n(2n-1)$

The distance between (-4, -5) and (-4, -10) is________units

1. 15

2. 10

3. 5

4. 2

Correct Option: C
Explanation:

Distance between two points $({x} _{1}, {y} _{1})$ and $({x} _{2}, {y} _{2})$ is $\sqrt {{({x} _{2}-{x} _{1})}^{2} + {{(y} _{2}-{y} _{1})}^{2} }$

So, distance between $(-4,-5) ; (-4,-10)$ is $\sqrt {{(-4+4)}^{2} + {(-10+5)}^{2} } = 5$

The two numbers which results 5 on subtracting are

1. 11 and 12

2. 4 and 10

3. 4 and 9

4. 5 and 6

Correct Option: C

If $14y-4=24y+26$, then $12y=$.

1. $-24$

2. $-36$

3. $-12$

4. $12$

Correct Option: B
Explanation:

Given, $14y - 4 = 24y + 26$
$\Rightarrow 14y-24y = 26 + 4$
$\Rightarrow -10y = 30$
$\Rightarrow y = -3$
Thus $12y = 12 \times (-3) = -36$

$\left (1 - \dfrac {1}{2}\right ) + \left (\dfrac {3}{4} - \dfrac {1}{4}\right )=$

1. $0$

2. $1$

3. $\dfrac {1}{2}$

4. $\dfrac {3}{4}$

Correct Option: B
Explanation:
$\left ( 1-\dfrac{1}{2} \right )+\left ( \dfrac{3}{4}-\dfrac{1}{4} \right )$
$=\left ( \dfrac{2-1}{2} \right )+\left ( \dfrac{3-1}{4} \right )$
$=\dfrac{1}{2}+\dfrac{2}{4}= \dfrac{1}{2}+\dfrac{1}{2}= 1$

Grace has 16 jellybeans in her pocket. She has 8 red ones, 4 green ones, and 4 blue ones. What is the minimum number of jellybeans she must take out of her pocket to ensure that she has one of each color?

1. 4

2. 8

3. 12

4. 13

5. 16

Correct Option: D
Explanation:
• Grace has $8$ red , $4$ green , $4$ blue jellybeans
• In order to have one of each color , she should take out $7$ red, $3$ green , $3$ blue jellybeans
• So she has to take out $7+3+3=13$ jellybeans

$\dfrac {2}{5} + \dfrac {4}{9} =$ _____

1. $\dfrac {10}{23}$

2. $\dfrac {8}{45}$

3. $\dfrac {38}{45}$

4. $\dfrac {6}{13}$

Correct Option: C
Explanation:
$\dfrac{2}{5}+\dfrac{4}{9}$
$=\dfrac{18+20}{45}$
$=\dfrac{38}{45}$

Sum of greatest five digits number and smallest three digits number is :

1. $10099$

2. $100099$

3. $1099$

4. $10990$

Correct Option: B
Explanation:

Smallest three digit number $=100$

Largest five digit number $=99999$
Sum $=99999+100=100099$
Option $B$ is correct.

Difference of greatest three digits number and smallest five digits number is :

1. $19001$

2. $9011$

3. $9001$

4. $9091$

Correct Option: C
Explanation:

Greatest three digit number $=999$

Smallest five digit number $=10000$
Difference $=10000-999=9001$
So option $C$ is correct.

Sum of greatest three digit number and smallest five digit number is

1. $10999$

2. $1999$

3. $19990$

4. $10099$

Correct Option: A
Explanation:

Smallest three digit number $=999$

Greatest five digit number $=10000$
Sum $=999+10000=10999$
So option $A$ is correct.

A girl goes $30$ meters North, then turns right and walks $40$ meters, then turns right and walks $20$ meters, then again turns right and walks $40$ meters. How many meters is she from the original position?

1. $0$ meter

2. $40$ meter

3. $20$ meter

4. $10$ meter

Correct Option: D
Explanation:
First goes $30$ m north
Then turn right and go $40$ m
Then turn right and go $20$ m
Then turn right and go $40$ m
Finally, distance from starting point $= 30 - 20 = 10$ m

Fill in the blanks by using appropriate alternative:
6409*2 + 28764* = _______

1. 928779

2. 838879

3. 928879

4. 928579

Correct Option: D

Fill in the blanks by using appropriate alternative:
370500 - 280575 = _______

1. 89725

2. 89952

3. 89825

4. 89925

Correct Option: D

Fill in the blanks by using appropriate alternative:
_________ - 452567 = 253510

1. 706087

2. 708087

3. 706077

4. 706057

Correct Option: C

If three is subtracted from each of the following numbers, then which of the following options is the difference between the second highest number and the second digit of the highest number?
$489$     $541$     $654$      $935$       $873$.

1. $0$

2. $3$

3. $1$

4. $4$

Correct Option: D
Explanation:
Given Numbers  489  541  654  935  873
Subtraction  -3  -3  -3  -3  -3
Required Numbers  486  538  651  932  870

Highest Number $\rightarrow$ $932$

Second digit of $932$  $\rightarrow$ $3$
Second highest Number $\rightarrow$ $870$
Second digit of $870$ $\rightarrow$  $7$
Difference between 7 and 3 $\rightarrow$ $4$
Hence, the required answer is $4$.

The population of a city is $2,09,32,714$. Out of these, $90,47,314$ are men; $984,35,784$ are women and the rest are children. Find the number of children in the city.

1. $34,94,616$

2. $34,49,616$

3. $34,49,661$

4. $34,94,661$

Correct Option: B
Explanation:

Population of City $\rightarrow$ Number of Men $+$ Number of Women $+$ Number of Children

Population of city $\rightarrow$ $2,09,32,714$
Number of Men $\rightarrow$ $90,47,314$
Number of Women $\rightarrow$ $84,35,784$
$2,09,32,714$ $\rightarrow$  $90,47,314$ $+$ $84,35,784$ $+$ Number of children
Number of Children $\rightarrow$ $3449616$
Hence, Option B is correct.

Select the INCORRECT statement.

1. Tina has $1556$cm long cloth. She cut $13$m $50$cm from it. The length of cloth left with her is $2.06$m

2. Neetu bought $500$g potatoes, $250$g capsicums, $700$g onions, $500$g tomatoes, $100$g gingers and $300$g radish. The total weight of the vegetables she bought is $2.350$kg

3. Rita got Rs. $500$ and spent Rs. $117.35$ on stationary items and Rs. $50.75$ on eatables. The amount left with Rita is Rs. $331.09$

4. Yashika has to cover a distance of $20$km $50$m. She walked $1$km and went by bus for $15$km and hired an auto for rest of the distance. The distance she covered by auto is $4.05$km

Correct Option: C
Explanation:

(A) Total length of cloth Tina had $=1566$cm $=15.56$m
Length of cloth she cut from it $=13$m $50$cm
$=13.50$m
$\therefore$ Length of cloth left with her $=15.56-13.50$
$=2.06$m
(B) Total weight of vegetables Neetu bought $=500g+250g+700g+500g+100g+300g=2350$g i.e., $2.350$kg
(C) Total amount spent by Rita$=Rs. (117.35+50.75)=Rs. 168.10$
Amount left will Rita $=Rs. (500-168.10)$
$=Rs. 331.90$
(D) Total distance covered by Yashika $=20$km $50$m $=20.050$km
Distance covered by auto $=20.050-(1+15)=20.050-16=4.05$km
So, option (C) is incorrect.

Rita's watch was 10 minutes fast.Her watch showed 1:05 p.m.when she left home.She travelled for 35 minutes and arrived 5 minutes early for her dental appointment.At what time was her dental appointment?

1. 13 : 20 hrs

2. 13 : 25 hrs

3. 13 : 35 hrs

4. 13 : 55 hrs

Correct Option: C
Explanation:

Rita's watch was 10 min fast

when she left home her watch shows time 1:05 p. m
then actual time when she left home is=$1:05 p.m.-10 min=12:55 p.m.$
now she travelled 35 min then the time goes to=$12:55 p.m.+35 min= 13:30 p.m.$
now she reach at dental hospital 5 min. before the,
actual time was her dental appointment= $13:30 p.m.+5min.=13:35$ hrs

$2\ +\ 3\ =?$

1. $0$

2. $2$

3. $5$

4. $4$

Correct Option: C
Explanation:

$2+3=5$

If 300 jellybeans cost you x dollars. How many jellybeans can you purchase for 50 cents at the same rate?

1. 150/x

2. 150x

3. 6x

4. 1500/x

5. 600x

Correct Option: A
Explanation:
• $1$ dollar is equal to $100$ cents
• Given $300$ jellybeans is equal to $x$ dollar , which implies $100x$ cents
• For $50$ cents , we get $300/2x = 150/x$ jellybeans
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