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  • Real Numbers Class 10 MCQ

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CHAPTER 1 – REAL NUMBERS Class 10

For some integer m, every odd integer is of the form

(A) m

(B) m + 1

(C) 2m

(D) 2m + 1

Answer: D

Explanation: As the number 2m will always be even, so if we add 1 to it then, the number will always be odd.

3. If two positive integers a and b are written as a = p3q2 and b = pq3; p, q are prime numbers, then HCF (a, b) is:

VDO.AI

(A) pq

(B) pq2

(C) p3q3

(D) p2q2

Answer: B

Explanation: Since a = p × p × p × q × q,

b = p × q × q × q

Therefore H.C.F of a and b = pq2

4. The product of a non-zero number and an irrational number is:

(A) always irrational

(B) always rational

(C) rational or irrational

(D) one

Answer: A

Explanation: Product of a non-zero rational and an irrational number is always irrational i.e.,

jagran josh

5. If the HCF of 65 and 117 is expressible in the form 65 m – 117, then the value of m is

(A) 4

(B) 2

(C) 1

(D) 3

Answer: B

Explanation: By Euclid’s division algorithm,

jagran josh

6. The largest number which divides 70 and 125, leaving remainders 5 and 8, respectively, is

(A) 13

(B) 65

(C) 875

(D) 1750

Answer: A

Explanation: Since 5 and 8 are the remainders of 70 and 125, respectively. Thus after subtracting these remainders from the numbers, we have the numbers

65 = (70 − 5), 117 = (125 − 8) which is divisible

—————————————————–118

Which of the following will have a terminating decimal expansion?
(b) 1600
(c) 2400
(d) 3600

(a)

(b)

(c)

(d)
—————————————————–123

n2 – 1 is divisible by 8, if n is
an integer
a natural number
an odd integer
an even integer

—————————————————–119
—————————————————–124

If x = 0.7 , then 2x is

(a) 1.4
(b) 1.5 (c) 1.54 (d) 1.45

—————————————————–120

Which of the following rational number have non- terminating repeating decimal expansion?
When 2256 is divided by 17 the remainder would be
1
16
14
None of these

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Assertion : 13 is a terminating decimal fraction.

(a)
31
3125
Reason : If q = 2m 5n where m, n are non-negative

71 512
integers, then p is a terminating decimal fraction.
Both assertion (A) and reason (R) are true and

(c)
23 200
reason (R) is the correct explanation of assertion (A).

(d) None of these

—————————————————–121

The number 313 – 310 is divisible by
2 and 3
3 and 10
2, 3 and 10
2, 3 and 13

Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
Assertion (A) is true but reason (R) is false.
Assertion (A) is false but reason (R) is true.

—————————————————–126

Assertion : 34.12345 is a terminating decimal fraction.

Reason : Denominator of 34.12345, when expressed

in the form
p , q ! 0, is of the form 2m # 5n , where

m and n are non-negative integers.
Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
Assertion (A) is true but reason (R) is false.
Assertion (A) is false but reason (R) is true.

—————————————————–127

Assertion :

The HCF of two numbers is 5 and their product is 150, then their LCM is 30.
Reason : For any two positive integers a and b, HCF a, b + LCM a, b = a # b .
Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).

Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).

Assertion (A) is true but reason (R) is false.
Assertion (A) is false but reason (R) is true.

—————————————————–128

a and b are two positive integers such that the least prime factor of a is 3 and the least prime factor of b is 5. Then the least prime factor of (a + b) will be ………..
1
2
3
4

—————————————————–129

Select the least number that is divisible by all numbers between 1 and 10 (both inclusive).
(a) 2520
(b) 5040
(c) 1010
(d) 2020

The number 7 will have –
non-terminating repeating decimal expansion.
terminating decimal expansion.
non-terminating non repeating decimal expansion.
terminating non repeating decimal expansion

—————————————————–131

The decimal representation of 16 21 15 will …………..
terminate after 2 decimal place
terminate after 3 decimal place
terminate after 4 decimal places
terminate after 5 decimal places

—————————————————–132

The sum of exponents of prime factors in the prime- factorisation of 1764 is ……………
3
4
5
6

—————————————————–133

In the given factor tree what is the composite number
x ?

(a) 65
(b) 585
(c) 130
(d) 195

—————————————————–134

The HCF and LCM of 378, 180 and 420 of will be
6 and 3980
(b) 12 and 3780
(c) 6 and 3780
(d) 12 and 3980

—————————————————–135

In the given factor tree what is the composite number
x ?

(a) 53 (b) 11130 (c) 5565 (d) 19438

—————————————————–136
What is the HCF of smallest primer number and the smallest composite number?
2
4
6
8

—————————————————–137

38. If HCF(336, 54) = 6, LCM(336, 54) will be
(a) 2024
(b) 3024
(c) 1012
(d) 1512

—————————————————–138

What are the missing numbers c and d in the given factor tree:

3 and 7
13 and 11
6 and 9
5 and 4

Real numbers class 10 mcq pdf

Real numbers class 10 mcq

—————————————————–139

COMPETENCEY BASED QUESTIONS

Direction For Question : (40-41)
When the marbles in a bag are divided evenly between two friends, there is one marble left over. When the same marbles are divided evenly among three friends, there is one marble left over. When the marbles are divided evenly among five friends, there is one marble left over.

What is the least possible number of marbles in the bag?
31
30
32
34

—————————————————–140

What is another possible number of marbles in the bag?
31
61
52
34

—————————————————–140

Direction For Question : (42-45)
An online shopping website sells 10 types of items which are packed into various sizes of cartons which are given below.

The company places supporting thermocol sheets inside every package along the edges. The company thought of procuring same sized sheets for all types of cartons.

What should be the maximum size of the sheet that fits into all type of cartons?
6 by 4
6 by 2
4 by 2
4 by 4

—————————————————–141

How many such sheet sizes are possible?
1
2
3
4

—————————————————–141

The company later introduced a new size of carton called semi large whose measurements are 14 # 15. Whether the existing maximum size sheet fits this
shape?
yes it will fit
It will not fit because 14 is not multiple of 6 and

15 is not multiple of 4.
It will not fit because 14 # 15 is not multiple of 6 # 4.
can’t say

—————————————————–141
Direction For Question : (48-49)
Taniya have 54 football cards, 72 volleyball cards, and 63 basketball cards and she want to put them in a binder. Each page of the binder should have cards from a single sport, and there should be the same number of cards on each page.

What should have been the size of the semi large carton (which is larger than medium carton but smaller than large carton) so that the maximum sized sheet remains same?
(a) 12 # 28
(b) 18 # 28
(c) 12 # 24
(d) 18 # 24

—————————————————–141

Direction For Question : (46-47)
Two oil tankers contain 825 litres and 675 litres of kerosene oil respectively.

What is the maximum capacity of a container which can measure the kerosene oil of both the tankers when used an exact number of times?
50 litre
75 litre
150 litre
225 litre

—————————————————–142

How many times we have to use container for both tanker to fill ?
11 and 9 times
22 and 18 times
10 and 8 times
8 and 6 times

—————————————————–142

What is the greatest number of cards, Taniya can put on a page?
9
12
15
18
—————————————————–143

How many pages will Taniya need for each sport?
for football 6, for volleyball 8 and for basketball 7 pages
for football 9, for volleyball 7 and for basketball 6 pages
for football 7, for volleyball 6 and for basketball 8 pages
for football 9, for volleyball 6 and for basketball 7 pages
—————————————————–143

Tina has 39 pairs of headphones and 13 music players. Tina wants to sell all of the headphones and music players in identical packages. What is the greatest number of packages Tina can make?

4
9
13
26

—————————————————–144

Direction For Question : (51-52)
A patient admitted to the Jaipur Golden hospital was prescribed a pain medication to be given every
4 hr and an antibiotic to be given every 5 hr. Bandages applied to the patient’s external injuries needed changing every 12 hr. The nurse changed the bandages and gave the patient both medications at 6:00 A.M. Monday morning.

How many hours will pass before the patient is given both medications and has his bandages changed at the same time?
60 hours
40 hours
20 hours
90 hours

—————————————————–145

What day and time will this be?
Wednesday at 8 PM
Wednesday at 6 PM
Thursday at 6 PM
Thursday at 8 PM

—————————————————–145
A tile floor is to be made from 10 inch, 12 inch, and 15 inch square tiles. A design is made by alternating rows with different size tiles. The first row uses only 10 inch tiles, the second row uses only 12 inch tiles, and the third row uses only 15 inch tiles. Neglecting the grout seams, what is the shortest length of floor space that can be covered evenly by each row?

20 inch
39 inch
60 inch
10 inch

—————————————————–146

The traffic lights at three different road crossings change after every 48 seconds, 72 seconds and 108 seconds respectively. If they change simultaneously at 7 AM, at what time will they change simultaneously again?

7 min 12 sec
8 min 12 sec
6 mni 24 sec
9 min 24 sec

—————————————————–147

Mercury, Venus, and Earth revolve around the Sun

approximately once every 3 months, 7 months, and 12 months, respectively. If the planets begin lined up, what is the minimum number of months required for them to be aligned again? (Assume that the planets lie roughly in the same plane.)
respectively. What is the minimum distance each should walk so that all can cover the same distance in complete steps?

4 years
6 year
7 years
8 year

—————————————————–148

Lina is preparing dinner plates. She has 12 pieces of chicken and 16 rolls. If she wants to make all the plates identical without any food left over, what is the greatest number of plates Lina can prepare ?

1 plate
2 plate
3 plate
4 plate

—————————————————–149

In a morning walk, three persons step off together. Their steps measure 75 cm, 80 cm and 90 cm

38 m
30 m
32 m
36 m

—————————————————–150

Four satellites revolve around the earth once every 6, 8, 10, and 15 hr, respectively. If the satellites are initially lined up, how many hours must pass before they will again be lined up?

90 hours
200 hours
120 hours
180 hours

—————————————————–151

At a train station, the blue line has a train leaving every 15 minutes, the green line has a train leaving every 24 minutes, and the red line every 10 minutes. If the first train on each line leaves at the same time, how often will there be trains on all three lines departing the train station at the same time?

60 minute
90 minute
120 minute
150 minute

—————————————————–152

Jasmin is completing an art project. She has two pieces of construction paper. The first piece is
44 centimeters wide and the second piece is 33 centimeters wide. Jasmin wants to cut the paper into strips that are equal in width and are as wide as possible. How wide should Jasmin cut each strip?

10 cm
11 cm
22 cm
33 cm

—————————————————–153

Direction For Question : (61-65)
Ashish supplies bread and jams to a hospital and a school. Bread and jam are supplied in equal number of pieces. Bread comes in a packet of 8 pieces and Jam comes in a pack of 6 pieces.

On a particular day, Ashish has supplied x packets of bread and y packets of jam to the school. On the same day, Ashish has supplied 3x packets of bread along with sufficient packets of jam to hospital. It is known that the number of students in the school are between 500 and 550.
How many students are there in school?
(a) 544
(b) 504
(c) 608
(d) 456

—————————————————–154

How many packets of bread are supplied in the school?
94
63
74
84

—————————————————–154

How many packets of jams are supplied in the school?
(a) 129
64

74
84

—————————————————–154

How many packets of bread are supplied in the hospital?
(a) 189
64
74
(d) 124

—————————————————–154

How many packets of jams are supplied in the hospital?
(a) 120
(b) 164
(c) 252
(d) 224

—————————————————–154

Direction For Question : (66-70)
Shalvi is a tuition teacher and teaches mathematics to some kids at her home. She is very innovative and always plan new games to make her students learn concepts.

Today, she has planned a prime number game. She announce the number 2 in her class and asked the
first student to multiply it by a prime number and then pass it to second student. Second student also multiplied it by a prime number and passed it to third student. In this way by multiplying to a prime number the last student got 173250. He told this number to Shalvi in class. Now she asked some questions to the students as given below.
How many students are in the class?
6
7
8
9

—————————————————–155

What is the highest prime number used by student?
2
3
5
11

—————————————————–155

What is the least prime number used by students ?
2
3
5
11

—————————————————–155

Which prime number has been used maximum times
?
2
3
5
11

—————————————————–155

Which prime number has been used minimum times
?
2
3

7
11

—————————————————–155

Direction For Question : (71-75)
Mahesh works as a manager in a hotel. He has to arrange chairs in hall for a function. The hall has a certain number of chairs. Guests want to sit in different groups like in pairs, triplets, quadruplets, fives and sixes etc. Mahesh want to arrange chairs in such a way that there are no chair left after arrangement.

When Mahesh arranges chairs in such pattern like in 2’s, 3’s, 4’s 5’s and 6’s then 1, 2, 3, 4 and 5 chairs are left respectively. But when he arranges in 11’s, no chair will be left.
In the hall, how many chairs are available?
(a) 539
(b) 234
(c) 689
(d) 456

—————————————————–156

If one chair is removed, which arrangement is possible now?
2
3
4
5

—————————————————–156

If one chair is added to the original number of chairs,
how many chairs will be left when arranged in 11’s.
1
2
3
4

—————————————————–156

How many chairs will be left in original arrangement if same number of chairs are arranged in 7’s?
1
2
3
0

—————————————————–156

How many chairs will be left in original arrangement if same number of chairs will be arranged in 9’s?
8
7
8
4

—————————————————–156

Direction For Question : (76-80)
The Republic Day parade, first held in 1950, has been a yearly ritual since. The parade marches from the Rashtrapati Bhawan along the Rajpath in New Delhi. Several regiments of the army, navy, and air force, along with their bands, march to India Gate. The parade is presided over by the President of India, who is the Commander-in-Chief of the Indian Armed Forces. As he unfurls the tricolour, the national anthem is played. The regiments of the Armed Forces then start their march past. Prestigious awards like Kirti Chakra, Ashok Chakra, Paramvir Chakra and Vir Chakra are given out by the President. Nine to twelve different regiments of the Indian Army, in addition to the Navy and Air Force march toward India Gate along with their bands. Contingents of paramilitary forces and other civil forces also participate in the parade.

On 71th republic day parade, captain RS Meel is planing for parade of following two group:
First group of Army troops of 624 members behind an army band of 32 members.
Second group of CRPF troops with 468 soldiers behind the 228 members of bikers.
These two groups are to march in the same number of columns. This sequence of soldiers is followed by different states Jhanki which are showing the culture of the respective states.
What is the maximum number of columns in which the army troop can march?
(a) 8 (b) 16
(c) 4 (d) 32

—————————————————–157

What is the maximum number of columns in which the CRPF troop can march?
4
8
12
16

—————————————————–157

What is the maximum number of columns in which total army troop and CRPF troop together can march past?
2
4
6
8

—————————————————–157
What should be subtracted with the numbers of CRPF soldiers and the number of bikers so that their maximum number of column is equal to the maximum number of column of army troop?
4 Soldiers and 4 Bikers
4 Soldiers and 2 Bikers
2 Soldiers and 4 Bikers
2 Soldiers and 2 Bikers

—————————————————–157

What should be added with the numbers of CRPF soldiers and the number of bikers so that their maximum number of column is equal to the maximum number of column of army troop?
4 Soldiers and 4 Bikers
12 Soldiers and 12 Bikers
6 Soldiers and 6 Bikers
12 Soldiers and 6 Bikers

—————————————————–157

Direction For Question : (81-85)
Lavanya wants to organize her birthday party. She is very happy on her birthday. She is very health conscious, thus she decided to serve fruits only in her birthday party.

She has 36 apples and 60 bananas at home and decided to serve them. She wants to distribute fruits among guests. She does not want to discriminate among guests, so she decided to distribute fruits equally among all.

How many maximum guests Shalvi can invite?
12
(b) 120
(c) 6
(d) 180

——————————————————

How many apples and bananas will each guest get?
3 apple 5 banana
5 apple 3 banana
2 apple 4 banana
4 apple 2 banana

——————————————————

Lavanya decide to add 42 mangoes also. In this case how many maximum guests Lavanya can invite ?
12
(b) 120
(c) 6
(d) 180

——————————————————

How many total fruits will each guest get?
6 apple 5 banana and 6 mangoes
6 apple 10 banana and 7 mangoes
3 apple 5 banana and 7 mangoes
3 apple 10 banana and 6 mangoes

——————————————————

If Lavanya decide to add 3 more mangoes and remove 6 apple in total fruits, in this case how many maximum guests Lavanya can invite ?
12
30
15
24

——————————————————
Direction For Question : (86-90)
Amar, Akbar and Anthony are playing a game. Amar climbs 5 stairs and gets down 2 stairs in one turn. Akbar goes up by 7 stairs and comes down by 2 stairs every time. Anthony goes 10 stairs up and 3 stairs down each time.

Doing this they have to reach to the nearest point of 100th stairs and they will stop once they find it impossible to go forward. They can not cross 100th stair in anyway.
Who reaches the nearest point?
Amar
Akbar
Anthony
All together reach to the nearest point.

———————————————————

How many times can they meet in between on same stair ?
3
4
5
No, they cannot meet in between on same stair.

———————————————————

Who takes least number of steps to reach near hundred?
Amar
Akbar
Anthony
All of them take equal number of steps.

———————————————————

What is the first stair where any two out of three will meet together?
Amar and Akbar will meet for the first time on 15th stair.
Akbar and Anthony will meet for the first time on 35th stair.
(b) Amar and Anthony will meet for the first time on 21th stair.
(d) Amar and Akbar will meet for the first time on 21th stair.

———————————————————

What is the second stair where any two out of three will meet together?
Amar and Akbar will meet on 21th stair.
Akbar and Anthony will meet on 35th stair.
Amar and Anthony will meet on 21th stair.
Amar and Anthony will meet on 35th stair.

———————————————————

***********

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