MCQ Questions for Class 8 Maths: Ch 6 Squares and Square Roots

1. Find the least number that must be subtracted from 5607 so as to get a perfect square.

(a) 130

(b) 135

(c) 131

(d) none of these

► (c) 131

2. Which of the following would end with digit 1?

(a) 123²

(b) 161²

(c) 77²

(d) 82²
► (b) 161²

3. Find the square of 39.
(a) 1500
(b) 78
(c) 1521
(d) none of these
► (c) 1521

4. The square of 23 is :
(a) 529
(b) 526
(c) 461
(d) 429
► (a) 529

5. Sum of squares of two numbers is 145. If square root of one number is 3, find the other number.
(a) 136
(b) 8
(c) 9
(d) 64
► (b) 8

6. If a number has 1 or 9 in the unit’s place, then it’s square ends in ________.
(a) 3
(b) 9
(c) 1
(d) none of these
► (c) 1

7. The largest perfect square between 4 and 50 is
(a) 25
(b) 36
(c) 49
(d) 45
► (c) 49

8. What will be the number of digits in the square root of 1296?
(a) 2 
(b) 3
(c) 1
(d) 4
► (a) 2 

9. How many natural numbers lie between 9² and 102?
(a) 15
(b) 19
(c) 18
(d) 17
► (c) 18

10. Without adding,find the sum of 1+3+5+7+9+11+13+15+17+19
(a) 100
(b) 64
(c) 49
(d) 81
► (a) 100

11. Which is the greatest three-digit perfect square?
(a) 999
(b) 961
(c) 962
(d) 970
► (b) 961

12. Find the perfect square numbers between 30 and 40.
(a) 936
(b) 49
(c) 25
(d) none of these
► (a) 936

13. How many numbers lie between square of 12 and 13
(a) 22
(b) 23
(c) 24
(d) 25
► (c) 24

14. Without doing any calculation, find the numbers which are surely perfect squares.

(a) 441

(b) 408

(c) 153

(d) 257

► (a) 441

15. The square root of 1.21 is

(a) 1.1

(b) 11

(c) 21

(d) 2.1

► (a) 1.1

16. Find the greatest 4-digit number which is a perfect square.

(a) 9990

(b) 9801

(c) 9999

(d) none of these

► (b) 9801

17. Sum of squares of two numbers is 145. If square root of one number is 3, find the other number. 

(a) 136

(b) 9

(c) 64

(d) 8

► (d) 8

18. Which of the following are the factors of ac+ ab + bc + ca  

(a) (a – c)(a – b)

(b) (a + c)(a + b)

(c) (a – c)(a + b)

(d) (a + c)(a – b)

► (b) (a + c)(a + b)

19. What could be the possible “one’s digit” of the square root of 625?

(a) 5        

(b) 0

(c) 4

(d) 8

► (a) 5        

20. What is the length of the side of a square whose area is 441 cm² ?

(a) 21

(b) 22

(c) 20

(d) 12

► (a) 21

21. The square root of 169 is
(a) 13
(b) 1.3
(c) -1.3 
(d) 13/10
► (a) 13

22. What is smallest number with which 5400 may be multiplied so that the product is perfect cube?
(a) 5
(b) 3
(c) 4
(d) 6
► (a) 5

Squares and Square Roots Class 8 Extra Questions Very Short Answer Type

Question 1.
Find the perfect square numbers between 40 and 50.
Solution:
Perfect square numbers between 40 and 50 = 49.

Question 2.
Which of the following 24², 49², 77², 131² or 189² end with digit 1?
Solution:
Only 49², 131² and 189² end with digit 1.

Question 3.
Find the value of each of the following without calculating squares.
(i) 27² – 26²
(ii) 118² – 117²
Solution:
(i) 27² – 26² = 27 + 26 = 53
(ii) 118² – 117² = 118 + 117 = 235

Question 4.
Write each of the following numbers as difference of the square of two consecutive natural numbers.
(i) 49
(ii) 75
(iii) 125
Solution:
(i) 49 = 2 × 24 + 1
49 = 25² – 24²
(ii) 75 = 2 × 37 + 1
75 = 38² – 37²
(iii) 125 = 2 × 62 + 1
125 = 63² – 62²

Question 5.
Write down the following as sum of odd numbers.
(i) 7²
(ii) 9²
Solution:
(i) 7² = Sum of first 7 odd numbers = 1 + 3 + 5 + 7 + 9 + 11 + 13
(ii) 9² = Sum of first 9 odd numbers = 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17

Question 6.
Express the following as the sum of two consecutive integers.
(i) 15²
(ii) 19²
Solution:

Question 7.
Find the product of the following:
(i) 23 × 25
(ii) 41 × 43
Solution:
(i) 23 × 25 = (24 – 1) (24 + 1) = 24² – 1 = 576 – 1 = 575
(ii) 41 × 43 = (42 – 1) (42 + 1) = 42² – 1 = 1764 – 1 = 1763

Question 8.
Find the squares of:
(i) −37
(ii) −917
Solution:

Question 9.
Check whether (6, 8, 10) is a Pythagorean triplet.
Solution:
2m, m² – 1 and m² + 1 represent the Pythagorean triplet.
Let 2m = 6 ⇒ m = 3
m² – 1 = (3)² – 1 = 9 – 1 = 8
and m² + 1 = (3)² + 1 = 9 + 1 = 10
Hence (6, 8, 10) is a Pythagorean triplet.
Alternative Method:
(6)² + (8)² = 36 + 64 = 100 = (10)²
⇒ (6, 8, 10) is a Pythagorean triplet.

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Question 10.
Using property, find the value of the following:
(i) 19² – 18²
(ii) 23² – 22²
Solution:
(i) 19² – 18² = 19 + 18 = 37
(ii) 23² – 22² = 23 + 22 = 45

Squares and Square Roots Class 8 Extra Questions Short Answer Type

Question 11.
Using the prime factorisation method, find which of the following numbers are not perfect squares.
(i) 768
(ii) 1296
Solution:

768 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3
Here, 3 is not in pair.
768 is not a perfect square.

1296 = 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3
Here, there is no number left to make a pair.
1296 is a perfect square.

Question 12.
Which of the following triplets are Pythagorean?
(i) (14, 48, 50)
(ii) (18, 79, 82)
Solution:
We know that 2m, m² – 1 and m² + 1 make Pythagorean triplets.
(i) For (14, 48, 50),
Put 2m =14 ⇒ m = 7
m² – 1 = (7)² – 1 = 49 – 1 = 48
m² + 1 = (7)² + 1 = 49 + 1 = 50
Hence (14, 48, 50) is a Pythagorean triplet.
(ii) For (18, 79, 82)
Put 2m = 18 ⇒ m = 9
m² – 1 = (9)² – 1 = 81 – 1 = 80
m² + 1 = (9)² + 1 = 81 + 1 = 82
Hence (18, 79, 82) is not a Pythagorean triplet.

Question 13.
Find the square root of the following using successive subtraction of odd numbers starting from 1.
(i) 169
(ii) 81
(iii) 225
Solution:
(i) 169 – 1 = 168, 168 – 3 = 165, 165 – 5 = 160, 160 – 7 = 153, 153 – 9 = 144, 144 – 11 = 133, 133 – 13 = 120, 120 – 15 = 105, 105 – 17 = 88, 88 – 19 = 69,
69 – 21 = 48, 48 – 23 = 25, 25 – 25 = 0
We have subtracted odd numbers 13 times to get 0.
√169 = 13
(ii) 81 – 1 = 80, 80 – 3 = 77, 77 – 5 = 72, 72 – 7 = 65, 65 – 9 = 56, 56 – 11 = 45, 45 – 13 = 32, 32 – 15 = 17, 17 – 17 = 0
We have subtracted 9 times to get 0.
√81 = 9
(iii) 225 – 1 = 224, 224 – 3 = 221, 221 – 5 = 216, 216 – 7 = 209, 209 – 9 = 200, 200 – 11 = 189, 189 – 13 = 176, 176 – 15 = 161, 161 – 17 = 144, 144 – 19 = 125,
125 – 21 = 104, 104 – 23 = 81, 81 – 25 = 56, 56 – 27 = 29, 29 – 29 = 0
We have subtracted 15 times to get 0.
√225 = 15

Question 14.
Find the square rootofthe following using prime factorisation
(i) 441
(ii) 2025
(iii) 7056
(iv) 4096
Solution:
(i) 441 = 3 × 3 × 7 × 7
√441 = 3 × 7 = 21

(ii) 2025 = 3 × 3 × 3 × 3 × 5 × 5
√2025 = 3 × 3 × 5 = 45

(iii) 7056 = 2 × 2 × 2 × 2 × 3 × 3 × 7 × 7
√7056 = 2 × 2 × 3 × 7 = 84

(iv) 4096 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
√4096 = 2 × 2 × 2 × 2 × 2 × 2 = 64

Question 15.
Find the least square number which is divisible by each of the number 4, 8 and 12.
Solution:
LCM of 4, 8, 12 is the least number divisible by each of them.
LCM of 4, 8 and 12 = 24
24 = 2 × 2 × 2 × 3
To make it perfect square multiply 24 by the product of unpaired numbers, i.e., 2 × 3 = 6
Required number = 24 × 6 = 144

Question 16.
Find the square roots of the following decimal numbers
(i) 1056.25
(ii) 10020.01
Solution:

Question 17.
What is the least number that must be subtracted from 3793 so as to get a perfect square? Also, find the square root of the number so obtained.
Solution:
First, we find the square root of 3793 by division method.

Here, we get a remainder 72
61² < 3793
Required perfect square number = 3793 – 72 = 3721 and √3721 = 61

Question 18.
Fill in the blanks:
(а) The perfect square number between 60 and 70 is …………
(b) The square root of 361 ends with digit …………..
(c) The sum of first n odd numbers is …………
(d) The number of digits in the square root of 4096 is ………..
(e) If (-3)² = 9, then the square root of 9 is ……….
(f) Number of digits in the square root of 1002001 is …………
(g) Square root of 36625 is ………..
(h) The value of √(63 × 28) = …………
Solution:
(a) 64
(b) 9
(c) n²
(d) 2
(e) ±3
(f) 4
(g) 625
(h) 42

Question 19.
Simplify: √900 + √0.09 + √0.000009
Solution:
We know that √(ab) = √a × √b
√900 = √(9 × 100) = √9 × √100 = 3 × 10 = 30
√0.09 = √(0.3 × 0.3) = 0.3
√0.000009 = √(0.003 × 0.003) = 0.003
√900 + √0.09 + √0.000009 = 30 + 0.3 + 0.003 = 30.303

Squares and Square Roots Class 8 Extra Questions Higher Order Thinking Skills (HOTS)

Question 20.
Find the value of x if
1369−−−−√+0.0615+x−−−−−−−−−√=37.25
Solution:

Question 21.
Simplify:

Solution:

Question 22.
A ladder 10 m long rests against a vertical wall. If the foot of the ladder is 6 m away from the wall and the ladder just reaches the top of the wall, how high is the wall? (NCERT Exemplar)

Solution:
Let AC be the ladder.
Therefore, AC = 10 m
Let BC be the distance between the foot of the ladder and the wall.
Therefore, BC = 6 m
∆ABC forms a right-angled triangle, right angled at B.
By Pythagoras theorem,
AC² = AB² + BC²
10² = AB² + 6²
or AB² = 10² – 6² = 100 – 36 = 64
or AB = √64 = 8m
Hence, the wall is 8 m high.

Question 23.
Find the length of a diagonal of a rectangle with dimensions 20 m by 15 m. (NCERT Exemplar)
Solution:
Using Pythagoras theorem, we have Length of diagonal of the rectangle = l2+b2−−−−−√ units

Hence, the length of the diagonal is 25 m.

Question 24.
The area of a rectangular field whose length is twice its breadth is 2450 m2. Find the perimeter of the field.
Solution:
Let the breadth of the field be x metres. The length of the field 2x metres.
Therefore, area of the rectangular field = length × breadth = (2x)(x) = (2x²) m²
Given that area is 2450 m².
Therefore, 2x² = 2450
⇒ x² = 1225
⇒ x = √1225 or x = 35 m
Hence, breadth = 35 m
and length = 35 × 2 = 70 m
Perimeter of the field = 2 (l + b ) = 2(70 + 35) m = 2 × 105 m = 210 m.

MCQ Questions for Class 8 Maths: Ch 5 Data Handling

1. In the class- interval 70-80, 80 is the

(a) upper limit

(b) frequency

(c) range

(d) lower limit

► (a) upper limit

2. If a coin is flipped in the air, what is the probability of getting a tail?

(a) 0

(b) ½

(c) 1

(d) 2

► b) ½

3. The class mark of 95-100 is

(a) 95.5

(b) 97.5

(c) 95

(d) 100

► (b) 97.5

4. The number of times an observation occurs in a data is called its

(a) Range

(b) Interval

(c) Frequency

(d) Raw data

► (c) Frequency

5. The pie-chart is divided into

(a) circles

(b) squares

(c) sectors

(d) segments

► (c) sectors

6. Numbers 1 to 10 are written on ten separates slips (one number on one slip), kept in a box and mixed well. One slip is chosen from the box without looking in to it. What is the probability of getting a number less than 6?

(a) 1

(b) 0

(c) 1/10

(d) 1/2

► (d) 1/2

7. When a die is thrown, total number of possible outcomes is ______.

(a) 6

(b) 36

(c) 2

(d) None of these

► (a) 6

8. There are 2 Red, 3 Blue and 5 Black balls in a bag. A ball is drawn from the bag without looking in to the bag. What is the probability of getting a red ball?

(a) 2/5

(b) 3/5

(c) 1/5

(d) None of these

► (c) 1/5

9. 18 out of 36 people love reading, so reading in the pie chart will be represented by

(a) 36 degree sector

(b) quarter sector

(c) semi circular sector

(d) None of these

► (c) semi circular sector

10. Which of the following is the probability of an impossible event?

(a) 0

(b) 1

(c) 2

(d) None of these

► (a) 0

11. There are 2 Red, 3 Blue and 5 Black balls in a bag. A ball is drawn from the bag without looking in to the bag. What is the probability of getting a blue ball?

(a) 3/5

(b) 2/5

(c) 3/10

(d) None of these

► (c) 3/10

12. Two dice are thrown, find and number of outcomes.

(a) 36

(b) 6

(c) 12

(d) None of these

► (a) 36

13. The central total angle in a pie chart is

(a) 180°

(b) 210°

(c) 360°

(d) None of these

► (c) 360°

14. There are 2 Red, 3 Blue and 5 Black balls in a bag. A ball is drawn from the bag without looking in to the bag. What is the probability of getting a non-black ball?

(a) 3/5

(b) 2/5

(c) 1/2

(d) None of these

► (c) 1/2

15. There are 2 Red, 3 Blue and 5 Black balls in a bag. A ball is drawn from the bag without looking in to the bag. What is the probability of getting a non-red ball?

(a) 3/5

(b) 4/5

(c) 2/5

(d) None of these

► (b) 4/5

16. Numbers 1 to 10 are written on ten separates slips (one number on one slip), kept in a box and mixed well. One slip is chosen from the box without looking in to it .What is the probability of getting a number 6?

(a) 1

(b) 0

(c) 1/10

(d) 1/2

► (c) 1/10

17. A coin is tossed. Which of the following is the probability of getting a head or tail?

(a) 0

(b) 1

(c) 1/2

(d) None of these

► (b) 1

18. There are 2 Red, 3 Blue and 5 Black balls in a bag. A ball is drawn from the bag without looking in to the bag. What is the probability of getting a black ball?

(a) 3/5

(b) 2/5

(c) 1/2

(d) None of these

► (c) 1/2

19. There are 2 Red, 3 Blue and 5 Black balls in a bag. A ball is drawn from the bag without looking in to the bag. What is the probability of getting a non-blue ball?

(a) 7/10

(b) 3/5

(c) 2/5

(d) None of these

► (a) 7/10

20. Numbers 1 to 10 are written on ten separates slips (one number on one slip), kept in a box and mixed well. One slip is chosen from the box without looking in to it. What is the probability of getting a 1-digit number ?

(a) 1

(b) 0

(c) 1/10

(d) 9/10

► (d) 9/10

21. Numbers 1 to 10 are written on ten separates slips (one number on one slip), kept in a box and mixed well. One slip is chosen from the box without looking in to it. What is the probability of getting a number greater than 6?

(a) 1

(b) 0

(c) 1/2

(d) 1/10

► (d) 1/10

22. When a coin is thrown, total number of possible outcomes is ______.

(a) 2

(b) 5

(c) 6

(d) None of these

► (a) 2

MCQ Questions for Class 8 Maths: Ch 4 Practical Geometry

1. A parallelogram whose all sides are equal is called ________.

(a) triangle

(b) trapezium

(c) square

(d) rectangle

► (c) square

2. What do we require to construct a quadrilateral if lengths of four sides are given?

(a) One of the angle

(b) Length of a diagonal

(c) Length of two diagonals

(d) None of these

► (b) Length of a diagonal

3. The quadrilateral whose diagonals are equal and bisect each other at right angle is ________. 

(a) Triangle

(b) Square

(c) Rhombus

(d) None of these

► (b) Square

4. A polygon with minimum number of sides is  

(a) Pentagon

(b) Square

(c) triangle 

(d) angle

► (c) triangle 

5. The diagonals of a square bisect each other at  _________  angle.

(a) acute

(b) right

(c) obtuse

(d) reflex

► (b) right

6. What do we require to construct a square?

(a) Length of one side

(b) Lengths of three sides

(c) Lengths of two sides

(d) None of these

► (a) Length of one side

7. All the angles of a regular polygon are of ________________.

(a) 90°

(b) 60°

(c) equal length

(d) equal measure

► (d) equal measure

8. What do we require to construct a quadrilateral if measures of two adjacent angles are given?

(a) Lengths of three sides

(b) Length of one side

(c) Lengths of two sides

(d) None of these

► (a) Lengths of three sides

9. To construct a quadrilateral uniquely, it is necessary to know at least_________ of its parts.

(a) 5

(b) 4

(c) 3

(d) 2

► (a) 5

10. A quadrilateral can be constructed uniquely if the lengths of its four sides and ____ diagonal are given.

(a) 3

(b) 2

(c) 1

(d) none of these

► (c) 1

11.A simple closed curve made up of only _____________ is called  a polygon .

(a) lines

(b) curves

(c) closed curves

(d) line segments

► (d) line segments

12. A quadrilateral can be constructed uniquely if the lengths of its ______ sides and a diagonal are given.

(a) 3

(b) 1

(c) 2

(d) 4

► (d) 4

13. Diagonals of a rectangle:

(a) equal to each other

(b) not equal

(c) one is double of the other

(d) none of these

► (a) equal to each other

14. The measure of each interior angle of a regular polygon is 140o, then number of sides that regular polygon has ___

(a) 15

(b) 12

(c) 9

(d) 10

► (c) 9

15. A parallelogram must be a rectangle if its diagonals 

(a) bisect the angles to which they are drawn

(b) are perpendicular to each other

(c) bisect each other

(d) are congruent

► (d) are congruent

16. A parallelogram each of whose angles measures 90o is _____________.

(a) rectangle

(b) rhombus

(c) kite

(d) trapezium

► (a) rectangle

17. What is the number of sides in Hexagon ?

(a) 4      

(b) 7    

(c) 6    

(d) 5

► (c) 6    

18. What do we require to construct a quadrilateral if measures of three angles are given?

(a) Length of one side

(b) Two adjacent sides

(c) Length of one diagonal

(d) None of these

► (b) Two adjacent sides

19. Polygons that have no portions of their diagonals in their exteriors are called 

(a) triangles

(b) convex

(c) concave

(d) squares

► (b) convex

20. The ratio of two adjacent sides of a parallelogram is 4:5. If its perimeter is 72 cm, find its adjacent sides. 

(a) 18 cm and 25 cm

(b) 16 cm and 25 cm

(c) 18 cm and 20 cm

(d) 16 cm and 20 cm

►(d)16 cm and 20 cm

21. Sum of all interior angles of a polygon with (n) sides is given by

(a) (n – 2) x 180°

(b) n – 2 x 180°

(c) (n + 2) x 180°

(d) n + 2 x 180°

► (a) (n – 2) x 180°

22. A quadrilateral can be constructed uniquely if its _____ sides and two included angles are given.

(a) 1

(b) 2

(c) 3

(d) none of these

► (c) 3

Practical Geometry Class 8 Extra Questions Maths Chapter 4

Extra Questions for Class 8 Maths Chapter 4 Practical Geometry

Question 1.
Construct a quadrilateral PQRS, given that QR = 4.5 cm, PS = 5.5 cm, RS = 5 cm and the diagonal PR = 5.5 cm and diagonal SQ = 7 cm.

Solution:
Construction:
Step I: Draw QR = 4.5 cm.
Step II: Draw an arc with centre R and radius 5 cm.
Step III: Draw another arc with centre Q and radius 7 cm to meet the previous arc at S.
Step IV: Join RS and QS.
Step V: Draw two arcs with centre S and R and radius 5.5 cm each to meet each other at P.
Step VI: Join RP, SP and PQ.
Thus PQRS is the required quadrilateral.

Question 2.
Construct a quadrilateral ABCD in which AB = 4 cm, BC = 3.5 cm, CD = 5 cm, AD = 5.5 cm and ∠B = 75°.

Solution:
Construction:
Step I: Draw AB = 4 cm.
Step II: Draw an angle of 75° at B and cut BC = 3.5 cm.
Step III: Draw an arc with centre C and radius 5 cm.
Step IV: Draw another arc with centre A and radius 5.5 cm to meet the previous arc at D.
Step V: Join CD and AD.
Thus ABCD is the required quadrilateral.

Question 3.
Construct a square whose side is 5 cm.

Solution:
Construction:
Step I: Draw AB = 5 cm.
Step II: Draw an angle of 90° at B and cut BC = 5 cm.
Step III: Draw two arcs with centre A and C and same radii of 5 cm which meet each other at D.
Step IV: Join AD and CD.
Thus, ABCD is the required square.

Question 4.
Construct a rhombus ABCD in which AB = 5.8 cm and AC = 7.5 cm.

Solution:
Construction:
Step I: Draw AB = 5.8 cm.
Step II: Draw an arc with centre B and radius 5.8 cm.
Step III: Draw another arc with centre A and radius 7.5 cm to meet the previous arc at C.
Step IV: Draw two arcs with centres A and C and of the same radius 5.8 cm to meet each other at D.
Step V: Join BC, AC, CD and AD.
Thus ABCD is the required rhombus.

Question 5.
Construct a rhombus whose diagonals are 6 cm and 8 cm.

Solution:
Construction:
Step I: Draw SQ = 8 cm.
Step II: Draw a right bisector of SQ at O.
Step III: Draw two arcs with centre O and radius 3 cm each to cut the right bisector at P and R.
Step TV: Join PQ, QR, RS and SP.
Thus PQRS is the required rhombus.

Question 6.
Construct a rectangle whose diagonal is 5 cm and the angle between the diagonal is 50°.


Solution:
Construction:
Step I: Draw AC = 5 cm.
Step II: Draw the right bisector of AC at O.
Step III: Draw an angle of 50° at O and product both sides.
Step IV: Draw two arcs with centre O and of the same radius 2.5 cm to cut at B and D.
Step V: Join AB, BC, CD and DA.
Thus, ABCD is the required rectangle.

Question 7.
Construct a quadrilateral ABCD in which BC = 4 cm, ∠B = 60°, ∠C = 135°, AB = 5 cm and ∠A = 90°.

Solution:
Construction:
Step I: Draw AB = 5 cm.
Step II: Draw the angle of 60° at B and cut BC = 4 cm.
Step III: Draw an angle of 135° at C and angle of 90° at A which meet each other at D.
Thus, ABCD is the required quadrilateral.

Question 8.
Construct a parallelogram ABCD in which AB = 5.5 cm, AC = 7 cm and BD = 8 cm.

Solution:
Construction:
Step I: Draw AB = 5.5 cm.
Step II: Draw an arc with centre B and radius 82 cm = 4 cm.
Step III: Draw another arc with centre A and radius 72 cm = 3.5 cm which cuts the previous arc at O.
Step IV: Join AO and produce to C such that AO = OC.
Step V: Join BO and produce to D such that BO = OD.
Step VI: Join BC, CD and AD.
Thus ABCD is the required parallelogram.

Question 9.
Construct a rhombus PAIR, given that PA = 6 cm and angle ∠A = 110°.
Solution:
Since in a rhombus, all sides are equal, so PA = AI = IR = RP = 6 cm
Also, rhombus is a parallelogram
so, adjacent angle, ∠I = 180° – 110° = 70°

Steps of construction
Step I. Draw AI = 6 cm
Step II. Draw ray AX¯ such that ∠IAX = 110° and draw IY¯ such that ∠AIY = 70°.
Step III. With A and I as centres and radius 6 cm draw arcs intersecting AX and IY at P and R respectively.
Step IV. Join PR.
Thus, PAIR is the required rhombus.

MCQ Questions for Class 8th Maths: Ch 3 Quadrilaterals

1. The sum of all the angles of a quadrilateral is equal to:

(a) 180°

(b) 270°

(c) 360°

(d) 90°

► (c) 360°

2. A diagonal of a parallelogram divides it into two congruent:

(a) Square

(b) Parallelogram

(c) Triangles

(d) Rectangle

► (c) Triangles

3. The diagonals of a parallelogram:

(a) Equal

(b) Unequal

(c) Bisect each other

(d) Have no relation

► (c) Bisect each other

4. Each angle of rectangle is:

(a) More than 90°

(b) Less than 90°

(c) Equal to 90°

(d) Equal to 45°

► (c) Equal to 90°

5. If ABCD is a trapezium in which AB || CD and AD = BC, then:

(a) ∠A = ∠B

(b) ∠A > ∠B

(c) ∠A < ∠B

(d) None of the above

► (a) ∠A = ∠B

6. The diagonals AC and BD of a parallelogram ABCD intersect each other at the point O. If ∠DAC = 32°, ∠AOB = 70°, then ∠DBC is equal to:

(a) 32°

(b) 88°

(c) 24°

(d) 38°

► (d) 38°

7. In parallelogram ABCD, if ∠A = 2x + 15°, ∠B = 3x – 25°, then value of x is:

(a) 91°

(b) 89°

(c) 34°

(d) 38°

► (d) 38°

8. The opposite angles of a parallelogram are (3x – 2)° and (50 – x)° the measure of these angles is ______.​

(a) 140°, 140°

(b) 20°, 160°

(c) 37°, 143°

(d) 37°, 37°

► (d) 37°, 37°

9. In quadrilateral PQRS, if ∠P = 60° and ∠Q : ∠R : ∠S = 2 : 3 : 7, then ∠S =

(a) 175°

(b) 210°

(c) 150°

(d) 135°

► (a) 175°

10. Two angles of a quadrilateral are 50° and 80° and other two angles are in the ratio 8 : 15. Find the measure of the remaining two angles.​

(a) 100°, 130°

(b) 140°, 90°

(c) 80°, 150°

(d) 70°, 160°

► (c) 80°, 150°

11. The diagonals of rhombus are 12 cm and 16 cm. The length of the side of rhombus is:

(a) 12 cm

(b) 16 cm

(c) 8 cm

(d) 10 cm

► (d) 10 cm

12. In a parallelogram the sum of two consecutive angles is

(a) 360°

(b) 100°

(c) 180°

(d) 90°

► (c) 180°

13. The angles of a quadrilateral are (5x)°, (3x + 10)°, (6x – 20)° and (x + 25)°. Now, the measure of each angle of the quadrilateral will be

(a) 115°, 79°, 118°, 48°

(b) 100° 79°, 118°, 63°

(c) 110°, 84°, 106°, 60°

(d) 75°, 89°, 128°, 68°

► (a) 115°, 79°, 118°, 48°

14. Which of the following is not a parallelogram?

(a) Rectangle

(b) Rhombus

(c) Square

(d) Trapezium

► (d) Trapezium

15. In a Quadrilateral ABCD, AB = BC and CD = DA, then the quadrilateral is a

(a) Triangle

(b) Kite

(c) Rhombus

(d) Rectangle

► (b) Kite

16. If ABCD is a Parallelogram with 2 Adjacent angles ∠A =∠B, then the parallelogram is a

(a) Rhombus

(b) Triangle

(c) Rectangle

(d) Square

► (c) Rectangle

17. All the angles of a convex quadrilateral are congruent. However, not all its sides are congruent. What type of quadrilateral is it?

(a) Parallelogram

(b) Square

(c) Rectangle

(d) Trapezium

► (c) Rectangle

18. Perimeter of a parallelogram is 22 cm. If the longer side, measures 6.5 cm, the measure of the shorter side will be

(a) 4.5 cm

(b) 6.5 cm

(c) 2.5 cm

(d) 3.0 cm

► (a) 4.5 cm

19. If angles A, B, C and D of the quadrilateral ABCD, taken in order, are in the ratio 3:7:6:4, then ABCD is 

(a) rhombus

(b) parallelogram

(c) trapezium

(d) kite

► (c) trapezium

20. Angles of a quadrilateral are in the ratio 3 : 6 : 8: 13. The largest angle is :

(a) 178°

(b) 156°

(c) 90°​

(d) 36°​

► (b) 156°

21. The diagonals of a rectangle PQRS intersects at O. If ∠QOR = 44°, ∠OPS =?

(a) 82°

(b) 52°

(c) 68°

(d) 75°

► (c) 68°

22. In a parallelogram ABCD, if ∠A = 75°, then ∠B = ?

(a) 95°

(b) 80°

(c) 105°

(d) 15°

► (c) 105°

23. A diagonal of a Rectangle is inclines to one side of the rectangle at an angle of 25∘. The Acute Angle between the diagonals is :

(a) 115°

(b) 50°

(c) 40°

(d) 25°

► (b) 50°

24. If an angle of a parallelogram is two-third of its adjacent angle, the smallest angle of the parallelogram is:

(a) 81°

(b) 54°

(c) 108°

(d) 72°

► (d) 72°

Understanding Quadrilaterals Class 8 Extra Questions Very Short Answer Type

Question 1.
In the given figure, ABCD is a parallelogram. Find x.

Solution:
AB = DC [Opposite sides of a parallelogram]
3x + 5 = 5x – 1
⇒ 3x – 5x = -1 – 5
⇒ -2x = -6
⇒ x = 3

Question 2.
In the given figure find x + y + z.

Solution:
We know that the sum of all the exterior angles of a polygon = 360°
x + y + z = 360°

Question 3.
In the given figure, find x.

Solution:
∠A + ∠B + ∠C = 180° [Angle sum property]
(x + 10)° + (3x + 5)° + (2x + 15)° = 180°
⇒ x + 10 + 3x + 5 + 2x + 15 = 180
⇒ 6x + 30 = 180
⇒ 6x = 180 – 30
⇒ 6x = 150
⇒ x = 25

Question 4.
The angles of a quadrilateral are in the ratio of 2 : 3 : 5 : 8. Find the measure of each angle.
Solution:
Sum of all interior angles of a quadrilateral = 360°
Let the angles of the quadrilateral be 2x°, 3x°, 5x° and 8x°.
2x + 3x + 5x + 8x = 360°
⇒ 18x = 360°
⇒ x = 20°
Hence the angles are
2 × 20 = 40°,
3 × 20 = 60°,
5 × 20 = 100°
and 8 × 20 = 160°.

Question 5.
Find the measure of an interior angle of a regular polygon of 9 sides.
Solution:
Measure of an interior angle of a regular polygon

Question 6.
Length and breadth of a rectangular wire are 9 cm and 7 cm respectively. If the wire is bent into a square, find the length of its side.
Solution:
Perimeter of the rectangle = 2 [length + breadth]
= 2[9 + 7] = 2 × 16 = 32 cm.

Now perimeter of the square = Perimeter of rectangle = 32 cm.
Side of the square = 324 = 8 cm.
Hence, the length of the side of square = 8 cm.

Question 7.
In the given figure ABCD, find the value of x.

Solution:
Sum of all the exterior angles of a polygon = 360°
x + 70° + 80° + 70° = 360°
⇒ x + 220° = 360°
⇒ x = 360° – 220° = 140°

Question 8.
In the parallelogram given alongside if m∠Q = 110°, find all the other angles.

Solution:
Given m∠Q = 110°
Then m∠S = 110° (Opposite angles are equal)
Since ∠P and ∠Q are supplementary.
Then m∠P + m∠Q = 180°
⇒ m∠P + 110° = 180°
⇒ m∠P = 180° – 110° = 70°
⇒ m∠P = m∠R = 70° (Opposite angles)
Hence m∠P = 70, m∠R = 70°
and m∠S = 110°

Question 9.
In the given figure, ABCD is a rhombus. Find the values of x, y and z.

Solution:
AB = BC (Sides of a rhombus)
x = 13 cm.
Since the diagonals of a rhombus bisect each other
z = 5 and y = 12
Hence, x = 13 cm, y = 12 cm and z = 5 cm.

Question 10.
In the given figure, ABCD is a parallelogram. Find x, y and z.

Solution:
∠A + ∠D = 180° (Adjacent angles)
⇒ 125° + ∠D = 180°
⇒ ∠D = 180° – 125°
x = 55°
∠A = ∠C [Opposite angles of a parallelogram]
⇒ 125° = y + 56°
⇒ y = 125° – 56°
⇒ y = 69°
∠z + ∠y = 180° (Adjacent angles)
⇒ ∠z + 69° = 180°
⇒ ∠z = 180° – 69° = 111°
Hence the angles x = 55°, y = 69° and z = 111°

Question 11.
Find x in the following figure. (NCERT Exemplar)

Solution:
In the given figure ∠1 + 90° = 180° (linear pair)
∠1 = 90°
Now, sum of exterior angles of a polygon is 360°, therefore,
x + 60° + 90° + 90° + 40° = 360°
⇒ x + 280° = 360°
⇒ x = 80°

Understanding Quadrilaterals Class 8 Extra Questions Short Answer Type

Question 12.
In the given parallelogram ABCD, find the value of x andy.

Solution:
∠A + ∠B = 180°
3y + 2y – 5 = 180°
⇒ 5y – 5 = 180°
⇒ 5y = 180 + 5°
⇒ 5y = 185°
⇒ y = 37°
Now ∠A = ∠C [Opposite angles of a parallelogram]
3y = 3x + 3
⇒ 3 × 37 = 3x + 3
⇒ 111 = 3x + 3
⇒ 111 – 3 = 3x
⇒ 108 = 3x
⇒ x = 36°
Hence, x = 36° and y – 37°.

Question 13.
ABCD is a rhombus with ∠ABC = 126°, find the measure of ∠ACD.

Solution:
∠ABC = ∠ADC (Opposite angles of a rhombus)
∠ADC = 126°
∠ODC = 12 × ∠ADC (Diagonal of rhombus bisects the respective angles)
⇒ ∠ODC = 12 × 126° = 63°
⇒ ∠DOC = 90° (Diagonals of a rhombus bisect each other at 90°)
In ΔOCD,
∠OCD + ∠ODC + ∠DOC = 180° (Angle sum property)
⇒ ∠OCD + 63° + 90° = 180°
⇒ ∠OCD + 153° = 180°
⇒ ∠OCD = 180° – 153° = 27°
Hence ∠OCD or ∠ACD = 27°

Question 14.
Find the values of x and y in the following parallelogram.

Solution:
Since, the diagonals of a parallelogram bisect each other.
OA = OC
x + 8 = 16 – x
⇒ x + x = 16 – 8
⇒ 2x = 8
x = 4
Similarly, OB = OD
5y + 4 = 2y + 13
⇒ 3y = 9
⇒ y = 3
Hence, x = 4 and y = 3

Question 15.
Write true and false against each of the given statements.
(a) Diagonals of a rhombus are equal.
(b) Diagonals of rectangles are equal.
(c) Kite is a parallelogram.
(d) Sum of the interior angles of a triangle is 180°.
(e) A trapezium is a parallelogram.
(f) Sum of all the exterior angles of a polygon is 360°.
(g) Diagonals of a rectangle are perpendicular to each other.
(h) Triangle is possible with angles 60°, 80° and 100°.
(i) In a parallelogram, the opposite sides are equal.
Solution:
(a) False
(b) True
(c) False
(d) True
(e) False
(f) True
(g) False
(h) False
(i) True

Question 16.
The sides AB and CD of a quadrilateral ABCD are extended to points P and Q respectively. Is ∠ADQ + ∠CBP = ∠A + ∠C? Give reason.
(NCERT Exemplar)
Solution:
Join AC, then
∠CBP = ∠BCA + ∠BAC and ∠ADQ = ∠ACD + ∠DAC (Exterior angles of triangles)

Therefore,
∠CBP + ∠ADQ = ∠BCA + ∠BAC + ∠ACD + ∠DAC
= (∠BCA + ∠ACD) + (∠BAC + ∠DAC)
= ∠C + ∠A

Understanding Quadrilaterals Class 8 Extra Questions Higher Order Thinking Skills (HOTS)

Question 17.
The diagonal of a rectangle is thrice its smaller side. Find the ratio of its sides.

Solution:
Let AD = x cm
diagonal BD = 3x cm
In right-angled triangle DAB,
AD² + AB² = BD² (Using Pythagoras Theorem)
x² + AB² = (3x)²
⇒ x² + AB² = 9x²
⇒ AB² = 9x² – x²
⇒ AB² = 8x²
⇒ AB = √8x = 2√2x
Required ratio of AB : AD = 2√2x : x = 2√2 : 1

Question 18.
If AM and CN are perpendiculars on the diagonal BD of a parallelogram ABCD, Is ∆AMD = ∆CNB? Give reason. (NCERT Exemplar)
Solution:

In triangles AMD and CNB,
AD = BC (opposite sides of parallelogram)
∠AMB = ∠CNB = 90°
∠ADM = ∠NBC (AD || BC and BD is transversal.)
So, ∆AMD = ∆CNB (AAS)

MCQ Questions for Class 8 Maths: Ch 1 Rational Numbers

1. The value of ½ x ⅗ is equal to:

(a) ½

(b) 3/10

(c) ⅗

(d) ⅖

► b) 3/10

2. Find the reciprocal of -2.

(a) 2

(b) -2

(c) -1/2

(d) None of these

► c) -1/2

3. How is -28/84 expressed as a rational number with numerator 4?

(a) 4/7

(b) -4/12

(c) 4/12

(d) 4/-7

► (b) -4/12

4. Which of the following statements is true?

(a) Every fraction is a rational number.

(b) Every rational number is a fraction.

(c) Every integer is a rational number.

(d) Both (a) and (c).

► (d) Both (a) and (c).

5. Which of the following is the reciprocal of the reciprocal of a rational number?

(a) -1

(b) 1

(c) 0

(d) The number itself

► (d) The number itself

6. What is the sum of the additive inverse and multiplicative inverse of 2?

(a) 3/2

(b) -3/2

(c) 1/2

(d) -1/2

► (b) -3/2

7. Which among the following is a rational number equivalent to -5/-3 ?

(a) -25/15

(b) 25/-15

(c) 25/15

(d) -25/30

► (c) 25/15

8. Which of the following is the reciprocal of a rational number?

(a) -1

(b) 1

(c) 2

(d) Both a and b

► (d) Both a and b

9. Write the additive inverse of 4/5.

(a) 1

(b) -4/5

(c) 4/5

(d) 0

► (b) -4/5

10. Find the multiplicative inverse of 1/4.

(a) 4

(b) -1/4

(c) -4

(d) 1/4

► (a) 4

11. What is the additive inverse of -2/3?

(a) 0

(b) 1

(c) 2/3

(d) -2/3

► (c) 2/3

12. The value of ½ + ¼ is equal to:

(a) ¾

(b) 3/2

(c) ⅔

(d) 1

► (a) ¾

13. Which of the following is the identity element under addition?

(a) 1

(b) -1

(c) 0

(d) None of these

► (c) 0

14. A number which can be written in the form, p/q where p and q are integers and _____ is called a rational number.

(a) q = 0

(b) q ≠ 0

(c) q = 1

(d) none of these

► (b) q ≠ 0

15. Which of the following statements is true?

(a) Every fraction is a rational number.

(b) Every rational number is a fraction.

(c) Every integer is a rational number.

(d) Both (a) and (c).

► (d) Both (a) and (c).

16. Which of the following is the Multiplicative identity for rational numbers?

(a) 1

(b) -1

(c) 0

(d) None of these

► (a) 1

17. Find the multiplicative inverse of -13.

(a) 13

(b) -13

(c) -1/13

(d) 12

► (c) -1/13

18. ________ is not associative for rational numbers.

(a) Subtraction or Division

(b) Addition or Multiplication

(c) Addition or Division

(d) Multiplication or Division

► (a) Subtraction or Division

19. Which number is in the middle if -1/6, 4/9, 6/-7, 2/5 and -3/4 arranged in descending order?

(a) 2/5

(b) 4/9

(c) -1/6

(d) -6/7

► (c) -1/6

20. Which of the following is the Multiplicative identity for rational numbers?

(a) 1

(b) -1

(c) 0

(d) None of these

► (a) 1

21. Which of the following forms a pair of equivalent rational numbers? 

(a) 24/40 and 35/50

(b) -25/35 and 55/-77

(c) -8/15 and -24/48 

(d) 9/72 and -3/21

► (b) -25/35 and 55/-77

22. What should be subtracted from -7/11 to get −2?

(a) 15/11

(b) -15/11

(c) 29/11

(d) -29/11

► (a) 15/11

Rational Numbers Class 8 Extra Questions Maths Chapter 1

Question 1.
Pick up the rational numbers from the following numbers.
67, −12, 0, 10, 1000
Solution:
Since rational numbers are in the form of ab where b ≠ 0.
Only 67, −12 and 0 are the rational numbers.

Question 2.
Find the reciprocal of the following rational numbers:
(a) −34
(b) 0
(c) 611
(d) 5−9
Solution:
(a) Reciprocal of −34 is −43
(b) Reciprocal of 0, i.e. 10 is not defined.
(c) Reciprocal of 611 is 116
(d) Reciprocal of 5−9 = −95

Question 3.
Write two such rational numbers whose multiplicative inverse is same as they are.
Solution:
Reciprocal of 1 = 11 = 1
Reciprocal of -1 = 1−1 = -1
Hence, the required rational numbers are -1 and 1.

Question 4.
What properties, the following expressions show?
(i) 23+45=45+23
(ii) 13×23=23×13
Solution:
(i) 23+45=45+23 shows the commutative property of addition of rational numbers.
(ii) 13×23=23×13 shows the commutative property of multiplication of rational numbers.

Question 5.
What is the multiplicative identity of rational numbers?
Solution:
1 is the multiplicating identity of rational numbers.

Question 6.
What is the additive identity of rational numbers?
Solution:
0 is the additive identity of rational numbers.

Question 7.
If a = 12, b = 34, verify the following:
(i) a × b = b × a
(ii) a + b = b + a
Solution:

Question 8.
Multiply 58 by the reciprocal of −38
Solution:

Question 9.
Find a rational number between 12 and 13.
Solution:
Rational number between

Question 10.
Write the additive inverse of the following:
(a) −67
(b) 101213
Solution:

Question 11.
Write any 5 rational numbers between −56 and 78. (NCERT Exemplar)
Solution:

Question 12.
Identify the rational number which is different from the other three : 23, −45, 12, 13. Explain your reasoning.
Solution:
−45 is the rational number which is different from the other three, as it lies on the left side of zero while others lie on the right side of zero on the number line.

Rational Numbers Class 8 Extra Questions Short Answer Type

Question 13.
Calculate the following:

Solution:

Question 14.
Represent the following rational numbers on number lines.
(a) −23
(b) 34
(c) 32
Solution:

Question 15.
Find 7 rational numbers between 13 and 12.
Solution:

Question 16.
Show that:

Solution:

Question 17.
If x = 12, y = −23 and z = 14, verify that x × (y × z) = (x × y) × z.
Solution:
We have x = 12, y = −23 and z = 14
LHS = x × (y × z)

Question 18.
If the cost of 412 litres of milk is ₹8912, find the cost of 1 litre of milk.
Solution:

Question 19.
The product of two rational numbers is 1556. If one of the numbers is −548, find the other.
Solution:
Product of two rational numbers = 1556
One number = −548
Other number = Product ÷ First number

Hence, the other number = −187

Question 20.
Let O, P and Z represent the numbers 0, 3 and -5 respectively on the number line. Points Q, R and S are between O and P such that OQ = QR = RS = SP. (NCERT Exemplar)
What are the rational numbers represented by the points Q, R and S. Next choose a point T between Z and 0 so that ZT = TO. Which rational number does T represent?
Solution:

As OQ = QR = RS = SP and OQ + QR + RS + SP = OP
therefore Q, R and S divide OP into four equal parts.

Question 21.
Let a, b, c be the three rational numbers where a = 23, b = 45 and c = −56 (NCERT Exemplar)
Verify:
(i) a + (b + c) = (a + b) + c (Associative property of addition)
(ii) a × (b × c) – (a × b) × c (Associative property of multiplication)
Solution:

Rational Numbers Class 8 Extra Questions Higher Order Thinking Skills (HOTS)

Question 22.
Rajni had a certain amount of money in her purse. She spent ₹ 1014 in the school canteen, bought a gift worth ₹ 2534 and gave ₹ 1612 to her friend. How much she have to begin with?
Solution:
Amount given to school canteen = ₹ 1014
Amount given to buy gift = ₹ 2534
Amount given to her friend = ₹ 1612
To begin with Rajni had

Question 23.
One-third of a group of people are men. If the number of women is 200 more than the men, find the total number of people.
Solution:
Number of men in the group = 13 of the group
Number of women = 1 – 13 = 23
Difference between the number of men and women = 23 – 13 = 13
If difference is 13, then total number of people = 1
If difference is 200, then total number of people
= 200 ÷ 13
= 200 × 3 = 600
Hence, the total number of people = 600

Question 24.
Fill in the blanks:
(a) Numbers of rational numbers between two rational numbers is ……….

Solution:
(a) Countless
(b) 611
(c) −32
(d) 35
(e) Commutative
(f) associative
(g) equivalent
(h) 311