CODE-A

16/10/2016

Corporate Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.: 011-47623456

MM : 60

ONLINE TEST SERIES - TEST 1

Time : 1 Hr.

for

International Mathematics Olympiad (IMO) (Based on Mathematics Olympiad Syllabus) (For Class-VIII) Topics Covered in Various Subjects : Mental Ability

:

Verbal Series, Logical sequence of words, Coding-Decoding, Verbal Analogy, Inserting the missing character, Logical Venn diagram, Verbal Classification, Number, Ranking & Time sequence test, Alphabet Test

Mathematics

:

Rational Numbers, Exponents and Powers, Direct and Indirect Variations, Comparing Quantities, Algebraic Expressions and Identities, Factorization of Algebraic expressions, Linear Equations in One Variable, Congruent Triangle, Understanding Quadrilaterals

GENERAL INSTRUCTIONS : (i) (ii)

All questions are compulsory. There are four sections, 15 questions in section-I (Logical Reasoning), 20 questions in section-II (Mathematical Reasoning), 10 questions in section-III (Everyday Mathematics) and 5 questions in section-IV (Achievers Section). (iii) Section-I, II & III carries 1 mark and Section-IV carries 3 marks. (iv) There is no negative marking.

SECTION-I (LOGICAL REASONING) Choose the correct answer : 1.

2.

3.

Find the odd one out. (1) 4

(2) 9

(3) 25

(4) 36

In the code of ‘ABCD’ is ‘1234’, then code of ‘IFEH’ will be (1) 1965

(2) 6583

(3) 9658

(4) 9237

5 7 9

24 48 80

126 344 ?

(1) 728

(2) 729

(3) 730

(4) 792

Directions (Q.4 & Q.5) : In each of the following questions, find the missing term(s) in the given sequence. -1-

Class VIII

4.

5.

6.

International Mathematics Olympiad (IMO) Online Test Series - Test 1

10. Arpit is ranked 7th from top and Shashi is 4 rank behind the Arpit’s rank. If their ranks are interchanged, then Arpit is 10th from the last. The total number of students in the class is

5, 8, 14, 23, 35, ? (1) 55

(2) 45

(3) 52

(4) 50

WUS_ _MKIGEC (1) PN

(2) QO

(3) OO

(4) QP

If BOOK is coded as 5449 and BANK as 5789, then KNOB is coded as

(2) 9847 (3) 8947

(4) 20

(1) 12

(2) 23

(3) 8

(4) 17

12. Bones : Orthopaedics : : Skin : ?

(4) 7845

8.

(2) 22

(3) 21

11. The difference between the ranks of Amar and Ayush is Eight and Pradeep ranks 17th from top and 10th from bottom. If Pradeep’s rank is exactly in the middle of Amar and Ayush’s ranks and Amar’s rank is ahead of Ayush’s rank, then total number of students in class who are ranked before Amar and after Ayush is

(1) 9845

7.

(1) 24

(1) Cardiology

4 : 8 : : 9 : 27 : : 25 : 125 : : 64 : ? (1) 216

(2) 343

(3) 512

(4) 729

(2) Dermatology (3) Genetics (4) Haematology

Which of the following figure best represent the relationship between “Students, Employed and Women”?

13. Which of the following group is best represented by the given Venn diagram?

(1)

(1) Plastic, cotton, bottle (2) Liquid, water, milk (2)

(3) Trees, oaks, jeans (4) Players, cricketers, umpire Directions(Q.14 & Q.15): If ‘Aa ba Ca’ means ‘Ram Eat Food’, ‘Da Ea ba’ means ‘Food is Good’ and ‘Ea Da Fa’ means ‘Good is Best’. Now answer the following questions :

(3)

14. Food is coded as

(4) 9.

(1) Aa

(2) Ca

(3) ba

(4) Da

15. Good Food is Best’ is coded as

How many ‘2s are followed by ‘4’ and preceded by ‘1’ in the given sequence?

(1) Aa Ea Da Fa (2) ba Ea Da Fa

61247954612447891245 (1) 3

(2) 4

(3) Aa ba Da Fa

(3) 2

(4) 1

(4) Aa Ca Da ba -2-

International Mathematics Olympiad (IMO) Online Test Series - Test 1

Class VIII

SECTION-II (MATHEMATICAL REASONING) 22. One of the factors of a4 – a2 + 16 is

16. Which of the following is not a property of a parallelogram?

(1) a2 – 3a + 4

(1) Opposite sides are equal

(2) a2 + 4a – 3

(2) Opposite angles are equal

(3) a2 – 4a + 3

(3) Diagonals must bisect each other at right angle

(4) a2 + 3a – 4 23. The difference between the compound interests on

(4) Co-interior angles are supplementary

1 years at 20% per annum 2 1 compounded half yearly and ` 24000 for year 2 at 20% per annum compounded quarterly is

` 24000 for 1

17. If a and b are any two non-zero rational numbers and m is a positive integer, then which of the following is correct? (1) (a + b)m = am + bm (3)

m

am  bm  a  b

(2)

ma

(4)

m

 b  ma  mb

 a  b m

ab

average cost price of resulting mixture is ` 30 per litre, then the original cost price of milk is (assuming that water is available free of cost) (2) ` 40 per litre

(3) ` 45 per litre

(4) ` 50 per litre

(2) x–2y–2

(3) xy

(4) x –1y –1

(3) ` 5484

(4) ` 2580

(1) 3a2x2 – 8abxy + 5b2y2 (2) 3a2x2 – 12abxy – 5b2y2 (3) 3a2x2 – 12abxy + 5b2y2 (4) 3a2x2 – 8abxy – 5b2y2 25. In the given figure, ABCD is a kite, AC and BD are diagonals. If AO = x cm, DO = (2x + 3) cm, and BO = (x + 4) cm, then the length of side AB is

19. If a = bxy, b = cyz and c = azx, then the value of z2 is (1) x2y2

(2) ` 2904

24. On dividing (6a2x2 – abxy – 15b2y2)(ax – by) by (2ax + 3by), we get

18. Milk and water are mixed in the ratio 3 : 1. If the

(1) ` 35 per litre

(1) ` 6216

D

1 ⎛3 4⎞ ⎛1 3⎞ ⎛1 4⎞ 20. If  ⎜ – ⎟  ⎜  ⎟ – ⎜  ⎟ , then which of 2 ⎝2 5⎠ ⎝2 2⎠ ⎝2 5⎠

x

A

2x + 3 O

C

x+4

the following properties is represented by above statement?

B

(1) Associative law (2) Distributive law of division (3) Distributive law of multiplication over addition (4) Distributive law of multiplication over subtraction x  5 x  3 2  x  5    x  – 1, – 3  , then x x  3 x 1 x 1 equals

(2) – 4

(3) – 2

(4) Zero

(2)

26 cm

(3) 2 cm

(4)

13 cm

26. Rahul can do a piece of work in 50 days. He works at it for 5 days and then Prateek finished it in 18 days. They will together complete the work in

21. If

(1) – 6

(1) 1 cm

(1) 15 days (3) 14 -3-

2 days 7

(2) 22

2 days 9

(4) 24 days

Class VIII

International Mathematics Olympiad (IMO) Online Test Series - Test 1

27. If Samar pours 105 molecules of water per second in a bottle with a capacity of 1 gallon, then it takes 3.5 × 107 years to fill it. How much time (in years) will it take to fill the bottle if Samar was pouring at the rate of 108 molecules per second?

31. In the given figure, WXA  ZCY and AY = BX, then ABC is always a/an W A

X

(1) 0.035 × 1014 (2) 35 ×

Y

Z

108

(3) 0.35 × 1011 (4) 3.5 × 109 28. Five years ago, Rahul’s father was 5 times as old as Rahul. But 5 years from now, Rahul’s father will be 3 times as old as his son. The present age of Rahul is (1) 10 years

(2) 12 years

(3) 15 years

(4) 18 years

B (1) Equilateral triangle

C (2) Isosceles triangle

(3) Right triangle

(4) Scalene triangle

32. In an n-sided regular polygon, the sum of the interior angles and the sum of the exterior angles is same if and only if n equals (1) 3

(2) 4

(3) 5 4a 2

(4) 6

33. If + + 12ab – 36c 2 = (2a + pb – qc) (2a + pb + qc), where p and q are natural

27 5 29 33 31 , , , , in ascending order 41 7 43 47 45 can be written as

29. The fractions

9b 2

(1) 45

pq is pq (2) 9

(3) 18

(4) 2

numbers, then the value of

5 33 31 29 27 , , , , (1) 7 47 45 43 41

34. A sum of money invested at compound interest

(2)

27 29 31 33 5 , , , , 41 43 45 47 7

amounts to ` 1,300 in 4 years and to ` 1,365 in 5 years. The rate of interest per annum is

(3)

5 33 27 29 31 , , , , 7 47 41 43 45

(4)

33 5 29 27 31 , , , , 47 7 43 41 45

(1) 5% (2) 10% 1 (4) 3% (3) 2 % 2 35. If, p,q, r and s are in proportion (pq > rs), then the mean proportional between (p2 – r2) and (q2 – s2) is

30. The value of (123456789)(123456789) – (123456795)(123456783) is (1) 64

(2) 89

(3) 36

(4) 28

(1)

pr qs

(3) pq – rs

(2) ps – qr (4)

p s – q r

SECTION-III (EVERYDAY MATHEMATICS) 36. A bed in the form of a rectangle has length and breadth (2x + 3y) cm and (3x – 5y) cm respectively, then the diagonal of the bed is equal to (1)

13 x 2  28 y 2  18 xy cm

(2)

17 x 2  27 y 2  16 xy cm

(3)

18 x 2  30 y 2  16 xy cm

(4)

2

37. A car travels 672 km on 56 litres of petrol. How far would it travel on 30 litres of petrol? (1) 360 km

(2) 300 km

(3) 260 km

(4) 280 km

38. The ratio of A’s income to that of B is 3 : 4 and their expenses are in the ratio 2 : 3. If A saves ` 7000, while B saves ` 8000, then A’s income is

2

13 x  34 y  18 xy cm -4-

(1) ` 10,000

(2) ` 12,000

(3) ` 15,000

(4) ` 16,000

International Mathematics Olympiad (IMO) Online Test Series - Test 1

42. If 18 persons can do a piece of work in 7 days, then the number of persons required to complete the work in 42 days is

39. Mr. Ramaiah joins a company with a starting salary of ` 50,000 per month. After every 1 year of service, he gets an increment of 20% of his current salary. After 3 years of service, his monthly salary is (1) ` 60,000

(2) ` 72,000

(3) ` 86,400

(4) ` 1,03,680

(2) 10 t seconds

(3) 1000 t seconds

(4) 500 t seconds

(1) 4

(2) 8

(3) 6

(4) 3

43. Rahul spends

40. The growth of bacteria is such that it doubles itself after every ‘t’ seconds. Initially their population in a specified region and time is 1 million. The minimum time taken for the population to cross 1 billion is (1) 9 t seconds

Class VIII

3 1 of his salary on rent, on 10 5

1 1 on travelling and on miscellaneous 10 6 expenses. The remaining amount that he saves is food,

41. Sudhir follows a path for morning walk as shown in the figure given below. Which of the following statements is correct?

(1)

1 of his salary 10

(2)

7 of his salary 30

(3)

2 of his salary 15

(4)

3 of his salary 20

44. In a parking, there are few autos and cars in the ratio 3 : 5. If there are 116 wheels in all, then the number of autos in the parking is (1) 32

(2) 20

(3) 12

(4) 9

45. Ram moves along the boundary of a regular polygon shaped field whose one interior angle is 144°. The shape of the field is

(1) Path is not a simple curve (2) Path is a convex polygon (3) Path is a concave polygon (4) Path is not a closed curve

(1) Regular octagon

(2) Regular nonagon

(3) Regular decagon

(4) Regular dodecagon

SECTION-IV (ACHIEVERS SECTION) 46. In the given figure, ABCD and BEDF are parallelogram. If 2FDC = ADE, ABE = x and ADE = y, then the value of x + y is A

y

47. The value of

⎛ xa ⎞ ⎜⎜ b ⎟⎟ ⎝x ⎠

D

E

a2  ab  b 2

⎛ xb  ⎜⎜ c ⎝x

⎞ ⎟⎟ ⎠

b2  bc  c 2

⎛ xc  ⎜⎜ a ⎝x

⎞ ⎟⎟ ⎠

(1) Zero

(2) 1

(3) x

(4) x a  b  c

c 2  ca  a2

is

3

x

48. For any positive real number x, if x 2 

F

then the value of x12 

C

B

(1) 2x

(2) 3x

(3) 4x

x (4) 2 -5-

1 x12

can be

(1) 416 12

(2) 816 2

(3) 864 2

(4) 340 12

1 3 x2

 2,

Class VIII

International Mathematics Olympiad (IMO) Online Test Series - Test 1

49. x8 + x4 + 1 can be factorised as

50. A store prices an item in x rupees and y paise so that 4% sales tax is added and no rounding is necessary because the result is exactly (x + 1) rupees. Which of the following is true?

(1) (x4 – 1 – x2)(x4 – 1 – x2) (2) (x4 +1 – x2)(x4 + 1 – x2) (3) (x4 + 1 + x2)(x4 + 1 – x2)

(1) 15y – 14x = 1560

(2) 4x + 19y = 3245

(4) (x4 – 1 + x2)(x4 + 1 – x2)

(3) 20y – 7x = 2250

(4) 13y + 50x = 1250





-6-



CODE-A

16/10/2016

Corporate Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.: 011-47623456

ONLINE TEST SERIES - TEST 1

MM : 60

Time : 1 Hr.

for

International Mathematics Olympiad (IMO) (Based on Mathematics Olympiad Syllabus) (For Class-VIII)

ANSWERS 1.

(4)

11.

(4)

21.

(2)

31.

(2)

41.

(3)

2.

(3)

12.

(2)

22.

(1)

32.

(2)

42.

(4)

(3)

33.

(4)

43.

(2)

3.

(3)

13.

(4)

23.

4.

(4)

14.

(3)

24.

(1)

34.

(1)

44.

(3)

5.

(2)

15.

(2)

25.

(2)

35.

(3)

45.

(3).

6.

(1)

16.

(3)

26.

(3)

36.

(4)

46.

(2)

(3)

37.

(1)

47.

(2)

7.

(3)

17.

(4)

27.

8.

(2)

18.

(2)

28.

(3)

38.

(3)

48.

(2)

9.

(1)

19.

(2)

29.

(2)

39.

(3)

49.

(3)

10.

(4)

20.

(4)

30.

(3)

40.

(2)

50.

(4)

-1-

CODE-A

16/10/2016

Corporate Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.: 011-47623456

ONLINE TEST SERIES - TEST 1 for

International Mathematics Olympiad (IMO) (Based on Mathematics Olympiad Syllabus) (For Class-VIII)

ANSWERS & HINTS SECTION-I (LOGICAL REASONING) 1.

Answer (4) Except option (4), all the numbers are perfect squares of prime numbers.

2.

Answer (3) In English alphabet’s sequence, ABCD have place values of 1234 respectively. Similarly, IFEH have place values of 9658 respectively.

3.

Answer (3)

4.

Answer (4) The difference between the numbers is the consecutive multiple of 3. 5

5.

+3

8

+6

14

+9

23

+12

35

Answer (2) Only alternate letters are taken in the series.

6.

Answer (1) B O O K

B A N K

5 4 4 9

5 7 8 9

K N O B 9 8 4 5 -2-

+15

50

Answers & Hints - International Mathematics Olympiad (IMO) Online Test Series - Test 1

7.

Class VIII

Answer (3) x2 : x3

8.

Answer (2)

Women

Students

Employed 9.

Answer (1)

612 47954612 4478912 45 10. Answer (4) th

I

11

th

7 Arpit

6

3

Shashi 11

II

th

th

7 6

3

Shashi

Arpit 9 th 10

6 + 1 + 3 + 1 + 9 = 20 11. Answer (4) th

10

5 12 3 3  Amar  Pradeep  Ayush  th

17

12 + 5 = 17 12. Answer (2) Orthopaedics is the branch of medical science deal in bones. Similarly dermatology is the branch of medical science deals in skin etc. 13. Answer (4)

Players Umpire

Cricketers 14. Answer (3) Aa ba Ca  Ram Eat Food Da Ea ba  Food is Good Ea Da Fa  Good is Best 15. Answer (2) ba Ea Da Fa -3-

Class VIII

Answers & Hints - International Mathematics Olympiad (IMO) Online Test Series - Test 1

SECTION-II (MATHEMATICAL REASONING) 16. Answer (3) 17. Answer (4) 18. Answer (2) Let the resulting mixture is 1 litre and its price = ` 30. In resulting mixture, Proportion of milk =

3 3  3 1 4

and proportion of water =

1 1  3 1 4

Assuming original cost price of milk = ` x per litre Then, according to question,

3 1  x   0 = 30 4 4

[Here, we assume water is available at free of cost, so its cost price = ` 0 per litre] 

3 x  30 4 4 = ` 40 per litre 3

 x = 30  19. Answer (2) a = bxy, b =

...(i)

cyz

and c =

...(ii) azx

...(iii)

Substituting the value of b from (ii) into (i) a = (cyz)xy  a = cyz × xy xy  a= c

2

z

[(am)n = amn] ...(iv)

Now, substituting the value of c from (iii) into (iv),

 

a = azx x  a= a

x2y 2z

2 2 2

y z

On equating the exponents of common bases on both sides, we get x2y2z2 = 1  z2 = 

z2

1 2 2

xy

= x–2y–2

-4-

Answers & Hints - International Mathematics Olympiad (IMO) Online Test Series - Test 1

20. Answer (4) 21. Answer (2) 22. Answer (1) a4 – a2 + 16 = (a2)2 + 2(4)a2 + 42 – 9a2 = [(a2)2 + 2(4)a2 + 42] – (3a)2 = (a2 + 4)2 – (3a)2

[∵ x2 + 2xy + y2 = (x + y)2]

= (a2 + 4 + 3a)(a2 + 4 – 3a)

[∵ x2 – y2 = (x + y)(x – y)]

23. Answer (3) 3

10 ⎞ 5 ⎞ ⎛ ⎛ Required difference = ` 24000 ⎜ 1  ⎟  ` 24000 ⎜ 1  100 ⎟ ⎝ 100 ⎠ ⎝ ⎠ ⎡⎛ 11 ⎞ ⎛ 21 ⎞ = ` 24000 ⎢⎜ ⎟  ⎜ ⎟ ⎢⎣⎝ 10 ⎠ ⎝ 20 ⎠ 3

2

2⎤

⎥ ⎥⎦

⎛ 1331 441 ⎞ = ` 24000 ⎜  ⎟ ⎝ 1000 400 ⎠ = ` 24000 

457 2000

= ` 5484 24. Answer (1) 25. Answer (2) For given kite ABCD, OD = OB [ Smaller diagonal is bisected by the longer diagonal] and AOD is a right triangle. 26. Answer (3) Work done by Rahul in 5 days = Remaining work = 1  Now,

1 1 5  50 10

1 9  10 10

9 work is done by Prateek in 18 days. 10

10 ⎞ ⎛  Whole work will be done by Prateek in ⎜ 18  ⎟ days = 20 days 9 ⎠ ⎝ 1 1 and Prateek’s 1 day’s work =  Rahul’s 1 day’s work = 50 20 Rahul’s and Prateek’s together 1 day’s work =

1 1 7   50 20 100

Hence, Rahul and Prateek will together complete the work in 27. Answer (3) 28. Answer (3) Let Rahul’s present age be x years. So, father’s age 5 years from now = 10 + Father’s age 5 years ago  3(x + 5) = 10 + 5 (x – 5)  x = 15 -5-

100 2 days = 14 days. 7 7

Class VIII

Class VIII

Answers & Hints - International Mathematics Olympiad (IMO) Online Test Series - Test 1

29. Answer (2) 27 29 31 33 35 , , , , . 41 43 45 47 49 Each number is less than 1. Also, adding 2 to numerator and denominator of each fraction, we get the next fraction. So, they are in ascending order as given above.

Given numbers are

30. Answer (3) Let x = 123456789.  x + 6 = 123456795 and x – 6 = 123456783  (123456789)(123456789) – (123456795)(123456783) = x2 – (x + 6)(x – 6) = x2 – (x2 – 62) = 62 = 36 31. Answer (2) 32. Answer (2) 33. Answer (4) 34. Answer (1) Let the rate of interest be r%. Simple interest for 1 year = `(1365  1300)  ` 65 According to the question,

1300  r  1 100 65  100  r= 1300  1  r=5 65 =

Hence, the rate of interest is 5%. 35. Answer (3) Since p, q, r and s are in proportion, 

p r  q s

 ps = qr Let x be the mean proportional between (p2 – r2) and (q2 – s2).  x=

( p2 – r 2 )(q 2 – s 2 )

 x=

p 2q 2 – r 2q 2 – p 2s 2  r 2s 2

 x=

p2q 2 – r 2q 2 – q 2 r 2  r 2s 2

 x=

p2q 2 – 2q 2 r 2  r 2s 2

 x=

p2q 2 – 2pqrs  r 2s 2

 x=

( pq – rs )2

 x = pq – rs

[∵ ps = qr]

[∵ ps = qr]

[∵ pq > rs] -6-

Answers & Hints - International Mathematics Olympiad (IMO) Online Test Series - Test 1

SECTION-III (EVERYDAY MATHEMATICS) 36. Answer (4) 37. Answer (1) 38. Answer (3) Let the incomes of A and B be 3x and 4x respectively.

A’s expenses 2  B’s expenses 3 

A’s income – ` 7000 2  B’s income – ` 8000 3



3 x  7000 2  4 x  8000 3

(Given)

 9x – 21000 = 8x – 16000  x = 5000 So, A’s income = 3x = ` 15000 39. Answer (3) 3

20 ⎞ ⎛ After 3 years, Ramaiah’s monthly salary = ` 50,000 ⎜ 1  ⎟  ` 86,400 ⎝ 100 ⎠ 40. Answer (2) 1billion  1000 1million

Now, 29 = 512 and 210 = 1024  Required time = 10t seconds 41. Answer (3) 42. Answer (4) 43. Answer (2) Let the fraction of salary that he saves be ‘x’ 

3 1 1 1     x 1 10 5 10 6

⎛9  6  3  5⎞ 7  x = 1– ⎜ ⎟  30 30 ⎝ ⎠ 44. Answer (3) Let the number of autos = 3x and the number of cars = 5x Then, according to the question, (3x) × 3 + (5x) × 4 = 116  9x + 20x = 116  29x = 116  x=4 Therefore, the number of autos = 3 × 4 = 12 -7-

Class VIII

Class VIII

Answers & Hints - International Mathematics Olympiad (IMO) Online Test Series - Test 1

45. Answer (3) Let the number of sides of the regular polygon = n We know that, Each interior angle of polygon of n sides =

 n – 2   180 n

Then according the question :

144° =

 n – 2   180 n

 144°n = 180°n – 360°  180°n – 144°n = 360°  n=

360  10 36

So, the polygon has 10 sides.

SECTION-IV (ACHIEVERS SECTION) 46. Answer (2) In given figure, ABCD and BEDF are parallelograms and BD is their diagonal. A

y

D

E

x

F C

B

ABD = BDC

...(i)

⎡alternate interior angle ⎤ ⎢∵ AB || CD ⎥ ⎣ ⎦

...(ii)

⎡alternate interior angles ⎤ ⎢∵ BE || FD ⎥ ⎣ ⎦

and EBD = BDF

Subtracting (ii) from (i), ABD – EBD = BDC – BDF ABE = FDC = x

ABE  x, Given

Then, according to the given question, 2FDC = ADE  2x = y

∵ ADE  y, Given

Therefore, the value of x + y = x + 2x = 3x -8-

Answers & Hints - International Mathematics Olympiad (IMO) Online Test Series - Test 1

47. Answer (2)

x  a –b

a = x

= x

3

a

a2  ab  b2

– b

3

 xb

3



 xb – c

– c3

 

 xc

3



b2  bc  c 2



 xc – a



c 2  ca  a2

– a3

 

– b3  b3 – c 3  c 3 – a3



= x0 = 1 48. Answer (2) Given,

3 x2



1 3 x2

2

…(i)

On squaring both the sides of equation (i), we get x3 



x3 

1 x3 1

2  4

…(ii) 6 x3 On squaring both the sides of equation (ii), we get x6 

1 x6

 34

…(iii)

2

2

1 ⎞ 1 ⎞ ⎛ ⎛ Now, ⎜ x 6  6 ⎟  ⎜ x 6  6 ⎟  4 x ⎠ x ⎠ ⎝ ⎝ = 342 – 4

[From (iii)]

= 1152 1   24 2 x6 1 1 ⎞⎛ 1 ⎞ ⎛  12  ⎜ x 6  6 ⎟⎜ x 6  6 ⎟ x x ⎠⎝ x ⎠ ⎝



x6 



x12

=  24 2(34) =  816 2 49. Answer (3) x8 + x4 + 1 = (x4)2 + x4 + 1 + 2x4 – 2x4 = (x4)2 + 1 + 2x4 + x4 – 2x4 = (x4 + 1)2 – x4 = (x4 + 1)2 – (x2)2 = (x4 + 1 + x2)(x4 + 1 – x2) 50. Answer (4) The price marked by the store is x rupees and y paise. According to the question, (100 x  y )  4  100 x  y  100( x  1) 100  400x + 4y + 10000x + 100y = 10000x + 10000

 400x + 104y = 10000  13y + 50x = 1250



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Class VIII