IMO Level 2 Class 10

(1)

LEVEL - 2

Year 2011-12

5

th

(2)

SECTION I : LOGICAL REASONING

1.

1. There are There are six perssix persons ons A, B, C, D, E A, B, C, D, E and Fand F. C is the . C is the sister sister of Fof F. B is the br. B is the brother of E's other of E's husband. Dhusband. D is the father of A and grandfather of F. There are two fathers, three brothers and a mother in the is the father of A and grandfather of F. There are two fathers, three brothers and a mother in the group. Which of the following is a group of brothers?

group. Which of the following is a group of brothers? (A)

(A) ABFABF (B)(B) ABDABD (C)(C) BFCBFC (D)(D) BDFBDF

2.

2. Anita, MAnita, Mahima, Rajan, Latahima, Rajan, Lata and Dea and Deepti are epti are five cousins. five cousins. Anita is Anita is twice as twice as old as Maold as Mahima. Rajan ishima. Rajan is half the age of Mahima. Anita is half the age of Deepti and Rajan is twice the age of Lata.

half the age of Mahima. Anita is half the age of Deepti and Rajan is twice the age of Lata. If Mahima is 16 years old, then what is the age of Lata?

If Mahima is 16 years old, then what is the age of Lata? (A)

(A) 4 4 yearsyears (B)(B) 5 5 yearsyears (C)(C) 7 7 yearsyears (D)(D) 14 14 yearsyears

3.

3. If secIf second Saturday ond Saturday and all Sundays and all Sundays are are holidays in a holidays in a 30 da30 days ys month beginning on Saturdaymonth beginning on Saturday, then, then how many working days are there in that month?

how many working days are there in that month? (A)

(A) 2525 (B)(B) 2222 (C)(C) 2424 (D)(D) 2323

4.

4. If the sIf the same fame function is aunction is applied to reach pplied to reach the rethe results in esults in each ach of the throf the three see sets ets of numberof numbers given s given thenthen which number will replace the question mark in the third set of numbers?

which number will replace the question mark in the third set of numbers? (A) (A) 2424 (B) (B) 3030 21 21 55 17 17 77 24 24 28 16 28 13 13 16 22 25 10 25 7 7 10 88 30 ? 30 ? (C) (C) 3636 (D) (D) 4040 5.

5. If the If the first first and the and the second lesecond letters tters of the of the word UNPRECEDENTED word UNPRECEDENTED are are interchanged with interchanged with the last the last andand the second last letters and similarly the third and the fourth letters are interchanged with the third the second last letters and similarly the third and the fourth letters are interchanged with the third and the fourth letters from the last respectively and so on, then what will be the seventh letter to and the fourth letters from the last respectively and so on, then what will be the seventh letter to the right of the third letter fr

the right of the third letter from the left endom the left end ?? (A)

(A) CC (B)(B) EE (C)(C) PP (D)(D) RR

6.

6. Ravi wants Ravi wants to go to to go to the universitythe university. He st. He starts arts from his home from his home which is in the which is in the East and East and comes to comes to aa crossing. The road to the left ends in a theatre, and straight ahead is the hospital. In which direction crossing. The road to the left ends in a theatre, and straight ahead is the hospital. In which direction is the university if all the four places are in different directions ?

is the university if all the four places are in different directions ? (A)

(A) North North (B)(B) South South (C)(C) East East (D)(D) West West

7.

7. Find out Find out the the wrong wrong term term in in the the number number series.series.

105, 85, 60, 30, 0, – 45, – 90 105, 85, 60, 30, 0, – 45, – 90 (A)

(A) 105105 (B)(B) 6060 (C)(C) 00 (D)(D) – – 4545

8.

8. Choose Choose the the number-letter number-letter group group which is which is different different from from the the others.others. (A)

(A) M5SM5S (B)(B) B9LB9L (C)(C) T4YT4Y (D)(D) F4JF4J

9.

9. Select Select a figure a figure from amongst from amongst the options the options which will continue which will continue the sthe series eeries established stablished by the by the fivefive problem figures. problem figures. Problem Figures Problem Figures

?

(A) (A) (B) (B) (C) (C) (D)(D)

(3)

3

3 ₅₅thth_{IMO | Level-II | Class 10 |}_{IMO | Level-II | Class 10 |}

10.

10. In the question, therIn the question, there are e are seven figures, seven figures, the first the first and last of and last of which are which are unmarked and tunmarked and the remaininghe remaining are marked as P, Q, R, S and T. These seven figures form a series. However, one of the five marked are marked as P, Q, R, S and T. These seven figures form a series. However, one of the five marked figures does not fit into the series. Select that figure from the options.

figures does not fit into the series. Select that figure from the options.

P

P Q Q R R S S TT

(A)

(A) PP (B)(B) QQ (C)(C) RR (D)(D) TT

1

11. 1. In the given figure, if the triangle representIn the given figure, if the triangle represents girls, the circle represents girls, the circle representss athletes, the rectangle represents boys and the square represents disciplined, athletes, the rectangle represents boys and the square represents disciplined, then the boys who are athletes and disciplined are indicated by which then the boys who are athletes and disciplined are indicated by which numbe numberr ?? (A) (A) 11 6 6 2 2 3 3 4 4 5 5 7 7 1 1 9 9 10 10 8 8 (B) (B) 22 (C) (C) 66 (D) (D) 1010 12.

12. Five boys took part in a raceFive boys took part in a race. Raj finished before Mohit but behind Gaurav. A. Raj finished before Mohit but behind Gaurav. Ashish finished beforeshish finished before Sanchit but behind Mohit. Who won the race?

Sanchit but behind Mohit. Who won the race? (A)

(A) RajRaj (B)(B) Gaurav Gaurav (C)(C) Mohit Mohit (D)(D) Ashish Ashish

13.

13. In In a a certain coding certain coding system,system,

'816321' means 'the brown dog frightened the cat'; '64851' means 'the frightened cat ran away'; '816321' means 'the brown dog frightened the cat'; '64851' means 'the frightened cat ran away'; '7621' means 'the cat was brown'; '341' means 'the dog ran'.

'7621' means 'the cat was brown'; '341' means 'the dog ran'. What is the code for 'the dog was frightened'?

What is the code for 'the dog was frightened'? (A)

(A) 5438 5438 (B)(B) 8263 8263 (C)(C) 8731 8731 (D)(D) None None of of thesethese

14.

14. Choose that set of numberChoose that set of numbers from the options, that is similar to the given set : (9, 15, 21)s from the options, that is similar to the given set : (9, 15, 21) (A)

(A) (10, (10, 14, 14, 16)16) (B)(B) (7, (7, 21, 21, 28)28) (C)(C) (5, (5, 10, 10, 25)25) (D)(D) (4, (4, 8, 8, 12)12)

15.

15. Find tFind the mhe missing issing number?number?

3 3C C 27 27 A A 9 9BB 2 2BB ? ? 4 4 A A 4 4 A A 64 64BB 16 16C C (A) (A) 88C C (B) (B) 1212BB (C) (C) 1616C C (D) (D) 1818C C 16.

16. Find the Find the odd one odd one out.out.

(A)

(A) (B) (B) (C) (C) (D)(D)

17.

17. The question consists of The question consists of a set of threa set of three figures X, Y e figures X, Y and Zand Z

X Y Z

showing a sequence of folding of a piece of paper. Fig. (Z) showing a sequence of folding of a piece of paper. Fig. (Z) shows the manner in which the folded paper has been cut. shows the manner in which the folded paper has been cut. Choose a figure from the options which would most closely Choose a figure from the options which would most closely resemble the unfolded form of fig. (Z).

resemble the unfolded form of fig. (Z).

(A)

(4)

18.

18. Group the given figures Group the given figures into three classinto three classes using eaes using each figure only once.ch figure only once.

1 1 2 2 33 4 4 5 5 66 7 7 88 99 (A) (A) 1, 2, 1, 2, 5; 3, 5; 3, 7, 8; 7, 8; 4, 6, 4, 6, 99 (B) (B) 1, 7, 1, 7, 2; 3, 2; 3, 9, 6; 9, 6; 4, 5, 4, 5, 88 (C) (C) 2, 3, 2, 3, 8; 4, 8; 4, 6, 9; 6, 9; 1, 5, 1, 5, 77 (D) (D) 5, 6, 5, 6, 9; 3, 9; 3, 4, 1; 4, 1; 2, 7, 2, 7, 88 19.

19. When the giveWhen the given figure is folded to fn figure is folded to form a cube, how maorm a cube, how many dots would lieny dots would lie opposite the face bearing five dots?

opposite the face bearing five dots? (A) (A) 11 (B) (B) 22 (C) (C) 33 (D) (D) 44 20.

20. Select a figure frSelect a figure from the options which satisfies om the options which satisfies the same conditions of placemthe same conditions of placement of the dots aent of the dots ass in fig. (X). in fig. (X). Fig. (X) Fig. (X) (A) (A) (B) (B) (C) (C) (D)(D)

SECTION II : MATHEMATICAL REASONING

21.

21. A person invested sA person invested some amount at the rate of 10% ome amount at the rate of 10% simple interest and some other asimple interest and some other amount at themount at the rate of 12% simple interest. He received yearly interest of

rate of 12% simple interest. He received yearly interest of 130. But if he had interchanged the130. But if he had interchanged the amounts invested, he would have received

amounts invested, he would have received 4 more as interest. How much amount did he invest at4 more as interest. How much amount did he invest at different rates ?

different rates ? (A)

(A) ``_{700 at 12%,}_{700 at 12%,} ``_{500 at 10%}_{500 at 10%} _(B)_(B) ``_{700 at 10%,}_{700 at 10%,} ``_{500 at 12%}_{500 at 12%}

(C)

(C) ``_{700 each at 10% and 12%}_{700 each at 10% and 12%} _(D)_(D) ``_{500 each at 10% and 12%}_{500 each at 10% and 12%}

22. In

22. In PDPD QR QR such that such that DD lies on lies on QR QR . . If If PQ PQ == aa,, PR PR == bb,, QDQD == c c andand DR DR == d d , then, then ((aa ++ bb)()(aa –– bb) = _____.) = _____.

(A)

(A) 11 (B)(B) ((c c ++ d d )()(d d –– c c )) (C)(C) ((c c ++ d d )()(c c –– d d )) (D)(D) 00

23.

23. Two Two circles circles with rwith radiiadii aa andand bb respectively touch each other externally. Let respectively touch each other externally. Let c c be the radius of a circle be the radius of a circle that touches these two circles as well as a common tangent to these two circles. Then ___.

that touches these two circles as well as a common tangent to these two circles. Then ___.

(A) (A) 1 1 -- 1 1 == 11 a a b b c c (B)(B) 1 1 1 1 11 0 0 a a b b c c + + ++ == _(C)_(C) 1 1 ++ 1 1 == 11 a

a b b c c (D)(D) None None of of thesethese

24.

24. AA.. DEFG DEFG is a square inscribed in triangle as side is a square inscribed in triangle as side DE DE is on is on BC BC andand G G && F F are two points at

are two points at ABAB andand AC AC respectively. Then respectively. Then DE DE 22 ₌₌

(A)

(A) BDBD´´ _EC_EC _(B)_{(B) BD}_{BD =}_{= 2}_2EC_EC

A A 1 1 PQ PQR R ,, ABC

(5)

5

25.

25. If from twice the greIf from twice the greater of two positive numbers 1ater of two positive numbers 16 is subtract6 is subtracted, the result is half the other numbered, the result is half the other number.. If from half the greater number 1 is subtracted, the result is still half the other number. What are If from half the greater number 1 is subtracted, the result is still half the other number. What are the numbers ?

the numbers ? (A)

(A) 16, 16, 88 (B)(B) 12, 12, 1010 (C)(C) 6, 6, 88 (D)(D) 10, 10, 88

26. If

26. If P P andand Q Q are two points whose coordinates are ( are two points whose coordinates are (at at 22_{, , 2}_2at_{at ) and}_{) and}

2 2 2 2 ,, a a aa tt t

t respectively and S respectively and S is the point is the point

((aa, 0), then, 0), then 1 1 11 S

SP P SSQ Q (A)

(A) Dependent Dependent of of t t (B)(B) Independent Independent of of t t (C)(C) Independent Independent of of aa (D)(D) None None of of thesethese

27. If

27. If T T ₁₁,, T T ₂₂,, T T ₃₃, ...,, ..., TT_n_n are consecutive terms of an A.P., thenare consecutive terms of an A.P., then 1 1 2 2 2 2 3 3 11 1 1 11 11 ... ... n n T T T T T T T T ____. ____. (A) (A) 1 1 1 1 n n n n T T T T -×× (B)(B) 1 1 nn n n T T T ××T (C)(C) 2 2 1 1 ( ( 11)) n n T T nn T T T T

-×× (D)(D) None None of of thesethese

28.

28. In the given figure, the diameters of two In the given figure, the diameters of two wheels have measures wheels have measures 2 cm 2 cm and 4 and 4 cm. Determine the lengthscm. Determine the lengths of the belts

of the belts ADAD andand BC BC that pass around the wheels if it is given that belts cross each other at right that pass around the wheels if it is given that belts cross each other at right angle.

angle. (A)

(A) 4 4 cm cm eacheach _A_A BB

O O C C P P D D O O ¢¢ (B) (B) 3 3 cm cm eacheach (C) (C) 5 5 cm cm eacheach (D) (D) 6 6 cm cm eacheach 29.

29. In the given figure, three circles of rIn the given figure, three circles of radius 2 cm touch one anotheradius 2 cm touch one another externally. These circles are circumscribed by a circle of radius

externally. These circles are circumscribed by a circle of radius R R cm. cm. Find the approximate value of

Find the approximate value of R R .. (A) (A) 5.4 5.4 cmcm A A C C B B (B) (B) 5.0 5.0 cmcm (C) (C) 4.0 4.0 cmcm (D) (D) 4.3 4.3 cmcm 30.

30. A A number is selected at number is selected at random from the numbers :random from the numbers :

5, 8, 10, 12, 14, 15, 16, 18, 20, 22, 24, 24, 25, 25, 27, 30, 30, 36, 37, 37, 39, 40, 40, 46. 5, 8, 10, 12, 14, 15, 16, 18, 20, 22, 24, 24, 25, 25, 27, 30, 30, 36, 37, 37, 39, 40, 40, 46. Find the probability that the selected number is their average.

Find the probability that the selected number is their average.

(A) (A) 00 (B)(B) 11 (C)(C) 11 6 6 (D)(D) 1 1 12 12 31.

31. A A cone is cut into two parts cone is cut into two parts by a horizontal plane passby a horizontal plane passing through the midpoint of its axis. The ratioing through the midpoint of its axis. The ratio of the volume of the upper part to the volume of lower part is ____.

of the volume of the upper part to the volume of lower part is ____. (A)

(A) 1 1 : : 77 (B)(B) 1 1 : : 88 (C)(C) 7 7 : : 11 (D)(D) 7 7 : : 88

32.

32. The ratio of the aThe ratio of the areas of reas of the right angled trianglesthe right angled triangles ABC ABC andand DEF DEF in which in which AC

AC = 4 cm, = 4 cm, DE DE = 4 cm is ___. = 4 cm is ___. (A)

(A) 1 1 : : 22 (B)(B) 4 4 : : 11 (C)(C) 1 1 : : 44 (D)(D) 2 2 : : 11

33.

33. If If (( x x ++ aa) is a factor of the polynomial) is a factor of the polynomial x x 22 ₊_{+ px}_{px +}_{+ q}_{q and}_{and x}_x22 ₊_{+ mx}_{mx +}_{+ n}_{n, then}_{, then a}_{a = ___.}_{= ___.}

(A)

(A) n n q--q (B)(B) m m q--q (C)(C) n n p--p (D)(D) None None of of thesethese is _____. is _____. n n T T T T A A = 30°, = 30°, BB = 90°, = 90°, D

(6)

34. If

34. If AA is the area of a right-angled triangle and is the area of a right-angled triangle and bb is one of the sides containing the right angle, then is one of the sides containing the right angle, then the length of altitude on the hypotenuse is ____.

the length of altitude on the hypotenuse is ____.

(A) (A) + + 4 4 22 2 2 4 4 Ab Ab b b AA (B)(B) 4 4 ++ 22 2 2 4 4 A A b b AA (C)(C) ++ 2 2 4 4 22 2 2 4 4 A A b b AA (D)(D) 4 4 ++ 22 2 2 4 4 b b b b AA 35.

35. Find the inter-rFind the inter-relationship of the elationship of the variables for variables for the quadratic the quadratic equationequation y y == ax ax 22 ₊_{+ bx}_{bx +}_{+ c}_{c from given}_{from given}

graph. graph. (A) (A) aa ++ bb ++ c c = = 00 x x y y (–1, (–1, 0) 0) (2, (2, 0)0) –x –x ¢¢ y y ¢¢ (B) (B) aa –– bb ++ c c = = 00 (C) (C) 22aa ++ bb ++ c c = = 00 (D) (D) 44aa – – 22bb ++ c c = = 00 36.

36. The houses of a row are numbereThe houses of a row are numbered consecutively from d consecutively from 1 to 49. If there is a1 to 49. If there is a x x such that the sum such that the sum of the numbers of the house preceding the house numbered

of the numbers of the house preceding the house numbered x x is equal to the sum of the numbers is equal to the sum of the numbers of the house following it. Find the value of

of the house following it. Find the value of x x .. (A)

(A) 3535 (B)(B) 3434 (C)(C) 3030 (D)(D) 3333

37.

37. IIf f ssiin n cocos s anand d ssiin n cocoss , , tthheenn si sin n cocoss a a qq qq bb q q qq q q qq ____. ____. (A) (A) ₂₂22 1 1 a a b b a a = = -- (B)(B) 22 2 2 1 1 b b a a b b = = -- (C)(C) abab == bb 2 2_–_{– 1}₁ _(D)_{(D) a}_{a +}_{+ b}_{b =}_{= 1}₁ 38.

38. In In the the given given figure,figure, PT PT is a tangent to the circle at is a tangent to the circle at T T . . If If PPAA = 4cm and = 4cm and ABAB = 5 cm, find = 5 cm, find PT PT .. (A) (A) 7 7 cmcm A A B B P P T T (B) (B) 6 6 cmcm (C) (C) 8 8 cmcm (D) (D) 2 2 cmcm 39.

39. Consider Consider a a cylinder of cylinder of heightheight nn cm and radius cm and radius 33cm.cm.

p

p A string of width hA string of width h cm, when wound around cm, when wound around

the cylinder without keeping any space between two turns, covers the lateral surface of the cylinder the cylinder without keeping any space between two turns, covers the lateral surface of the cylinder completely

completely. What is the required length of the string. What is the required length of the string ??

(A) (A) 66nncmcm h h (B)(B) 12 12 cm cm h h n n (C)(C) 36 36 cm cm n n h

h (D)(D) None None of of thesethese

40. If

40. If AA(( x x 22 ₊_{+ m}_m22₎_{) +}_{+ Amx}_{Amx + cm}_{+ cm}22_x_x22 _{= 0, then}_{= 0, then A}_A(( ₊₊ ₊_{+ A}_A ₊_{+ c}_c ₌₌

____. ____.

(A)

(A) 00 (B)(B) 11 (C)(C) –1–1 (D)(D) None None of of thesethese

SECTION III : EVERYDAY MATHEMATICS

41.

41. Piyush gave one-fourth of Piyush gave one-fourth of the amount he hthe amount he had to Mahesh. Mahad to Mahesh. Mahesh in turn gave esh in turn gave half of what half of what he recehe receivedived from Piyush to Suraj. If the difference between the remaining amount with Piyush and the amount from Piyush to Suraj. If the difference between the remaining amount with Piyush and the amount received by Suraj is

received by Suraj is 500, how much money did Mahesh receive from Piyush ?500, how much money did Mahesh receive from Piyush ? (A)

(A) ``₁₀₀₁₀₀ _(B)_(B) ``₂₀₀₂₀₀ _(C)_(C) ``₄₀₀₄₀₀ _(D)_{(D) Data}_{Data inadequate}_inadequate

42.

42. 10 years 10 years ago, thago, th e average e average age of a age of a family of 4 members was family of 4 members was 24 y24 years. Two children having bears. Two children having b eeneen born (with age difference of 2 years), the present average age of the family is the same. The present born (with age difference of 2 years), the present average age of the family is the same. The present age of the youngest child is ____.

age of the youngest child is ____. and

(7)

7

43.

43. AA,, BB andand C C start cycling around a circular path in the same direction at same time. Circumference start cycling around a circular path in the same direction at same time. Circumference of the path is 1980 m. If the speed of

of the path is 1980 m. If the speed of AA is 330 m/min, speed of is 330 m/min, speed of BB is 198 m/min and is 198 m/min and C C is 220 m/min is 220 m/min and they start from the same point, then after what time interval will they be together at the starting and they start from the same point, then after what time interval will they be together at the starting point?

point? (A)

(A) 30 30 minsmins (B)(B) 9 9 minsmins (C)(C) 90 90 minsmins (D)(D) 60 60 minsmins

44.

44. A pA part of the monthly expenses of a famart of the monthly expenses of a family is constant and the remaining varies with the price ofily is constant and the remaining varies with the price of wheat. When the price of wheat is

wheat. When the price of wheat is 250 per quintal, the total monthly expenses are250 per quintal, the total monthly expenses are 1000 and when1000 and when it is

it is 240 per quintal, the total monthly expenses are240 per quintal, the total monthly expenses are 980. Find the total monthly expenses of the980. Find the total monthly expenses of the family when the cost of wheat is

family when the cost of wheat is 350 per quintal.350 per quintal. (A)

(A) ``₁₁₀₀₁₁₀₀ _(B)_(B) ``₁₂₀₀₁₂₀₀ _(C)_(C) ``₁₃₀₀₁₃₀₀ _(D)_(D) ``₁₅₀₀₁₅₀₀

45.

45. In the Maths Olympiad at In the Maths Olympiad at Animal Planet, two represAnimal Planet, two representatives entatives from the donkeyfrom the donkey's side, while solving's side, while solving a quadratic equation, committed the following mistakes :

a quadratic equation, committed the following mistakes : (i)

(i) One of them mOne of them made a ade a mistake mistake in the consin the constant term tant term and got the and got the roots aroots as 5 and 9s 5 and 9.. (ii)

(ii) The other cThe other committed an ommitted an error error in the coein the coefficient of fficient of x x and he got the roots as 12 and 4. and he got the roots as 12 and 4.

In the meantime, they realised that they were wrong and together they managed to get it right. Find In the meantime, they realised that they were wrong and together they managed to get it right. Find the quadratic equation.

the quadratic equation. (A)

(A) x x 22₊_{+ 4}_4 x_{x + 14 = 0}_{+ 14 = 0} _{(B) 2}_(B) _2 x_x22 ₊_{+ 7}_7 x_{x – 24 = 0}_{– 24 = 0} _(C)_{(C) x}_x22_{– 14}_–_14 x_{x + 48 = 0}_{+ 48 = 0} _{(D) 3}_(D) _3 x_x22_–_{– 17}_17 x_{x + 52 = 0}_{+ 52 = 0}

46.

46. Hari wishes Hari wishes to determine to determine the the distance between distance between two objectstwo objects AA andand BB, but there is an obstacle between, but there is an obstacle between these two objects which prevents him from making a direct measurement. He devises an clever way these two objects which prevents him from making a direct measurement. He devises an clever way to overcome this difficulty.

to overcome this difficulty.

First he fixes a pole at a convenient point

First he fixes a pole at a convenient point O O so that from so that from O O , both, both AA andand BB are are visible. Then he fixes another pole at the point

visible. Then he fixes another pole at the point DD on the line on the line AO AO (produced) such (produced) such that

that AO AO == DO DO . In a similar way he fixes a third pole at the point. In a similar way he fixes a third pole at the point C C on the line on the line BO BO (produced) such that

(produced) such that BO BO == CO CO . Then he measures. Then he measures CDCD which is equal to 170 cm. which is equal to 170 cm. The distance between the objects

The distance between the objects AA andand BB is ____. is ____.

A A _B_B D D C C O O (A) (A) 170 170 cmcm (B)(B) 340 340 cmcm (C)

(C) 85 85 cmcm (D)(D) None None of of thesethese

47.

47. AA,, BB,, C C are three points on the same horizontal line and are three points on the same horizontal line and CT CT is a vertical pole. The angle of is a vertical pole. The angle of elevation of

elevation of T T , as seen from, as seen from AA, , isis x° x° and the angle of elevation of and the angle of elevation of T T , as seen from, as seen from BB isis y° y° ((y° y° >> x° x° ).). If

If ABAB == d d , then the height of the pole is ____., then the height of the pole is ____.

(A) (A) ccoos s ccooss s siinn( ( )) d d x x yy y y x x °° °° °° -- °° (B)(B) ttaan n ttaann ttaan n ttaann d d x x yy y y x x °° °° °° -- °° (C)(C) c coos s ccooss c cooss( ( )) d d x x yy y y x x °° °° °° -- °° (D)(D) s siin n ssiinn c cooss( ( )) d d x x yy y y x x °° °° °° -- °° 48.

48. A buckeA bucket is 40 cm in t is 40 cm in diameter at diameter at the top, 28 cm in diametthe top, 28 cm in diameter at ter at the bottom and 21 cm dehe bottom and 21 cm deep. Theep. The cost of tin sheet used in making the bucket, if the cost of tin is

cost of tin sheet used in making the bucket, if the cost of tin is 1.50 per sq. dm is ____.1.50 per sq. dm is ____. (A)

(A) ``_32.25_32.25 _(B)_(B) ``_40.25_40.25 _(C)_(C) ``_44.25_44.25 _(D)_{(D) None}_{None of}_{of these}_these

49.

49. There are 100 There are 100 transistotransisto rs in a rs in a box. 20 of them are box. 20 of them are defectidefecti ve. ve. At random two transistors are tAt random two transistors are takenaken one by one consecutively without replacement. What is the probability that both of them are one by one consecutively without replacement. What is the probability that both of them are good ?

good ?

(A)

(8)

50.

50. A A boy is standing on the ground and flying a kite boy is standing on the ground and flying a kite with 100 m length of string at an with 100 m length of string at an elevation of 30°.elevation of 30°. Another boy is standing on the roof of a 10 m high building and is flying his kite at an elevation Another boy is standing on the roof of a 10 m high building and is flying his kite at an elevation of 45°. Both the boys are on opposite sides of both the kites. Find the length of the string that the of 45°. Both the boys are on opposite sides of both the kites. Find the length of the string that the second boy must have so that the two kites meet.

second boy must have so that the two kites meet. (A)

(A) 550 0 3 3 mm (B)(B) 440 0 2 2 mm (C)(C) 50 50 mm (D)(D) 100 100 mm

SPACE FOR ROUGH WORK SPACE FOR ROUGH WORK

(9)

LEVEL - 2

Year 2012-13

6

th

(10)

SECTION-I : LOGICAL REASONING

1.

1. Study Study the the following information following information carefully carefully to to answer answer the the given given question.question.

M

M K K K K I I D D N N E E T T T T Q Q O O B B F F H H A A A A G G T T U U U U X X W W L L S S R R II

Each

Each of of these these letters letters gets gets a a numerical numerical value value based based on on its its position position in in the the above above arrangement, arrangement, suchsuch

as, 1 for M, 2 for K, 4 for I and so on.

Value

Value of of A A is is exactly exactly equal equal to to the the total total value value of of which which of of the the following following pairspairs??

(i)

(i) DO DO (ii) (ii) QE QE (iii) (iii) MHMH

(A)

(A) Only Only (i)(i) (B)(B) Only (ii)Only (ii) (C)(C) Only Only (iii)(iii) (D)(D) Both Both (i) (i) and and (ii)(ii)

2.

2. Seven villages Seven villages A, B, A, B, C, D, C, D, E, F E, F and G and G are sare situated as ituated as follows:follows:

E is

E is 2 km 2 km to the to the west of west of B. F B. F is 2 is 2 km to km to the north the north of of A. C is A. C is 1 km 1 km to the to the west of west of A. D is A. D is 2 km 2 km toto

the south of G. G is 2 km to the east of C. D is exactly in the middle of B and E.

How

How far far is is E E from from F F (in (in km)?km)?

(A)

(A) 44 (B)(B) 2020 (C)(C) 55 (D)(D) 2626

3.

3. In the In the given diagram, given diagram, the circle the circle stands fostands for educated, r educated, square for square for hard-working, triangle hard-working, triangle for urban for urban andand

the rectangle for honest people. Different regions in the diagram are numbered from 1 to 12.

Region 4 is best described as consisting of ______.

(A)

(A) People who are non-urban, honest, uneducated and hard-working.People who are non-urban, honest, uneducated and hard-working.

(B)

(B) People who People who are are uneducated, urban, uneducated, urban, honest and honest and hard-working.hard-working.

(C)

(C) People who are uneducated, urban, hard-working and dishonest.People who are uneducated, urban, hard-working and dishonest.

(D)

(D) People who are urban, hard-working, honest and educated.People who are urban, hard-working, honest and educated.

4.

4. Read Read the the following information following information carefully carefully to to answer answer the the given given question.question.

Fifty

Fifty books books belonging belonging to to different different subjects,subjects, viviz z . History (8), Geography (7), Literature (13),. History (8), Geography (7), Literature (13),

Psychology (8) and Science (14), are placed on a shelf. They are arranged in an alphabetical order

subject to the condition that no two books of the same subject are placed together so long as books

of other subjects are available. Unless otherwise mentioned, all counting is done from the left.

Counting

Counting from from the the right right end, end, the the fth fth book book from from the the right right of of 3939thth_{book is ______.}_{book is ______.}

(A)

(A) History History (B)(B) Psychology Psychology (C)(C) Geography Geography (D)(D) Science Science

5.

5. If the word If the word TERMINATION is TERMINATION is coded as coded as 12345671586, what should 12345671586, what should be the be the code for the code for the wordword

MOTION?

(A)

(A) 438586 438586 (B)(B) 458586458586 (C)(C) 481586 481586 (D)(D) 485186 485186

6.

6. Read Read the the following information following information carefully carefully and and answer answer the the question question given given below below itit..

(i)

(i) A, A, B, B, C, C, D D and and E E are are ve ve friends. friends. (ii) (ii) B B is is elder elder to to E, E, but but not not as as tall tall as as C.C.

(iii)

(iii) C C is is younger younger to to A, A, and and is is taller taller to to D D and and E. E. (iv) (iv) A A is is taller taller to to D, D, but but younger younger than than E.E.

(v)

(v) D D is is elder elder to to A A but but is is shortest shortest in in the the group.group.

Which

Which of of the the following following statements statements is is correct correct about about BB??

(i)

(i) B B is is not not the the tallest.tallest.

(ii)

(ii) B B is is shorter shorter to to E.E.

(iii)

(iii) When When they they are are asked asked to to stand stand in in ascending ascending order order with with respect respect to to their their heights, heights, B B is is in in thethe

middle.

(A)

(11)

3

3 66thth_{IMO | Level-II | Class 10 |}_{IMO | Level-II | Class 10 |}

7.

7. Pointing to Pointing to a photograph, a photograph, a person a person tells his tells his friend, "She friend, "She is the is the grand daughter grand daughter of the of the elder brotherelder brother

of my father." How is the girl in the photograph related to this man?

(A)

(A) Niece Niece (B)(B) SisterSister (C)(C) Aunt Aunt (D)(D) Sister-in-law Sister-in-law

8.

8. Study Study the the following information following information and and answer answer the the question question given given below below itit..

The

The admission admission ticket ticket for for an an exhibition exhibition bears bears a a password password which which is is changed changed after after every every clock clock hourhour

based on set of words chosen for each day. The following is an illustration of the code and steps

of rearrangement for subsequent clock hours. The time is 9 a.m. to 3 p.m.

Batch

Batch I I (9 (9 a.m. a.m. to to 10 10 a.m.) a.m.) : : is is not not ready ready cloth cloth simple simple harmony harmony burningburning

Batch

Batch II II (10 (10 a.m. a.m. to to 11 11 a.m.) a.m.) : : ready ready not not is is cloth cloth burning burning harmony harmony simplesimple

Batch

Batch III III (11 (11 a.m. a.m. to to 12 12 noon) noon) : : cloth cloth is is not not ready ready simple simple harmony harmony burningburning

Batch

Batch IV IV (12 (12 noon noon to to 1 1 p.m.) p.m.) : : not not is is cloth cloth ready ready burning burning harmony harmony simplesimple

Batch

Batch V V (1 (1 p.m. p.m. to to 2 2 p.m.) p.m.) : : ready ready cloth cloth is is not not simple simple harmony harmony burningburning

Batch

Batch VI VI (2 (2 p.m. p.m. to to 3 3 p.m.) p.m.) : : is is cloth cloth ready ready not not burning burning harmony harmony simplesimple

If the

If the password password for Bafor Batch I tch I was was – 'rate – 'rate go long go long top top we let we let have', have', which which batch batch will have will have thethe

password–'go rate top long have let we'?

(A)

(A) IIII (B)(B) III III (C)(C) IVIV (D)(D) VV

9.

9. N ranks fth N ranks fth in a class. S in a class. S is eighth from the is eighth from the last. If T is last. If T is sixth after N sixth after N and just in and just in the middle of Nthe middle of N

and S, then how many students are there in the class?

(A)

(A) 2323 (B)(B) 2424 (C)(C) 2525 (D)(D) 2626

10.

10. Which one of Which one of the four intercthe four interchanges in signs hanges in signs and numbers and numbers would make thwould make the given equate given equation correction correct??

4

×

6 – 2 = 146 – 2 = 14

(A)

×

toto

÷

, 2 and 4, 2 and 4 (B)(B) – – toto

÷

, 2 and 6, 2 and 6 (C)(C) – – to to +, +, 2 2 and and 66 (D)(D)

×

to +, 4 and 6to +, 4 and 6

11.

11. A total of A total of 324 coins of 20 324 coins of 20 paise and 25 paise make paise and 25 paise make a sum ofa sum of ``_{71. The number of 25 paise coins}_{71. The number of 25 paise coins}

is _______.

(A)

(A) 120 120 (B)(B) 124 124 (C)(C) 144 144 (D)(D) 200200

12.

12. Select a gure from amongst Select a gure from amongst the options which will continue the sathe options which will continue the same series as established byme series as established by

the ve Problem Figures.

(A)

(A) (B) (B) (C) (C) (D)(D)

13.

13. In the given question, there are seven In the given question, there are seven gures, the rst and last of gures, the rst and last of which are unnumbered and thewhich are unnumbered and the

remaining are numbered as 1, 2, 3, 4 and 5. These seven gures form a series. However, one of the

ve numbered gures does not t into the series. The number of that gure is the answer.

M M EE UUHH UU EE EE SS HHSS EE NNNN UU SSBB SS EEUU EE BB S L P U E Y J S L P U E Y J L S L S UU PP YY UU SS 1 2 3 4 5 1 2 3 4 5 (A) (A) 11 (B)(B) 22 (C)(C) 44 (D)(D) 55

(12)

14.

14. There is a set of ve gures There is a set of ve gures labelled Plabelled P, Q, R, S and T called the Problem gures. Fig. (R) contains, Q, R, S and T called the Problem gures. Fig. (R) contains

a question mark. Select a suitable gure from the options which will substitute this question mark

so that a series is formed by the gures P, Q, R, S and T taken in order.

(A)

(A) (B)(B) _(C)_(C) _(D)_(D)

15.

15. There is a deThere is a denite relationship between gures nite relationship between gures P and R. P and R. Establish a similar relationship betweenEstablish a similar relationship between

gures Q and S by selecting a suitable gure from the options that would replace the question

mark (?) in g. (S).

(A)

(A) (B) (B) (C) (C) (D)(D)

16.

16. Which term Which term comes next comes next in the in the given series?given series?

AC,

AC, FH, FH, KM, KM, PR, PR, ??

(A)

(A) UWUW (B)(B) VWVW (C)(C) UXUX (D)(D) TVTV

17.

17. Count the Count the number of penumber of pentagons in the ntagons in the given gure.given gure.

(A)

(A) 1616 (B)(B) 1212 (C)(C) 88 (D)(D) 44

18.

18. Choose the correct mirror-image of the Fig. (X) from amongst Choose the correct mirror-image of the Fig. (X) from amongst the four options given along withthe four options given along with

it, if the mirror is placed along M

it, if the mirror is placed along M₁₁ MM₂₂..

(A)

(A) (B) (B) (C) (C) (D)(D)

19.

19. A cube, painted yellow on A cube, painted yellow on all faces is cut into 27 smaall faces is cut into 27 small cubes of equal size. How many small cubesll cubes of equal size. How many small cubes

are painted on

are painted on one face onlyone face only??

(A)

(13)

5

20.

20. Find out whFind out which of the ich of the options will complete options will complete the gure mathe gure matrixtrix..

(A) (A) (B)(B)

?

(C) (C) (D)(D)

SECTION-II : MATHEMATICAL REASONING

21.

21. The The value value ofof

3 311 5 5 22 7 7 11 11 4 4 77 10 10 11 17 17 22 22 5 5 11 11 77 8 8 55 2 2 4 4 55 8 8 11 3 3

++

−−

÷÷

++

−−

is _______. is _______. (A) (A) 77₈₈ (B)(B) 00 (C)(C) ₁₆₁₆1111 (D)(D) 11 22. If

22. If aa x x – – 11 ₌₌ _bc_bc_,_, _b_by y – – 11 ₌₌ _ca_ca _and_and _c_cz z – – 11 ₌₌ _ab_ab _then_then_xy_xy₊₊ _yz_yz₊₊ _zx_zx_{= ______.}_{= ______.}

(A)

(A) xyz xyz (B)(B) x x 22_y_y22_z_z22 _(C)_(C) ₂₂_xyz_xyz _(D)_(D) _1/(_1/(_xyz_xyz₎₎

23.

23. A railway half ticket costs half the full fare and the A railway half ticket costs half the full fare and the reservation charge is the same on half ticketreservation charge is the same on half ticket

as on full ticket. One reserved rst class ticket from Chennai to Trivandrum costs

as on full ticket. One reserved rst class ticket from Chennai to Trivandrum costs ``_{216 and one}_{216 and one}

full and one half reserved rst class tickets cost

full and one half reserved rst class tickets cost ``_{327. What is the cost of basic rst class full}_{327. What is the cost of basic rst class full}

fare and the reservation charge?

(A)

(A) ``_{105 and}_{105 and} `` ₆₆ _(B)_(B) ``_{216 and}_{216 and} `` ₁₂₁₂ _(C)_(C) ``_{210 and}_{210 and} ``₁₂₁₂ _(D)_(D) ``_{210 and}_{210 and} ``₆₆

24. If

24. If p pandandq q are the roots of the equationare the roots of the equation x x 22_–_–_bx_bx₊₊_c_c_{= 0, then what is the equat}_{= 0, then what is the equat}_{ion if the roots are (}_{ion if the roots are (}_pq_pq₊₊_p_p₊₊_q_q₎₎

and ( and ( pq pq – – p p –– q q )?)? (A) (A) x x 22 _{– 2}_{– 2}_cx_cx_{+ (}_{+ (}_c_c22_–_– _b_b22_{) = 0}_{) = 0} _(B)_(B) _x_x22_–_–₂₂_bx_bx₊₊₍₍_b_b22₊₊ _c_c22_{) = 0}_{) = 0} (C) (C) 33cx cx 22 _{– 2(}_{– 2(}_b_b ₊₊ _cx_cx₊₊ _c_c22_{) = 0}_{) = 0} _(D)_(D) _x_x22₊₊₂₂_bx_bx_–_–₍₍_c_c22_–_– _b_b22_{) =}_{) =}₀₀ 25.

25. Given intersecting chords, ndGiven intersecting chords, nd x x ..

(A) (A) 20° 20° B B C C E Ex x 4 4 0 0 ° ° 8 800°° O O D D A A (B) (B) 40° 40° (C) (C) 60°60° (D) (D) 80°80° 26. If

26. If ABC ABC is a right angled triangle withis a right angled triangle with

∠

A A = 90° and 2= 90° and 2ss == aa ++ bb ++ c c , where, where aa >> bb >> c c and notations and notations

have their usual meanings, then which one of the following is correct?

(A)

(A) ((ss – – bb) () (ss – – c c ) >) > ss((ss ––aa)) (B)(B) ((ss – – aa) () (ss –– c c ) >) > ss((ss –– bb))

(C)

(C) (s (s –– aa) () (ss –– bb) <) < ss((ss – – c c )) (D)(D) 44ss((ss – – aa) () (ss –– bb) () (ss – – c c ) =) = bc bc

27.

27. Six fruit baskets contain peSix fruit baskets contain peaches, apples and oranges. Three aches, apples and oranges. Three of the baskets of the baskets contain two apples andcontain two apples and

one orange each, two other baskets contain three apples and one peach each, and the last basket

contains two peaches and two oranges. You select a basket at random and then select a fruit at

random from the basket. Which of the following is the probability that the fruit is an apple?

(A)

(14)

28.

28. A A is three times as old as is three times as old as BB. Four years ago,. Four years ago, C C was twice as old as was twice as old as A A. In four years time,. In four years time, A A will will

be 31. What are the present ages of

be 31. What are the present ages of BB and and C C respectively? respectively?

(A)

(A) 9, 469, 46 (B)(B) 9, 9, 5050 (C)(C) 10, 10, 4646 (D)(D) 10, 10, 5050

29. If

a

,,

b

and and

g

are in A.P., then cot are in A.P., then cot

b

= _______. = _______.

(A)

(A) ssiinn ssiinn

c cooss ccooss

a

g

a

−−

(B)(B) s siinn ssiinn c cooss ccooss

g

a

g

a

−−

(C)(C) s siinn ssiinn ((ccooss ccooss ))

a

g

a

g

−−

2 2 (D)(D) 2 2((ssiinn ssiinn )) c cooss ccooss

g

a

g

a

−−

30.

30. Water ows at the rate of 10 metres per minute through a cylindrical pipe 5 mm in diameter.Water ows at the rate of 10 metres per minute through a cylindrical pipe 5 mm in diameter.

How long would it take to ll a conical vessel whose diameter at the base is 40 cm and depth

24 cm?

(A)

(A) 60 60 mins mins 15 15 secssecs (B)(B) 50 50 mins mins 15 15 secssecs (C)(C) 51 51 mins mins 12 12 secssecs (D)(D) 49 49 mins mins 8 8 secssecs

31. Points

31. Points A A,, BB,, C C and and DD are midpoints of the sides of squareare midpoints of the sides of square JETS JETS . If the area of. If the area of JETS JETS is 36 sq. cm,is 36 sq. cm,

then the area of

then the area of ABCD ABCD is ________.is ________.

J J A A E E B B T T C C S S D D (A) (A) 3 3 sq. sq. cmcm (B)(B) 7.5 7.5 sq. sq. cmcm (C)(C) 9 9 sq. sq. cmcm (D)(D) 18 18 sq. sq. cmcm 32.

32. The mean of The mean of 1, 3, 4, 5, 1, 3, 4, 5, 7 and 4 7 and 4 isis mm. The numbers 3, 2, 2, 4, 3, 3 and. The numbers 3, 2, 2, 4, 3, 3 and p p have mean have mean mm – – 1 1 andand

median

median q q , then, then p p ++ q q = ______.= ______.

(A)

(A) 77 (B)(B) 66 (C)(C) 55 (D)(D) 44

33.

33. What approximaWhat approximate value should come in place of the question mark (?) in the followingte value should come in place of the question mark (?) in the following

equation? equation? 158.25 158.25

×

4.6 + 4.6 + 21% of 21% of 847 + 847 + ? = ? = 950.935045950.935045 (A) (A) 3535 (B)(B) 4444 (C)(C) 5050 (D)(D) 4545 34.

34. If the ratio of mean and median of If the ratio of mean and median of a certain data is 2 : 3, then a certain data is 2 : 3, then nd the ratio of its mode andnd the ratio of its mode and

mean.

(A)

(A) 2 2 : : 55 (B)(B) 3 3 : : 22 (C)(C) 5 5 : : 22 (D)(D) 1 : 1 : 22

35.

35. In In the the given given diagram,diagram, ABCD ABCD is a square, diagonalis a square, diagonal BDBD is extended through is extended through

D

D toto E E .. AD AD == DEDE andand AE AE is drawn. What isis drawn. What is mm

∠

DAE DAE ??

(A) (A) 22.5° 22.5° (B) (B) 45° 45° E E D D B B C C A A (C) (C) 112.5° 112.5° (D) (D) 135° 135° 36.

36. What is the probability of getting at least one What is the probability of getting at least one six in a single throw of three unbiased dice?six in a single throw of three unbiased dice?

(A) (A) ₆₆11 (B)(B) 125125 216 216 (C)(C) 1 1 36 36 (D)(D) 91 91 216 216 37.

37. ABC ABC is a right angled triangle, right angled at is a right angled triangle, right angled at A A. A circle is inscribed in it and the lengths of the. A circle is inscribed in it and the lengths of the

two sides containing the right angle are 12 cm and 16 cm. Find the area of the circle.

(A)

(15)

7

38.

38. A person of height 2 m wanA person of height 2 m wants to get a fruit which is on the top of a pole of heightts to get a fruit which is on the top of a pole of height 1010 3 3 m if he m if he stands at distance of stands at distance of 44 3 3













mm from the foot from the foot of the pole, theof the pole, then the angle an the angle at which he should t which he should throwthrow

the stone, so that it hits the fruit is _____.

(A)

(A) 15° 15° (B)(B) 30° 30° (C)(C) 45° 45° (D)(D) 60°60°

39.

39. The point (–4, –2) lies on The point (–4, –2) lies on a circle. What is the length oa circle. What is the length of the radius of this circle, if the f the radius of this circle, if the centre iscentre is

located at (–8, –10)?

(A)

(A) 4848 (B)(B) 8080 (C)(C) 108108 (D)(D) 288288

40.

40. The ratio between the The ratio between the length and the breadth length and the breadth of a rectangular park of a rectangular park is 3 : 2. If a is 3 : 2. If a man cycling along theman cycling along the

boundary of the park at the speed of 12 km/hr

boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, completes one round in 8 minutes, then the area of the parkthen the area of the park

(in sq. m) is ______.

(A)

(A) 15360 15360 (B)(B) 153600 153600 (C)(C) 30720 30720 (D)(D) 307200 307200

SECTION-III : EVERYDAY MATHEMATICS

41.

41. In a garden, there are 10 In a garden, there are 10 rows and 12 columns of marows and 12 columns of mango trees. The distance between tngo trees. The distance between the two treeshe two trees

is 2 metres and a distance of one metre is left from all sides of the boundary of the garden. The

length of the garden is ______.

(A)

(A) 20 20 mm (B)(B) 22 22 mm (C)(C) 24 24 mm (D)(D) 26 m26 m

42.

42. 3 years ago, the average 3 years ago, the average age of a family of 5 members age of a family of 5 members was 17 years. A was 17 years. A baby having been born,baby having been born,

the average age of the family is the same today. The present age of the baby is _____.

(A)

(A) 1 1 yearyear (B)(B) 1111 2

2 years years (C)(C) 2 2 yearsyears (D)(D) 3 3 yearsyears

43.

43. Rajan got Rajan got married 8 married 8 years ago. years ago. His present His present age isage is 66

5

5 times his age at the time of his marriage. times his age at the time of his marriage. Rajan's sister was 10 years younger to him at the time of his marriage. The present age of Rajan's

Rajan's sister was 10 years younger to him at the time of his marriage. The present age of Rajan's

sister is ______.

(A)

(A) 32 32 yearsyears (B)(B) 36 36 yearsyears (C)(C) 38 38 yearsyears (D)(D) 40 years40 years

44.

44. In a History examination, the average for the entire class was 80 marks. If 10% of thIn a History examination, the average for the entire class was 80 marks. If 10% of the studentse students

scored 95 marks and 20% scored 90 marks, what was the average marks of the remaining students

of the class?

(A)

(A) 65.5 65.5 (B)(B) 72.5 72.5 (C)(C) 7575 (D)(D) 8585

45.

45. Padma purchased Padma purchased 30 kg of 30 kg of rice at the rice at the rate ofrate of ``_{17.50 per kg and another 30 kg rice at a certain}_{17.50 per kg and another 30 kg rice at a certain}

rate. She mixed the two and sold the entire quantity at the rate of

rate. She mixed the two and sold the entire quantity at the rate of `` _{18.60 per kg and made 20%}_{18.60 per kg and made 20%}

overall prot. At what price per kg did she purchase the lot of another 30 kg rice?

(A)

(A) ``_12.50_12.50 _(B)_(B) `` _13.50_13.50 _(C)_(C) `` _14.50_14.50 _(D)_(D) ``_15.50_15.50

46.

46. Three partners shared the prot in a business in the ratio 5 : 7 : 8. They had partnered forThree partners shared the prot in a business in the ratio 5 : 7 : 8. They had partnered for

14 months, 8 months and 7 months respectively. What was the ratio of their investments?

(A)

(A) 5 5 : : 7 7 : : 88 (B)(B) 28 : 49 : 6428 : 49 : 64 (C)(C) 38 : 28 : 2138 : 28 : 21 (D)(D) None of theseNone of these

47.

47. Simi can do a work in 3 days, wSimi can do a work in 3 days, while Meeta can do the same hile Meeta can do the same work in 2 days. Both of them nishwork in 2 days. Both of them nish

the work together and get

the work together and get ``_{150. What is the share of Simi?}_{150. What is the share of Simi?}

(A)

(16)

48.

48. A bicycle A bicycle can be can be purchased on purchased on cash payment cash payment ofof ``_{1500. The same bicycle can also be purchased}_{1500. The same bicycle can also be purchased}

at the down payment (initial payment, at the time of purchasing) of

at the down payment (initial payment, at the time of purchasing) of `` _{350 and rest can be paid in}_{350 and rest can be paid in}

3 equal installments of

3 equal installments of `` _{400 for next 3 months. The rate of SI per annum charged by the dealer}_{400 for next 3 months. The rate of SI per annum charged by the dealer}

is _____. is _____. (A) (A) ₂₃₂₃ 99 17 17%% (B)(B) 1717 9 9 23 23%% (C)(C) 1313 9 9 17

17%% (D)(D) None of theseNone of these

49.

49. The question given below consists of The question given below consists of a question followed by three statementa question followed by three statements. Ys. You have to studyou have to study

the question and the statements and decide which of the statement(s) is/are necessary to answer

the question.

A

A solid solid metallic metallic cone cone is is melted melted and and recast recast into into a a sphere. sphere. What What is is the the radius radius of of the the sphere?sphere?

I.

I. The The radius radius of of the the base base of of the the cone cone is is 2.1 2.1 cm.cm.

II.

II. The The height height of of the the cone cone is is four four times times the the radius radius of of its its base.base.

III.

III. The The height height of of cone cone is is 8.4 8.4 cm.cm.

(A)

(A) Only Only I I and and IIII (B)(B) Only Only II II and and IIIIII (C)(C) Only Only I I and and IIIIII (D)(D) Any Any two two of of threethree

50.

50. Yash Yash invesinvested a certain sum of money at 8% p.a. simple interest for ‘ted a certain sum of money at 8% p.a. simple interest for ‘nn’ years. At the end of ‘’ years. At the end of ‘nn’’

years, Yash got back 4 times his original investment. What is the value of

years, Yash got back 4 times his original investment. What is the value of nn??

(A)

(A) 50 50 yearsyears (B)(B) 25 25 yearsyears (C)(C) 12 12 years years 6 6 monthsmonths (D)(D) 37 37 years years 6 6 monthsmonths

SPACE FOR ROUGH WORK SPACE FOR ROUGH WORK

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LEVEL - 2

Year 2013-14

7

th

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1.

1. There are There are ve persons ve persons PP, Q, , Q, R, S R, S and and T. T. One is One is aa football player, one is a chess player and one is a football player, one is a chess player and one is a hockey player. P and S are unmarried ladies and hockey player. P and S are unmarried ladies and do not participate in any game. None of the ladies do not participate in any game. None of the ladies plays

plays chess chess or or footfootballball. T. There here is is a a marrmarried ied couplcouple e inin which T is the husband. Q is the brother of R and is which T is the husband. Q is the brother of R and is neither a chess player nor a hockey player. Who is neither a chess player nor a hockey player. Who is the football player?

the football player? A. A. PP B. B. QQ C. C. R R D. D. SS 2.

2. How How many many such such pairs pairs of of digits digits are are there there in in the the numbernumber 95137248 each of which has as many digits between 95137248 each of which has as many digits between them in the number as when they are arranged in them in the number as when they are arranged in ascending order? ascending order? A. A. NoneNone B. B. OneOne C. C. TwoTwo D. D. ThreeThree 3.

3. In In a a certain certain code code language, language, ''bring the white board bring the white board ' is' is written as '

written as 'ka na di paka na di pa' and '' and 'white and black board white and black board '' is written as '

is written as 'na di sa rana di sa ra'. How is ''. How is 'thethe' written in that' written in that code? code? A. A. kaka B. B. pa pa C. C. kaka oror pa pa D.

D. None None of of thesethese

4.

4. Read Read the the following following information information and and answer answer the the questionquestion given below it.

given below it. (i)

(i) L, L, M, M, N, N, O, O, PP, , Q, Q, R R and and S S are are sitting sitting around around aa circle facing the centre.

circle facing the centre. (ii)

(ii) N, N, who who is is third third to to the the left left of of PP, , is is not not a a neighbourneighbour of R and M.

of R and M. (iii)

(iii) S S is is the the neighbour neighbour of of ‘O’ ‘O’ and and ‘R’ ‘R’ and and is is third third toto the right of M.

the right of M. (iv)

(iv) L L is is not not the the neighbour neighbour of of O, O, who who is is second second to to thethe left of N.

left of N. What

What is is the the position position of of Q?Q? A.

A. Immediate Immediate right right of of R R B.

B. Immediate Immediate left left of of NN C.

C. Third Third to to the the right right of of MM D.

D. Second to the left of SSecond to the left of S

5.

5. TwTwo o different different positions positions of of the the same same dice dice has has beenbeen shown below. If digit 1 is on the top what will come shown below. If digit 1 is on the top what will come just

just belobelow w it?it?

4 4 33 22 33 5 5 66 A. A. 22 B. B. 33 C. C. 44 D. D. 55 6.

6. Figures Figures (i) (i) and and (ii) (ii) of of the the Problem Problem Set Set bears bears a a certaincertain relationship. Establish a similar relationship between relationship. Establish a similar relationship between gures (iii) and (iv) by selecting a suitable gure fr gures (iii) and (iv) by selecting a suitable gure fr omom the options that would replace the question mark in the options that would replace the question mark in g.(iv).

g.(iv).

??

((ii) ) ((iiii) ) ((iiiiii) () (iivv)) Problem Set Problem Set A. A. B. B. C. C. D. D. 7.

7. If 'tall' is equivalent to 'circle', 'army men' to 'triangle'If 'tall' is equivalent to 'circle', 'army men' to 'triangle' and 'strong' to 'square', indicate which number will and 'strong' to 'square', indicate which number will represent only strong army men?

represent only strong army men? A. A. 33 B. B. 44 C. C. 55 D. D. 66 8.

8. Select Select a a gure gure from from the the options options which which will will continuecontinue the series

the series established by established by the Problem the Problem Figures.Figures. Problem Figures Problem Figures A. A. B. B. C. C. D. D. 5 5 4 4 7 7 6 6 3 3 2 2 1 1 LOGICAL REASONING LOGICAL REASONING

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7

7thth_{IMO | Class-10 | Level 2}_{IMO | Class-10 | Level 2}

3 3 9.

9. Three Three of of the the following following four four are are alike alike in in a a certain certain wayway and so form a group. Which is the one that does not and so form a group. Which is the one that does not belo

belong ng to to that that grougroup?p? A. A. 215215 B. B. 247247 C. C. 9191 D. D. 6565 10.

10. Group the Group the given gures given gures into three into three classes classes using eachusing each gure only once.

gure only once.

A. A. 1,2,5 1,2,5 ; ; 3,7,8; 3,7,8; 4, 4, 6, 6, 99 B. B. 1, 1, 7, 7, 2; 2; 3, 3, 9, 9, 6; 6; 4, 4, 5, 5, 88 C. C. 2, 2, 3, 3, 8; 8; 4, 4, 6, 6, 9; 9; 1, 1, 5, 5, 77 D. D. 5, 5, 6, 6, 9; 9; 3, 3, 4, 4, 1; 1; 2, 2, 7, 7, 88 11.

11. Choose Choose the the option which option which most most closely closely resembles theresembles the water-image of the given combination.

water-image of the given combination. GR98AP76ES GR98AP76ES A. A. B. B. C. C. D. D. 12.

12. Identify Identify which which one one of the of the alternative alternative gures gures completescompletes the pattern in the given matrix.

the pattern in the given matrix.

A. A. B. B. C. C. D. D. 13.

13. If it If it is is possible to possible to make a make a meaningful word frommeaningful word from the second, fourth, seventh and tenth letters of the the second, fourth, seventh and tenth letters of the word UNDENOMINATIONAL, using each letter word UNDENOMINATIONAL, using each letter only once, third letter of the word would be your only once, third letter of the word would be your answer. If more than one such word can be formed answer. If more than one such word can be formed your answer would be ‘X’, whereas if more than your answer would be ‘X’, whereas if more than two such words can be formed your answer would two such words can be formed your answer would be

be ‘Y’‘Y’, , and and if if no no such such word word can can be be forformedmed, , answanswerer would be ‘Z’. would be ‘Z’. A. A. XX B. B. ZZ C. C. YY D. D. NN 14.

14. The following problem consists of The following problem consists of a set a set of sixof six figures, the first of which is unnumbered and marks figures, the first of which is unnumbered and marks the beginning of the series which is continued in the the beginning of the series which is continued in the successive figures numbered from 1 to 5. However, successive figures numbered from 1 to 5. However, the series will be established only if the positions the series will be established only if the positions of two of the numbered figures are interchanged. of two of the numbered figures are interchanged. The number of the earlier of the two figures is the The number of the earlier of the two figures is the answer. If no two figures need to be interchanged, answer. If no two figures need to be interchanged, then the answer is 5.

then the answer is 5.

A. A. 11 B. B. 22 C. C. 33 D. D. 55 15.

15. Study Study the the following following arrangement arrangement carefully carefully and and answeranswer the question given below:

the question given below:

How many many such such consonants consonants are are there there in in the the aboveabove arrangement, each of which

arrangement, each of which is immediately precededis immediately preceded by

by a a lettlett er er and and immeimmediatdiately ely folfollowelowed d by by a a numbnumber?er? A. A. NoneNone B. B. OneOne C. C. TwoTwo D. D. ThreeThree 16.

16. Mohit lives Mohit lives to the to the North of North of Rajesh wRajesh who lives ho lives to theto the West of Tanuj. Arun who lives to the South of Mohit West of Tanuj. Arun who lives to the South of Mohit have his house in which direction with respect to have his house in which direction with respect to Tanuj? Tanuj? A. A. North-EastNorth-East B. B. NorthNorth C. C. South-WestSouth-West D.