IMO Level 2 Class 10

January 11, 2019 | Author: Nilesh Gupta | Category: Circle, Elementary Mathematics, Elementary Geometry, Geometric Shapes, Space
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IMO Level 2 Class 10...

Description

5th

LEVEL - 2 Year 2011-12

2

| 5th IMO | Level-II | Class 10

SECTION I : LOGICAL REASONING 1.

There are six persons persons A, B, C, D, E and F. F. C is the sister of F. F. B is the brother brother of E's husband. D 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? (A) ABF

2.

(D) BDF

(B) 5 years

(C) 7 years

(D) 14 years

If second second Saturday and all Sundays are holidays in a 30 days days month beginning on Saturday, Saturday, then how many working days are there in that month? (A) 25

4.

(C) BFC

Anita, Mahima, Mahima, Rajan, Lata Lata and Deepti Deepti are five cousins. Anita is twice as old as Mahima. Mahima. Rajan is 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? (A) 4 years

3.

(B) ABD

(B) 22

(C) 24

(D) 23

If the same same function function is applied applied to reach the results results in each each of the three three sets sets of numbers numbers given then which number will replace the question mark in the third set of numbers? (A) 24 21 5 28 13 (B) 30 24 30 (C) 36 7 7 17 25 (D) 40

5.

16

2 ?

10

8

If the first and the second letters letters of the word UNPRECEDENTED are interchanged with the last and 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 the right of the third letter from from the left end ? (A) C

6.

(B) E

(C) P

(D) R

Ravi wants to go to the university. university. He starts starts from his home which is in the East and comes to a 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 ? (A)  (A)  North

7.

(B)  (B)  South

(C)  (C)  East

(D)  (D)  West

Find out the wrong term in the number series. 105, 85, 60, 30, 0, – 45, – 90 (A) 105

8.

(C) 0

(D) – 45

Choose the number-letter group which is different from the others. (A) M5S

9.

(B) 60

(B) B9L

(C) T4Y

(D) F4J

Select a figure from amongst the options which will continue the series series established established by the five problem figures. Problem Figures

? (A)

(B)

(C)

(D)

3 10.

5th IMO | Level-II | Class 10 |

In the question, there there are seven figures, the first and last of which are unmarked and the the remaining 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.

P

(A)

P

Q

R

(B) Q

S (C) R

T

(D) T

11. In the given figure, if the triangle represents represents girls, the circle represents represents athletes, the rectangle represents boys and the square represents disciplined, then the boys who are athletes and disciplined are indicated by which number number ? (A) 1 (B) 2 (C) 6 (D) 10

10

7 6 5

9 3 2 4 1

8

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

Raj

(B)  (B)  Gaurav

(C)  (C)  Mohit

(D)  (D)  Ashish

13. In a certain coding system, '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'. What is the code for 'the dog was frightened'? (A)  (A)  5438

(B)  (B)  8263

(C)  (C)  8731

(D) None of these

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

(10, 14, 16)

(B) (7, 21, 28)

(C) (5, 10, 25)

(D) (4, 8, 12)

15. Find the the missing missing number? (A)

8C 

(B)

12B 12B

(C)

16C  16C 

(D)

18C  18C 

3C  2B

4 A

27 A ?

64B

9B 4 A 16C 

16. Find the odd one out. (A)

(B)

(C)

17. The question consists of a set of three three figures X, Y and Z showing a sequence of folding of a piece of paper. Fig. (Z) shows the manner in which the folded paper has been cut. Choose a figure from the options which would most closely resemble the unfolded form of fig. (Z). (A)

(B)

(C)

(D)

X

Y

(D)

Z

4

| 5th IMO | Level-II | Class 10

18. Group the given figures into three classes classes using each each figure only once. (A) 1, 2, 5; 3, 7, 8; 4, 6, 9 (B) 1, 7, 2; 3, 9, 6; 4, 5, 8

1

2

3

4

5

6

7

8

9

(C) 2, 3, 8; 4, 6, 9; 1, 5, 7 (D) 5, 6, 9; 3, 4, 1; 2, 7, 8 19. When the given given figure is folded to form form a cube, how many many dots would lie opposite the face bearing five dots? (A) 1 (B) 2 (C) 3 (D) 4 20. Select a figure from from the options which satisfies the same conditions of placement placement of the dots as as in fig. (X).

Fig. (X)

(A)

(B)

(C)

(D)

SECTION II : MATHEMATICAL REASONING 21. A person invested some some amount at the rate of 10% simple interest and some other amount amount at the rate of 12% simple interest. He received yearly interest of  130. But if he had interchanged the amounts invested, he would have received

4 more as interest. How much amount did he invest at

different rates ? (A)

` 700

(C)

`

at 12%,

` 500

at 10%

(B)

`

700 at 10%,

700 each at 10% and 12%

(D)

`

500 each at 10% and 12%

`

500 at 12%

22. In PQR  PQ R , PD QR   such that D  lies on QR . If  PQ  = a, PR  = b, QD = c  and DR  = d , then (a + b)(a )( a – b) = _____. (A) 1

(B) (c  + d )(d  )(d  – c )

(C) (c  + d )(c  )(c  – d )

(D) 0

23. Two circles with radii radii a and b respectively touch each other externally. Let c  be the radius of a circle that touches these two circles as well as a common tangent to these two circles. Then ___. (A) 24.

1 a

-

1 b

=

1 c 

(B)

1 a

+

1 b

+

1 c 

=

0

(C)

1 a

+

1

=

b

1 c 

(D) None of these

 ABC   is right angled at A.  DEFG   is a square inscribed in triangle as side DE   is on BC  and G  & F  are two points at AB and AC   respectively. Then DE 2 = (A) BD ´ EC  1

(B) BD = 2EC 

 A

5

5th IMO | Level-II | Class 10 |

25. If from twice the greater greater of two positive numbers 16 16 is subtracted, subtracted, the result is half the other number. number. If from half the greater number 1 is subtracted, the result is still half the other number. What are the numbers ? (A)

16, 8

(B) 12, 10

(C) 6, 8

(D) 10, 8 a 2a , respectively and S  is the point t 2 t

26. If  P and P and Q  are   are two points whose coordinates are (at  (at 2, 2at ) and (a, 0), then (A)

1 SP

1 is _____. SQ  

Dependent of  t 

(B) Independent of  t 

(C) Independent of  a

27. If  T 1, T 2, T 3, ......., Tn are consecutive terms of an A.P., then

(A)

n -1 T1 × T n

(B)

n T1 × T n

(C)

1

1

T1T2

T 2T3

T2 (n - 1) T1 × T n

(D) None of these 1

......

 ____.

Tn 1Tn  

(D) None of these

28. In the given figure, the diameters of two wheels have measures 2 cm and 4 cm. Determine the lengths of the belts AD and BC  that   that pass around the wheels if it is given that belts cross each other at right angle. (A)

4 cm each

(B)

3 cm each

(C)

5 cm each

(D)

6 cm each

B  A P

O

D

29. In the given figure, three circles of radius radius 2 cm touch one another externally. These circles are circumscribed by a circle of radius R   cm. Find the approximate value of  R . (A)

5.4 cm

(B)

5.0 cm

(C)

4.0 cm

(D)

4.3 cm

¢



C

 A

B

C

30. A number is selected at 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. Find the probability that the selected number is their average. (A)

0

(B) 1

(C)

1 6

(D)

1 12

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

1:7

(B) 1 : 8

(C) 7 : 1

(D) 7 : 8

32. The ratio of the areas areas of the right angled triangles ABC  and DEF   in which  A   A  = 30°,  AC   = 4 cm, D  = 60°, E   = 90° and DE   = 4 cm is ___. (A)

1:2

(B) 4 : 1

(C) 1 : 4

B  = 90°,

(D) 2 : 1

33. If ( x   x  + a) is a factor of the polynomial x 2 + px  + q  and x 2 + mx  + n, then a  = ___. (A)

n-q

(B)

m-q

(C)

n-p

(D) None of these

6

| 5th IMO | Level-II | Class 10

34. If  A  is the area of a right-angled triangle and b  is one of the sides containing the right angle, then the length of altitude on the hypotenuse is ____. 2 Ab

(A)

b

4

+

4A

2 A2

2 A

(B)

2

b

4

+

4A

(C)

2

b4

+

4 A2

2b

(D)

b

4

+

4A

2

35. Find the inter-relationship inter-relationship of the variables for the quadratic equation y  = ax 2 + bx  + c   from given graph. y  (A) a + b + c = c  = 0 (B) a – b + c = c  = 0  –x   x (–1, 0) (2, 0) (C) 2a + b + c = c  = 0 y  (D) 4a – 2b + c = c  = 0 ¢

¢

36. The houses of a row are numbered numbered consecutively from 1 to 49. If there is a x   such that the sum of the numbers of the house preceding the house numbered x   is equal to the sum of the numbers of the house following it. Find the value of  x . (A) 35

37.

(B) 34

If sin q

(A)

b

cos q

2a

=

a2

-1

a and

sin q

c os q

sin sin q cos cos q

(B)

a

=

(C) 30

(D) 33

(C) ab = b2 – 1

(D) a + b = 1

b, then  ____.

2b b2

-1

38. In the given figure, PT   is a tangent to the circle at T . If  PA  = 4cm and AB  AB  = 5 cm, find PT . B

(A) 7 cm (B) 6 cm (C) 8 cm

 A P

(D) 2 cm

39. Consider a cylinder of height n  cm and radius

3 p



cm. A string of width h  cm, when wound around

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 ? (A)

6n h

cm

40. If  and  ____. (A) 0

(B)

12h n

cm

(C)

36n h

cm

are roots of the equation A( x   x 2 + m2) + Amx   + cm2 x 2 = 0, then A( (B) 1

(C) –1

(D) None of these 2

+

2

) + A

+ c

2

2

=

(D) None of these

SECTION III : EVERYDAY MATHEMATICS 41. Piyush gave one-fourth of the amount he had had to Mahesh. Mahesh Mahesh in turn gave half of what he received received from Piyush to Suraj. If the difference between the remaining amount with Piyush and the amount received by Suraj is 500, how much money did Mahesh receive from Piyush ? (A)

`

100

(B)

`

200

(C)

`

400

(D) Data inadequate

42. 10 years ago, th e average age of a family of 4 members was 24 years. years. Two children having b een 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 ____.

7

5th IMO | Level-II | Class 10 |

43. A, B and C   start cycling around a circular path in the same direction at same time. Circumference of the path is 1980 m. If the speed of  A  is 330 m/min, speed of  B  is 198 m/min and C   is 220 m/min and they start from the same point, then after what time interval will they be together at the starting point? (A)

30 mins

(B) 9 mins

(C) 90 mins

(D) 60 mins

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

250 per quintal, the total monthly expenses are

240 per quintal, the total monthly expenses are

family when the cost of wheat is (A)

`

1100

(B)

1000 and when

980. Find the total monthly expenses of the

350 per quintal.

` 1200

(C)

`

1300

(D)

` 1500

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

One of them made made a mistake in the constant constant term and got the roots as as 5 and 9. 9.

(ii)

The other committed committed an error in the coefficient coefficient of  x   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 the quadratic equation. (A)

x 2 + 4 x   + 14 = 0

(B) 2 x 2 + 7 x   – 24 = 0

(C) x 2  – 14 x   + 48 = 0

(D) 3 x 2  – 17 x   + 52 = 0

46. Hari wishes to determine the distance between two objects A and B, but there is an obstacle between these two objects which prevents him from making a direct measurement. He devises an clever way to overcome this difficulty. First he fixes a pole at a convenient point O   so that from O , both A and B  are

 A

B

visible. Then he fixes another pole at the point D  on the line AO  (produced)   (produced) such that AO = AO  = DO . In a similar way he fixes a third pole at the point C   on the line BO  (produced) such that BO  = CO . Then he measures CD  CD  which is equal to 170 cm. O 

The distance between the objects A and B  is ____. (A)

170 cm

(B) 340 cm

(C)

85 cm

(D) None of these

C

D

47. A, B, C   are three points on the same horizontal line and CT   is a vertical pole. The angle of elevation of  T , as seen from A, is x°   and the angle of elevation of  T , as seen from B is y° ( y°  > x° ). ). If  AB = d , then the height of the pole is ____. (A) 48.

d cos x ° cos y ° sin( y ° - x ° )

(B)

d tan x° tan y ° tan y ° - tan x °

(C)

d cos x ° cos y ° cos( y ° - x ° )

(D)

d sin x° sin y ° cos( y ° - x °)

A bucket bucket is 40 cm in diameter at the top, 28 cm in diameter diameter at the the bottom and 21 cm deep. deep. The cost of tin sheet used in making the bucket, if the cost of tin is (A)

`

32.25

(B)

` 40.25

(C)

`

44.25

1.50 per sq. dm is ____. (D) None of these

49. There are 100 transisto rs in a box. 20 of them are defecti ve. At random two transistors are taken taken one by one consecutively without replacement. What is the probability that both of them are good ? (A)

316

(B)

19

(C)

16

(D)

32

8

| 5th IMO | Level-II | Class 10

50. A boy is standing on the ground and flying a kite with 100 m length of string at an elevation of 30°. 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 second boy must have so that the two kites meet. (A)

50 3 m

(B)

40 2 m

(C) 50 m

SPACE FOR ROUGH WORK

(D) 100 m

6th

LEVEL - 2 Year 2012-13

| 6th IMO | Level-II | Class 10

2

SECTION-I : LOGICAL REASONING 1.

Study the following information carefully to answer the given question. M K K I D N E T T Q O B F H A A G T U U X W L S R I Each of these letters gets a numerical value based on its position in the above arrangement, such as, 1 for M, 2 for K, 4 for I and so on. Value of A is exactly equal to the total value of which of the following pairs ? (i) DO (A) Only (i)

2.

(ii) QE (B) Only (ii)

(iii) MH (C) Only (iii)

(D) Both (i) and (ii)

Seven villages A, B, C, D, E, F and G are situated situated as follows: E is 2 km to the west of B. F is 2 km to the north of A. C is 1 km to the west of A. D is 2 km to the south of G. G is 2 km to the east of C. D is exactly in the middle of B and E. How far is E from F (in km)? (A) 4

3.

(B)

20

(C) 5

(D)

26

In the given diagram, the circle stands for for educated, square for hard-working, triangle for urban and 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) People who are non-urban, honest, uneducated and hard-working. (B) People who are uneducated, urban, honest and hard-working. (C) People who are uneducated, urban, hard-working and dishonest. (D) People who are urban, hard-working, honest and educated.

4.

Read the following information carefully to answer the given question. Fifty books belonging to different subjects, vi viz  z . 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 from the right end, the fth book from the right of 39 th  book is ______. (A)   History (A) (B)  Psychology (B)  (C)   Geography (C) (D)  Science (D) 

5.

If the word TERMINATION is coded as 12345671586, what should be the code for the word MOTION? (A)   438586 (A)

6.

(B) 458586

(C)   481586 (C)

(D)   485186 (D)

Read the following information carefully and answer the question given below it . (i)

A, B, C, D and E are ve friends.

(iii) C is younger to A, and is taller to D and E. (v)

(ii)

B is elder to E, but not as tall as C.

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

D is elder to A but is shortest in the group.

Which of the following statements is correct about B ? (i)

B is not the tallest.

(ii)

B is shorter to E.

(iii) When they are asked to stand in ascending order with respect to their heights, B is in the middle. (A) Only (i)

(B) Only (i) and (ii)

(C) (i), (ii) and (iii)

(D)  All are incorrect

6th IMO | Level-II | Class 10 |

3 7.

Pointing to a photograph, a person tells his friend, "She is the grand daughter of the elder brother of my father." How is the girl in the photograph related to this man? (A)   Niece (A) (B) Sister (C)   Aunt (C)

8.

(D)   Sister-in-law (D)

Study the following information and answer the question given below it . The admission ticket for an exhibition bears a password which is changed after every clock hour 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 I (9 a.m. to 10 a.m.)

:

is not ready cloth simple harmony burning

Batch II (10 a.m. to 11 a.m.)

:

ready not is cloth burning harmony simple

Batch III (11 a.m. to 12 noon) :

cloth is not ready simple harmony burning

Batch IV (12 noon to 1 p.m.)

:

not is cloth ready burning harmony simple

Batch V (1 p.m. to 2 p.m.)

:

ready cloth is not simple harmony burning

Batch VI (2 p.m. to 3 p.m.)

:

is cloth ready not burning harmony simple

If the password for Batch Batch I was – 'rate go long top we let have', which batch will have the password–'go rate top long have let we'? (A) II (B)   III (B) 9.

(C) IV

(D) V

N ranks fth in a class. S is eighth from the last. If T is sixth after N and just in the middle of N and S, then how many students are there in the class? (A) 23

(B) 24 24  

(C) 25 25  

(D) 26

10. Which one of the four interchanges interchanges in signs and numbers would make the the given equation equation correct? correct ? 4 × 6 – 2 = 14 (A)

× to ÷,

2 and 4

(B) – to

÷,

2 and 6

(C)  – to +, 2 and 6

11. A total of 324 coins of 20 paise and 25 paise make a sum of is _______. (A)   120 (A)

(B)   124 (B)



(D)

× to

+, 4 and 6

71. The number of 25 paise coins

(C)   144 (C)

(D) 200

12. Select a gure from amongst the options which will continue the same same series as established by the ve Problem Figures.

(A)

(B)

(C)

(D)

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

L

P

U

E

Y

J

M E UH U E E S HS E NN U SB S E U E B L S U P Y U S 1

 

(A) 1

(B) 2 

2

3

4

(C) 4 

5

(D) 5

| 6th IMO | Level-II | Class 10

4

14. There is a set of ve gures labelled P, P, 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)

(B)

(C)

(D)

15. There is a denite denite relationship between gures P and R. Establish 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)

(B)

(C)

(D)

16. Which term comes next in the given series? (A) UW

(B) VW VW  

AC, FH, KM, PR, ? (C) UX UX  

(D) TV

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

(A) 16

(B) 12

(C) 8

(D) 4

18. Choose the correct mirror-image of the Fig. (X) from amongst the four options given along with it, if the mirror is placed along M 1 M2.

(A)

(B)

(C)

(D)

19. A cube, painted yellow on all faces is cut into 27 small small cubes of equal size. How many small cubes are painted on one face only ? (A) 1 (B) 6

(C) 8

(D) 12

6th IMO | Level-II | Class 10 |

5 20. Find out which which of the options will complete the gure matrix matrix . (A)

(B)

(C)

(D)

?

SECTION-II : MATHEMATICAL REASONING 1 7 +2 5 11 21. The value of 7 17 4 −1 10 22 3

(A)

7 8

5

÷

7

11 +

8+

5

−4

8−

5 2

1 3

is _______.

(B) 0

(C)

11 16

(D) 1

 x  –  – 1 22. If  a x  = bc , by  – 1 = ca and c z  – 1 = ab then  xy  + yz  + zx  = ______. (A) xyz  (B)  x 2y 2z 2 (C) 2 xyz 

 xyz ) (D) 1/( xyz 

23. A railway half ticket costs half the full fare and the reservation charge is the same on half ticket as on full ticket. One reserved rst class ticket from Chennai to Trivandrum costs full and one half reserved rst class tickets cost

`  327.

fare and the reservation charge? (A) ` 105 and ` 6 (B) ` 216 and

(C)

`

12

`  216

and one

What is the cost of basic rst class full

` 210

and ` 12

(D)

` 210

and ` 6

24. If p If p and q  q are are the roots of the equation x  equation  x 2 – bx  bx + + c  =  = 0, then what is the equat ion if the roots are ( pq  ( pq  + p  + p +  + q ) and ( pq  –  pq  –  p – q )? )? 2 2 (A)  x  – 2 cx  + ( c   – b2) = 0 (C) 3cx 2 – 2( b + cx  +  + c 2) = 0

(B)  x 2 – 2bx  +  + (b2 + c 2) = 0 (D)  x 2 + 2bx  –  – (c 2 – b2) = 0 C 

25. Given intersecting chords, nd  x .  A

(A)   20° (A)

E x  80°    °    0   4 O 

(B)   40° (B) (C) 60°

B

D

(D) 80° 26. If  ABC  is a right angled triangle with

∠ A

= 90° and 2s 2s = a + b + c , where a > b > c   and notations

have their usual meanings, then which one of the following is correct? (A) (s  – b) ( s – c ) > s(s – a) (B) (s – a) ( s – c ) > s(s – b) (C) (s – a) ( s – b) < s(s – c ) (D) 4s(s – a) ( s – b) ( s – c ) = bc  27. Six fruit baskets contain peaches, peaches, apples and oranges. Three of the baskets contain 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)   0.32 (A) (B)  0.4 (B)  (C)  0.46 (C)  (D)  0.58 (D) 

| 6th IMO | Level-II | Class 10

6

28.  A  A   is three times as old as B. Four years ago, C   was twice as old as  A  A.. In four years time,  A  A   will be 31. What are the present ages of B  and C   respectively? (A) 9, 46 (B) 9, 50 (C) 10, 46 29. If

a, b  and  g   are

(A)

(D) 10, 50

in A.P., then cot b  = _______.

sin a − sin g  cos g − cos a

(B)

sin g − sin a cos g − cos a

(C)

sin a − sin g  2(cos a − cos g )

(D)

2(sin g − sin a ) cos g − cos a

30. 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) 60 mins 15 secs

(B) 50 mins 15 secs

(C) 51 mins 12 secs

(D) 49 mins 8 secs

31. Points  A  A,, B, C   and D are midpoints of the sides of square JETS . If the area of JETS  is 36 sq. cm, then the area of  ABCD is ________. J

A

B

D



(A) 3 sq. cm

(B) 7.5 sq. cm







(C) 9 sq. cm

(D) 18 sq. cm

32. The mean of 1, 3, 4, 5, 7 and 4 is m. The numbers 3, 2, 2, 4, 3, 3 and  p  p   have mean m  – 1 and median q , then  p + q  = ______. (A) 7 (B) 6

(C) 5

(D) 4

33. What approxima te value should come in place of the question mark (?) in the following equation? (A) 35

158.25 (B) 44

×  4.6

+ 21% of 847 + ? = 950.935045 (C) 50

(D) 45

34. If the ratio of mean and median of a certain data is 2 : 3, then nd the ratio of its mode and mean. (A) 2 : 5

(B) 3 : 2

(C) 5 : 2

(D) 1 : 2

35. In the given diagram,  ABCD is a square, diagonal BD BD   is extended through D to E .  AD = DE and  AE is drawn. What is m∠DAE ?

B



 A

D

(A)   22.5° (A) (B)   45° (B) (C)   112.5° (C)



(D)   135° (D) 36. What is the probability of getting at least one six in a single throw of three unbiased dice? (A)

1 6

(B)

125 216

(C)

1 36

(D)

91 216

37.  ABC   is a right angled triangle, right angled at  A  A.. 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) 25.56 sq. cm (B) 50.28 sq. cm (C) 75.65 sq. cm (D) 20.34 sq. cm

6th IMO | Level-II | Class 10 |

7

38. A person of height 2 m wants wants to get a fruit which is on the top of a pole of height stands at distance of

  

10 3

  m if he

  m from the foot of the pole, then then the angle at at which he should throw  3 

4

the stone, so that it hits the fruit is _____. (A)   15° (A) (B)  30° (B) 

(C)   45° (C)

(D) 60°

39. The point (–4, –2) lies on a circle. What is the length of of the radius of this circle, if the centre is located at (–8, –10)? (A)

48

(B)

80

(C)

(D)

108

288

40. The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is ______. (A)   15360 (A)

(B)   153600 (B)

(C)   30720 (C)

(D)   307200 (D)

SECTION-III : EVERYDAY MATHEMATICS 41. In a garden, there are 10 rows and 12 columns of mango mango trees. The distance between the the 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) 20 m

(B) 22 m

(C) 24 m

(D) 26 m

42. 3 years ago, the average age of a family of 5 members was 17 years. A baby having been born, the average age of the family is the same today. The present age of the baby is _____. (A) 1 year

1 (B) 1   years 2

(C) 2 years

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

(D) 3 years

6

  times his age at the time of his marriage. 5 Rajan's sister was 10 years younger to him at the time of his marriage. The present age of Rajan's sister is ______. (A) 32 years

(B) 36 years

(C) 38 years

(D) 40 years

44. In a History examination, the average for the entire class was 80 marks. If 10% of the the students scored 95 marks and 20% scored 90 marks, what was the average marks of the remaining students of the class? (A)   65.5 (A)

(B)   72.5 (B)

45. Padma purchased 30 kg of rice at the rate of

(C) 75 `  17.50

(D) 85

per kg and another 30 kg rice at a certain

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

`

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)

`

12.50

(B)

`

13.50

(C)

`

14.50

(D)

`

15.50

46. Three 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) 5 : 7 : 8 (B) 28 : 49 : 64 (C) 38 : 28 : 21 (D) None of these 47. Simi can do a work in 3 days, while while Meeta can do the same work in 2 days. Both of them nish the work together and get `  150. What is the share of Simi? (A) ` 30 (B) ` 60 (C) ` 70

(D)

`

75

| 6th IMO | Level-II | Class 10

8

48. A bicycle can be purchased on cash payment of

`  1500.

The same bicycle can also be purchased

at the down payment (initial payment, at the time of purchasing) of 3 equal installments of

`

`

350 and rest can be paid in

400 for next 3 months. The rate of SI per annum charged by the dealer

is _____. (A)

23

9 17

%

(B) 17

9 23

%

(C) 13

9 % 17

(D) None of these

49. The question given below consists of a question followed by three statements. statements. You You have to study the question and the statements and decide which of the statement(s) is/are necessary to answer the question. A solid metallic cone is melted and recast into a sphere. What is the radius of the sphere? I.

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

II.

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

III. The height of cone is 8.4 cm. (A) Only I and II (B) Only II and III

(C) Only I and III

(D) Any two of three

50. Yash inves invested ted a certain sum of money at 8% p.a. simple interest for ‘ n ’ years. At the end of ‘ n ’ years, Yash got back 4 times his original investment. What is the value of n? (A) 50 years (B) 25 years (C) 12 years 6 months (D) 37 years 6 months SPACE FOR ROUGH WORK

7th

LEVEL - 2 Year 2013-14

7th IMO | Class-10 | Level 2

2 LOGICAL REASONING

1.

There are ve persons P, Q, R, S and T. One is a football player, one is a chess player and one is a hockey player. P and S are unmarried ladies and do not participate in any game. None of the ladies  plays chess or football foot ball.. There T here is a married marr ied coupl e in which T is the husband. Q is the brother of R and is neither a chess player nor a hockey player. Who is the football player? A. B. C. D.

2.

A. B. C. D.

6.

None One Two Three

ka  pa ka or  pa None of these

5.

Immediate right of R 

B.

Immediate left of N

C.

Third to the right of M

D.

Second to the left of S

Two Two different positions of the same dice has been shown below. If digit 1 is on the top what will come  just below belo w it?

2

3

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

(ii)

(iii)

(i (iv)

A. B. C.

D. 7.

(i)

A.

3

2 3 4 5

(i)

Read the following information and answer the question given below it. L, M, N, O, P, Q, R and S are sitting around a circle facing the centre. (ii) N, who is third to the left of P, is not a neighbour of R and M. (iii) S is the neighbour of ‘O’ and ‘R’ and is third to the right of M. (iv) L is not the neighbour of O, who is second to the left of N. What is the position of Q?

6

?

In a certain code language, ' bring the white board ' is written as ' ka na di pa ' and ' white and black board ' is written as ' na di sa ra '. How is ' the ' written in that code? A. B. C. D.

4.

4

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

3.

P Q R  S

5

8.

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

3

B.

4

C.

5

D.

6

1 4 2 7 3 6 5

Select a gure from the options which will continue the series established by the Problem Figures. Problem Figures

A. B. C. D.

7th IMO | Class-10 | Level 2

9.

Three of the following four are alike in a certain way and so form a group. Which is the one that does not  belong  belo ng to that group? grou p? A. B. C. D.

10.

3

13.

215 247 91 65

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

If it is possible to make a meaningful word from the second, fourth, seventh and tenth letters of the word UNDENOMINATIONAL, using each letter only once, third letter of the word would be your answer. If more than one such word can be formed your answer would be ‘X’, whereas if more than two such words can be formed your answer would  be ‘Y’, ‘Y’ , and if no such word can be formed for med,, answer answ er would be ‘Z’. A. B. C. D.

A. B. C. D. 11.

1,2,5 ; 3,7,8; 4, 6, 9 1, 7, 2; 3, 9, 6; 4, 5, 8 2, 3, 8; 4, 6, 9; 1, 5, 7 5, 6, 9; 3, 4, 1; 2, 7, 8

X Z Y N

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

Choose the option which most closely resembles the water-image of the given combination. GR98AP76ES A. B. C. D.

12.

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

A. B. C. D.

15.

1 2 3 5

Study the following arrangement carefully and answer the question given below: [email protected]©2HD%38BIM6*UWY5$9GJ#7A How many such consonants are there in the above arrangement, each of which is immediately preceded  by a lett er and imme diat ely followe fol lowed d by a numb number? er? A. B. C. D.

A.

16. B.

C.

D.

None One Two Three

Mohit lives to the North of Rajesh who who lives to the West of Tanuj. Arun who lives to the South of Mohit have his house in which direction with respect to Tanuj? A. B. C. D.

North-East North South-West Can't be determined

7th IMO | Class-10 | Level 2

4

17.

Find the suitable alternative alternative to t into the blank space in Fig. (X) in order to complete the pattern.

(v)

If an odd number is followed by an even number, the second one is to be subtracted from the rst one. 58 17 5 85 5 n If n is the resultant of the r st row what is the resultant of the second row? A. B. C. D.

A.

19. B.

255 32 49 34

There is a denite relationship between gures 1 and 2. Establish a similar relationship between gures 3 and 4 by selecting a suitable gure from the option that would replace the question mark (?) in g. 4.

C.

D. A.

18.

In the following question, two rows of numbers are given. The resultant number in each row is to be worked out separately based on the following rules and the question below the rows of numbers is to be answered. The operation of numbers progresses from left to right.

B.

C.

Rules: (i)

If an odd number is followed by another composite odd number, they are to be multiplied.

(ii)

If an even number is followed by an odd number, they are to be added.

D.

20.

(iii) If an even number is followed by a number which is a perfect square, the even number is to be subtracted from the perfect square.

Pointing to a woman woman in a photograph photograph a man says; says; “She “She is the only daughter of my father’s mother-in-law”. How is the woman related to the man? A. B. C. D.

(iv) If an odd number is followed by a prime odd number, the rst number is to be divided by the second number.

Daughter  Mother  Daughter-in-law Mother-in-law

MATHEMATICAL REASONING

21.

Determine the value of k  so   so that the following linear

22.

Find the value of 

equations have no solution.

sec39°

 + 1) x + (3k  (3k  +  x + 3 y –  y – 2 = 0 2  – 2) y – (k   + 1) x +  x + (k  –  y – 5 = 0

cosec 51°

A.

–1

B.

–2

C.

1

D.

4

 +

2 3

tan17° tan38° tan60° tan52° tan73° –

3(sin231° + sin259°) A. –1 B. 0 C. 1 D. 2

7th IMO | Class-10 | Level 2

23.

5

Let  f (  f ( x) =  x 2 + bx + c   where b , c   are integers. I f  f (  f ( x ) is a factor of both  x 4 + 6 x 2   + 25 and

A. B. C. D.

3 x 4 + 4 x2 + 28 x + 5, then the value of  f (1) (1) is _____  A. B. C. D.

1 2 3 None of these

29.

24.  A ,  B , C   are three towns connected by straight roads from  A to  B,  B to C   and C  to  A.  A.  AB   = 5 km,  BC   = 6 km and CA   = 7 km. Two cyclists start simultaneously from A and go in different roads with same speed. They meet at  D, then  BD =  BD = _______.

A. B. C. D. 25.

26.

Triangle ABC  is  is equilateral of side length 8 cm. Each arc shown in the diagram is an arc of a circle with the opposite vertex of the triangle as its centre. The total area enclosed within the entire gure shown (in cm2) ________.

A.

48( p − 3 )

B.

30

C. D.

32( p − 3 ) 90 p

30.

31.

125 sq. units 110 sq. units 148 sq. units 132 sq. units

A boy is cycling such that the wheels of the cycle are making 140 revolutions per minute. If the diameter of the wheel is 60 cm, calculate the speed per hour with which the boy is cycling. A. B. C. D.

32.

1 6 3 7

Find the area of the quadrilateral ABCD  whose vertices are respectively  A (1, 1),  B (7, –3), C (12, ( 12, 2) and  D (7, 21). A. B. C. D.

15.82 km/hour  15.84 km/hour  15.96 km/hour  20 km/hour 

A conical vessel of radius 6 cm and height 8 cm is completely ll ed with water. A sphere is lowered in to the water and its size is such that when it touches the sides, it is just immersed as shown in gure. What fraction of water overows?

(a + 1), (– a + 2) (a + 1), (a + 2) (– a + 1), (a + 2) (a + 1), – ( a + 2)

The radii of two concentric circles circles are 13 cm and 8 cm.  AB  is a diameter of the bigger circle.  BD is a tangent to the smaller circle touching it at  D. Find the length  AD.  AD . A. B. C. D.

28.

3p

A bag contains 12 balls out of which  x  are white. If 6 more white balls are put in the bag, the probability of drawing a white ball will be double than that of drawing a white ball before adding the balls. Find the value of  x.  x. A. B. C. D.

Solve for  x :  x2 +  x – (a  + 1)(a  + 2) = 0 A. B. C. D.

27.

2 km 4 km 6 km 8 km

100 m 120 m 60 m 125 m

19 20 25 30

cm cm cm cm

The angle of elevation of a cloud from a point 60 m above a lake is 30° and the angle of depression of the reection of cloud in the lake is 60°. Find the height of the cloud.

A. B. C. D. 33.

3/8 8/3 5/4 6/7

The sum of 5th and 9th  terms of an A.P. is 72 and the sum of 7 th  and 12 th  terms is 97. Find the A.P. A. B. C. D.

5, 10, 15, 20 ...... 15, 30, 45, 60 ....... 6, 11, 16, 21, 26, ..... 2, 4, 6, 8, 10 ......

7th IMO | Class-10 | Level 2

6

34.

Find the median of the following data.

Class

sec θ cosec(90° − θ) − tan θ cot(90° − θ )

010

1020

2030

3040

4050

5060

6070

7080

8090

90100

5

3

4

3

3

4

7

9

7

8

Frequency

A.

64

B.

48.93

C.

63.43

D.

66.43

35.

Evaluate :

A.

+ sin 2 55° + sin 2 35° tan 10° tan 20° tan 60° tan 70° tan 80°

1

2

B.

3 C.

3

3

D.

1

EVERYDAY MATHEMATICS

36.

The speed of a boat in still water is 15 km/hr. It can go 30 km upstream and return downstream to the original point in 4 hours 30 minutes. Find the speed of the stream. A. B. C. D.

37.

4 5 6 7

km/hr  km/hr  km/hr  km/hr 

Two Two cars start start together in the same direction from the same place. The rst goes with uniform speed of 10 km/h. The second goes at a speed of 8 km/h in the rst hour and increases the speed by 1/2 km in each succeeding hour. After how many hours will t he second car overtake the rst car if both cars go non-stop? A. B. C. D.

40.

A. B. C. D.

41.

9 hours 10 hours 12 hours None of these

39.

2772 litres 9979 litres 9979.2 litres 9297.4 litres

A mason has to fit a bathroom with square marble tiles of the largest possible size. The size of the  bathroo  bat hroo m is 10 ft. by 8 ft. What woul d be the size (in inches) of the tile required that has to be cut and how many such tiles are required respectively? A. B. C. D.

42. 38.

Water is being pumped out through a circular pipe whose internal diameter is 7 cm. If the flow of water is 72 cm per second, how many litres of water are  bein g pum pumped ped out in one hou hour? r?

24, 20, 20, 41,

20 24 43 6

An aeroplane at an altitude of 200 metres observes the angles of depression of opposite points on the two  banks of a river r iver to be 4 5° and 60°. Find the width widt h of the river.

Reena has pens and pencils which together are 40 in number. If she has 5 more pencils and 5 less pens, then number of pencils would become 4 times the number of pens. Find the original number of pens and pencils respectively.

A. B. C. D.

A. B. C. D.

115.47 metres 200 metres 215.47 metres 315.47 metres

Aarushi sold sold 100 lottery tickets in which 5 tickets carry prizes. If Priya purchased a ticket, what is the  probabil  prob ability ity of Priya Priy a winning winn ing a prize? priz e? A. B. C. D.

43.

20 1 25 1 20 17 20

44.

12 28 13 27

Two Two poles of of height 9 m and 14 m stand on a plane plane ground. If the distance between their feet is 12 m, find the distance between their tops. A. B. C. D.

19

28, 12, 27, 13,

12 13 14 15

m m m m

A sum of `  700  700 is to be used to give seven cash prizes to students of a school for their overall academic  perf  pe rf or ma nc e. If each ea ch pr iz e is  `   20 less than its  preceding  prec eding prize, priz e, nd the value valu e of each prize. priz e.

7th IMO | Class-10 | Level 2 A. B. C. D.

45.

7

20 more candidates appeared and 2 more passed, the ratio of successful candidates to unsuccessful candidates would have been 2 : 1. Find the number of candidates who appeared in the examination originally.

  100,  `  `  100,

120,  ` 140,  ` 160,  ` 80,  ` 40,  ` 20   140,  ` 120,  ` 100,  ` 80,  ` 40,  ` 20  ` 160,  `  140,  ` 160,  ` 140,  ` 120,  ` 100,  ` 80,  ` 60,  ` 40  ` 380,  ` 360,  ` 340,  ` 320,  ` 300,  ` 280,  ` 260

A. B. C. D.

In an examination the ratio of the number of of successful successful candidates and unsuccessful candidates is 4 : 1. Had

85 92 34 17

ACHIEVERS SECTION

46.

CAB  is an angle whose measure is 70°.  ACFG and  ABDE  are squares drawn outside the angle. The diagonal FA meets G  B E  a t H . Then the measure of the angle  EAH   EA H  is   is _____.

A. B. C. D. 47.

There is only one

 F 

A. B. C. D.



 A

70°

 B

49.

 E   H 

 D

Study the statements carefully and select the correct option. Statement- 1 : The distance between two points ( x1,  y 1) and ( x 2,  y 2) is

( x1 − x2 ) 2

A. B. C. D.

+ ( y1 − y2 )2

48.

Fill in the blanks. the circle at A P to a circle is a line that meets the only one one point. It is a special special case of Q , when the two end points of its corresponding chord R .

S tangent tangent secant tangent

Match the columns. Co lu mn II

th

(i)

The 8  term from the end of the (p) A.P. 7, 10, 13, …, 184 is

(ii)

The 10th term from the end of the (q)  –142 A.P. 8, 10, 12, …, 126 is

A. B. C. D.

or (–9, (–9, 0). 0).

Both the statements are true. Statement-1 is true but statement-2 is false. Statement-1 is false but statement-2 is true. Both the statements are false.

R intersect coincide coincide meet

(iii (iii)) The rst term of an A.P. A.P. is 5 (r) th and its 100  term is – 292. The 50th  term is

Statement-2 : The point(s) on the  x-axis which has its distances from the points (7, 6) and (–3, 4) in

 35 , 0    3  

at a point of circle.

Q tangent secant chord tangent

C ol umn I

45° 25° 65° 70°

the ratio 1 : 2 is

P secant tangent tangent line

S

50.

108

163

(i) →  (q), (ii) →  (p), (iii) → (r ) (i) →  (r), (ii) →  (p), (iii) →  (q) (i) →  (p), (ii) →  (q), (iii) →  (r) (i) →  (q), (ii) →  (r), (iii) →  (p) 5

% 16 without changing the shape, what will be the percentage increase in the surface area?

If the volume of a sphere is increased increased by 95

A. B. C. D.

SPACE SPACE FOR ROUGH WORK

56.25% 50 % 28.56% Remains same

9th

LEVEL - 2 Year 2015-16

MATHEMATICS

1.

2.

3.

If one of the zeros of a quadratic polynomial of the form  x 2 + ax + b   is negative of the other, then it  ______.  ____ __. A.

Has no linear term and the constant term is negative.

B.

Has no linear term and the constant term is  positive  posi tive..

C.

Can have a linear term but the constant term is negative.

D.

Can have a linear term but the constant term is  positive  posi tive..

6.

None of these

Frequency (in `) A.

8

Solve for  x   x  and  y :

B.

16

 1 + b  x +  1 + a  y = b − a , x − 4 y = 5 ; ab ≠ 0.  b    a   b a

C.

12

D.

4

A.

 x = – a,  y = b

B.

 x = b 2 ,  y = a 2

C.

 x = a 2 ,  y = b 2

D.

 x = b,  y = – a – a

7.

In the given gure, ABC  gure,  ABC  is   is a triangle right angled at  B and  B and  BD ^  AC . If  AD =  AD  = 4 cm and CD = CD  = 5 cm, nd  BD   BD  and  AB respectively.

 D

 B



B.

36 years

C.

40 years

D.

46 years

40 - 50

50- 6 0

 Number  Numb er of  students

12

35

45

25

13

2 5 cm cm, 6 cm

D.

60.43

D.

3 5 cm cm, 8 cm

9.

In D ABC  right  right angled at B at B,, BC  =  = 5 cm and AC  and AC  – AB  – AB =  = 1 cm. 1 + sin C  . Evaluate cos C  5 A. 13 B. 13 12 13 5

The value of sin

q  increases as q  decreases

4

30 -4 0

C.

B.

5

2 0- 30

33.33

sin ( A +  B)  B) = sin  A +  A + sin  B

?

10 -2 0

C.

A.

13

M ar ks

3 5 cm,  6 cm

Which of the following statements is correct ?

9

Find the mode of the following frequency distribution :

30.12

D.

6

30 years

B.

B.

3

A.

20.33

2 5 cm, 3 5 cm

as q  increases

Three years ago, the average age of Latika, Garima and Megha was 27 years and that of Garima and Megha 5 years ago was 20 years. Latika’s present age is _______.

A.

A.

C.

2

D.

q  increases

Class Class inter interval val 11-13 11-13 13-15 13-15 15-17 15-17 17-1919-2 17-1919-21 1 21-23 21-23 23-25 23-25

8.

5.

The value of cos

The following table shows the daily pocket allowance given to the children of a multistorey building. The mean of the pocket allowance is `  18. Find out the missing frequency.

 A

4.

C.

10.

A small scale industry produces a certain number of items per day. The cost of production of each item (in rupees) was calculated to be 74 minus twice the number of articles produced in a day. On a particular day, the total cost of production was `  540. Which of the following equations represent how to nd the number of items produced on that day? A.

74 + 2 x =  x  = 540

B.

 x 2 + 74 x –  x – 540 = 0

C.

74 – 2 x =  x = 540

D.

 x 2 – 37 x +  x + 270 = 0

The sum of rst n terms of an A.P. is given by ( n2 + 8n 8n). th th Find the 12  term of the A.P. Also nd the n   term of the A.P. th

-

11.

A.

31, 2 n + 9

B.

31, 2 n + 7

C.

30, 2 n + 6

one expected by Beena. Which one of the following  pai rs of num ber s wil l t in the des cri pti on of the question?

D.

30, 2 n + 8

A.

14, 22

B.

13, 62

C.

19, 33

D.

42, 28

In the given gure,  PQ   PQ   is the chord of circle and  PT   is the tangent at  P  such   such that ∠QPT   = 60°. Then  PRQ is ________. ∠ PRQ is 15.

Q

For what values of k  will   will the following pair of linear equations have innitely many solutions? 2 x + 3 y =  y = 4 and (k  ( k  +   + 2)  x + 6 y = 3 k  + 2

 R  P 

12.



–1

C.

2

B.

150°

D.

–2

C.

120°

D.

110°

16.

In the given gure, arcs are drawn by taking vertices  A,  A,  B and  B and C  of   of an equilateral triangle of side 10 cm to intersect the sides BC  sides  BC , CA and CA  and AB  AB at  at their respective mid-points  D,  D,  E   and  F . Find the area of the shaded region. [Use p  = 3.14]

A.

39.25 cm 2

B.

48.50 cm 2

C.

78.50 cm 2

D.

28.25 cm 2

Two Two cleanliness cleanliness hoardings are put on two poles poles of equal heights standing on either side of a roadway 50 m wide between the poles. The elevations of the tops of the poles from a point between them are 60° and 30°. Find the height of the pole.

B. C. D.

th

B.

135°

A.

14.

1

A.

50 3 m 25 3m 3 25 3 m 25

3m

2

Beena gave a simple multiplication question to her students. But one student reversed the digits of  both numbers numb ers and carried carr ied out the multipli mult ipli cation catio n and found that the product was exactly the same as the -

The values of l   for which the quadratic equation  x 2 + 5lx  lx   + 16 = 0 has no real root is _____. A.

l  > 8

B.

l  < –5 8 8 − < l  < 5 5 8 − ≤ l  < 0 5

C. D. 17.

13.

A.

18.

A straig ht highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of 30°, which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to  be 60°. Find the time taken by the car to reach the foot of the tower from this point. A.

3 seconds

B.

6 seconds

C.

9 seconds

D.

5 seconds

Two dice are thrown simultan eously. What is the  probabil  prob ability ity of getting gett ing two numbe rs whose whos e pr oduct is odd ? A. C.

19.

1

B.

2 3

D.

8

3 4 1 4

Find the median of the following data : M ar ks

0- 10

 No. of students stud ents

10

A.

51.5

B.

25.5

C.

28.5

D.

31

10 -2 0 2 0- 30 30 -4 0 18

40

20

40 - 50 12

3

20.

A number is selected at random from the numbers :

24.

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 a  prime  prim e number. numb er. A. B. C. D. 21.

0 1 8 1 6 1

(The shaded portion is cut off from the quadrant. The radius of quadrant OAB  OAB   is 5 cm and radius of each semicircle is 1 cm)

12

The value of expression

 1 1/ 4 (0.3) ⋅   ⋅ (9)1/ 6 ⋅ (0.81)2 /3  27  − 1 2 (0.9) 2 / 3 ⋅ (3) −1/ 2 ⋅   ⋅ ( 243)−1/ 4  3  − (0.6)0 − (0.1) 1 ÷ − −  3  1 ⋅  3 3 +  − 1  1  3        1/ 3

2

22.

A.

– 0.2

B.

0.9

C.

1.27

D.

– 0.06

25. 25.

3

25 : 16

B.

25 : 9

C.

20 : 9

D.

None of these

There are 100 apples in a box. 20 of them are rotten. At random, two apples are taken one by one consecutively without replacement. What is the  probabil  prob ability ity that both of them are good ? 316 495 19

B.

There are two circles intersecting each other. Another smaller circle with centre O, is lying between the common region of two larger circles. Centres of the circle (i ( i.e.,  A,  A, O  and  B)  B) are lying on a straight line.  AB   AB   = 16 cm and the radii of the larger circles are 10 cm each. What is the area of the smaller circle ?

O

495 16

C.

99 32

D. 26.

B

99

Which of the following statements is INCORRECT ? (i)

In order to divide a line segment internally in the ratio m : n, both m  and n are real numbers.

(ii)

A pair of tangents can be constructed to a circle inclined at an angle of 165°.

A.

Only (i)

A.

4p cm 2

B.

Only (ii)

B.

2p cm 4 cm 2

C.

Both (i) and (ii)

D.

Neither (i) nor (ii)

C. D.

4

2

is

A.

A.

 A

23.

A circular paper is folded along its diameter, then again it is folded to form a quadrant. Then it is cut as shown in the gure, after it the paper was reopened in the original circular shape. Find the ratio of the original paper to that of the remaining paper?

2

p p 4

27. cm

2

If the points  A(–2, ( 4, –1) are  A (–2, 1),  B(  B ( a , b) and C (4, collinear and a – b  = 1, nd the values of a  and b respectively. A.

1, 0

B.

1, –1

C.

0, 1

D.

–1, 1

If

a and b be two zeros of the quadratic polynomial

 p(  p ( x)  x) = 2 x 2 – 3 x   x  + 7, evaluate A. B. C. D.



3

1 2a − 3

+

1 2b − 3

14

3 7



5 4

3 14 th

-

.

28.

29.

5 − 3 − 2  is _____. A.

A rational number

B.

A natural number 

C.

Equal to zero

D.

An irrational number 

33.

In gure, the line segment  LM  is   is parallel to side  XZ  of D XYZ   X YZ  and   and it divides the triangle into two parts of  XL . equal areas. Find the ratio  XY 

A.

50°

B.

45°

C.

35°

D.

55°

In the given gure,  XW  is  is a tangent to the circle with centre O at  X   and YZW  YZ W   is a straight line. Find the value of  y.  y.  X  O

 X 

 y

Y   L



30.

A.

2 −1: 2

B.

2 +1: 2

C.

1− 2 : 2

D.

2− 2 : 2

lighthouse. 100 A. m 3 B. 100 m

32.

34. 34.

Two ships are sailing in the sea on the either side of the lighthouse, the angles of depression of two ships as observed from the top of the lighthouse are 60° and 45° respectively. If the distance between the

 

ships is 200 

31.





3 + 1 

C.

200 m

D.

(1 + 3 ) m

3

  metres,  

30°

B.

35°

C.

40°

D.

50°

A.

5

B.

20

C.

30

D.

25

26 24 14

B.

13 24

C.

26 13

D.

14

units units units

units

A.

4.50 m

If the point  P ( x,  x, 2) divides the line segment joining the points  A(12,  A(12, 5) and  B(4,  B(4, – 3) in the ratio k   : 1, then nd the value of  x.  x.

B.

2.125 m

A.

C.

1.125 m

D.

3.25 m

C.

In the given gure, if equal to

 POQ  = 130°, then ∠SOR ∠ POQ =

Q

O



-

36.



If the points A points A(1, (1, –2), B –2), B(2, (2, 3), C (–3, (–3, 2) and D and D(–4, (–4, –3) are the vertices of parallelogram  ABCD  ABC D, then taking  AB as  AB  as the base, nd the height of this parallelogram. A.

A well of diameter 3 m is dug 14 m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4 m to form an embankment. Find the height of the embankment.

20°

 Z 

If the common difference of an A.P. A.P. is 5, then a18 – a13  = _____.

nd the height of the

 P 

th

35.

A.

70°

 R

is

8

B.

67 3

D.

67 8 9

37.  ABC   is a right-angled triangle, right angled at  A.  A. A circle is inscribed in it. The lengths of the two sides containing the right angle are 5 cm and 12 cm. Find the radius of the circle. A.

1/2 cm

B.

13 cm

C.

2 cm

D.

10 cm 5

38.

In figure,  ABC  A BCDE DE F   is any regular hexagon with different vertices  A,  A,  B,  B, C ,  D,  D,  E   and  F   as the centres of circles with same radius ‘r  ‘ r ’ units are drawn. Find the area of the shaded portion.

A.

2pr 2 sq. units

B.

4pr 2 sq. units

C.

pr 2 sq. units 6pr 2 sq. units

D. 39.

40.

41.

42.

43.

C.

 x 2 – 14 x +  x + 48 = 0

D.

3 x 2 – 17 x +  x + 52 = 0

What must be added to the polynomial 3l  3 l 4 + 5l  5 l 3 – 7l  7 l 2 + 5 l   + 3 so that the resulting polynomial is exactly divisible by l 2 + 3 l  + 1 ? A.

–3l  –3 l  + 1

B.

–3l  –3 l  – 1

C.

3 l  + 1

D.

3 l  – 1

In the given gure,  DE  | |  BC . If  DE  :  BC   = 3 : 5, nd the ratio of the area of D ADE   AD E   to the area of trapezium  BCED.  BCED .  A

A cylindrical pipe has inner diameter diameter of 4 cm cm and water ows through it at the rate of 20 m per minute. How long would it take to ll a conical tank, with diameter of base as 80 cm and depth 72 cm ?

 D

A.

5 minutes

B.

3 minutes 56 seconds

A.

9 : 16

C.

4 minutes 20 seconds

B.

25 : 9

D.

4 minutes 48 seconds

C.

16 : 9

D.

9 : 25

 B

If sum of the squares of zeros of the polynomial 25 6 x 2 +  x + k  is ,  nd k . 36 A. 2

44.

If

cos q − sin q cos q + sin q

B.

–2

the angle q.

C.

1

A.

30°

D.

–1

B.

60°

C.

90°

D.

45°

In the Maths Olympiad Olympiad in a school, two representatives from two teams, while solving a quadratic equation, committed the following mistakes : (i)

One of them made a mistake in the constant term and got the roots as 5 and 9.

(ii)

The other committed an error in the coefcient of  x   x   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 the right quadratic equation. A.

 x 2 + 4 x +  x + 14 = 0

B.

2 x 2 + 7 x –  x  – 24 = 0



45.



=

1− 3 1+ 3

  and 0° <

q  <

90°, then nd

Evaluate : 4 (sin4 30° + cos 4 60°) – 3 (cos 2 45° – sin2 90°) + (sin2 60° + sin 2 45°) A. B. C. D.

3

1 4

1 4 3 4 7 16

ACHIEVERS SECTION

46.

Which of the following options hold ?

( x – a) ( x – b) + ( x – b) ( x – c) + ( x – c) ( x – a) = 0

 p, q, r   and  s   s  are real numbers such Statement 1 :  I f  p, that pr  that  pr  = 2 ( q +  s),  s), then atleast one of the equations 2  x +  px + q = 0 and  x 2 + rx +  s =  s = 0 has real roots.

has real and distinct roots.

Statement 2 : If a , b, c   are distinct real numbers, then the equation 6

A.

Statement 1 is true, Statement 2 is false

B.

Statement 1 is false, Statement 2 is true

C.

Both Statement 1 and Statement 2 are true

D.

Both Statement 1 and Statement 2 are false th

-

47.

Rakesh has to buy a TV. TV. He can buy TV either making cash down payment of ` 14000 at once or by making 12 monthly instalments as below : st

`   1500

nd

(1   month), ` 1450 (2   month), (3  month), `  1350 (4 th   month), ........

1400

`

A.

3, 4, 2, 1

B.

2, 4, 3, 1

C.

3, 1, 4, 2

D.

2, 4, 1, 3

rd

Each instalment except the rst is ` 50 less than the  previous  prev ious one. Amount of the instalment paid in the 9 th month.

Find (i)

50.

Match the columns : (i)

(ii) Total amount paid in 12 instalments . (iii) How much extra he has to pay in addition to the amount of cash down payment ? (i)

48.

(ii)

`

1100

`

16700

`

900

B.

`

1200

`

14700

`

600

C.

`

1100

`

14700

`

700

D.

`

1100

`

14700

`

900



 No. of students

4

A.

48.904

B.

50.909

C.

62.804

D.

64.324

10

28

 B

 D

(ii)

Find the mode of the distribut ion from the following table : Less Less Less than 20 than 40 than 60

(a) 10 cm In gure, a circle touches all four sides of quadrilateral  ABCD  ABC D with  AB =  AB  = 18 cm,  BC  = 21 cm and CD  CD   = 12 cm,  AD = ..........

(iii)

A.

Marks

36

50

Q

5 cm

 P 

 x

3 cm



(b) 9 cm

 R

  m   2  c



(iii) Perimeter of D PST   with  PQ = (c) 3 cm 10 cm is ......  P 



S  Q

2.

Draw a line through C ′  parallel  para llel to the line CA to intersect  BA at  A′ .

3.

Draw any ray  BX   making an acute angle with  BC   on the side opposite to the vertex  A.  A.

4.

Join B Join  B4C  and   and draw a line through  B3 parallel to  B4C   to intersect  BC  at C ′ .

Then, D A ′ BC   BC ′   is the required triangle.

 A

In gure, value of  x of  x is  is ........

Less Less than 80 than 100

49. Arrange the given steps in correct order while constructing a triangle similar to a given triangle ABC  triangle  ABC  3 with its sides equal to   of the corresponding sides 4 3 of the triangle  ABC  (i.e., of scale factor ). 4 1. Locate 4 points  B1,  B2,  B3 and B  and  B4 on  BX  so  so that  BB1 =  B1 B2 =  B2 B3 =  B3 B4.

 

Column - II

Column - I

U  R

(iv) In gure, PQ gure, PQ =  = 6 cm, QR = QR = 7 cm, (d) 20 cm  RS  =   = 4 cm,  PS   = ........... S 



 D

 P 

A. B. C. D.

R

 B

 A

Q

→ (b), (ii) → (a), (iii) → (c), (iv) → (d) (i) → (a), (ii) → (b), (iii) → (d), (iv) → (c) (i) → (b), (ii) → (d), (iii) → (a), (iv) → (c) (i) → (b), (ii) → (a), (iii) → (d), (iv) → (c)

(i)

SPACE SPACE FOR ROUGH WORK

th

-

7

10 th

LEVEL - 2 Year 2016-17

CLASS-10 MATHEMATICS

Q.1

Q.2

Q.3

If 3 is the least prime factor of number a and 7 is the least prime factor of number b, then the least prime factor of a + b, is (A) 2 (B) 3 (C) 5 (D) 10

Evaluate :

Q.6

(B) (B)

2

(C) (C) – 2

(D)

5

In the given figure (not drawn to scale) ABCD is a trapezium in which AB || DC and AD = BC. If P, Q, R, S be respectively the mid-points of BA, BD, CD and CA. Then PQRS is a

2

If , , are the roots of x  – (k + 1) x +

1 2

2

(k 

2

+ k + 1) = 0, then ( ( –  )  ________. 2 (A) –(k   + 1) 2 (B) k   + 1 2 (C) 2k   + k 2 (D) k  – 1

2  3  4  5  17  4 15

(A) (A) 1

Date : 12-02-2017

Q.7

If (5  2 6 ) x

2

3

+ (5  2 6 ) x

2

3

  = 10, then

x = _________. (A) 2 (B) – 2 (C) –2 (D) All of these Q.8

If cot  + tan  = x and sec  – cos  = y, then 2

(A) (x + 2y)  = 2 2 2 (B) x  + y  = 2 2 2/3 2 2/3 (C) (x y)  – (xy )  = 1 2 1/3 2 1/3 (D) (x y)  + (xy )  = 1

(A) Rhombus (C) Parallelogram Parallelogram Q.4

Q.5

(B) Rectangle Rectangle (D) Square

A right cone and a hemisphere lie on opposite sides of a common base of 2.5 m diameter and the cone is right angled at the vertex. If a cylinder circumscribe them in this position, approximate what additional space will be enclosed? 3 3 (A) 7.12 m (B) 6.14 m 3 3 (C) 6.69 m (D) 5.25 m The HCF of 3 2 x  + (a + b)x  + (ab + 1) x + b and 3 2 2 x  + 2ax  + (a  + 1)x + a is 2 2 (A) x + ax + 1 (B) x  + bx + 1 2 2 (C) x + x + a (D) x  + x + b

Q.9

In the given figure, the common tangents PR and QS intersect at the point T. A and B are centres of the two circles. Given that PAQ = 108º and PR = 8 cm, find

(a) RBS (b) The length of QS. (a) (A) 120º (B) 108º (C) 115º (D) 112º

(b) 8 cm 8 cm 6 cm 6 cm

Q.10

Q.11

Q.12

Q.13

The point A divides the join of of P(–5, 1) and Q(3, 5) in the ratio k : 1. The values of k for which the area of ABC where B(1, 5) C(7, –  2) is 2 sq. units units is 31 31 (A) 7, (B) –7, 9 9 31 31 (C) 7, – (D) –7, –  9 9

Q.17

P(4, 3) and Q lies on the same straight line which is parallel to the y-axis. If Q is 3 units from the x-axis, the possible coordinates of Q are _________. (A) (–3, 0) (B) (3, 4) (C) (4, –3) (D) (3, 8)

Q.18

The coordinates of A, B, C are (6, 3), (–3, 5) and (4, –2) respectively and P is any point

If 2x 2x – 3y = 7 and (a + b)x – (a + b – 3) y = 4a + b represent coincident lines, then a and b satisfy the equation (A) a + 5b = 0 (B) 5a + b = 0 (C) a – 5b = 0 (D) 5a – b = 0

(x, y). Find (A)

A bag contains 11 white balls and some red  balls. If the t he probability of drawing a red ball is double that of a white ball, find the number of red balls in the bag. (A) 22 (B) 33 (C) 11 (D) 0

(B) (C) (D)

2

If ,  are the roots of the equation ax  + bx + c = 0 and

1  1 ,   are the roots of the  

Q.19

2

equation px  + qx + r = 0, then r = ________. (A) a + 2b (B) a + b + c (C) ab + bc + ca (D) abc Q.14

Let Sn denote the sum of the first 'n' terms of S an A.P. S2n = 3Sn. Then the value of 3n is Sn equal to (A) 4

Q.15

Q.16

(B) 6

(C) 8

(D) 10

Sum of the the length, length, width and depth depth of a cuboid is 's' and its diagonal is 'd'. Find its surface area. 2 2 2 2 (A) s  + d (B) s  – d 2 2 (C) d  – s (D) None of these In a rectangle ABCD, P and Q are the mid points of BC and AD respectively. If R is any  point on PQ, then area ( (ARB) equals 1 (A) (area of ABCD) 2 1 (B) (area of ABCD) 3 1 (C)  (area of ABCD) 4 (D) None of these

area (PBC) area ( ABC)

.

2x  y  2 7 3x  2 y  2 7 x  y 7 x  y 2 7

A tree standing on a horizontal horizontal plane is leaning towards east. At two points situated at distance a and b exactly due west on it, the angles of elevation of the top of the tree are respectively   and . Find the height of the top of the tree from the ground. tan   tan  (A) a  b (B)

( b  a ) tan  tan  tan   tan 

(C) (a – b)(tan b)(tan + 2 tan tan) (D)

ab(tan   tan ) tan   tan 

Q.20

Find the number of coins, 1.5 cm in diameter diameter and 0.2 cm thick, to be melted to form a right circular cylinder of height 10 cm and diameter diameter 4.5 cm. (A) 435 (B) 231 (C) 450 (D) 520

Q.21

In the given given figure, RTP and STQ are common tangents to the two circles with centres A and B of radii 3 cm and 5 cm respectively. If ST : TQ = 1 : 3 and RT = 4 cm, find

(a) The length of QT (b) The length of AB

Q.27

The minute hand of a block is

Find the area described by the minute hand on the face of the clock between 7:00 AM and 7:05 AM. 2

(A) 8.21 cm 2 (C) 6.25 cm

(A) (B) (C) (D) Q.22

Q.23

(a) 10 cm 16 cm 15 cm 12 cm

(b) 14 cm 25 cm 20 cm 18 cm

4 x

 +

x

 is __________.

2

2

 a  b  (A)      a  b  2

  a       a  b 

(C) 

Q.25

Q.26

In the given figure, ABCD is a rectangle with AB = 14 cm and BC = 7 cm. Taking DC, BC

2

(A) 59 cm 2 (C) 60 cm

2

4

 a  b  (B)    a  b 

2

(B) 4.32 cm 2 (D) 5.5 cm

and AD as diameters, three semi-circles are drawn as shown in the figure. Find the area of the shaded region.

If abx   = (a – b) (x + 1), then the value of 1+

Q.24

Q.28

Two dice are thrown simultaneously. Find the  probability of getting a multiple of 2 on the dice and a multiple of 3 on the other dice. (A) 1/3 (B) 7/36 (C) 1/6 (D) 11/36 2

21 cm long.

Q.29

In ABC, P divides the side AB such that AP : PB = 1 : 2. Q is a point in AC such that

2

   b     a  b 

2

(B) 59.5 cm 2 (D) 60.5 cm

PQ || BC. Find the ratio of the areas of APQ and trapezium BPQC. (A) 1 : 6 (B) 1 : 7

2

(D) 

The coefficient coeffici ent of x in a quadratic equation 2 x  + px + q = 0 was taken as 17 in place of 13 and its roots were found to be –2 and –15. The roots of the original equation are ______. (A) 2, 15 (B) 10, 3 (C) –10, –3 (D) –2, –15 P is the point point (–5, 3) and Q is the point point (–5, m). If the length of the straight line PQ is 8 units, then the possible values of 'm' are  ________. (A) –5, 5 (B) –5, 11 (C) –5, –11 (D) 5, 11 How many odd integers beginning with 15 must be taken for their sum t o be 975? (A) 27 (B) 25 (C) 23 (D) 21

(C) 1 : 8 (D) None of these Q.30

In a competitive competiti ve examination, examinati on, one mark is awarded for each correct answer while 1

mark is deducted for each wrong answer. 2 Jayanti answered 120 questions and got 90 marks. How many questions did the answer correctly? (A) 100 (B) 110 (C) 90 Q.31 

(D) 115 3

2

Find a  and b  in order that x – 6x   + ax + b 2 may be exactly divisible by x  – 3x + 2. (A) –7, 9 (B) 11, –6 (C) 8, 4

(D) 5, 4

Q.32

circle with AO as radius. radius. Step IV : Draw a circle This circle cuts the circle drawn in step II at B and P. Step V : Joint AP. AP. AP and AB are desired tangents drawn from A to the circle passing through B, C and D. (A) Only I (B) Only IV (C) Only III (D) Only V

In the given figure, M =  N = 46º. Express x in terms of a, b and c where a, b, c are lengths of LM, MN and NK respectively.

Q.36

(A) (C)

Q.33

ac  b  c a    b ac

 

(B)

 

(D)

Q.35

a a  b(a  c)

 90,000 in A man arranges arra nges to pay a debt of  –  40 monthly installments which are in A.P. When 30 installments are paid, he dies leaving one third of the debt unpaid. Find the value of second installments.  1500  1800 (A)  –  (B)  –   1400 (C)  – 

Q.34

ab  bc

Marks 0-10 10-20 20-30 30-40 40-50 50-60 Total obtained  No. of a b 10 25 30 10 100 students (A) 9, 16 (B) 10, 15 (C) 15, 13 (D) 8, 9

Q.37

 1325 (D)  – 

Two years ago, a father was five times as old old as his son. Two years later, his age will be 8 more than three times the age of the son. Find the present ages of father and son respectively. (A) 42 years, 10 years (B) 46 years, 12 years years (C) 56 years, 18 years years (D) 64 years, 20 years Let ABC be a right angled triangle in which AB = 3 cm, BC = 4 cm and B = 90º. BD is the perpendicular from B on AC. The circle through B, C, D is drawn. Given below are steps of construction of tangents from A to this circle. Identify the wrong step. Steps of construction : Step I :  Draw ABC and perpendicular BD from B on AC. Step II :   Draw a circle with BC as a diameter. This circle will pass through D. Step III : Let O be the mid point of BC. Join AO.

Find the value of a  and b respectively in the following frequency distribution table, if  N = 100 and median is 32.

In the given figure points A, B, C and D are the centres of four circles that each have a radius of length 2 units. If a point is selected at random from the interior of square ABCD. What is the probability that the point will be chosen from the shaded region?

(A) 7/15 (C) 3/14

(B) 8/19 (D) 5/7

Q.38

X takes takes 3 hours hours more more than Y to walk 30 km. km. But, if X doubles his pace, he is ahead of Y 1  by 1  hour. Find their speed of walking. 2 (A) 7 km/h, 4 km/h (B) 10/3 km/h, 5 km/h (C) 2 km/h, 3/2 km/h (D) 3 km/h, 7 km/h

Q.39

Find the square root of 2 (ab – ac – bc)  + 4abc(a + b). (A) ab – b – ca (B) ab + bc + ca (C) 1/2 (a + 2b + c) (D) (a – b + c)

Q.40

Q.41

Q.42

The vertices of ABC are A(4, 6), B(1, 5) and C(7, 2). A line is drawn to intersect sides AB and AC at D and E respectively such that AD AE 1  =  = . Find the area of ADE. BD CE 4 (A) 7/2 sq. units (B) 11/3 sq. units (C) 12 sq. units (D) None of these The coordinates of one end point of a diameter of a circle are (4, –1) and the coordinates of the centre of the circle are (1, –  3). Find the coordinates of the other end of the diameter. (A) (–2, –5) (B) (–2, 5) (C) (2, –5) (D) (2, 5) 42  42  42  ...

The value of

Q.44

A man standing on the deck of a ship, which is 10 m above water level. He observes the angle of elevation of the top of a hill as 60º and the angle of depression of the base of the hill as 30º. Find the height of the hill (Ignore the height of the man). (A) 30 m (B) 42 m (C) 40 m (D) 35 m

Q.45

In the given figure (not drawn to scale), two circles with centres A and B of radii 3 cm and 4 cm respectively intersect at two points C and D such that AC and BC are tangents to the two circles. Find the length of the common chord CD.

 is

6  6  6  ... (A) 7/3 Q.43

(B) 6/8

(C) 5

(D) 8

Two circles of radii 5 cm and 3 cm and centres A and B touch internally. If the  perpendicular  perpendicular bisector of segment AB meets the bigger circle in P and Q, find the length of PQ. (A) 5 7 cm

(B) 3 2 cm

(C) 10 6 cm

( D ) 4 6 cm

(A) 3.2 cm (B) 2.4 cm (C) 4.8 cm (D) 5.6 cm

ACHIEVERS SECTION

Q.46

Match the following : 2

 p.

(1 – sin )sec

q.

cos  +

r. s.

1  sin  2



2



+ 1 = ii. 2sec

1 1  sin  2

cosec  + sec



=

=



2

2

iii. cosec sec iv. 1

(A) p  iii, q  iv, r  ii, s  i (B) p  i, q  ii, r  iii, s  iv (C) p  iv, q  ii, r  i, s  iii (D) p  iv, q  i, r  ii, s  iii

A peacock peacock is sitting on the top of a pillar, which is 9 m high. From a point 27 m away from the bottom of the pillar, a snake is coming to its hole at the base of the pillar.

i. 2 2

1  cot +

Q.47

=

1

2

1

2



Seeing the snake the peacock pounces on it. If their speeds are equal, at what distance from the hole is the snake caught? (A) 10 m (B) 11 m (C) 12 m (D) 13 m

Q.48

Study the following statements statements and state 'T' for true and 'F' for false. (i) The common common difference difference of an A.P., the sum of whose n terms is S n, is Sn – 2 Sn–1 + Sn–2. (ii) If the sums of n terms of two arithmetic  progressions are in the ratio

3n 5n

th

their n  terms are in the ra tio

 

5 7

3n

1

5n

1

, then

(A) (B) (C) (D) Q.49

d

such

that

Sx Skx

is

independent of x, then d = 2a. (i) (ii) (iii) T T T F F F T F T F T F

In the given figure, ABC is a right angled triangle in which A = 90º, AB = 21 cm and AC = 28 cm. Semi-circles are described on AB, BC and AC as diameters. Find the area of the shaded region.

2

(A) 294 cm 2 (B) 296 cm 2 (C) 298 cm (D) None of these

Read the statements carefully and select the correct option. Statement I :  For any positive integer n, 3

n  – n divisible by 6. Statement II : If a and b are two odd positive integers such that a > b, then one of the two numbers

a    b 2

  and

a

  b

2

  is odd and the

other is even. (A) Both Statement-1 and Statement S tatement-II -II are

.

(iii) If Sn  denote the sum of an terms of an A.P. with first term a and common difference

Q.50

true. (B) Both Statement-1 and Statement-II are false. (C) Statement-1 is true and Statement-II is false. (D) Statement-1 is false and Statement-II is true.

ANSWER KEYS

5th IMO 1. 8. 15. 22. 29. 36. 43. 50.

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

2. 9. 16. 23. 30. 37. 44.

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

3. 10. 17. 24. 31. 38. 45.

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

4. 11. 18. 25. 25. 32. 32. 39. 46.

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

5. 12. 19. 19. 26. 33. 40. 47. 47.

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

6. 13. 20. 27. 27. 34. 34. 41. 48. 48.

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

7. 14. 21. 28. 35. 42. 49.

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

5. 12. 19. 26. 33. 33. 40. 47.

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

6. 13. 20. 27. 34. 41. 48. 48.

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

7. 14. 21. 28. 35. 42. 49.

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

5. 12. 19. 26. 33. 33. 40. 47.

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

6. 13. 20. 27. 34. 41. 48.

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

7. 14. 21. 28. 35. 42. 49.

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

6th IMO 1. 8. 15. 22. 29. 36. 43. 50.

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

2. 9. 16. 23. 30. 37. 44.

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

3. 10. 17. 24. 31. 38. 45.

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

4. 11. 18. 25. 25. 32. 39. 46. 46.

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

7th IMO 1. 8. 15. 22. 29. 36. 43. 50.

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

2. 9. 16. 23. 30. 37. 44.

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

3. 10. 17. 24. 31. 38. 45.

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

4. 11. 18. 25. 25. 32. 32. 39. 46.

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

8th IMO-Level 2 was an online exam. Hence, paper cannot be included in the booklet.

9th IMO 1. 2. 3. 4. 5. 6. 7. 8.

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

9. 10. 11. 12. 13. 14. 15. 16.

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

17. 18. 19. 20. 21. 22. 23. 24.

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

25. 26. 27. 28. 29. 30. 30. 31. 32.

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

33. 34. 35. 36. 37. 38. 39. 40.

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

41. 42. 43. 44. 45. 46. 46. 47. 48.

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

49. 50.

(C) (D)

10th IMO

Ques   1

2

3

4

5

6

7

8

9

10

11 11

12 12

13 13

14 14

15 15

16 16

17 17

18 18

19 19

20 20

21 21

22 22

23 23

24 24

25 25

Ans.   A

A

A

B

A

A

D

C

B

A

C

A

B

B

B

C

C

D

B

C

D

A

B

C

B

26 Ques   26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

Ans.   B

D

B

C

A

B

A

D

A

B

A

C

B

B

D

A

A

D

C

C

D

C

D

A

C

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