Imo Level1 Class 10 Set 3

DO NOT OPEN THIS BOOKLET UNTIL ASKED TO DO SO

Total Questions: 50

Time: 1 hr.

CLASS

10 SET 3

Level - 1 Guidelines for the Candidate 1. You will get additional ten minutes to fill up information about yourself on the OMR Sheet, before the start of the exam. 2. Write your Name, School Code, Class, Section, Roll No. and % of marks/grade in last class clearly on the OMR Sheet and do not forget to sign it. 3. The Question Paper comprises four sections : Logical Reasoning (15 Questions), Mathematical Reasoning (20 Questions), Everyday Mathematics (10 Questions) and Achievers Section (5 Questions) Each question in Achievers Section carries 3 marks, whereas all other questions carry one mark each. 4. All questions are compulsory. There is no negative marking. Use of calculator is not permitted. 5. There is only ONE correct answer. Choose only ONE option for an answer. 6. To mark your choice of answers by darkening the circles in the OMR Sheet, use HB Pencil or Blue / Black ball point pen only. E.g. Q. 16: Rahul bought 4 kg 90 g of apples, 2 kg 60 g of grapes and 5 kg 300 g of mangoes. The total weight of all the fruits he bought is______. A. 11.450 kg B. 11.000 kg C. 11.350 kg D. 11.250 kg

As the correct answer is option A, you must darken the  circle corresponding to option A in the OMR Sheet.

7. Rough work should be done in the blank space provided in the booklet. 8. Return the OMR Sheet to the invigilator at the end of the exam. 9. Please fill in your personal details in space on top of this page before attempting the paper.

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LOGICAL REASONING 1.



Ten executives A, B, C, D, E, F, G, H, I and J stay in flats in two rows opposite to each other. One row has 5 flats facing North and the other row has 5 flats facing South. F's flat is second to the right of J's flat, which is exactly opposite of C's flat facing North. D's flat is on the immediate left of J's flat and A's flat is on the immediate left of C's flat. B's flat is on the right of C's flat. I and E have flats at the two ends of the same row. Flats of E and H are opposite to each other. Which of the following is the correct position of G's flat ?



A. B. C. D.

Facing North Opposite to C's flat To the left of F's flat To the left of J's flat

2.

There is a definite relationship between figures (1) and (2). Establish the similar relationship between figures (3) and (4) by selecting a suitable figure from the options that would replace the question mark (?) in figure (4).

A.

B.

C.

D.

6.

In a certain code language, the letters of English alphabet are arranged in such a manner that the letters immediate next to vowels are replaced with D, all other consonants are replaced with preceding letters and the vowels are replaced with Z. How will the word S TA N D I N G be written in that code language ?

A. RSZMCZMF B. TSZMCZFM C. RSZMCZDF D. TUZOCZFM 7.

Which of the following options satisfies the same conditions of placement of the dots as in Fig. (X)?

Fig. (X)

A.

A.

B.

B. C.

C.

D.

3.





A. C.

ccaac cacac

B. D.

cbabc bccab

4.

If '+' denotes 'division', '–' denotes 'addition', '×' denotes 'subtraction' and '÷' denotes 'multiplication', what will be the value of the following expression ?

A boy rode his bicycle northwards, then turned left and rode 1 km and again turned left and rode 2 km. He found himself exactly 1 km west of his starting point. How far did he ride northwards initially ?



A. C.

9.

Select a figure from the options which will continue the same series as established by the Problem Figures.

1 km 3 km

In which of the given options, Fig. (X) is exactly embedded as one of its part?

 2

2 km 5 km

×× C

C

A.

C. Fig. (X)

B. D.

Problem Figures

[{(17 × 13) – (5 ÷ 5)} + (23 – 6)] A. 1 B. 0 C. 118 D. 219 5.



8.

Which of the following options complete the letter series given below? aab_bbc_c_ab_ab_

D.



S

S N

 S

B. N

D.  Class-10 | Level-1 | Set-3

10. Among five persons M, N, T, R and D each having a different height, T is taller than D but shorter than M. R is taller than N but shorter than D. Who among them is the tallest ? A. D C. M

B. T D. R

X

11. Select a figure from the options, which when placed in the blank space of Fig. (X) would complete the pattern.

A.

B.

C.

D.



12. The six faces of a cube are coloured, each with a different colour. I. The white face is between yellow and green. II. The red face is adjacent to brown. III. The green face is opposite to the yellow side. IV. The blue face is adjacent to red. V. The yellow face is the top face of the cube.

The face opposite to the red face is ________ . A. Green B. White C. Blue D. Brown

13. A set of three figures X, Y and Z showing folding of a piece of paper is given. Figure Z shows the manner in which the folded paper has been cut. Select a figure from the options which would most closely resemble the unfolded form of figure Z.

Y

Z

A.

B.

C.

D.

14. Which of the following Venn diagrams best represent the relationship amongst "Star, Moon and Mars" ? A.

B.

C.

D.

15. Find the correct mirror image of Fig. (X).

A.

B.

C.

D.

MATHEMATICAL REASONING 16. The decimal expansion of the rational number 14587 1250 will terminate after ________ .

A.

One decimal place B.

Two decimal places



C.

Three decimal places D.

Four decimal places

17. The perimeter of a right-angled triangle is five times the length of its shortest side. The numerical value of the area of the triangle is 15 times the numerical value of the length of the shortest side. Then the lengths of the three sides of the triangle are ________ .

A.

6, 8 and 10

B.

10, 24 and 26



C.

5, 12 and 13

D.

16, 30 and 34

Class-10 | Level-1 | Set-3

18. Find the mode for the following data. Age

0-6 6-12 12-18 18-24 24-30 30-36 36-42

Frequency



A. C.

6

19.32 21.44

11

25

35

18

B. D.

20.22 23.14

12

6

19. If a is the first term of an A.P. and the sum of first n terms of an A.P. is zero, then the sum of next m terms is ________ . − an(n + m) − am(m + n) A. B. n −1 n −1 nm ( n − m) am(n + m) C. D. n +1 n −1  3

20. In a trapezium ABCD, AB || DC and DC = 2AB. EF drawn parallel to AB cuts AD at F and BC at E such BE 3 that = . Diagonal DB intersects EF at G. Then EC 4 FE value of is ________ . AB 9 8 A. B. 6 7 11 10 C. D. 8 7

27. The least number of complete years in which a sum of money put out at 20% compound interest will be more than double is ________ .

A. C.

3 5

B. D.

4 6

21. If P(2, –1), Q(3, 4), R(–2, 3) and S(–3, –2) are four points in a plane, then PQRS is a _______.

28. A jar contains 54 marbles of colour either blue, green or white. The probability of selecting a blue marble 1 at random from the jar is , and the probability of 3 4 selecting a green marble at random is . How many 9 white marbles does the jar contain?





A. C.

Rectangle Rhombus

B. D.

Square Parallelogram

22. In the given figure, ∠CAB = 90° and AD ^ BC. If AC = 75 cm, AB = 1 m and BC = 1.25 m, find AD.

A. C.

12 4

B. D.

3 5

29. If the roots of the equation (c 2 – ab)x2 – 2(a 2 – bc)x + b 2 – ac = 0 are equal, then which of the following options is correct? A. a=0 B. a3 + b3 + c3 = 3abc C. Both A and B D. None of these



A. C.

45 cm 70 cm

B. D.

80 cm 60 cm

23. The expression Ax3 + x2 + Bx + C leaves a remainder 21 when divided by 1 – 2x and 18 when divided 4 by x. Also (x – 2) is the factor of the expression, then the values of A, B and C respectively are ________ .

A. C.

4, – 27, 18 3, – 25, 12

B. D.

6, 27, 15 8, – 27, 20

24. If a and b be the zeroes of the polynomial ax2 + bx + c, then find the value of

α β . + β α

−a −c A. B. bc ab −b C. ac

D.

c ba



25. A hollow sphere of internal and external radii 2 cm and 4 cm respectively is melted into a solid cone of base radius 4 cm. Find the slant height of the cone.

A. C.

13.30 cm 16.50 cm

B. D.

30. The diameters of two circles are in the ratio 3 : 4 and the sum of areas of the circles is equal to the area of a circle whose diameter measures 30 cm. Find the diameters of the given circles.

A. C.

17 cm, 20 cm 15 cm, 18 cm

31. If tanq =

12 2 sin θ cos θ , find the value of . 13 cos 2 θ − sin 2 θ

318 C. 25

D.

 4

B. 0 D. 2



312 25

32. Given figure shows a kite in which BCD is the shape of a quadrant of a circle of radius 42 cm. ABCD is a square and DCEF is an isosceles right angled triangle whose equal sides are 6 cm long. Find the area of the shaded region. A

B

D

C

26. If the system of equations 3x + y = 1 and (2k – 1) x + A. 1 C. –1

18 cm, 24 cm 16 cm, 22 cm

311 309 A. B. 21 23

14.56 cm 12.12 cm

(k – 1)y = 2k + 1 is inconsistent, then k = _______ .

B. D.

E

F



A.

1404 cm2

B.

1350 cm2



C.

1410 cm2

D.

1400 cm2

 Class-10 | Level-1 | Set-3

33. In an acute angled triangle ABC, if tan (A + B – C) = 1 and sec(B + C – A) = 2, then the values of A, B and C respectively are ________ . °

°

°

°

 1  1 A. 55°,  50  ,  65   2  2 ° °  1  1 B. 57 ° , 52 , 68     2  2

A. 50 2 ( 2 − 1) m

B.

50 2 ( 3 + 1) m

C. 50 3 ( 3 − 1) m

D.

45 2 ( 2 + 1) m

35. Two concentric circles of radii 3 cm and 5 cm are given. Then length of chord BC which touches the inner circle at P is equal to ________ .

 1  1 60°,  50  ,  70  C.  2  2 ° °  1  1 D. 60°,  52  ,  67   2  2 34. Two boats approach a light house in mid-sea from opposite directions. The angles of elevation of the top of the light house from two boats are 60° and 45° respectively. If the distance between two boats is 100 m, find the height of the light house.



A.

4 cm

B.

6 cm



C.

8 cm

D.

10 cm

EVERYDAY MATHEMATICS 36. A manufacturer company of mobile phones produced 6000 units in 3 rd year and 6500 units in 5 th year. Assuming that production increases uniformly by a fixed number every year, find the production in 8th year.

A. C.

7250 units 7500 units

B. D.

6700 units 8250 units

37. Sudha is going away from the lamp post at a speed of 1.5 m/sec. If the lamp post is 3.9 m above the ground and height of Sudha is 120 cm, then find the length of her shadow after 3 seconds.

A. C.

3 m 4 m

B. D.

2m 5m

38. A merchant has 1000 kg of sugar, some part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The quantity sold at 18% profit is ________ .

A. C.

400 kg 600 kg

B. D.

560 kg 640 kg

39. A rectangular courtyard 3.78 metres long and 5.25 metres wide is to be paved exactly with square tiles, all of the same size. What is the largest size of the tile which could be used for the purpose?

A. C.

14 cm 42 cm

B. D.

21 cm None of these

40. In an examination, 5% of the applicants were found ineligible and 85% of the eligible candidates belonged to the general category. If 4275 eligible candidates belonged to other categories, then how many candidates applied for the examination ?

A. C.

30,000 37,000

Class-10 | Level-1 | Set-3

B. D.

35,000 None of these

41. Two years ago, a father was five times as old as his son. Two years later, his age will be 8 more than three times the age of the son. Then present ages of son and father respectively are ________ . A. 10 yrs, 42 yrs B. 15 yrs, 30 yrs C. 13 yrs, 40 yrs D. 14 yrs, 35 yrs 42. The price of a VCR is marked at ` 12,000. If successive discounts of 15%, 10% and 5% be allowed, then at what price does a customer buy it ? A. ` 8400 B. ` 8721 C. ` 8856 D. None of these 43. Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 km/h. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 km/h. At what time will they meet ? A. 9 a.m. B. 10 a.m. C. 10:30 a.m. D. 11 a.m. 44. A person lent out a certain sum on simple interest and the same sum on compound interest at a certain rate of interest per annum. He noticed that the ratio between the difference of compound interest and simple interest of 3 years and that of 2 years is 25 : 8. The rate of interest per annum is ________ . A. 10% B. 11% 1 C. 12% D. 12 % 2 45. A tank 4 m long, 2.5 m wide and 1.5 m deep is dug in a field 31 m long and 10 m wide. If the earth dug out is evenly spread out over the field, the rise in level of the field is ________ . A. 3.1 cm B. 4.8 cm C. 5 cm D. 6.2 cm  5

ACHIEVERS SECTION  46. PQR is a tangent to the circle at Q. PUS is a straight line and ST = SQ. Given that ∠PQU = 25° and ∠SQR = 62°, then find: (i) ∠TSQ (ii) ∠UPQ S



Step-1: Draw a circle with centre at O and radius 4 cm.



Step-2: Draw a diameter AOA′.



Step-3: At O, construct ∠A′OB = 40° and let OB intersect the circle at B. (Hence, ∠AOB = 140°)



T

A and B. Let them intersect at P.

R



62° U

25° Q

(i) 38° 65° 58° 56°

Step-5: PA and PB are tangents to the circle and they are inclined to each other at 30°.

P

A. B. C. D.

Step-4: Draw perpendiculars OA and OB respectively at

(ii) 32° 40° 37° 37°



A.

Step-2

B.

Step-3



C.

Step-4

D.

None of these

50. Match the following.

47. In the following figure (not drawn to scale) PQRS is a rectangle. Area of the rectangle is 15 sq. units and point A lies on PQ such that PQ = 3QA. Find coordinates of A and R respectively. Y P(2, 7)

) –1,1 A

Q(

Column II



(a) Length of CP is____.

(i) 6 3 cm

(b) Radius of the given

(ii) 4.5 cm



S



X

O R

Column I

circle is____. T



A. C.

(0, 8) and (2, 0) (0, 6) and (2, 2)

B. D.

(0, 5) and (0, 1) (0, 3) and (1, 0)

6 cm

A

P

48. Read the given statements carefully and select the correct option. 1 Statement I : If 43t + 156(4t ) = 216(42t ), then t = 2 Statement II : If ax2 + 2a2 x + b3 is exactly divisible by x + a, then a2 + ab + b2 = 0, where a ≠ b A. Both Statement I and Statement II are true. B. Both Statement I and Statement II are false. C. Statement I is true but Statement II is false. D. Statement I is false but Statement II is true.



49. Which of the given steps is incorrect while constructing pair of tangents to a circle of radius 4 cm which are inclined to each other at 30°.



2 cm

O

(c) The length of OP is ____. (iii) 8 cm



A.

(a)-(ii), (b)-(i), (c)-(iii)



B.

(a)-(i), (b)-(ii), (c)-(iii)



C.

(a)-(ii), (b)-(iii), (c)-(i)



D.

(a)-(iii), (b)-(i), (c)-(ii)

SPACE FOR ROUGH WORK

 6

 Class-10 | Level-1 | Set-3