Imo Level1 Class 10 Set 2

DO NOT OPEN THIS BOOKLET UNTIL ASKED TO DO SO

Total Questions: 50

Time: 1 hr.

CLASS

10

SET 2

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.

Find the missing term in the series given below.

4.

0, 2, 3, 5, 8, 10, 15, 17, 24, 26, ?

A. 28 B. 30 C. 32 D. 35

2.

Select a figure from the options which is exactly embedded in the given Fig. (X) as one of its part.

Which of the following options would complete the pattern in Fig. (X)?

A.



B.

Fig.(X)

A.

C. D.



5.

In a certain code language, 'dom pul ta' means 'bring hot food', 'pul tir sop' means 'food is good' and 'tak da sop' means 'good bright boy'. Which of the following does means 'hot' in that language ?



A. dom B. pul C. ta D. Cannot be determined

6.

Count the number of cubes in the following figure.



A. 80 B. 87 C. 89 D. 90

B.

C.





D.

3.

A word arrangement machine when given an input line of words, rearranges them following a particular rule in each step. The following is an illustration of the input and the steps of rearrangement.



Input : going but for crept te light sir



Step I : crept going but for te light sir



Step II : crept going light but for te sir



Step III : crept going light but for sir te



If Step III is the last step of the rearrangement and the same rule is followed for below input, then which of the following will be the step III for the given input?

7.



Input : the in car as he may me



Which of the following options is not true ?



A. B. C. D.



A. B. C. D.

2

car car car car

the in as he may may the as in he as may he the in may the in as he

me me me me

A, B, C, D, E, F and G are playing cards sitting around a circular table. D is not neighbour of C or E. A is neighbour of B and C. G, who is second to the left of D, is the neighbour of E and F. A is to the immediate right of B. B is to the immediate left of D. F is between G and D. E is between G and C. Class-10 | Level-1 | Set-2

8.

Select the correct mirror-image of the Fig. (X). A.



Fig. (X)

A.



B.

C.



D.

Mirror

12. Showing a photograph, Rajeev told Shweta. "His mother is the only daughter of your father'. How is Shweta related to the man in the photograph ?

B.

A. C.

Aunt Wife

B. D.

Mother Daughter



D.

13. In the given Venn diagram, the smaller triangle represents the teachers; the big triangle represents the politicians; the circle represents the graduates and the rectangle represents the members of Parliament. Different regions are being represented by the letters of English alphabet. Which letters represent politicians that are graduates but not the members of Parliament ?

9.

Rakhi starts from point Q and moves 25 m southward, then she turns left and moves 30 m, then she turns right and moves 15 m to reach point P. What is the distance of P from Q and in which direction is she with respect to point Q? A. 50 m South-West B. 50 m South-East C. 45 m South-East D. 40 m South



C.





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

A.

Problem Figures



B. C.



D.

A. B, C C. D, L

B. D.

14. Find the number of triangles in the given figure.



A. 12 B. 18 C. 22 D. 26

15. Find the missing number if same rule is followed in all three figures. 916

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

Class-10 | Level-1 | Set-2

L, B A, H, L

3



49 4

2

? 3

1

5

A. 125 B. 215 C. 251 D. 512 3

MATHEMATICAL REASONING 1458 16. The decimal expansion of the rational number 125 will terminate after ____________ .

A. B. C. D.

One decimal place Two decimal places Three decimal places Four decimal places

A. 2 B. 3 C. 5 D. 10

a 18. If tan θ = , then value of b 2

A. 46th C. 51st

B. 53rd D. 49th

21. Determine the value of k so that the following linear equations have no solution.

17. 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 ____________ .

20. Find the term of the arithmetic progression 9, 12, 15, 18, ... which is 39 more than its 36th term.

a sin θ − b cos θ = a sin θ + b cos θ

2

a −b A. a 2 + b2

(3k + 1) x + 3y – 2 = 0 (k 2 + 1) x + (k – 2) y – 5 = 0 A. 1 B. –1 C. –2 D. 0 22. F i n d t h e m e a n o f t h e f o l l o w i n g f r e q u e n c y distribution. Class Interval Frequency

40-50 50-60 60-70 70-80 80-90 90-100 Total 10

25

28

12

A. 68.2 C. 59.31

a 2 + b2 B. a 2 − b2 2ab C. 2 a + b2 2ab D. 2 a − b2

10

15

100

B. 70 D. 65.12

23. In figure, there are two concentric circles with centre O. PR and PQS are tangents to the inner circle from point lying on the outer circle. If PR = 7.5 cm, then PS is equal to __________ . S

19. Which of the following is not a graph of cubic polynomial?

Q O

P

Y

R

A. O

X



Y

B.

O

X

X

O

B. 12 cm D. 18 cm

24. The sum of the squares of two integers is 306. If the square of the larger integer is 25 times the smaller integer, find the integers.

Y

C.

A. 10 cm C. 15 cm

A. 8 and 15 C. 9 and 16

25. In the given figure, if AB || CD, find the value of x. D 6 x– 5

– 3x

Y

D.

4

O

B. 9 and 15 D. 8 and 16

X

1

O

C

–3

5x

2x

+1

A

A. 2 C. 1

B

B. 3 D. 4 Class-10 | Level-1 | Set-2

26. If x = r sin q cos f, y = r sin q sin f and z = r cos q, then A. x 2 + y 2 + z2 = r 2 B. x 2 + y 2 – z2 = r 2 C. x 2 – y 2 + z2 = r 2 D. z2 + y 2 – x 2 = r 2 27. The radii of the bases of two right circular solid metallic cones of same height h are r 1 and r 2 . The cones are melted together and recast into a solid sphere of radius R. Then the value of h is ______ .



A. 117.2 m B. 95.1m C. 109.28 m D. 96.2 m

31. In the given figure (not drawn to scale), ABCD is trapezium with AB || DC and ∠ BCD = 60°. If BFEC is a sector of a circle with centre C and AB = BC = 7 cm and DE = 4 cm, then find the area of the shaded 22 and 3 = 1.732]. region [Use π = 7 A

2R 2 A. 2 r1 + r22

B

F

3 B. R

60°

r12 + r22 3

C. 4R r12 + r22 8R 2 D. 2 2 r1 + r2 28. If – 5 is a root of the quadratic equation 2x2 + px – 15 = 0 and the quadratic equation p(x2 + x) + k = 0 has equal roots, find the value of k. 7 A. 4 5 B. 2 11 C. 5 3 D. 7

D



A. B. C. D.

30.33 28.89 25.32 32.49

E

L

C

2

cm cm2 cm2 cm2

32. Find the circumcenter of the triangle whose vertices are (–2, –3), (–1, 0), (7, –6).

A. (2, 1) C. (1, –5)

B. (3, –3) D. (0, 4)

33. If a and b are the zeros of the quadratic polynomial x2 + ax + b, evaluate

α 2 β2 + . β α

2ab − b 2 a 3 − b3 A. B. a ab a 2 − b2 C. 2ab

D.



3ab − a3 b

17 A. 25

34. The area of a rectangle is increased by 76 square units, if the length and breadth are increased by 2 units. However, if the length is increased by 3 units and breadth is decreased by 3 units, the area gets reduced by 21 square units. Then the length and breadth of the rectangle respectively are ____________ .

2 B. 5



16 C. 25

35. Through the mid-point M of the side CD of a parallelogram ABCD, the line BM is drawn intersecting AC at L and AD and BM are produced to meet at E. EL Then, = ____________ . BL 4 A. B. 4 3 5 C. 2 D. 3

29. Find the probability that a number selected from the number 1 to 25 is not a prime number when each of the given numbers is equally likely to be selected.

3 D. 7 30. The angle of elevation of the top Q of a vertical tower PQ from a point X on the ground is 60°. At a point Y, 40 m vertically above X, the angle of elevation is 45°. Find the distance XQ. [Use 3 = 1.732] Class-10 | Level-1 | Set-2

A. C.

18 units, 15 units 21 units, 17 units

B. D.

20 units, 16 units 12 units, 10 units

5

EVERYDAY MATHEMATICS 36. The area of a circular playground is 22176 m2 . Find the cost of fencing this ground at the rate of ` 50 per metre. A. ` 28,000 B. ` 26,400 C. ` 29,125 D. ` 25,420 37. In the given figure, the shape of a solid piece (made of two pieces with dimensions as shown). The face ABCDEFA is the uniform cross-section. Assume that the angles at A, B, C, D, E and F are right angles. Calculate the volume of the piece. 22 cm

A B

2 cm 5 cm

F

C 8 cm

D 3 cm



E

A. B. C. D.

432 780 952 880

3

cm cm3 cm3 cm3

38. In an examination, a pupil's average marks were 63 per paper. If he had obtained 20 more marks for his Geography paper and 2 more marks for his History paper, his average per paper would have been 65. How many papers were there in the examination ?

A. 8 B. 11 C. 10 D. 12

39. The electricity bill of a certain establishment is partly fixed and partly varies as the number of units of electricity consumed. When in a certain month 540 units are consumed the bill is ` 1800. In another month 620 units are consumed and the bill is ` 2040. In yet another month 500 units are consumed. The bill for that month would be __________. A. ` 1560 B. ` 1680 C. ` 1840 D. ` 1950 6

40. A, B and C start at the same time in the same direction to run around a circular stadium. A completes a round in 252 seconds, B in 308 seconds and C in 198 seconds, all starting at the same point. After what time will they meet again at the starting point ? A. 26 minutes 18 seconds B. 42 minutes 36 seconds C. 45 minutes D. 46 minutes 12 seconds 41. At his usual rowing rate, Rahul can travel 12 km downstream in a certain river in 6 hours less than it takes him to travel the same distance upstream. But if he could double his usual rowing rate for his 24 km round trip, then the downstream 12 km would take only one hour less than the upstream 12 km. What is the speed of the current (in km per hour) ? 2 1 1 1 B. A. 3 3 1 2 2 D. 2 C. 3 3 42. On selling a chair at 7% loss and a table at 17% gain, a man gains ` 296. If he sells the chair at 7% gain and the table at 12% gain, then he gains ` 400. The actual price of the table is __________. A. ` 1600 B. ` 1800 C. ` 2200 D. ` 2400 43. Four circular cardboard pieces, each of radius 7 cm are placed in such a way that each piece touches two other pieces. The area of the space enclosed by the four pieces is __________. A. 21 cm2 B. 42 cm2 C. 84 cm2 D. 168 cm2 44. A and B started a business jointly. A's investment was thrice the investment of B and the period of his investment was two times the period of investment of B. If B received ` 4000 as profit, then their total profit is __________. A. ` 16,000 B. ` 20,000 C. ` 24,000 D. ` 28,000 45. A, B and C enter into a partnership with a capital in which A's contribution is ` 10,000. If out of a total profit of ` 1000, A gets ` 500 and B gets ` 300, then C's capital is __________. A. ` 4000 C. ` 6000

B. ` 5000 D. ` 9000 Class-10 | Level-1 | Set-2

ACHIEVERS SECTION  46. Which of the following statements is incorrect? A. There exist no positive integer n, for which n − 1 + n + 1 is rational. B. There exist a natural number n for which 4n end with the digit 0. C. For every natural number n, n2 – n is divisible by 2. D. If a and b are rational numbers and c is an irrational number such that a + bc = 0, then a = b = 0. 47. The radius of the circle inscribed in a D ABC is 4 cm. (as shown in figure). The circle touches the sides BC, CA and AB at P, Q and R respectively. If AQ = 8 cm. and CQ = 6 cm, find the lengths of the sides AB and BC respectively. A

O

4 cm 4 cm



Step 1 : Draw BX at an acute angle to base BC. Step 2 : Cut 4 equal parts on BX as : BB1, B1B2 , B2B3, B3B4. Step 3 : Join B4C and drawn B3C′||B4C. Step 4 : B3C′ meets AB at C′. Step 5 : Draw C′A′||CA. Step 6 : C′A′ meets BA at A′ and DA′BC′ is the required triangle. A. Step 1 B. Step 2 C. Step 3 D. Step 4

50. In the given figure, ABCD is a rectangle of dimensions 20 cm × 10 cm. A semi-circle is drawn with centre at O and radius 10 2 cm and it passes through A and B. Find the area of shaded region in the figure.

8 cm R 4 cm

49. Which of the following steps is incorrect while constructing a triangle similar to given D ABC with 3 its sides equal to th of the corresponding sides of 4 D ABC?

Q 6 cm C

P

20 cm



A. 14 cm, 11 cm C. 15 cm, 13 cm

B. 11 cm, 13 cm D. 16 cm, 18 cm

G A

48. Fill in the blanks. If two zeros of the polynomial x4 – 6x3 – 26x2 + 138x – 35 are 2 − 3 and 2 + 3 . Then, other two zeros are P and Q . (ii) A linear polynomial has always R zero(s). (iii) A quadratic polynomial has at most S distinct real roots.   P Q R S A. –5 7 1 2 B. 3 –2 1 2 C. –5 6 0 3 D. 4 7 2 2

C 10 cm

D

B

(i)

B

10 2 cm

L

A. 162 cm2

10 2 cm

O

M

20 2 cm

1000 B. cm2 7 500 C. cm2 3

D. 175 cm2

SPACE FOR ROUGH WORK

Class-10 | Level-1 | Set-2

7