SL. No.

: G

CCE PF

BΔ«M•⁄ O⁄}⁄°¬“
Jlflo Æ⁄√ÀÊ-V⁄◊⁄ —⁄MSÊ¿ : 50 ] [ Jlflo »⁄flfl¶√}⁄ Æ⁄‚¥lV⁄◊⁄ —⁄MSÊ¿ : 12
] [ Total No. of Printed Pages : 12
Total No. of Questions : 50
CCE PR
—⁄MOÊfi}⁄ —⁄MSÊ¿ : 81-E Code No. : 81-E
…Œ⁄æ⁄fl : V⁄{}⁄
Subject : MATHEMATICS
(
BMW«ŒÈ ∫¤Œ¤M}⁄¡⁄ / English Version )
( ‘ʇ—⁄ Æ⁄p⁄¿O⁄√»⁄fl / New Syllabus )

(S¤—⁄W @∫⁄¥¿£% & Æ⁄‚¥´⁄¡¤»⁄~%}⁄ S¤—⁄W @∫⁄¥¿£%/ Private Fresh & Private Repeater)

¶´¤MO⁄ : 26. 03. 2018 ] [ Date : 26. 03. 2018

TEAR HERE TO OPEN THE QUESTION PAPER

—⁄»⁄flæ⁄fl : ∑ÊÿVÊX 9-30 ¬M•⁄ »⁄fl®¤¿‘⁄-12-45 ¡⁄»⁄¡ÊVÊ ] [ Time : 9-30 A.M. to 12-45 P.M.

Æ⁄√ÀÊ-Æ⁄~√OÊæ⁄fl´⁄fl-}Ê¡Êæ⁄flƒfl BΔ« O⁄}⁄°¬“

V⁄¬Œ⁄r @MO⁄V⁄◊⁄fl : 100 ] [ Max. Marks : 100

General Instructions to the Candidate :

1. This Question Paper consists of 50 objective and subjective types of

questions.

2. This question paper has been sealed by reverse jacket. You have to cut on
the right side to open the paper at the time of commencement of the
examination. Check whether all the pages of the question paper are intact.

3. Follow the instructions given against both the objective and subjective
types of questions.

4. Figures in the right hand margin indicate maximum marks for the
questions.

5. The maximum time to answer the paper is given at the top of the question
paper. It includes 15 minutes for reading the question paper.
Tear here

PF & PR-7008 [ Turn over

81-E 2 CCE PF & PR

I. Four alternatives are given for each of the following questions / incomplete

statements. Only one of them is correct or most appropriate. Choose the correct

alternative and write the complete answer along with its letter of alphabet.

8×1=8

1. In the given Venn diagram n ( A ) is

(A) 3 (B) 1

(C) 5 (D) 2

2. Sum of all the first ‘n’ terms of even natural number is

(A) n(n+1) (B) n(n+2)

(C) n2 (D) 2n 2

3. A boy has 3 shirts and 2 coats. How many different pairs, a shirt and a

coat can he dress up with ?

(A) 3 (B) 18

(C) 6 (D) 5

4. In a random experiment, if the occurrence of one event prevents the

occurrence of other event is

(A) a complementary event (B) a certain event

(C) not mutually exclusive (D) mutually exclusive event

PF & PR-7008
CCE PF & PR 3 81-E

5. The polynomial p ( x ) = x 2 – x + 1 is divided by ( x – 2 ) then the

remainder is

(A) 2 (B) 3

(C) 0 (D) 1

6. The distance between the co-ordinates of a point ( p, q ) from the origin is

(A) p2 − q 2 (B) p2 − q 2

(C) p2 + q 2 (D) q 2 − p2

7. The equation of a line having slope 3 and y-intercept 5 is

(A) 3y = 5x + 3 (B) 5y = 3x + 5

(C) y = 3x – 5 (D) y = 3x + 5

8. The surface area of a sphere of radius 7 cm is

(A) 88 cm 2 (B) 616 cm 2

(C) 661 cm 2 (D) 308 cm 2

II. Answer the following : 6×1=6

9. Find the HCF of 14 and 21.

10. The average runs scored by a batsman in 15 cricket matches is 60 and

standard deviation of the runs is 15. Find the coefficient of variation of the

runs scored by him.

11. Write the degree of the polynomial f ( x ) = x 2 – 3 x 3 + 2.

PF & PR-7008 [ Turn over

81-E 4 CCE PF & PR

12. What are congruent circles ?

5
13. If sin θ = then write the value of cosec θ.
13

14. Write the formula used to find the total surface area of a right circular

cylinder.

III. 15. If U = { 0, 1, 2, 3, 4 } and A = { 1, 4 }, B = { 1, 3 } show that

( A U B )l = Al I B l . 2

16. Find the sum of the series 3 + 7 + 11 + .......... to 10 terms. 2

17. At constant pressure certain quantity of water at 24°C is heated. It was

observed that the rise of temperature was found to be 4°C per minute.

Calculate the time required to rise the temperature of water to 100°C at sea

level by using formula. 2

18. Prove that 2 + 5 is an irrational number. 2

19. If n P4 = 20 ( n P2 ) then find the value of n. 2

20. A die numbered 1 to 6 on its faces is rolled once. Find the probability of

getting either an even number or multiple of ‘3’ on its top face. 2

21. What are like surds and unlike surds ? 2

22. Rationalise the denominator and simplify : 2

5+ 3
.
5− 3

PF & PR-7008
CCE PF & PR 5 81-E

23. Find the quotient and the remainder when f ( x ) = 2x 3 − 3x 2 + 5x − 7

is divided by g ( x ) = ( x – 3 ) using synthetic division. 2

OR

Find the zeros of the polynomial p ( x ) = x 2 − 15x + 50 .

24. Solve the equation x 2 − 12x + 27 = 0 by using formula. 2

25. Draw a chord of length 6 cm in a circle of radius 5 cm. Measure and write

the distance of the chord from the centre of the circle. 2

26. In ABC ABC = 90°, BD ⊥ AC. If BD = 8 cm, AD = 4 cm, find CD

and AB. 2

OR

1
In Δ ABC, XY || BC and XY = BC . If the area of Δ AXY = 10 cm 2 , find
2

the area of trapezium XYCB.

PF & PR-7008 [ Turn over

81-E 6 CCE PF & PR

27. Show that, cot θ . cos θ + sin θ = cosec θ. 2

28. A student while conducting an experiment on Ohm’s law, plotted the graph

according to the given data. Find the slope of the line obtained. 2

X-axis I 1 2 3 4

Y-axis V 2 4 6 8

29. Draw the plan for the information given below : 2

( Scale 20 m = 1 cm )

Metre To C

140

To D 50 100

60 40 to B

To E 30 40

From A

PF & PR-7008
CCE PF & PR 7 81-E

30. Out of 8 different bicycle companies, a student likes to choose bicycle from

three companies. Find out in how many ways he can choose the companies

to buy bicycle. 2

31. If A and B are two non-disjoint sets, draw Venn diagram to represent

A \ B. 2

32. What is an Arithmetic progression ? Write its general form. 2

33. There are 10 points in a plane such that no three of them are collinear.

Find out how many triangles can be formed by joining these points. 2

34. A student reads the books according to the given data. Draw a pie chart to

represent it.

Name of the books Novels Short stories Magazines Journals

No. of books 10 60 20 30

35. Simplify : 75 + 108 − 192 . 2

36. A polynomial p ( x ) = x 2 + 4x + 2 is divided by g ( x ) = ( x + 2 ). Find

the quotient by using division algorithm. 2

37. If v 2 = u 2 + 2as , solve for v and find the value of v, if u = 0, a = 2 and

s = 100. 2

PF & PR-7008 [ Turn over

81-E 8 CCE PF & PR

38. A vertical building casts a shadow of length 12 m. If the distance between

the top of the building to the tip of the shadow at a particular time of the

day is 13 m. Find the height of the building. 2

39. Show that ( sin θ + cos θ ) 2 = 1 + 2 sin θ cos θ. 2

40. Find the co-ordinates of the mid-point of the line segment joining the

points ( 14, 12 ) and ( 8, 6 ). 2

IV. 41. In a Geometric progression the sum of first three terms is 14 and the sum

of next three terms of it is 112. Find the Geometric progression. 3

OR

If ‘a’ is the Arithmetic mean of b and c, ‘b’ is the Geometric mean of c and

a, then prove that ‘c’ is the Harmonic mean of a and b.

42. Marks scored by 30 students of 10th standard in a unit test of

mathematics is given below. Find the variance of the scores : 3

Marks ( x ) 4 8 10 12 16

No. of students ( f ) 13 6 4 3 4

PF & PR-7008
CCE PF & PR 9 81-E

43. If p and q are the roots of the equation x 2 − 3x + 2 = 0 , find the value of
1 1
− . 3
p q

OR

A dealer sells an article for Rs. 16 and loses as much per cent as the cost

price of the article. Find the cost price of the article.

44. Prove that, “If two circles touch each other externally, their centres and the

point of contact are collinear.” 3

45. If 7 sin 2 θ + 3 cos 2 θ = 4 and ‘θ’ is acute then show that cot θ = 3. 3

OR

The angle of elevation of an aircraft from a point on horizontal ground is

found to be 30°. The angle of elevation of same aircraft after 24 seconds

which is moving horizontally to the ground is found to be 60°. If the height

of the aircraft from the ground is 3600 3 metre. Find the velocity of the

aircraft.

PF & PR-7008 [ Turn over

81-E 10 CCE PF & PR

46. A solid is in the form of a cone mounted on a right circular cylinder, both

having same radii as shown in the figure. The radius of the base and

height of the cone are 7 cm and 9 cm respectively. If the total height of the

solid is 30 cm, find the volume of the solid. 3

OR

The slant height of the frustum of a cone is 4 cm and the perimeters of its

circular bases are 18 cm and 6 cm respectively. Find the curved surface

area of the frustum.

V. 47. Solve the equation x 2 − x − 2 = 0 graphically. 4

48. Construct a direct common tangent to two circles of radii 4 cm and 2 cm

whose centres are 9 cm apart. Measure and write the length of the

tangent. 4

49. State and prove Basic Proportionality ( Thale’s ) Theorem. 4

PF & PR-7008
CCE PF & PR 11 81-E

50. A vertical tree is broken by the wind at a height of 6 metre from its foot and

its top touches the ground at a distance of 8 metre from the foot of the

tree. Calculate the distance between the top of the tree before breaking and

the point at which tip of the tree touches the ground, after it breaks. 4

OR

In Δ ABC, AD is drawn perpendicular to BC. If BD : CD = 3 : 1, then prove

that BC 2 = 2 ( AB 2 − AC 2 ) .

PF & PR-7008 [ Turn over

81-E 12 CCE PF & PR

PF & PR-7008