B∆«M•⁄ O⁄}⁄¬° “
6
B
Question Paper Serial No.
Jlflo »⁄flfl¶√}⁄ Æ⁄‚¥lV⁄◊⁄ —⁄MSÊ¿ : 16 ]
Total No. of Printed Pages : 16 ]
Jlflo Æ⁄√ÀÊ-V⁄◊⁄ —⁄MSÊ¿ : 38 ]
Total No. of Questions : 38 ] CCE RR
UNREVISED
411
—⁄MOÊfi}⁄ —⁄MSÊ¿ : 81-E
REDUCED SYLLABUS
Code No. : 81-E
…Œ⁄æ⁄fl : V⁄{}⁄
TEAR HERE TO OPEN THE QUESTION PAPER
Subject : MATHEMATICS
BMW«ŒÈ »⁄·¤®⁄¥¿»⁄fl / English Medium )
Æ⁄√ÀÊ-Æ⁄~√OÊæ⁄fl´⁄fl-}Ê¡Êæ⁄flƒfl B∆« O⁄}⁄°¬“
(
( Æ⁄‚¥´⁄¡¤»⁄~%}⁄ À¤≈¤ @∫⁄¥¿£% / Regular Repeater )
¶´¤MO⁄ : 17. 06. 2023 ] [ Date : 17. 06. 2023
—⁄»⁄flæ⁄fl : ∑Ê◊⁄VÊX 10-30 ¬M•⁄ »⁄fl®¤¿‘⁄-1-45 ¡⁄»⁄¡ÊVÊ ]
[ Time : 10-30 A.M. to 1-45 P.M.
V⁄¬Œ⁄r @MO⁄V⁄◊⁄fl : 80 ] [ Max. Marks : 80
General Instructions to the Candidate :
1. This question paper consists of objective and subjective types of
38 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
Tear here
question paper. It includes 15 minutes for reading the question paper.
RR-B(411)2108 [ Turn over
81-E 2 CCE RR
I. Four alternatives are given for each of the following questions /
incomplete statements. Choose the correct alternative and write
the complete answer along with its letter of alphabet. 8×1=8
1. Which of the following represents measures of the sides of a right
angled triangle ?
(A) 3 cm, 8 cm and 6 cm
(B) 5 cm, 8 cm and 10 cm
(C) 3 cm, 4 cm and 5 cm
(D) 6 cm, 7 cm and 8 cm
2. The formula to find the sum of first ‘n’ positive integers is
n (n +1) n (n −1)
(A) (B)
2 2
(C) n(n+1) (D) n(n–1)
RR-B(411)2108 6
CCE RR 3 81-E
3. The coordinates of the midpoint of the line segment joining the
points ( 3, 4 ) and ( 5, 6 ) is
(A) ( – 4, – 5 ) (B) ( 4, 5 )
(C) ( 4, – 5 ) (D) ( – 4, 5 )
4. The median of the scores 10, 6, 8, 11 and 15 is
(A) 8 (B) 11
(C) 6 (D) 10
5. In triangle ABC if DE || BC, then the correct relation among the
following is
AD AE AB EC
(A) = (B) =
BD EC AD BD
AD CE DE AE
(C) = (D) =
AE BD BC AD
RR-B(411)2108 6 [ Turn over
81-E 4 CCE RR
6. The distance between two parallel tangents in a circle of radius
3 cm is
(A) 3 cm (B) 1·5 cm
(C) 9 cm (D) 6 cm
7. The formula to find the volume of a solid cylinder having base
radius ‘r’ and height ‘h’ is
(A) V = 4 πr 2 (B) V = πr 2 h
1
(C) V = πr l (D) V = πr 2 h
3
8. If the n th term of an arithmetic progression is a n = 2n + 1 then
its ( n – 1 ) th term is
(A) ( 2n – 2 ) (B) ( 2n + 3 )
(C) ( 2n – 1 ) (D) 2n
RR-B(411)2108 6
CCE RR 5 81-E
II. Answer the following questions : 8×1=8
9. In right angled triangle ABC, ABC = 90° and BD ⊥ AC . If
AD = 8 cm and CD = 2 cm, find the length of BD.
10. How many solutions do the pair of linear equations x + 2y – 4 = 0
and 3x + 2y – 5 = 0 have ?
11. If x, 7, 10 .... are in arithmetic progression then write the value
of x.
12. If the pair of linear equations 2x + 3y + 7 = 0 and ax + 6y + 14 = 0
represents the coincident lines then find the value of a.
RR-B(411)2108 6 [ Turn over
81-E 6 CCE RR
13. Find the value of the discriminant of the quadratic equation
x 2 – 5x + 1 = 0.
14. Write the formula to find the area of a triangle PQR having
vertices P ( x1 , y1 ), Q ( x 2 , y 2 ) and R ( x 3 , y 3 ).
15. In the figure, name the side of triangle PQR which is
corresponding to the side AB of triangle ABC.
16. Write the formula to find the surface area of a sphere having
radius ‘r’ units.
RR-B(411)2108 6
CCE RR 7 81-E
III. Answer the following questions : 8 × 2 = 16
17. Find the ratio in which the point ( – 4, 6 ) divides the line
segment joining the points A ( – 6, 10 ) and B ( 3, – 8 ).
OR
Show that the points A ( 7, – 2 ), B ( 5, 1 ) and C ( 3, 4 ) are
collinear.
18. Find the solution for the given pair of linear equations :
x + y = 10
2x – y = 8
19. Find the 21 st term of the arithmetic progression 5, 9, 13, ..... by
using formula.
20. Find the roots of the equation x 2 – 3x + 1 = 0 using quadratic
formula.
OR
Solve the equation x 2 – 3x – 10 = 0 by factorisation method.
RR-B(411)2108 6 [ Turn over
81-E 8 CCE RR
21. In the given figure, find the values of cos α and tan θ.
22. If cos 9 θ = sin θ and 9 θ is acute, find the value of θ.
23. In triangle ABC, ABC = 90° and D is the midpoint of BC. Prove
that AC 2 = AD 2 + 3CD 2 .
RR-B(411)2108 6
CCE RR 9 81-E
24. Construct two tangents to a circle of radius 3 cm from a point
7 cm away from its centre.
IV. Answer the following questions : 9 × 3 = 27
25. Find the sum of the first 40 positive integers divisible by 6.
OR
The second and third terms of an arithmetic progression are 14
and 18 respectively. Find the sum of the first 26 terms of the
Arithmetic progression using the formula.
26. Simplify the equation ( x 2 + 5x + 3 ) = ( x + 2 ) ( x – 1 ) and
mention whether it is a quadratic equation or not.
27. Prove that ( sec A – cos A ) ( cot A + tan A ) = tan A . sec A.
OR
RR-B(411)2108 6 [ Turn over
81-E 10 CCE RR
If A, B and C are interior angles of a triangle then prove that
A+B C
1 + tan 2 = cosec 2 .
2 2
28. The points A, B and C are collinear. If A ( 1, 0 ), B ( 4, 4 ) and
AC = 8 cm, then find the coordinates of point C.
29. Calculate the mean for the data in the following frequency
distribution table :
Frequency ( f i )
Class-interval
5 – 15 4
15 – 25 6
25 – 35 5
35 – 45 6
45 – 55 4
∑ f i = 25
OR
RR-B(411)2108 6
CCE RR 11 81-E
Calculate the mode for the data in the following frequency
distribution table :
Class-interval Frequency
10 – 15 3
15 – 20 3
20 – 25 7
25 – 30 6
30 – 35 6
30. The daily income of 50 workers of a factory were recorded as
follows. Draw “less than type” ogive for the given data.
Daily income in Rs. Number of workers
( cumulative frequency )
Less than 100 10
Less than 120 25
Less than 140 35
Less than 160 40
Less than 180 50
RR-B(411)2108 6 [ Turn over
81-E 12 CCE RR
31. Prove that “The tangent at any point of a circle is perpendicular
to the radius through the point of contact”.
32. Construct a triangle with sides 5 cm, 6 cm and 8 cm. Then
3
construct another triangle whose sides are of the
4
corresponding sides of the first triangle.
33. The curved surface area of a cone is 550 cm 2 . If the slant height
of the cone is 25 cm then find the total surface area of the cone.
OR
Two cubes each of side 6 cm are joined end to end. Find the total
surface area of the resulting cuboid.
V. Answer the following questions : 4 × 4 = 16
34. Find the solution of the given pair of linear equations by
graphical method :
x+y = 5
2x + y = 6
RR-B(411)2108 6
CCE RR 13 81-E
35. The denominator of a fraction is 3 more than its numerator. If the
29
sum of this fraction and its reciprocal is then find the
10
fraction.
OR
A student bought some books for Rs. 60. Had he bought 5 more
books for the same amount each book would have cost him Re. 1
less. Find the number of books bought by him.
36. A 1·2 m tall girl spots a balloon moving with the wind in a
horizontal line at a height of 88·2 m from the ground. The angle
of elevation of the balloon from the eyes of the girl at any instant
is 60°. After some time the angle of elevation reduces to 30°
RR-B(411)2108 6 [ Turn over
81-E 14 CCE RR
( see the figure ). Find the distance travelled by the balloon during
the interval.
37. Prove that “The ratio of the areas of two similar triangles is equal
to the square of the ratio of their corresponding sides”.
VI. Answer the following question : 1×5=5
38. A dustbin in the form of a frustum of a cone is mounted on the
circular base of a hollow cylinder as shown in the figure. The
radii of circular top and bottom of the dustbin and its slant
height are 18 cm, 8 cm and 26 cm respectively. The radius and
RR-B(411)2108 6
CCE RR 15 81-E
height of the cylinder are 8 cm and 6 cm respectively. If the total
height of the given solid is 30 cm, then find the volume of the
dustbin and also the curved surface area of the entire solid.
RR-B(411)2108 6 [ Turn over
81-E 16 CCE RR
RR-B(411)2108 6
