l I • ·1

SECTION A

This section comprises Multiple Chotce Questions (MCQ,s) of 1 mark each.

1•• The pair of equations x "'2a and Y .. 3b (a, b ¢ 0) sraphfcally represents

strafght lines whfch are : 1

{A) coincident
(B.) parallel
{C) intersecting at (2a, 3b) ,
(D) inter~ctfng at (Jb, 2a)

2. PQ is a diameter of a circle with centre 0(2, - 4). If the coordinates of the

1'
point Pare(-_ 4, 5)., then the coordinates of the point Q will be:
(A) (- 3; 4.·S) ., .
(8.) (- 1, 0.5)
(C) (4, - 5)
• (D) (8, - 13) •
J '

3• If k + 7, 2k - 2 and 2k + -6 are three co~secutive -terms of an A.P., then the

1
. value of k is : .
' ' " 1 ,.' . !"
J l ~ ' ... \. • • I : A J
..
'
(A) ·15
(B) 17 •
I .
- - - ..
(C) 5 (D) 1

4. A cap is cylindrical in~.shap~.,_ surmq!,:f_n~ed _by a co11ical top. If the-vqlume of the 1

- J , .,, • ~ .... •

•cylindrical part is equal,~o-that Qf. ~h~:c;~pjc;.~! part,. the~ the ratf~ of the-height •
. . of the cylindrical part to the..h~~g~t.. of -th~11cRnica! p~r,t is : ., ,
.
(A): 1 :· 2
I
\ .
)·
(C) 2 : 1 ' (D) 3 : 1

5. . In a formula racing competition, ~he tfme taken by two racing cars A and B to 1
complete 1 round of the track is 30 minutes and p minutes· r~spectively. If the
cars meet again at the starting point for the first time after 90 ~inutes and the
HCF (30, p) = 15, then the value of p is

(a) 45 minutes (b) 60 minutes

(c) 75 minutes (d) 180 minutes

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 ,
i\- .
6. If tan2 8 + cot" a= 2, where 6 • 45 • and 0 • :S a S90 ·, then the value of a ts :
1

(A) Jo• (8) 45•

(C) 60° (D) 90°

) ' . 1
the numbers
7• I Tw o dfce are thro wn at the same~tfme and the product of
numbers
probabflfty tha t the pro duc t of the
appearfng ont the m fs noted.·The
lies bet we en 8 and 13 is :
s
(A)..!. (B) i6
36 .
-

(D) !.
. (C) ! 4
. 9.
1
8. f If a·= 2'.3
1
u an db = 2j.3 ', the n H_CF (a, b) is:

(BJ.]10. 311
(A) i1.3 10
'
7
(D) 2 .J!
(~) 23.37
11
the numbers - 3, - 2, - 1, O, 1, 2, 3.- The
9. I A number is chosen at random from ./ ••, -• , . . • ·' ,i,
-
➔
I
A • ·, • ft)

'
·is,tess than.or equal to· 1 is': ·,
•
•

probability tha t square of this number

(B) 2
(A) ! 7
7

(D) ! .
.(C) ! 7
1

perimeter of a square are·equal, then:1,:

1 1 11
and the
10. t ff the circum1erence of a circle

(a) Area of the circle = Area of the

square
~
square
•

(b) Area of the cfrcle > Area.of the

I

square
(c) Area of the cir cle ~ Area of the
the
ut the relation between the areas of
I

(d) Nothing de fini te can be said abo

circle and square~ 1

11. I For the following distribution:

-
Below I Below j Below Below I Below I. Below
Marks / 50 , I 60
10 I 20 I 30 40

\3 of 12
 Noof 3 12 75 80
27 57
students

the modal class fs

(a) 10-20 (b) 20-30 (c) .30-40 (d) 50-60

12 • 5x ~ 3, 1
• In the llABC, -DE II BC and AD = 3x - 2, AE = 5x - 4, 8D = 7x - 5, CE
then ffnd the value of x r

(a) 1 (b) 7 /10

(c) both (a) & (b) (d) none of these

nt of
13. Two cfr~l~s touch each other externally _at C and AB is common tange 1
circles, then LACB is , )

·(a) 70° (b) 60°

(c)-100° (d) 90°

14 r r ~ Ssin9- 3cos9 . I

• If 5_ tan 8 = 4, then
.
t~e va,tu,e
) L
~f ~ss·mti¼-z
.
cose .1s
I !,;) L.1 :, '
I

• 1· 1
(a)- (b) -7 t ·)
.
6-

r
1 (d) !_ '
(c). -4 s C \ (

15. •1n the .given figµr~, -if .AB =14 cm; then ~the value of tan B•i_s: ••
....
1 '

.
Ea..-.....................~
i
'

. ,,..
•
. ..i - • '""
(b) !!
(a)~ 3
3 • tt ' r
'. '

·s
(c)-
.3
(d) ¥ ;~ H:.

. ......, .....
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 •

,. 16. Ffnd the value of k for which the equatton xz+ k(2x + k - 1) 2 • o h~ -~ -
as real and r:1i - - -
+
equal roots.
' '

(a) 2 (b) 3

(C) 4 (d) 5

se circum' ference is 22 cm , fs 1
17. The area of a quadrant of a circle, who

(a) e<m
11 2 (b) ~c m2
\ 8 • J

77 2 2
(c) -cm (d) T!. cm
2 4

values of x and
18• In fig RS I I DB I I PQ. If CP=PD= 11 cm and DR=RA= 3cm. Then the 1
,, •u
y are .respectively

I -

·'

RO

vf

1 1 ·1 •
(a)12, 10 (b) 14,6

(c) 10,7 (d) 16,8

ertion and Reason based questions. Two

Questions number 19 and 20 are Ass
Asser~ion. (A) and the other is labelled as
statements are given, one labelled as '

correct answer to these questions ·from the codes (A),

Reason {R). Select the
(B), (C) and.(D) as given below.
.
are true and Reason (R) is the correct
·u
.
(A) Both Assertion (A) and Reason (R)

explanation of the Assertion (A). \

are true, but Reason (R) ls not the
(B) Both Assertion (A) and Reason (R)
. .
. .
(A).
correct explanatton o~ th~ Assertion
5 bf 12
 (C) Assertion (A) fs true, but Reason (R) fs false.
{D) Assertion (A) fs false, but Reason (R) fs true

19• Assertion (A) : .,ff, fs an frratfonal number.

Reason (R) : If m fs an odd number greater than 1, then fm fs frratfonat.

20. Assertion (A) : Points A(3, 2), B(-2, -3) and C(2, 3) form a triangle. 1

Reason (R) : Sum of the two sides of a triangle is always greater than the thfrd
side.

SECTION B
. .'
~

This section c'?mprises Very Short Answer (VSA) type questions of 2 marks
each.

21. A chord of a circle of radius 15 cm subtends an angle of 60° at the centre. Find 2
the areas of the corresponding minor segment of the circle. (Use n = 3.14 and
13 = 1.73)

·OR

PQRS is a diameter of a circle of radius 6 cm. The lengths PQ, QR and RS are
equal. Semi-circles are drawn on PQ and QS as diameters as ·shown in below
figure. Find the perimeter of shaded region

1.
'

..t ... ,
• tI....
,.•
J
, I •
'\ I
I .,

p
 With
In the giv
22. th en ft gure, PAQ and PBR are tangents to the circle ce ntr e •o•
. ch th at at
e points A and B respectively. If T Is a point on the circle su
45 . < Q.AT"
' 65 ., t~en fin d < ATB.
) and < TBR"

.P

1 d XN ar e drawn parallel to AB and AC

2
e BC of Ll4BC . XM an
23. Xis a point on the sid oduced at
ting AB in N an d AC in M· MN produced meet s CB pr
respectively· mee •
2 = TB x TC.· • • • • •• '
T-. Prove th at nc i •
I
1

ich ~h e fo l\o wi ng pa ir of -linear eq~ations have

r wh
24. :o ~ ~h at value of k fo = 3k is
so lution s: 2x + 3y = 7' (k - 1)x + (k + 2)y
1nf101tely ma ny
2
d the·
.
1
d tan (A - B) = wh ere O s A+ B < 90°, then fin
Jj,
~2 5. (a) If cos (A + B) = 2 an 1
; (!!) f 1r
i;--
value ~f sec·(2A: 38).
•

I"'.

O R·

ch that,
(b) Find the value of >.< su
2
sec 30° = 2 cosec 30°
2
3 tan2 60° -x sin 45 ° + .!4
2

SECTION C
3 marks each
I

co m pr ise s Sh or t An sw er (SA),type questions of

Th is se ct io n 3
. The
rd s ar e re mo ve d fro m a pcick of 52 playing cards
26. Al l th e bl ac k fa ce ca
fle d an
__ d th en a cf! rd, ~s drawn at random. fi'1,d the
sh uf
re m ain ing cards ar e. ~e ll • T •
•
, .
fa ce ca rd (ii ) red ca rd_ (ii i) bla·r ck card.
pr ob ab ilit y of ge tti ng (i) 3
co t A
(s inA + co se cA ) + (co sA + secA) '." 7 + ta n A+
27 Prove th at
3
ta ng en ts dr aw n fro m an external point to a circle
th e
Pr ov e th at th e len gt hs of
28. \
are equal.

7 of 12
 OR
p, • ' , (

In the figure XY and X'Y' are two parallel tangents to a circle with. centre O and
.

another tangent AB with point of contact C interesting XY at A and X'Y' at B,

what is the measure of LAOB
'
X p A y

X: Y'"' .\, l

t ·•
. < .... ' "'\ I , ·1
-1
!
r • I
1
/ 1
~
' !

29. A man wished to give Rs. 12 to each person and found that he fell short of Rs. 6 3
when he wanted to give to all the persons present. He, therefore, distrib~ted • ,
Rs. 9 to eacfi· person and· fol.incl that Rs.· 9 ·was left over. How ·much mon~y did
1
he· have and_ how many p~rson~ were the~e? • '"~ ,~
• ..J .
•
r _"QR • 9 , IV' . , = l :") ., - .J .

I
A father's age is three times the sum of the ages of h;s children. After 5 )fears,
his Iage •will be two times. the sum of their _ages; Find the present age of the
father. .I.J.. .

30. Prove that 7 - 3.,/5 is an irr~tional number, given that ../5 is an irratio_nal 3

Number

31. Find the zeroes of the quadratic po.lynomial 6x - 3 - 7x and verify the 3

relationship .betwe~n ~he zeroes ,and the ·cqefficiertts of the polynomial.

. .
SECTION D ' .; • I •

•. . I
• I 7 ~ , .... • 1

• • • 1 p·n·set5 •18na ·An~wer (LA) ~y~~ questions of 5 marks each.

Th1sc, sect1on com ... :, ' ' .
. • , .
•
. I .. , • .
h d is-18 km/h in still water takes 1 hour more to go
A motor boat w ose spee . ,- . ~~ • •
32. 5

, - • than to r~~ur~--~o~nst~eam to the same spot. Find the speed of 5

24 km upstream . . _ · . 1
- • t j:.., 11 1~~l,~. f,E ' •
the stteain. e:
OR

8 of 12
 An express train takes 1 hour less than a passenger tratn to travel 132 km
between Mysore and Bangalore (without taktns Into constderatton the ttme
they stop at intermediate stations). If t~e average speed of the express train is
11km/h more than that of the passenger train, find the average speed of the
two trains.
33 • If the median of the following distribution is 58 and sum of all the frequencies

is 140. What is the value of x an_d y?

5
CLASS #15-25 25-35 ·35.45 ·45.55 55-65 65-75 75-85 85-95

FREQUENCY 8 10 X 25 40 y 15 17

34. Prove that if a line is drawn parallel to one side of a triangle intersecting the 5
. .

other two sides in distinct points, then the other two sides are divided in the •
same ratio. Using the above theorem prove that a line through the point of
intersection of the diagonals and parallel to the base of the trapezium divides
the non parallel sides in the same ratio

35. Ramesh made a bird-bath~for h_is garden in the shape of a cylinder with a
.
hemispherical depression at one end. The height. of the cylinder 1s 1.45 m and
its radius is 30• cm. Find the total surfaae area of the bird-bath..
s

·1.45 m

OR

At nt is in shape of a cylinder slirmountecl i;y a conical top. If the height and

d. e eter of the cylindrical part are 2.1m and 4m respectively and the slant
iam . 2 8m Find the area of canvas used for making the tent.
height of the top 1s • • 2
Also find the cost of ~anvas. of the tent ~t the rate of 500 per m

g of 12
 SECTION E
This sectfon comprf ses 3 •
case study based questions of 4 marks each
36. A school has decfded to I •
Envfronment D . P ant some endangered trees on 51 st World
ay 1n the nearest park Th . '
I few concentric . l • ey have dec1ded to plant those trees tn
I
c1rcu ar rows such that h
than the prev· .. eac succeeding rr;,w has 20 more trees
1ous, one ••The f1rst circular row has 50 trees.

Based.on the above given information, answer the following questions:

._

(i) How many t~ees will be planted iri the 10th row ?
1
(ii) How many more tree-s will .be planted in· the 8th row than -in the 5th row ?

(iii) (a) If 3200 t~e~s are to be planted iJ1 th~ park, then how many.rows are ..

·required? t.

2
OR

(b) If 3200 trees are to be planted· in the park, •then how. many trees _are
2
s_till left to be planted after the 11th row ?

- . 37. A building is made by keeping the lower window of a building at a particular

height above the grourd and an ~pp~r wind~~ i_s c:onstructed at some height
- .J .

vertically _above the lower windo~. Posi~io.n of the bot~ windows is shown in .
the diagram.

Both windows are designed.and constructed in order to have proper sunlight..

10 of 12 1·.. '
 At a certain tnstant, the angle of elevation of the bal oon from thes e
th Windaws
·s shown. The balloon is flying at constant height H above e ground.
l

Now, answer the following:

(i) Find the length AR in terms of H.

(fi) Find the height H. 1
window.
(iii) Find the distance of the balloon from the lower 2
OR- 1
(iii) Find the distance of the balloon from the uppe
r window.

hood. They always want

38. Aditya, Ritesh and Damodar are fast friend since child
allow them and rotate the
to sit in a row in the class room. But teacher doesn't
s and he does distance
seats row-wise every day. Ritesh is very good in math
as origin a~d marks
calculation every day. He considers the centre of class
day Ritesh makes-the
thei r position .on a paper in a co-ordinate system. One
a as A, Ritesh as B and
following -diagram of thei r seating position marked Adity
Damodar as C.

11 of 12
 I
(i) What is the distance between A and B ? ,I -

1
(if) What fs the distance between B and C ? 1
(ffi) A point D lies on the line segment between points A and B such that

AD:DB = 4 : 3 . What are the coordinates of point D?

OR

(iii) If the point P(k, 0) divides the line segment joining the points A(2, -2) and
B(-7, 4) in the ratio 1 : 2, then find the value of k
2

' .