1. A document provides instructions for students taking an exam. It specifies the code number to write on the answer sheet, time limits for reading the question paper and providing answers, and other directions. 2. The exam contains questions divided into four sections - A, B, C and D. Section A contains 8 multiple choice questions worth 7 marks each. Section B has 6 questions worth 2 marks each. Section C has 10 questions worth 3 marks each. Section D has 70 questions worth 4 marks each. 3. Calculators are not permitted. Students must write down the question number before attempting each question and adhere to time limits for reading and answering.

1. Series RSH
)-:(st i.
Roll No.
o.Is f.
Code No.
3012
L
qteTnfi 6ls 61 s-d( gfu6T b g*-g*
q{ 3rdrq fui t
Candidates must write the Code on
the title page of the answer-book.
o gr4r fre s{ ii f6 {q yFr-rl:i fr gEK gu rs t r
. s{Er-qr fr qRt ETq *1 3ft Rq qq q}-s qq{ +} 6H Td{-gR*T h W-w w ffi r
o g.rrrr siq +l d fu {q yFT-Er fr g+ qva t l
o !ffir vFT i["r siR ftrg{r g6 il} + qEe, s{ET 6',T H,,qi6. sf,Ew ftrd r
o {H Yq;T-w +) q-qi t fiTq 15 fuaE 6r qrr{T fEqrrqr t r $sq-qd sr fuf,{uJ tqf6 q
10.15 qi r6qT qAn | 10.1b qi t 10.s0 c$ m* on *-+o rsT-tr{ +i Gi sil{
{q 3rqFr * Ehr{ a s-fl{-qk6T q{ q}$ sir-{ Tfr ftdn I
o Please check that this question paper contains lb printed pages.
o Code number grven on the right hand side of the question paper should be
written on. the title page of the answer-book by the candidate.
. Please check that this question paper contains 84 questions.
o Please write down the Serial Number of the question before
attempting it.
o 15 minutes time has been allotted to read this question paper. The question
paper will,be distributed at 10.1b a.m. From 10.1b a.m. to 10.80 a.m., the
students will read the question paper only and will not write any answer
on the answer-book during this period.
d6frd q0en - u
SUMIUA'TTVE ASSESSMENT - II
IVIATHEIT{ATICS
fuifftdwg:sqv|
Time alloweil :3 hours
30t2
Jtfqndq di6 : 90
Maximum Marks : 90
{ L P o I {
P.T. O.

2. srqq fidfn :
(,
(ii)
(iii)
wfrxwqffidt
W XYI-W q 34Wl d W 4K gagT
-
a{, 6{, g 37{ , q Wilfqd d I
sas er q ga.-qp eri6 qe I yw d', si, ag-ffi yfl{ a t ste q i
6 wt d Aa+ 0 rdir 2 ei6 ar d r sug" v if to xw ilTq-ilTq er*i-# d r
sue.E il to w+ d Aaa 0 eAir 4 ai6 ar d r
questions diuided into four
(iu) *qrdzr ar xqJrT +rffa d r
General Instructions :
(L) AII questions are compuls;ory.
(ii) The question paper consists of 34
sections
-
A, B, C and D.
(iii) Section A contains 8 qutestions of 7 mark each, which are multipl.e
choice type questions, Sectioi B contains 6 questions of 2 marks
e:o,ch, Section C contains 10 questions of 3 marlzs each and.
Section D contains 7O questions of 4 marks each-
(iu) Use of calculators is not permitted,
snffiola
wt ti@r r C e d6 rd+- wt 1 eiq w d r vs-+ €@T r 0 s i tAd v{? +
frq 4n f{Tw Rq Tq d, lY++ A #{d qir crd d I s-d fuq€.gfav r
Question numbers 1 to 8 carry 7 mark each. For each of the question
numbers 1 to 8, four alteritatiue choices haue been prouided, of which only
one is coryect. Select the correct choice.
c)9
r. qR n = 4 6, n) sO t* qrq ed qs qFq il{r ltd qffi{ ii aq 6i T$ (fr
I
rfra frl d
2-2
1.1
9-625
(A)
(B)
(c)
230t2
(D) s6-25

3. If n is taken as ?, tn" distance (in
I
diameter 35 cm, in one revolution, iq-_
.t
(A) '2.2
,r//
(B) 1.1 ./.a
(c) e.625
(D) e6.25
1b rfl,. eiafr q+ ffi'q* seqiw qrqn q R[s{
qrq 60' 61 6)ur q-{-fi t, A {qR *i *ni t
(A) 1b J5 ql.
metres) covered by a wheel of
nsqdffitrqR qE *6 SqR +
(B)
(c)
(D)
15J5 fi.
'
t-'tt:'
15
"t.2
15 fr.
A ladder 15 m long just reaches
ladder makes an angle of 60" wit
wall is
isJd *
15J5
-
fIl
2
L5
2
15m.
vertical wall.
wall, the height
If the
of the
(A)
(B)
(c)
(D)
3
to
30 t2 P.T.O.

4. 1
9
4
45
(c)
(D)
trqCfrtqTq-uqrq6
*rd f+*ror qqT | {s qrd qr 3iFF-d {qr + !$ Wf q.f EH dt Hfu*Tr tr1
rhr*,
.,
(B) 4
15
A box contains cards numbered 6 to 50.'A card is drawn at randorp
from the box. The probability that the drawn card has a number
which is a perfect square, is
sr5fd 1it, :r< Aq-A Td vt l5s qra fug o t A w{ ur( on dqr DF t I
qR On = 5 tfr den DE I DF t, A E-t *1 fi-q1 g
1
45
2
G
1
9
4
45
(A)
(B)
(c)
(D)
4:
(A)
(B)
(c)
(D)
3tfr
5 tql
4 +ql
6 tql
430t2

5. In Figure 1, DE and DF are tangents from an external point D to a
circle! with centre A. If DE = 5 cm and DE I DF, then the radius of
the circle is
Figure 1
(A) 3 cm
(B) 5 cm
(C) '4 cm.
(D) 6 cm
!_
qEfr z d, q*
=g$q
ABCD + sio'if, frqrrqr Tt; {s+1 Swii AB, Bc, cD
dqr AD qt 6q{r p, Q, R IEr S q{ {q{t 6561 $, I qR Td +1 f*qt t0 tfr,
BC = 88 t*, PB = 2z tfr f,erT AD t- cDt, A cD d tr t
RC
3ilryfu 2
(A)
(B)
(c)
(D)
11 tfr
20 tfr
21 t*
15 tfr
5
-----O
30t2 P,T.O.

6. In Figure- 2, a citcle is inscribed in a quadrilateral ABCD touching its
sides-rB, BC, CD and AD at P, Q, R and s respectively. If the radius of
the circle is 10 cm, BC - 38 cm, PB - 27 cm and AD r cD, then the
Iength of CD is
(A)
(B)
(c)
(D)
Figure 2
11 cm.
20 cm
2L cm
15 cm
l
t,
6. x-3rtT 6T 46 Gr€, fr tr€s (-1, 0) dql (5, g1 t qT{t€I t, t
(A) (0,2)
(B) (2;0)
(c) (3, o)
(D) (0, 3)
,:
The point on
(5, 0) is
(A) Q,2)
(B) . (2,0)
(c) (3, 0)
(D) -(0, 3)
3012
the x-axis which is equidistant from points (-1, 0) and
6
----{o

7. 7. q-6 qT+ d q6 eR ilffir qror t
(A) ?
3
(B) 1
'3
I qs sTqFr €qr + ant d qrtr+-dr t
1e)--+-a-- 2
(D) t6
A die is thrown once. The
(A) ?
3
(B)1'3
(c) I2
(D) 1
6
qqtdr4-dl s-b 3-2b
b' 3b ' 3b
probability of getting a prime number is
8.
1
(B) -^a
-
(c) 1
(U) _I
The common difference of the AP
1
5
c.
,...flqH3rfi6
13-b 3-2b
b' gb' gb
(A) 1
3
1S
(A)
3
1
-1
(c)
(D)
30t2 7 P.T.O.

8. Erug Er
SECTION B
. ,wdwrsi udqydoxw*z tioi t
Question nurnbers 9 to 14 carry 2 marks each'
e. qr5fr 3ii, aTdq{srfq-€ cTyriail t rR-qdftqfs cq{fiql .ri
3EqF1€ s{i tsr, P dzlT a qt fis q-$ 3q-qr{s qd GT 61 qffiq-q+ ocfi t t
atLTfu 3
InFigure3,twocirclestoucheachotheratthepointC.Provethat
the common tangent to the circles at c, bisects the common tangent
at P and Q.
P
Figure 3
10. srr5fr 4 ii, q-* 5 h qR'rd qs q-$tq ABCD dqrrqr i' r R-q dfqq ft
AB+CD=AD+BC.
I3012

9. 11.
In Figure 4, a quadrilateral ABCD is drawn to circumscribe a circle.
Prove that AB + CD = AD + BC.
APr-)
Figure 4
riq q)
"
* fr( 66 eifsq :
- J2t2+7x+ 5J2 =0
Solve the following for x :
J2*2+7x+|Ji=o
q+ q.S d 6o m Si qir ff 14 t* t r gs tuiz dt g{ ERr 5 fuas ii {tud
fu {rd +1Fsq I
The length of the minute hand of a clock is 14 cm. Find the area
swept by the minute hand in 5 minutes-
fi{-€}iqii Erfr sfi xrSn €ersii s1 €sT $6 dFq q} g t F'!{rFq-d ttfi t r
Find the number of all three-digit natural numbers which are
divisible by 9.
t4. n1-{ fueii +} q+ €Tsr sstrTr rrqr I fs-f6 d qR f{d 3Tri q1 xrE-*,dT {ro qifuq t
-ryr-*ihs
are tossed simultaneously. Find the probability of getting
,&ctly two heads.
t2.
13.
I3012 P_T.O.

10. Etug €
SECTION C
wt riwr ts g za d6 ,Flzg v7;7 o s eiq i t
Question numbers 15 to 24 carry 3 markseach./
,/
,/
tx s qrir qRT q1e,I qfi drg qrd s .irf, .ir lqqdr ql qqlHFI TH HT itcrtrhr{- (R- s
.r'v -
'r'-
- Fs q drqrrqr B r qFq dR sr ff rz rir. Et, dr nn qir tH ffi eiliqq r
A ,oiia metallic sphere of diameter 8 crn is melted and drawn into a
cylindrical wire of uniform widthl If the length of the wire is L2 m,
frnd its width.
16. q{ ns-dt{r Z tfr |*q1 q,6 3{ttrA qt eT?at-tFrd qqn f*qr q-A YiS * eTrf,R sr
d I qR ns-di ml gm ff B1'tfi t, E) fis-di 61 qE't Ydq *tq-d rTd
"iRq
| [n= ? Anqr
A toy is in
radius 7 cm.
surface area.
the form of a cone mounted on a hemisphere'of same
If the total height of-the toy is 31 cm, find its total
,.2. --'fUse ru - ::1...'
. 1.,//,/I
17. il6 +ifwq fd fuEuii A(-3, 10)dqr 8(6)-8)+l ffi qIA tuws q{ furd fr€
P(-1, y) {t fu'v eEwn ii 9"q6. oqar t I y sT qH $ {ra +1fuq t
Find the ratio in which poi P(-1, y). lyrng on the line segment
it. Also find the valuejoining points A(- 3, 10) 8(6, - 8) divides
of y. _--- ), ,1 f
4 u
J
30 t2 10

11. 18. qr5fr b ii, g* 91t *' qEEt{T OPBQ t ffd q+ +t OABC q-{r
€3{r t r qR
oA = 21 t* t, A gtqifu-d Qe or Q-{q-d $d dfuq I [r =
affis
In Figure 5, a square OABC is inscribed in a Quadrant OPBQ of a
circle. If OA = 2L cm, find the area of the shaded region.
rr' 22.
LUseT[=;lI
O-'eP
Figure 5
Egq-nn t eo fr- fi er-{c-6rgs + Rrgt + ts} q-{ A qgfr q-drcif t silq-{qq
qlor g0' Brt{ +5" t r qR €Ez-6rsq * qo A *{ q6 {{M {tr *o'q t *s m-d
E), ft A q-dFit t +q qfi
S {rd dfrq I t..6 = L-732 dfqqf
As observed from the top of a 60 m high lighthouse from the
sea-level, the angles of depression of two ships are 30" and 45". If
one'ship is exactly behind the other on the same side of the
lighthouse, find the distance between the two ships.
;1;se Jd = r.7}2l
f *ruu
a
19.
P.T.O.
_t
30t2 11

12. q{ a)q {ig', ffi eTrrTR +1 |*qr ro tfi t, +l sq-{i ff + qTq}-Et-q t E}si
wi gR, gs nET t A ,rT.il ii ora 'w t, qqfu qo no {g * enqn t q-qif,{ t r
yi$ t +ii -rT'il t 3ilTd-ii fr eqwn vra +1Re r
fisolid cone of base radius 10 cm is cut into two parts through the
nHh-point of its height, by a plane parallel to its base. Find the ratio
in the volumes of the two parts of the cone.
zL. kt fuq qH + Fdq RqTd q-qt+Tur (k- 12) x2 +2(k- 12)x + 2 = 0 t {g
qql-{t 2
. For what value of k, are the roots of the quadratic equation
(k - 12) x2 + 2(k - 12) x + 2 = 0 equal ?'
zz. qo erinr td qr sef w wt frd qq 6r fd'JqT t r qR g*r*r aqi qE 22 A, n)
qqim *.d vra qifqq t
The Bth term of an AP is equal to three times its third term. If its
6th term is 22', find the AP.
2s. 4.5 tS F*w1 q qs Tf, q{ q$ d,d twq OAq, m q}q qr q}nr +s'd t
fi1 Draw a pair of tangents to a circle of radius 4.5 cffi, which are
* i'nclined to each other at an angle of 45
24. fu€ dftq fu fd€ A(2, -r), B(8, 4), c(-2, 3) dqr D(- 3, -2) qs qq--q{q
ABCD t {fr{ fr€ d I F{I ABCD qs-q-f d ?
Prove that the points A(2, -1), B(3, 4), C(-2, 3) and D(- 3, - 2) are
the vertices of. a rhombus ABCD. Is ABCD a square ?
€ue, E
SECTION D
cw (i@r 2s t sa ao sdo sr+ A n aio d r
Question numbers 25 to 34 carry 4.marks each.
25. qs qgqT{ fr !-.dA qqq q-s qT* ql qta e'r 'r$ r qre-* i n-srar den qil{il st
qkqq td g{, sS erwors
"g*r}
q;r xiq f*-qr, Frst HKUT qrgqn 39 fu44 tfr t
qErT | :if,q q{, q} fu 1500 ffi qi (fr q{ t, vrFr rR
"gtt}
+ fdq qt-f,-s i
q1
'rR' 169 ffiuEia e--d-$ r .tg*" *1 p .TfdiEicT {t dFq I FIT 3{N
srekn gRT r-qfrTd {wl, t'fr e1 drr{ sdfirdl cler wfq q{ +qi * nqnii o1 srra+
q{it z
30t2 12

13. 0
While boarding an aeroplane, a passenger got hurt. The pilot,
showing promptness and concern, made ar:rangements to hospitalise
the injured and so the plane started late by 30 minutes. To reach the
destination, 1500 km away, in time, the pilot increased the speed by
lQO.km/hour. Find the original speed./hour of the plane. Do you
appreciate the values shown by the pilot, namely, promptness in
providing help to the injured and his efforts to reach in time ?
rlg qi qr<{ € q-iT oi{ g,q{ t gf,T qs eda rE; 4 fse-{ * eTrf,R 6r i, ffir
# ro ffi t dqT F1qa.s+{ sqfr mi + qRI *,ETI: 16 tt'i dPI 40 tqr t r gs
c -: , ,, :- r-,,qd;T 6r E;rFr s fdq rjffi srg 41 qK{ st Ts { 10 qfr 100 qri iqi 4t < t w
+ifqq | [n = 3'14 frfuq]
A container open at the top and made up of metal sheet is in the form
of a frustum of a cone of height 16 crn with diameters of its lower and
upper ends as 16 cm and 40 cm respectively. Find the co-st of metal
sheet used to make the container, if it costs { 10 per 100 cm".
lTake n = 3.14f
27. qd qt{R } qTq td€ t {d r+q t RTG{ 6I s{zFT q}ot 30" I I '{Eq
* *< RS
t qrqR + Rrcr 6I T*qq frq 60" t r qFq qHR 69 qi. g-+ A, R) trfi sl #
{Td sifqq I
The angle of elevation of the top of a building from the foot of a
tower is 30". The angle of elevation of the top of the tower from the
. foot of the building is 60'. If the tower is 60 m high, find the height
of the building.
26.
4
28. qd q-+t
qrf@qT
s .,It-l chls
qs 4.|g
ggfi
*c---^F-
€ lsFI q{ 3, 5, 7, 9, .... 35,
fq-+Tdl rlril I grfusdT FTd d,Fiq
tr
.e.:,_--__);+)
37 gGITq 3{i.5d € | qR q *l
fu Fffir-A qq fl-s r{ 3iird {i€qT
box contains cards numbered 3,
at random from the box. Find the
5, 7. 9, ..., 35, 37- A card is drawn
probability that the number on the
30 t2
drawn card is a prime number.
13 P.T.O.

14. zg. z tfr sridR-m qrs ql qs +dqTq,R qr{q t E]{dT gsTI qrfr qo qrd il rgz.s fua
qfr trTc +1 qr t qogr. t) ror t r q.rgq ii qrfr 61 'rfr ffi7q4 fr vra dfrq r
," = 'i dreqr
Water running in a cylindrical pipe of inner diameter 7 cm, is
collected in a container at the rate of 192.5 litres per mimrte. Find
99
. the rate of 'flow of water in the pipe in km/h. [Use n = "] I
s0. kd dfqq fs ffi qt-d tr€ t qs Tn q{ *qi 'r$ w{i t€Fri q1 @ wnt
6)-tr t
Prove that the lengths of tangents drawn from an external point to a
. circle are equal r ,
gl. qEfr 6 ii, Fgq ABC 6i g-utq AB, BC (nn cA, tc o dqr f{-qr r qrd gt e}
s'rrfl: P, Q dqr R qr s{t F-ffi t | .
A
Ba
ol7fu 6
A
Rl-q Sn-qq '
(i) AB+CQ=AC+BQ
(ii) *{s€ (A ABC) = 1 (o ABC 61 qfisq; ;a 1
,2
30t2
.1
rl I
--'--
o
I
lr
14

15. In Figure 6, the sides AB, BC and cA of triangle ABC touch a circle with
centre O and radius r atr P, Q and R respectively.
Figure 6
Provb that
(i) AB+CQ=AC+BQ
2x+3'
*+0.-9'2
:'
.15
II
i
@ Area (A ABC) =
1
lPurimeter of A ABC)
" r
sz. ** frq 6q frfrq :
!-s:x
Solve for x :
I-B: 5 ;x*g,-3-x 2x+3' 2
fr-€eil A(4, -6), B(3, - 2) nT C(5, 2)t qi trW ABg + idq scilvq +1fqq id
fuE-q
qi qrF4ql sS qqTq
@ qTa A ftgq t effi t r
For the triangle ABC formed' by the points A(4, - 6), B(3, - 2) and
C(5, 2), verifu that median divides the triangle into two triangles of
equal area. 'i
g4. gsqqif,r *.4*relrl mqdior+Ts-d 4m2_-t rqRE-s *frw ndqE rOz
t, ft n .Fr {Ft flC-dfqq | {q vqid{ }.d or 21d q( S an dfrq I
The sum of first m te"{ms of an AP is !^' - ^.
If its nth term is
- 107." frnd the value o{n. Also find the 21lt term of this AP'
30t2