"Q"�ciTT � -8�1 : 30 Total No. of Questions : 30

�: 3 -tie

Time: 3 Hrs.

-81 Jt I cii!i �u : General Instructions

1. ".cTa.ft "Q""�Gf 3-tfG'ia,d �,

All questions are compulsory.

WS&� Total No. o Pages :

l£?1fo.> : 8 0 Full Marks : 80

2- � "Q""�cifQ3f cA" 3 o "Q""�Gf "'cfR � A, B, C 3ITT D cA" fuA cA" 1 o "Q""�Gf q � cb 1 3fcf> "cbT, � 8 cA" 5 "Q"�Gf

"cbT, NUs C cA" 1 o i;r�Gf q � cb 3 3-icm- "cbT c=rm

Q � cb 6 3-icm- "cbT % I

This question paper consists of 30 questions divided into 4 sec tions A, B,C and D. Section A contains 10 questions of 1 mark each, Se tion questions of 2 marks each, Section C contains 10 questions of 3 n and Section D contains 5 questions of 6 marks each.

3. � c5 � cA" � 3fcf)Gf J1MQ I

4.

5.

Only sketches are to be given in the answers of constructio

Answers of the questions must be in the context of the instl ctio therein. ".cfa-fi � cnm "Q""�Gf � � 9,R-acb, cf) 3@ cA" � WS& ¢lMQ, 3� � � I

Do all rough work only on the last pages of the question-ct n ans and nowhere else.

�-A

"Q""�Gf -2i � I 1 if 1 0 cfcf5 Q� cb O 1 3fcf> "cbT � I

SECTION-A

Question Numbers I to 10 carry O 1 mark each.

, . 1 4 o cm- 31� <!!01ci1-8isl c5 <!!olci1QSc1 c5 � cA"

2.

Express 140 as a product of its Prime factors.

� � P(x) c5 mt!, Y=P(x) c5 cffitf5 i-r, P(x) � � cf5lflJ'IQ I

For some polynomials P(x), find the number of zeroes of of Y=P(x).

y

X

y

the Graph

Jharkhand Board Class 10

Maths Sample Paper-Set 2

3. uffu cblfuil! PcF.> x2 - 2x = (-2)(3-x) "(!en fut11a �-----.-........ � Check whether x2

- 2x = ( -2)(3 -x) is a quadratic equation

4. cRIGf �cf>lkil! ( Evaluate)

5.

6.

7.

8.

cot25°

tan 65°

-2-lcHlci-2. �: 6,9,12, 15, ........... cf> R1t! � 3h=R:° Write the common difference of an AP: 6,9,12,15, ......... .

ocfRf d � ¥ cf> tlgel"f�T cf5T �?fQ5c1 kiffill! I Write the area of quadrant of circle of diameter d.

<fl- cJT$ 3wp@ cit DE 11 BC m c=rr EC m cblfuil! 1 In given figure DE 11 BC, find EC.

1.5cm D

B C

Pcnm ¥ G5)- ��f nm- ¥ � fcf5<'1 � � � How many points a tangent to a circle intersects ?

9. erg U"cGlT fui�-lcf>I UIBcf 6lGfT �tlc=r � rcF.> IDTe:fcf.>illThe probability of an event that is certain to happen is -

Name the ogive given below.

I Ge

.SC

4C

Y- 3Hff(axis)

0 'IS !fi'R :s..!.f) �f Q s Ci €

(Upper limits)

�-B

U-�Gf � 1 1 i-l- 1 5 cfcf>" O�cf> 0 2 3fcBT cf5T � I

SECTION-B

Question Numbers 11 to 15 carry 02 marks each.

1 1. 6 3ITT 2 0 cf>f 3Hl-TT� c?J,Olci-i-8105 PcrR:r i-l- LCM Find LCM of 6 and 20 by the prime factorization method.

Gftt I

-3:r�(axis)

1 2. 1!c5 rnt11a � $fRl cblfu1Q.,

fu1-2icf.> �i�cm cf.> � cf2TT��T: - 3 "(!cf 2 t I Find a quadratic polynomial in which the sum and product and 2 respectively.

1 3. 3� � OA.OB=OC.OD t t

��Tfm! rco- LA= LC 3ITT LB= LD t IIn fig. OA.OB=OC.OD

A

1 4.

Show that LA= LC and LB= LD

D

� sec0 = _!2 ir ill SinA cBT cfTTGf $fRl cblfu1Q I12

Given sec0 = _!2 Calculate SinA.12

15. � cblfu1Q rc5 � � � <[R � � � ��fcst-llcst-2 itcfl- t IProve that the lengths of tangents drawn from an external pequal.

�-C "Q'�Gf � 1 6 � 2 5 cfcf> Oc-ilc.f> 0 3 3-fcf5T cBT t I

SECTION-C Question Numbers 16 to 25 carry 03 marks each.

1 6 . qfctc1 s fua-TT6TGf Q c-vn R&FT cBT � � s 6 7 3ITT s s cblfu1Q I Use Euclid's division algorithm to find the HCF of 867 an 255.

3l2TTTT (OR) � cbl fu1 Q rc5 ✓

5

1!c5 3-t Q R<A � -li -8<-11 t I Prove that ✓

5

is irrational number.

17- 6R cblM Q ( Solve) : 7r-2 11

• J = 5 xy

8x+ 7y = 15xy

1 s . <il I lhl � Pcmr &RT 6R cblM Q(Solve by Graphical Method)

y = 2x-2, y = 4x-4

1 9. � A.P. cBT 1 7UT � � 1 OU � � 7 3TTE % I

'-2Tict3fc'17 $fRl cbl fu1 Q I The 17st term of an A.P exceeds its 10th term by 7. Find th com difference.

C

B

circle are

HCF $fRl

312-TcTT (OR)

� � A.PcF.> i;rclcff 1 4 -qif- cBT -cilvT 1 050 % � 1 o % m 20-df � m cblRnl! 1

In the sum of the first 14 term of an A.P. is 1050 and its firs the 20th term.

2 o. Rlc& cblM Q (Prove that) :

l+sin A --- =SecA+tanA 1-sinA.

2 1. x 31� � cf6 � m cblRnl! un- (2., -5) 3fu (-2�i cf1 c;;_ U-<l" � I Find the point on the x-axis which is equidistant from (2, -

10, Find

22. 3cT � cBT ��ITTB m cblRnl! un- �3TT (-1 _, 7) 3ITT ( _, -3) cm

rn c1 16' cffR �-8116:i s cm 2 = 3 cf> 3-1 <1 q I a � rcra-rrMcr

Find the co-ordinates of the point which divides the join of -1, 7)in the ratio 2:3 .

312TTTT ( 0 R)

K cBT <ITTar � cblMQ � � A(2, 3), B(4, K) 3ITT Find the value ofK if the points A(2, 3), B(4, K) and C(6,

( 6, - ) �i�W � 1) are c llinear.

2 3. "Qcf> &3juf ABC ti!6-11$l! f'u1�➔cA AB = 5cm, BC= 6cm 3fu � "Qcf> &3juf -cB1- � cblMQ_, M�➔cbl � 1:,AB, �3TT -cB)- 3/4 � 6TI Draw a triangle ABC with side BC= 6cm, AB= 5cm an construct a triangle whose sides are ¾ of the corresponding triangle ABC.

312TcTT (OR)

4 cm f31 G'4 1 cBT "Qcf> � � 6 cm f31 G'4 1 cf> "Qcf>

� ir "[!cf> ��f � -cB)- � cblM Q I Construct a tangent to a circle of radius 4 cm from a point circle of radius 6cm.

2 4. "Qcf> � � "Qcf> aTcT �, "Qcf> G'flill � 3fu "Qcf>

"Ra-ft- � "Qcf> � -li I $61 -cB)- � I p@cbl � � cf> ir "[!cf> � frii cbl c1 ct1 % $�i cB) � Wefcbill % fm­� ? (ii) °c1lR � ? (iii) G'flill artt � ?A bag contains a red ball, a blue ball and a yellow ball, all the same size. Kritika takes out a ball from the bag withou looki What is the probability that she take out the (i) yellow ball ? (ii) e (iii) not blue ball ?

2 5 . 1 0 ira=fi f3l G'4 I cffR "Qcf> � -cB)- cf5f$ circ:rr � � � � 1 � � cra6:is cBT �5llhc1 m cblMQ 1

(n= 3.14 cBT � cblMl!) 1A chord of a circle of radius 10cm subtends a right angle the area of minor segment (use n= 3 .14)

3lercTT (OR)

AB 3fu CD� o c==rw 8'1R.l13TT 21cm 3ITT 7cm mc_q- � er> W<ff�T: � 7qrq % � L.AOB = 30° % ill e,1�iwx1 � m cf5Hu-1L:! 1 AB and CD are respectively arcs of two concentric circles 7cm at centre o. If L.AOB = 30° , find the area of the shaded

A

�-D

"Q"�Gf -2.-l -82-11 2 6 i-f 3 0 c=rc:5 Q c=i) cf.> 0 6 3-Tcf5T cf>f % I

SECTION-D

Question Numbers 26 to 30 carry 06 marks each.

1cm and

B

2 6. rnt.11a -2.-1ct-flcF.>-2.01 2x2-6x+3=0 cf>f RIRlmcF.>-2., � cBl- -r-rb:::-+-->r rnt.11cfl

27.

� cf>f 3q2..11cJ1 � � m cblfu-il! 1 Find out discriminant, nature of roots and root, using binor quadratic equation 2x2-6x+3=0.

3lercTT (OR) � ¢cH l<llc'1 c..16'1 lccHcf.> �01fcF.> $fR1 cB)fu-i Q M6icb cfvTT 3 6 5 it I Find two consecutive positive integers, sum of whose squa e is 3

1. 5 m clcsTT t!cf5 c1 $cf.> I 3 Om � t!cf5 cHcTG1 i-r �� c16 3;i) a-m cBl- 3ITT \J1Tc'1T % cfCsf 3-2_-1cB) 3rRJTcf>f 36-ui � 6i q5fUf Wcff�T: 3 0 ° 3ITT 6 0 ° it \J1Tc'1T

cHcTG1 cAf- 3ITT Rt:>a cA7 � c=rc:n 'cl c1 cF.>-2. vmi- % 1A 1.5111 tall boy is standing at some distance from a 30111 tc l buil ng. Theangle of elevations from his eyes to the top of the building increc s s from 30°

and 60° as he walks towards the building. Find the the dist nee h valkedtowards the building.

3lercTT (OR)

t!cf5 80111 � � er> � 3ITT 3�--2.ilcHcii :m-� RcJT g"C! � I � � :m-a-TT er> � � er> t!cf5

�m- er> 3 6-ui � 6i q5fUf Wcff �T: 60° 3ITT 3 o0 % I :m-a-n ____....::::...� 3ITT:m-a-it i-r � q§)- � � cl5lMQ I

The poles of equal heights are standing opposite each othe · on e·t er side of the road, which is 80m wide from a point between them 01 the r d, the angles of the top of the poles are 60° and 30°, respectively Find e height of the poles and the distances of the point from the poles.

2s. � cblfu-il! PcB- t!cn -2.-1cHcmu1 &� � cf.>Uf cf>f clcTT �TtST cfcJTT er> mvT er> isl-2.l<il-2. irc=rT % I Prove that in a right angle triangle, the square of the hypo en use i equal to the sum of the square of the other two sides.

2 9 "(Tcf5" iRr "(Tcf5" 3,� tR � "(Tcf5" �leg cf> 3ITTn R cf> % fui 6i cblf¾u-G11c! 1 cm % c=ren �leg � � 3-2➔ cb1 blu-G11 IB- GT-c1c1-c % , �iR=r cf>f 3-1,�acif n cF.> TTTit <ff m cblRiil!,A solid in the shape of a cone standing on a hemisphere v ith be th their radiibeing equal to I cm and the height of the cone is equal to ts rndit s. Find thevolume of the solid in terms of n.

3f2lcTT (OR) "(Tcf5" gcAf inft �leg cF.> IBciuict.> cF.> 3TTcBR � % � �f5 � �cBT" Blu-G!I 10cm �:, � � cf5l- blu-Gll 4cm � 3� � m � @def.> � 15cm %, m � � <ff !J,gchi "Q<TTe:f � �� �lt:>ci mcblfu-1 l! I A fez, the cap used by the Turks, is shaped like the frustu 11 of ;� �one. If itsradius on the open side is IO cm. radius at the upper base i� 4 cm a·1d its slantheight is 15 cm, Find the area of material used for making it

3 o � 3� it <il§cicf.> m cb'lfu-1 l! (Find the mode of th follo'v ng data)

qvf 3-R'R:Tcvf 10-25 2 5-40 40-55

(Class interval) cill�c:sll._>_cif 2 3 7

(Frequency)

3f2lcTT (OR)

� 3� it cffTE� $f@ a§)R:ii (!Find the mean of the following data.

55-70 70-E 5 8 !, - 1 0 0

6 5

mf 3TT'mc'l 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 ! 0-90 9(-100

Class

Interval �

Frequency 5 3 4 3 3 4 7 9 7 8