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JHARKAND BOARD CLASS- X SAMPLE PAPER- SET 1 Mathematics (Theory) Design of Question Paper

l lndcr�t.mding( l I)

Applic:1ti(m lligh Order (Al I hinking

<:;!..ills

E,t1hmtion ( I.)

otal J\ arks

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\ er� <:;hort An�" er (, 2 I - I I l< IO) ( \'SA l

( I Marl..) <;hurl Ans\\ cr-11 I J - I - 0( 5 l

( <;_i\-11 I (2 Marks)

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t3 Mark\) 1.nng An<,\\Cr I I I 2 - iOt 5 I

(I /\)(6 Mark,)

I 11tal l\larks 20 B 19 14 04 ODO) 0 o \\ eii;thtaS?c �5fJn 29

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Note: 3 3TTITT crrcr s v�arr cA" '3,erm � 3fl7 6 3TTITT crrcr 4 v�arr

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An internal choice wil I be provided in 5 questions of 3 marks an LI 4 questions of 6 marks.

Weight of content Units and Sub units

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Contcm Suh units W�1gl11agc

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Mathematics (Theory)

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a,11Se,q5 m � m 3rcn u�c;n c5)- � cm- c:-�rfcl �, Figures outside brackets indicate the marl,.s carried b) the concerned quc• lions and figures within brackets indicate the number of questions. (ii) *3fercTT i;:f�cf

OR questions*

MATHEMATICS Questionwise Analysis

Question Objective Group-A (01 marks} Number

01 R Ex - 1.2/l .4 -02 E Ex -2.1 03 u Ex -4.1

04 R Ex-8.3 05 u Ex -5.1

06 A Ex-12.1 07 R Ex -6. I /6.2/6.3/6.4/6.5 08 R Ex-10.l/l0.2 09 R Ex - 15.1

IO R Ex - 14.4

Grouo - B (02 Marks)

I I u Ex -1.212 u Ex -2.2/2.3

13 u Ex -6.2 lo 6.514 H Ex-8.1/8.2 15 R Ex-10.2 (� 10.1/10.2)

Grouo - C <03 Marks) 16 u Ex - I. I 3feffl"T 1.3

17 A Ex -3.3 � 3.6 18 A Ex-3.1/3.2 (3� mlR112) 19 A Ex -5.2 3:rerm 5.3 20 A Ex-8.4 21 R Ex - 7.1 22 R Ex - 7 .2 3:rerm 7.3

23 E Ex -11.1 3feffl"T 11.2

24 u Ex -15.1

25 lJ Ex - 12.2 3feffl"T 12.3

Grouo - D (06 Marks)

26 A Ex -4.3/4.44.2/4.3/4.4 3feffl"T a.nm �tft

27 If Ex -9.1 3:re.rm

28 ll � 6.1/6.6/6.8/6.9

29 u Ex - l 3.1/13.2/13.3

3feffl"T Ex - 13.4

30 R Ex -14.1/14.2/14.3

I

!Class- X]

Marks

01

01 I

01

01 01

01 01 Ol 01

01

02

02 02

02

02

03

03

03

03

03

03

03

03

03

03

06

06

06

06

06 (cRTt2:r m «s16. 01 c.n) 3feffl"T cR'T\:ZTq5

·-

��aIT c6\" -8-lii!t I : 3 0 � c6l- � Total No. of Questions : 30 Total No. of Pages

�: 3 � q:_u1fc15 : 8 0 Time: 3 Hrs. Full Marks : 80

..!-11 d1 I a,!I Parif�T :

General Instructions :

1 . �a-ft ��cf 3-tRlc.114 "l; I

All questions are compulsory. 2- � ,;f�'af'Q"5T cR" 3 0 ,;f�Gfi 'clR � A. B. C 3ITT D cR" Pcr� I �

A cfi- 1 o V�cJ !.l c::21 cb 1 3-fcf5 cf5T, � B cfi- 5 V�cJ !.l c::21 cb 2 3-rcmcf5T, � C cfi- 1 o "!.l"�cJ o c::21 cb 3 3-icm cf5T <'ferr � D cfi- "!.l"�cJ !.l c::21 cb 6 3-rcm cf5T � I

This question paper consists of 30 questions divided into four secti.o 1s /\.. B, C and D. Section /\. contains l O questions of 1 mark each. Section B c ntains 5 questions of 2 marks each. Section C contains IO questions of 3 mat ks each and Section D contains 5 questions of 6 marks each.

3. � cl5 3"'fR cR" c15cfR 3fcbc;f cflM l! IOnly sketches are to be given in the answers of construction.

4. V�aTT cl5 3TI7 V�aTT cl5 �cl KQ' .:>TT! Pcrif�T c5 3ilctlcb cR" t,- cflMQ IAnswers of the questions must be in the context of the instructions 1ventherein.

s . <:ra-ft � mm v�cJ <:16 3TI7 gR-a cb1 m 3m cfi- � � t1-c6lful l!, 3� cnt1- �I

Do all rough work only on the last pages of the question-cum answ r booklet and nowhere else.

�-A

V�cJ .!.1 ffe1 I 1 i)- l O c=rm \.lc::21 cf5 0 1 3fcb cf5T � I

SECTION-A

Question Numbers 1 to 10 carry O l mark each.

1. 1 2 o cl51" 3,� �u161-.!sis1 m �u16105e1 m

Express 120 as a product of its Prime factors.

2. � isl§QG P(x) m fFTI!, Y=P(x) m <1rfQ5 "R, P(x) m �r=-nt=+ �

;?.1 ffe-11 sf@" cf5l M Q I

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

y

X X 0

3. \7lfu c6lffilC? rcn x2 + 3x -t- I = (x - 2)2 12cn �u1c1 -2.-1ifflmlo1 � crtt 1

Check whether x2 + 3x + l = (x - 2)2 is a quadratic equation or not.

4. cFTTcf fatm,fc:il! ( Evaluate)Sin 18

°

Cos72°

s. AP : 4.10.16.22 ............ m � "Rrcf 3-hR" sm, c6lffil C? = Write the common difference ofan /\P: 4,10.16.22, .......... .

6. r � � 3-l<i{'<l'a "cbT qQa-,1q faf&l! IWrite the Perimeter or a semicircle or radius r.

7. "Rafi cJ<TT 61cf °t - -l1cR.MQ/-l-lclfol-l1cRAll Squares are - Similar/Congruent

a. 12cn � 'c6l Rbacif1 ..!➔<A ia-l <'Q"�f � it -l1mcf) 't?

9.

I lo\\ man) Parallel tangents can a circle have?

Uccff "'E .. mT IDT� 3fu UccTT ··E �-- mT IDT� cf5T

ircm?What will be the addition of the probability of incident .. E .. and incinot··?

10. fc:15-R � c.l5T c'fRUT �?What type of ogive is?

I 1

Y- 31Ett(axis)

0 � �(Lower limits)

�-B

i;T�cf -l-t-&.11 1 1 � 1 5 <'lcl5 08acb O 2 3fcITT c.l5T i I

SECTION- B

Question Numbers l l to 15 carry 02 marks each.

1 1 . 2 6 3fu 9 1 cBT 3T� <?Joiai&os fmu &RT" HCF � 'c6l Find HCF of 26 and 91 by the prime factorization method.

, 2 . 12cn mu, a � � m1 m112, ffil .[-I c6 ,!!,_cR.I cbl m mm cfe.:rr ��T: 4 "(!'cl 1 � I

-3Hff(axis)

Find a quadratic polynomial, the sum and product of whose zeroc. are 4 and I respectively.

l 3. -l-lct1C1dl �� /\BCD Rrl-l1<A /\B 11 CD � c,e;rf � fclq5of BD QU-Q-l O � �faiB<! � i ill c:-�� fiB

OA OB -=-

oc· OD

D C

� ;\ l3

3ITT

ABCD is a trapezium in\\ hich AB 11 CD and its diagonals AC and D

1 4.

intersect each other at the point o. Show that D C

(), I OB

()( OD [;� ;\ 11

� Sin A= l it- m tanA cm CfTTaf qRq5faa c61Rrn:! 14

If Sin, I= 1

then find the value or tan/\. 4

1 s. <[TI m qRJ1c1 l!cf5 �� ABCD � vrm �, � �� AB+ CD = /\D + BC

/\ quadrilateral ABCD is drawn to circumscribe a circle. Prove that AB+ CD = /\D + BC

�-C

��er -l� -&!I I 1 6 � 2 s cfcf5 •;tcil q5 o 3 3TTBT cm � ,

SECTION-C

Question Numbers 16 to 25 carry 03 marks each.

1 6. q:_Rrr-ls fu()ffijfcf l.!ci>rlRea:r cm 1FTT<TT � 1 3 5 3ITT 2 2 s �Rm!, Use Euclid"s division algorithm to (ind the HCF of 135 and 225.

3le.TcIT (OR)

� �Rm! 6 1r- ✓2 12cf.i 3ctoRJ.l.a �-&!II � 1 Prove that 6+ ✓2 is irrational.

1 7. 6Cf cf5lr01Q (Solve) :

I I -+-=2 2.Y J_r

I I 13 -+-=-

3.r 2.r 6

1 a. <JJ I c:61.a Fcrfu m 6Cf ml-Rm:!(Solve by Graphical Method)

X -2) 0

3x + 4) - 20

IICI $fTc'1"

1 9. 3R A.P. mr 3 1 cif 'Qc!" � c.&lfG:112 M..!.-lcbi 1 1 cif 'Qc!" 3 s 1 6UT 'Qc!" 7 3 % I Find the 3 i s1 term of an A.P whose l I th term is.38 and the 16th tern1, i 73.

3:rcTTTT (OR)

� A.P<B" � 'Qc!" 7 3i'R 1 3cif � 35 ir m -mcf3RR 1 3 L(c!T cf.)f -m.rr sITT'f 451M Q I

In an A.P. first term is 7 and 13th term is 35. rind the common diffc1 nee and sum of first 13th term.

20. � c5lMQ (Prove that):

Cos A 1 + Sin A 2 S I---+---= ec�

I +Sin A Cos A

2 1. �3IT (-5, 7) c=rm (-1, 3) ffl ffl ml- � � c$1ffirt:I t Find the distance between two points (-5. 7) and (-1. 3).

2 2. 3R � mr ��TicP srrc=r c.&lMC! cir �3rr (4, -3) 3ITT ( , s) cm-� cTTR �-8-11&5 cffi" 31ic'1Rcb � � 3: 1 ffl ;;s1<1,Ql<'1 <fl" 3-TTfG:R, cB«TT % I Find the co-ordinates of the point which divides the line segmcnljo ning the points (4. -3) and (8. 5) in the ratio 3: l internally.

3:rcTTTT (OR) 3R &� mr � '51 lf>c:1 � �c:6)4+f'U1-"----r�C! M -l-1 c?.i �fl-d ( 2 , 3 ) , (- 1 , o ) , (2, -4)°%1

Find the Area of the triangle whose ve1tiees are (2. 3). (-1. 0). (2. - ).

2 3. 4 cm. 5 cm 3ITT 6 cm �3TT cTTR � &� ml- ��......-=R 3ITTfcITT.- � ;[-IJ-l-li)Q l!cf5 3� Br� ml" � ml"ron::!, fui-<-lcffl �� of(! &� c$T � 3ji3ll3-Tl c$T 2 I 3 � N I Construct a triangle of sides 4 cm. 5 cm and 6 cm and then a triang c similar to it whose sides are 2/3 of the corresponding sides of the first trian le.

3fcTTTT ( 0 R)

6 cm bl&<!.ll mr � c[R" �TT.TT! I � � 10 cm � n:-em � � ¥ 1R ��f � � ml- � c5lMQ I

Draw a circles of radius 6 cm from a point 10 cm away from its Oe1trc,Construct the pair ort angents or the circle.

24. "Qcf5 � <fl" 5 � mit, s � � 3ITT 4 P �°%I � �<fl" � � cf5'm .:s:t I �'ci:.!>.:s:t I fat c.B I c:11 '5'lT<'1T % I tR-1 cf5) � � % rcf5fa:tcblc:11 cYfm cf5'm (i) cTTR % ? (ii) � �? (iii) e.Rf � % ?A box contains 5 red marbles, 8 while marbles and 4 green marble . Onemarble is taken out of the box at random. What is the probability ti at themarble taken out will be (i) red? (ii) white? (iii) not green?

2 s. � ¥ cf.> 'clgerl�T cf.>f �5JQ-jc1 � cf5)fu1Q M-8cl51 �T Find the area of a quadrant of a circle whose circumference is 22

• 3:rcTTTT (OR)

rn.:s:tim,a m mr �5llf>c1 sTTo c$1� � ABCD � 14 O<Jf � c=rm APO 3ITT BPC � 3:r� � 1

Find the area of the shaded region. Ir /\BCD is a square of side 14 c n and/\PD and BPC arc semicircles. /\ r:::::::;;======:;;::,-i (3

D

�-D

p

,;f�cf � 2 6 � 3 0 ?rcl5 OBacJ5 0 6 3fc15T mT � I

SECTION- D

Question Numbers 26 to 30 carrv 06 marks each.

C

26. � -.!-la-flcJ5l01 2x2-7x+3=0 m � � � $frc=f c61fG-t121 WIT mT J-IR:ac'cl 61", cTT fuEJtcfl � mT 3q,Q)a1 � � � �\-:'l::rn1

Find the nature of roots of quadratic equation 2x2-7x+3=0. If the re· I rootsexists then find roots using quadratic formula.

3fefcTT ( 0 R)

�r �3TT cf5 cfdTT mT 3rc=R 180 �I mt)-� mT crcrf �mT 3ffi'j � � I c:TclT <1 ,8,i!.11 (! slTff cB)fG-t C! Irhe di ffercnce of squares or two numbers is 180. The square of the smallernumber is 8 time the larger number. r:ind the h\O numbers.

2 7. � cf5 lTc5 � � 1Icn 20 m � :HcTcf m �ffiR "CR: c'fcJft �a-n cl I l m c=rc.vr 3'ft?:- �ffiR m 3iicl -a a1 cJ5TU1" 9'><ff�r= 4 s O 3'ft?:- o O � 1a-fl cl I< "c6I" � � c61fG-t C! IFrom a point on the ground. the angles of elevation of the bottom a 1d the topof a transmission to,\ers fixed at the top of a 20m high building ar 45° and60° respectively. Find the height of the tower.

3fefcTT (OR)

lTc5 -.!-I ct-1 a e1 61 a-fl cl "CR: � a-fl ii1 1 < � -mm 3"l-l �-errn- <it 4 m 3TTEicJ5� N i3fTcft- � i.il<ilW5 � mr 3iiclai�r 60° � E.lc.cb< 30° uTTaT � 1aftci11l -cB)- � slTc'f �fG-ti::! I The Shadow of a tower standing on a level ground is found to be➔ m longer"hen the Sun ·s altitude is 30° than "hen it is 60° . Find the height r the l()\\ er.

28. � �fG-ti::! � � �� � {!co � cf5 �3TT cffi" f'�-f'� �3rr "CR: ofame � m �fhft ulT(!, cTT cl" 3f«T cTT � {!co i;)" 3i '3q I c'1 <ff fu�I

Prove that if a line is dra\\ n parallel to one side of a triangle to • nterscct theother t,, o sides in distinct points. the other t\\ o sides arc divided in the sameratio.

29. � � {!co &1-wJl 31..if<>n&l m 3m cl5T �

&1&c11 � 3T&a1-i1Rta � 3�"')-&)- mr m 1 4cm("QT5l") -cB) � 3";mt 1 3cm � � � mr ..j1iaRq5$lTc'f c61ffi.lQ I

A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder The diameter of the hemisphere is 14cm and the total height of tre vessel is 13cm. Find the inner surface area of the vessel.

3:re.rcrr (OR)

mcft- � cfR.vlT l!c5 f.'l1c11-c1 14cm 3;'cll$ � l!c5 �� ci5 �c.r., ci5 3-ITTPR mr i 1 � t=a I ct51-l mit ci5 m 4cm 3� 2c 11 i �

22f.'l I c1 I {1 cf51 urfRTT $lTcl cJ5) M l' I ( ;r = - )

7 A drinking glass is in the shape of a frustum of a cone of height 14cm. The diameters of its two circular ends are 4cm and 2cm. Find the cap, city of the

22 glass. (1r=

7)

3 0. ra1 <t-al fc'1ffik1 <1 I {Of) � .3Rl-1<1 I c1 <R" "(!cf.) m�m c:nsf <R" :Hcf'f st! ii f.'l I ,!.11 mT 3� cffl" C:-�irf-cft- � :

5-15 15-25 25-35 35-45 45-55 55-55

6 11 21 23 14 5

3 q ii cfu 3� c5 di §c1 ct5 $l'lc1 cffi Ml' I The following table shows the ages of the patients admitted in a hos pi al during a year:

Age 5-15 1 5-25 2 5-3 5 35-45 45-55 5 s- 65

(in years)

Number 6 1 1 2 1 23 14 !:

of patients

Find the mode of the data given above. 312.TcTT (OR)

� 3� � -a:m� $l'lc1 mlfutl! Find the median of the following data.

nut 3fITT1c'f 65-85 85-105 105-125 125-145 145-165 165-185 185-205

Class Interval � 4 5 1 3 20 14 8 •l

Frequency