Maximum Marks: 80

� 3:/cn: 80

'nme allowed : 3 hours

RwtrrR1Fl:3 'E{TTZ

General Instructions :

(i) All questions are compulsory.

(ii) The question paper consists of 30 questions divided into four sections - A, B, C and D.

Section A comprises of ten questions of 1 mark each, Section B comprises of five

questions of 2 marks each, Section C comprises of ten questions of 3 marks each and

Section D comprises of five questions of 6 marks each

(iii) All questions in Section A are to be answered in one word, one sentence or as per the_

exact requirement of the question.

(iv) There is no overall choice. However, an internal choice has been provided in one

question of 2 marks each, three questions of 3 marks each and two questions of 6 marks

each. You have to attempt only one of the alternatives in all such questions.

(v) In question on construction, the drawings should be neat and exactly as per the given

measurement.

(vi) Use of calculators is not permitted.

CBSE QUESTION PAPER CLASS-XMATHS

"f1Tl1P:1�:

(i) ?tWJTR�t,

(ii) TT{ JTR-W -if 30 JT'FT t if 'cfT< � - 37, � "ff 3#( "E:: ff fcNrfirn t I � 37ff � "J(R" t � "ff � 'JTR I � cfiT !, � a! ff rifr.r JTR � � "ff JfPU

-srR t2 �t, �-«°ff"if'fl-srRt � # � JTFrt3 �ta?IT� "E:: -if 'QTr.T >TFf t � "ff JfPU 'JTR t6 � t I

(iii) � 37 -if � 'JTR "cfiT irf< TJ:cf) � TJ:cf) cWPl 37W JTR itl" 3fici�2/ctirt/riffl< f&:zrr"iifT "ffcfiffT r I

(iv) � 'JTR-W ff fcrq;f;q- � g I cffl'frr 2 3fri'i' cfTff � 'JTR #, 3 3fri'i' cfTff efR- ffl"-if a?IT 6 3frif � ?ft m ff � fcrq;f;q- � -,m t , � · "ff'4t m -if amcfiTffi � fcrq;f;q- ft <1iRT g I

(v) fq;::rT cfTff -srR -if fq;::rT � rtW Rii' -,m rrrrr t 37cfi � iRt' � I

(vi) J;eyi02fj' t ffl "Eh7 � � r ISECTION A

�3l

Questions number 1 to 10 carry 1 mark each.

m�1-s-10rfcfi�'JTR"cfiT1�t,

1. Complete the missing entries in the following factor tree :

. 2. If (x + a) is a factor of 2x2 + 2ax + 5x + 10, find a. ,.& . 2 -rn,-r-,.= � � ':rtt:m' '11� (x +a),� 2x + 2ax + 5x + 10 cf)]' 2UH,©Os ci, rn a cf)]' llR � 'flll"l" I

3. Show that x = - 3 is a solution of x2 + 6x + 9 = 0.

� fcl:i x = - 3, x2 + 6x + 9 = 0 cf)]' � � I

4. The first term of an A.P. is p and its common difference is q. Find its 10th term.

� � � cf)]' � '9'c!; p cf2TT � mcf � q t I � � '9'c!; � � I

5. If 5 tan A=-, 12 find the value of (sin A + cos A) sec A.

tan A=�. c'IT12 (sin A + cos A) sec A q;r llR � �

6. The lengths of the diagonals of a rhombus are 30 cm and 40 cm. Find the side of therhombus.� � � fcfcriuTf ctr (1�1��1 30 WTT (i2lf 40 WTT � I �� ctr � ctr ���I

7. In Figure 1, PQ II BC and AP : PB = 1 : 2. Find ar (�APQ)ar (�ABC)

A

B C Figure I

� 1 -q, PQ II BC om AP: PB = 1 : 2. ar (� APQ) � � 1ar(i1ABC) A

B C 3Wjifrr I

8. The surface area of a sphere is 616 cm2. Find its radius.

9. A die is thrown once. Find the probability of getting a number less than 3.� -gm cnT � � WfiT � I 3 "B mil" m:§lTT 31A ctr >ll�cfictl � �

10. Find the class marks of classes 10 -25 and 35 -55.� 10-25 � ,35-55 t cf7T � � � I

SECTION B �if

Questions number 11 to 15 carry 2 marks each.

w;:r ri&ff 11 "8 15 wli � w;:r t 2 3T<1i !' I

11. Find all the zeros of the polynomial x4 + x3 - 34x2 - 4x + 120, if two of its zeros are2 and -2 .

. � x4 + x3 - 34x2 - 4x + 120 � � � � �' * � � � 2 <i2IT-2 t I

12. A pair of dice is thrown once. Find the probability of getting the same number on eachdice.

13. If sec 4A = cosee (A - 20°), where 4A is an acute angle, find the value of A.

In a t.. ABC, right-angled at C, if

sin A cos B + cos A sin B.

OR

1 tan A =. .fa , find the value of

'lfR: sec 4A = cosec (A - 20°), � 4A � �-'q;TOT t, -al A cfiT llR � � 3l�

� t.. ABC if, � C � ;gJ.tc;fi)o1 �' 'lfR: tan A= � �' -al sin A cos B + cos A sin B cfiT. · v3 llH��I

14. Find the value of k if the points (k, 3), (6, - 2) and (- 3, 4) are collinear.

k cfiT lfR � � * � <k, 3), (6, -2) (i2IT <-3, 4) m �

15. E is a point on the side AD produced of a llgm ABCD and BE intersects CD at F. Showthat fl ABE ,.., 6 CFB.

� �� -ABCD chl � 71t· :PfT AD� � E � � t � BE :PfT CD cfiTF � Sl@-c{§� � � I � 1% t:,. ABE - t:,. CFB.

SECTION C

� lf

Questions number 16 to 25 carry 3 marks each.

JfR "ffi§!H 16 "R" 25 ffcfi � JfR i!t 3 3fcfi / I

16. Use Euclid's Division Lemma to show that the square of any positive integer is either ofthe form 3m or (3m + 1) for some integer m.

� � 51�f4cfil q;r ·m � � fen fcflm � � q;r cr,f fcfim �m t � 3m � (3m + 1) t � if QTdT t I

17. Represent the following pair of equations graphically and write the coordinates of pointswhere the lines intersect y-axis

X + 3y = 6 2x - 3y = 12

f.r-i:;:r wi'lcfi<o, "T1l � � mr f.i{<Zftrn � <f21T 6-1 �an t f--1��1icfi � �

� � y-3'.re;T � 51 fa-.i§c:: � �X + 3y = 6 2x - 3y = 12

18. For what value of n are the nth terms of two A.P.'s 63, 65, 67, ... and 3, 10, 17, ...equal ?

OR

If m times the mth term of an A.P. is equal to n times its nth term, find the (m ·+ nlh

term of the A.P.

D t � BR" t � 'c!,T fll-Jl.-rj{ � 63, 65, 67, ... cf217" 3, 10, 17, ... t nit 1lc!, m� )· (>

31'�

� M Bl-11.-d{ � t mil 'le!. cfiT m :fTT aZ!T nit 'le!. cfiT n :fTT m t ill � �cfiT (m + n)9T 'le!. � � I

19. In an A.P., the first term is 8, nth term is 33 and sum to first n terms is 123. Find n andd, the common difference.

"C[cn � � cfiT >f2Tlr 'le!. 8, n9T 'le!. 33 cf21T >f2Tlr n � cfiT lfl'llfici 123 � I n a21T

d('Bfcf �)��I

20. Prove that :(1 + cot A + tan A) (sin A - cos A) = sin A tan A - cot A cos A.

OR

Without using trigonometric tables, evaluate the following2 (cos 58°

) _ ls ( cos 38° cosec 52°

) · sin 32° tan 15° tan 60° t�n 75°

� � fcti (1 + cot A + tan A) (sin A - cos A) = sin A tan A - cot A cos A.

2 ( cos 58°

) - ls ( cos 38° cosec 52°

) 'sin 32° tan 15° tan 60° tan 75° .

21. If P divides the join of A(-2, -2) and B(2, -4) such that � = f, find the coordinatesof P.* �3TT A(-2, -2) � B(2, -4) cit � 9@ {@©O:S cit P � � � �

i fcti AP = � , or p � f.i��1icfi � -=AfurrAB 7 .

'-flll"I�

22. The mid-points of the sides of a triangle are (3, 4), (4, 6) and (5, 7). Find the coordinatesof the vertices of the triangle.� � ct>l �3lf t -i:rv:r-�;m t R��licfi (3, 4), (4, 6) <12TT cs, 7) � � % ffl � R��licfi � � I

23. Draw a right triangle in which the sides containing the right angle are 5 cm and 4 cm.Construct a similar triangle whose sides are. � times the sides of the above triangle.

. 3

� f!AchlOI � q)l' � � � f!AchlOI � qfffi :Pfl"3TT q)l' 1.1'41$-41 5 WTT �4-M)- �I������-���� :PfT � �

cfif��i 3

24: Prove that a parallelogram circumscribing a circle is a rhombus.

OR

In Figure 2, AD .l BC. Prove that AB2 + CD2 = BD2 + AC2.

C

B '--------___.,

A

Figure 2

�����ft -cmr@<if.TI � � � � m<TT t

�

� 2 "G", AD .l BC. � � fcfi AB2 + CD2 = BD2 + AC2.

C

B'--------___.,

25. In Figure 3, ABC is a quadrant of a circle of radius 14 cm and a semi-circle is drawnwith BC' as diameter. Find the area of the shaded region.

A C

Figure 3

3Wf@ 3 #, ABC � Tf1

���lltTTt f-Jl*lc:til � 14 "@TT t, cfiT 'tj�;qf:.tl * WTT BC chl" olfffi itHc:fi< 01-'-tifctia 'ITI1f ci)T � � ctlR!Q, I

A C

�3

SECTION D

�G

Questions number 26 to 30 carry 6 marks each.

� #<§!!r 26 "# 30 rrq; � "JfR t 6 afrF I I

26. A peacock is sitting on the top of a pillar, which is 9 m hig�. From a point 27 m awayfrom the bottom of the pillar, a snake is coming to its hole at the base of the pillar.Seeing the sn'ake the peacock pounces on it. If their speeds are equal, at what distancefrom the hole is. the snake caught ?

OR

4 The difference of two numbers is 4. If the difference of their reciprocals is - , find the 21

two numbers.

9 lft � � &i mm en: � -im: � t 1 21 lft cn1 � u � mer 3m fa@", � � &i 1lfc!: # W«=r �, cfi1 am � ® � I mq chl" ��ch< lITT � � 'CR � "J:Tm I *� 7ITTl<TT m �, m � c:tilf¼t; f&i � u � � en: mer � �

�

GT �3TT cfiT � 4 t I* ffl �&i41 cfiT � _±_ �' "f1T zy;rr fi@I� wa- c:tilf-JlQ, 21

27. The angle of elevation of an aeroplane from a point A on the ground is 60°. After a flightof 30 seconds, the angle of elevation changes to 30°. If the plane is flying at a constantheight of 3600 F3 m, find the speed, in km/hour, of the plane.

� ql�llH cfiT � -� � AU � "c:fi1UT 60° t I 30 �c:fiU:S cfi1 .� &i q�ill<(, �� irur 30° cfiT "ITT � � I � c11�llH 3600 .J3 lTT ch1 3fiR � 'CR � WT "ITT,m c111llH ch1 71fu (f&ilft;ek:r #) � chlMQ, I

28. If a Jine is drawn parallel to one side of a triangle to intersect the other two sides in

distinct points, prove that the other two sides are divided in the same ratio.

Using the above, prove the following :

In Figure 4, AB II DE and BC .II EF. Prove that AC II DF.

Figure 4

OR

Prove that the lengths of tangents drawn from an external point to a circle are equal.

Using the above, prove the following

ABC is an isosceles triangle in which AB = AC, circumscribed about a circle, as shown

in Figure 5. Prove that the base is bisected by the point of contact.

B p

Figure 5

C

<l'R � � qi! � :PTT ifi � 3Ff � :fiTTan qi) m-m �an 1n: sira�� w, � wr � �. m � � fcn � � c) �an qif � m amm �"' "' �wt,·

�qifffl�R8��:

� 4 �, AB II DE W-lT BC II EF. � � Ffi AC II DF.

rn;s: � fcn � ifi f<:fim � � � Tf 1n: � � � wran cf>1 ak11�24, � �i,

�qifffl�R8cfil��:

� 5�·ABC� B4f,<ills � �, � AB:::AC t, � � � � ifi lffi7To <iRT<TT 1"fcIT t I � � Fii 3ff'EITT: m � ID"U ffl� "ITTfil t I

B

A

p

3WfFrr 5

C

29. If the radii of the circular ends of a conical bucket, which is 16 cm high, are 20 cm and

8 cm, find the capacity and total surface area of the bucket. [Use n = 2

72]

� fchm �i¥tlcfiR �, � � 16 WTT t � � fuu cfi1 � 20 WTT cf2TT

8WTT ten�� ch1' � cf2l1 ¥J � �-� � h= � �1

30. Find mean, median and mode of the following data :

Classes Frequency

0-20 6

20-40 8

40-60 10

60-80 12

80-100 6

100-120 5

120- 140 3

91T ail�is!Hi:11

0-20 6

20-40 8

40-60 10

60-80 12

80-100 6

100-120 5

120-140 3