General Instuctions (ii) The question paper consists of three sections A,B and C Section A is compulsory for all students. In addition to Section A, every student has to att empt either Section B OR Section C (ii) For Section A Question numbers 1 to 8 are of 3 marks each. Question numbers 9 to 15 a of 4 marks each. Question numbers 16 to 18 are of 6 marks each. (iii) For Section B I Section C Question numbers 19 to 22 are of 3 marks each. 1 CBSE QUESTION PAPER MATHEMATICS �,1d Class-XII Ti me allowed : 3 hours f :3 � Maxi mum Marks: 100 � : 100
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General Instuctions
(ii) The question paper consists of three sections A,B and C. Section A is compulsory
for all students. In addition to Section A, every student has to attempt either
Section B OR Section C.
(ii) For Section A
Question numbers 1 to 8 are of 3 marks each.
Question numbers 9 to 15 are of 4 marks each.
Question numbers 16 to 18 are of 6 marks each.
(iii) For Section B I Section C
Question numbers 19 to 22 are of 3 marks each.
1
CBSE QUESTION PAPER
MATHEMATICS
�,(1)1d
Class-XII
Ti me allowed : 3 hours
f.:mfftrr-'ff1fll:3�
Maximum Marks: 100 � '3icFi: 100
Question numbers 23 to 25 are of 4 marks each.
Question number 26 is of 6 marks.
(iv) All question are compulsory.
(v) Internal choices have been provided in some questions. You have to attempt
only one of the choices in such questions.
(vi) Use of calculator is not permitted. However, you may ask for logarithmic
and statistical table. If required.
(i) W Jl�';f � "c6 efR' &1Js Jr, � Jff< N � I §fls i3' ?rJft' � "c6 fw:! ,:,{Pfq/q
-+ -+ -+ 20. Find the value of A whkh makes the vectors a, b and c coplanar, where
-+ A A A � /\ /\ /\ ....+ A /\ /\
a= 2 i -j + k, b = i + 2 j -3 k and c = 3 i -1 j + 5 k.
-+ -+ -+
A <of lfR ™ cfilRrt� Fct �T a, b � c ti9ct�l4 �' �
-+ I\ I\ I\ � I\ I\ A -+ /\ I\ I\
a=2i-j+k, b=i+2j-3k am c=3i-11.j+Sk%1
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21. A particle starting with initial vetocity of 30 m/sec moves with a uniformacceleration of 9 m/sec2• Find:
(a) the velocity of the particle after 6 seconds.
(b) how far it will go in 9 seconds.
(c) its velocity when is has traversed 150 m.
� cf>UT 20 lll.ffl. cf) '!mm � � am 9 lll.ffl.2 cf) Qcoft4H � � � i I f;rq
ffl cfil�Q
('3l) 6 �coos � colf cor �
(GI") 9 � coos � cf>UT fcbct .-i"1 � � ffl
(ft") 150 llt. c8 � � co"R "tTT" cf>UT coT � I
22. Find the resultant of two velocities 4 m/sec and 6 m/sec inclined to oneanother at an angle of 120° .
OR
A ball projected with a velocity of 28 m/sec has a horizontal range 40 m. Find
the two angles of projection.
4 lft.1�. am 6 lft.1�. cf> m � �-� � 120° cf> m "tTT" co14{a � 1 �
qf<u11'-i"I � ffl cfil�Q I
� � 28 lll./�. cf> � � � c8 � a"m � � 1TTffi 40 llT i I $ff
"Sfffl ffl ffl cfi1 � Q I
23. A body of weight 70 N is suspended by two strings of length 27 cm and 36 cm,fastened to two points in the same horizontal line 45 cm apart and is in equilibrium.
21 wfr c=rm 36 #1'.ft A smm � mn titlRla � � � m � 1 � irfr �
� � c:Q�q I
24. The resultant of two unlike parallel forces of 18 N and 10 N act along a line at adistance of 12 cm from the line of action of the smaller force. Find the distance
between the lines of action of two forces.
18 N cfm 10 N cf> � fclq{)a f?;�T ft4hH Gf'ffi coT qf<o11111 � � W 00 cf>
��T cor<f cR'ffi t � � � � � 00 � 12 WlT � � '(f{ i I � �
���A OOJTT cf)��� ffld" c:Q�q I
25. Find the equati on of the plane which is per pendicular to the p.lane
Sx + 3y + 6 z + 8 = 0 and which contains the Line of intersection of the planes
25. The total cost C(x), associated with the production and .making x units of an itemis given by
C(x) = 0.005x3 -0.02x2 +30x+5000
Find (i) the average cost function (ii) the average cost of output of 10 units (iii) the marginal cost function (iv) the marginal cost when 3 units are produced.