0 ratings0% found this document useful (0 votes) 79 views6 pagesMaths Paper PDF
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content,
claim it here.
Available Formats
Download as PDF or read online on Scribd
Class 11 - Mathematics
‘Time Allowed: 3 hours Maximum Marks: 80
General Instruetions:
1. This Question paper contains - five sections A, B, C, D and E. Each section is compulsory. However, there are
intemal choices in some questions.
2, Section A has 18 MCQ'’s and 02 Assertion-Reason based questions of 1 mark each,
3. Section B has 5 Very Short Answer (VSA)-type questions of 2 marks each,
4, Section C has 6 Short Answer (SA)-type questions of 3 marks each.
5. Section D has 4 Long Answer (LA)type questions of 5 marks each,
6, Section E has 3 source hased/case based/pascage based/Integrated units of assessment (4 marks each) with sub
pans.
Section A
1. Thevalue of (1-4 ¢08£) (1+c0s2) (1+ 00s) (14 e084) is a
ae ye
oF oF
2. The age distribution of 400 persons in a colony having median age 32 is given below: i)
Age (in years): pos asso faoas [asa aoas asso]
Frequency: 110 x |p 55 r 30 |
Then, x-yis
a) 20 b)-10
10 d) -20
3. Tf A and B are two events such that P(A U B) = P(A B), then the true relation is: ny
2) P(A) +P(B) =0 1b) P(A) + PCB) = (A) PEBIA)
©) P(A) + P(B) = 2P(A) PRIA) ) None of these
4 fim SSF is equal a
al bo
2 a3
5. A line L passes through the points (1, 1) and (2, 0) and another line M which is perpendicular to L passes iy
through the point (1/2, 0). The area ofthe triangle formed by these lines with y ax 10.
a
12,
13
4,
15,
a) 2518 by 2516
©) none of these 25/4
Ifa set A has n elements then the total number of subsets of A is
a)2n ba
on On
Ifzis any complex number such that lz + 4| < 3, then the greatest value of lz + 1)is
a6 DE
oa 5
Let R be the relation on N defined as by x + 2.y = 8. The domain of R is
2) (2,4,6,8) » G48)
(2,34) 4 2,4,6)
Solve the system of inequalities -2 < 6x-1<2
a-pSe<} b-pezcd
€) none of these a-tt
(ay
aE Dar
9 wen a WD
aE ae
1ECy2 = "Cp, then ns equal to
an bs
930 a2
‘Sum of n terms of the series ¥2+ VB+ VI8 + VI2+ .....is
. sion)
a) 2n(n+1) ye
au ame
In Pascal's triangle, each row begins with 1 and ends in
aa bo
92 a.
Hf|x—1] > 5, then
8) € [6,c0) by xe (6,00)
O@ € (-00,—4)U'6, 00) d) 2 € (—00,—4) U! 6,00]
‘A class has 175 students. The following data shows the number of students opting one or more subjects
Mathematics 100, Physics 70, Chemistry 40
Mathematics and Physics 30
Mathematics and Chemistry 28
Physics and Chemistry 23
io}
a
a
a
a
uy)
Ww
fy
io}
io} 16,
17,
18.
19,
20.
21
22,
2
24,
2.
‘Mathematics, Physics and Chemistry 18
How many students have opted for Mathematics alone?
a) 48, ») 60
924 ) 100
‘Mark the Correct alternative in the following: If 2 tance = 3 tan, then tan (a. - 8) =
of 1) None ofthese
oSam 9 far
Let 2 and zp be two complex numbers satisfying i|~9 and jz 3 il = 4. Then, the minimum value of [2x ~
zalis
a1 wo
ov a2
‘The number of all selections which a student can make for answering one or more questions out of 8 given
‘questions in a paper, when each question hasan alternative, is:
3) 255 by 6561
©) 6560 256
0
Assertion (A): Number of terms in the expansion of (22—-£) "is 1.
Reason (R): Number of terms inthe expansion of, (x + a)Pis n+
4) Both A and Rare true and R isthe comect —_b) Both A and R are true but R is not the
explanation of A. correct explanation of A.
©) A is true but R is false. 4) Ais false but Ris true,
Assertion (A): The relation R on the set A = (1, 2,3, 4, 5,6} is given by R= ((1, 1), (1,2) (1,3), 2,1), 2),
2,3), 1), 8,2), 8,3). 8.4) 4,3), 4 4),6, 5), (6, 6)}
Reason (R): The relation R is defined on A= (1, 2, 3,4, 5, 6} as {(@, b): Jab? <9)
a) Both A and Rare true and Ris the comect ——_b) Both A and R are true but R is not the
explanation of A. correct explanation of A.
©) Ais true but R is false, ) Ais false but Ris true.
Section B
E(x) = Ioge(1 - x) and f(x) = [xl then finds (F+ @)(X)
Find the equation of the parabola that satisfies the given conditions: Vertex (0, 0) Focus (-2, 0)
OR
Evaluate: Tiny
ath
Find the equations of the hyperbola satisfying the given conditions: vertices (0, ++ 5), foci (0, + 8),
Prove that A (AU B)'= 6.
FFind the equation ofa line with slope 2 and the length of the perpendicular from the origin equal to /5.
Section ©
a
uy)
ul)
fo}
uy)
fe}
Rl
Bl
fe}
B
Bl 26.
27.
28.
29.
30
31
32,
33,
34,
35.
36.
Itz, -1<2<0
Wflt)=¢ 22-1, O<2<2
22, 2 5
1? Pat Paya = find r
secon D
‘A bag contains 6 red, 4 white and 8 blue balls. If three balls are drawn at random, find the probability that:
i one is red and two are white
ii, two are blue and one is red
ii one ised.
Differentiate #8 from fist principle.
oR
Differentiate £% from first principle.
Prove that os%x sn 3x+ sin 2x cos 3x = Sin dx
oR
Prove that os 10° cos 30° cos 50° cos 70°=
Calculate the mean deviation about the median forthe following data:
Height(incm) | 95-105 | 105-115 | 115-125 | 125-135 | 135-145 | 145-155
Number of boys 9 13 5 30 13 10
‘Section E
Read the text carefully and answer the questions:
‘The girder of a railway bridge is a parabola with its vertex atthe highest point, 10 m above the ends. Its span is
100m.
Bi)
8)
BI
1
61
65)
(5)
(5)
wi >
>» 1
a i]
‘i
(Find the coordinates ofthe focus ofthe parabola,
(i) Find the equation of girder of bridge an find the length of lat return of girder of bridge
(ii) Find the height ofthe bridge at 20m fom the mid-point.
or
Find the ads of citcle with centre at focus ofthe parabola and pases through the vertex of parabola.
37. Read the text carefully and answer the questions: la)
Ratan wants to open an RD forthe marriage of his daughter, He visited the branch of SBI at sector3, Gurgaon
‘There he made an agreement with the bank.
According to this agreement, he would deposit % 100 x n® every month ( here n =1 to 15). Other terms and
conditions areas follows:
1. He has to pay a minimum of six instalments
I. If he continues the deposit up to 15 months then the bank will pay 20% extra as a bonus.
IIL If he breaks the deposit after 6 months then the bank will pay 10% extra as a honus
IV. Af he breaks the deposit after 10 months then the bank will pay 15% extra as a bonus.
YV. No other interest will be paid by the bank.
(How much amount would be accumulated after 15 months?
a) % 10,00,000 by) % 11,02,500
©) 15,00,000 ) 8 14,40,000
(i) How much total amount would Ratan get after 15 months?
a) ¥ 14,40,000 by % 13,23,000
©) 17,28,000 ) 8 15,00,000
(Gi) How mach total amount would Ratan get if he breaks the deposit after 10 months?
a) €3,50,000 by 8 3,23,000
8347875 a) 83,45,875
OR
How much total amount would Ratan get if he breaks the deposit after 6 months?
) % 60,000 by 850,715
©) 50,000 a) 865,875
38, Read the text carefully and answer the questions: la {In an University, out of 100 students 15 students offered Mathematics only, 12 students offered Statistics only, &
students offered only Physics, 40 students offered Physics and Mathematics, 20 students offered Physics and
Statistics, 10 students offered Mathematics and Statistics, 65 students offered Physics.
(Find the number of students who offered all the three subjects
(ji) Find the number of students who offered mathematics and statistics but not physics.
