HBSE Class 11 Question Paper 2021 Maths

Code No. 1531
CLASS : 11th (Eleventh) Series : 11-April/2021
Roll No.











xf.kr
MATHEMATICS
[ fgUnh ,oa vaxzsth ek/;e ]
[ Hindi and English Medium ]
(Only for Fresh/School Candidates)

le; : 2 21 ?k.Vs ] [ iw.kk±d : 80

Time allowed : 2 21 hours ] [ Maximum Marks : 80

• Ñi;k tk¡p dj ysa fd bl iz'u-i= esa eqfnzr i`"B 16 rFkk iz'u 13 gSaA
Please make sure that the printed pages in this question paper are 16 in number
and it contains 13 questions.
• iz'u-i= esa lcls Åij fn;s x;s dksM uEcj dks Nk= mÙkj-iqfLrdk ds eq[;-i`"B ij fy[ksaA
The Code No. on the top of the question paper should be written by the candidate
on the front page of the answer-book.
• Ñi;k iz'u dk mÙkj fy[kuk 'kq: djus ls igys] iz'u dk Øekad vo'; fy[ksaA
Before beginning to answer a question, its Serial Number must be written.
• mÙkj-iqfLrdk ds chp esa [kkyh iUuk / iUus u NksMsa+A
Don’t leave blank page/pages in your answer-book.
• mÙkj-iqfLrdk ds vfrfjDr dksbZ vU; 'khV ugha feysxhA vr% vko';drkuqlkj gh fy[ksa vkSj fy[kk mÙkj u
dkVsaA
Except answer-book, no extra sheet will be given. Write to the point and do not
strike the written answer.
• ijh{kkFkhZ viuk jksy ua0 iz'u&i= ij vo'; fy[ksaA
Candidates must write their Roll Number on the question paper.
• d`i;k iz'uksa dk mÙkj nsus lss iwoZ ;g lqfuf'pr dj ysa fd iz'u-i= iw.kZ o lgh gS] ijh{kk ds mijkUr bl
lEcU/k esa dksbZ Hkh nkok Lohdkj ugha fd;k tk;sxkA
Before answering the question, ensure that you have been supplied the correct and
complete question paper, no claim in this regard, will be entertained after
examination.

1531 P. T. O.

(2) 1531
lkekU; funsZ'k %
(i) lHkh iz'u vfuok;Z gSaA
(ii) bl ç'u-i= esa 13 ç'u gSa] tks fd pkj [k.Mksa % ^v*
^v*] ^c*] ^l* ,oa ^n* esa ck¡Vs x, gSa %
[k.M ^v* % bl [k.M ds ç'u la[;k 1 esa pkyhl (1-40) oLrqfu"B çdkj ds ç'u gSaA çR;sd
ç'u 1 vad dk gSA
[k.M ^^cc* % bl [k.M esa ç'u la[;k 2 ls 7 rd dqy N% ç'u gSaA çR;sd ç'u 2 vadksa dk gSA
[k.M ^^ll* % bl [k.M esa ç'u la[;k 8 ls 11 rd dqy pkj ç'u gSaA çR;sd ç'u 4 vadksa dk
gSA
[k.M ^^nn* % bl [k.M esa ç'u la[;k 12 ,oa 13 dsoy nks ç'u gSaA çR;sd ç'u 6 vadksa dk gSA
(iii) [k.M ^n* ds nksuks
uksa ç'uksa esa vkUrfjd fodYi fn;k x;k gSA vkidks dsoy ,d fodYi pquuk gSA
General Instructions :

(i) All questions are compulsory.

(ii) This question paper consists of 13 questions which are divided into four
Sections : 'A', 'B', 'C' and 'D' :

Section 'A' : Question No. 1 of this Section has forty (1-40) Objective Type
questions. Each question carries 1 mark.

Section 'B' : This Section contain six questions from Question Nos. 2 to 7.
Each question carries 2 marks.

Section 'C' : This Section contain four questions from Question Nos. 8 to
11. Each question carries 4 marks.

Section 'D' : This Section contain only two questions, Question Nos. 12 &
13. Each question carries 6 marks.

(iii) In both the questions of Section 'D' internal choices are given. You have to
attempt only one alternative.
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(3) 1531
SECTION – A

[k.M – v
fuEufyf[kr oLrqfu"B ç'uksa ds mÙkj nsa %
Answer the following objective type questions :

1. (1) A = {x : x ,d vHkkT; la[;k gS }] rks leqPp; A ,d ----------- leqPp; gSA 1

¼ifjfer] [kkyh] vuUr½

A = {x : x is a prime number}, Set A is ………….. set. (Finite, Null, Infinite)

(2) ;fn A = {a, e, i, o, u }, rks leqPp; A ds mileqPp;ksa dh la[;k gS -----------A 1

{5, 20, 32, 120}

A = {a, e, i, o, u }. Number of subsets of set A is …………. . {5, 20, 32, 120}

π π π  7 13 13 13 
(3) 2 sin2 − cos 2 + tan2 dk eku -------------- gSA  , , ,−  1
3 6 6  12 12 4 12 

π π π
The value of 2 sin2 − cos 2 + tan2 is equal to …………… .
3 6 6

 7 13 13 13 
 , , ,− 
 12 12 4 12 

(4) ;fn A = {a, b, c }, B = {a, b, c, d, e }, rks A ∩ B = ……….. . 1

¼A, B, u A u B)

If A = {a, b, c }, B = {a, b, c, d, e }, then A ∩ B = ……….. .

(A, B, neither A nor B)

1531 P. T. O.

(4) 1531
(5) ,d fo|ky; esa 20 f'k{kd gSa tks xf.kr ;k HkkSfrdh i<+krs gSaA muesa ls 12 xf.kr vkSj 4 nksuksa
fo"k; xf.kr vkSj HkkSfrdh i<+krs gSaA tks f'k{kd HkkSfrdh i<+krs gSa] mudh la[;k gS --------------A 1

In a school there are 20 teachers who teach Mathematics or Physics. Of
these 12 teach Maths and 4 teach Maths and Physics. The number of
teacher who teach Physics are ………….. .

(6) ;fn A = {0, 1, 2, 3, 4, 5, 6, 7}A ,d laca/k R tks A ij ifjHkkf"kr gS R = {(x, y) : y =
x + 5, x, y ∈ A}, rks laca/k A dk ijkl gS {………..} A 1

Let A = {0, 1, 2, 3, 4, 5, 6, 7}. A relation R is defined from A to A where
R = {(x, y) : y = x + 5, x, y ∈ A}. Then the relation R has the range
{………..}.

(7) ;fn 40 cm O;kl okys o`Ùk dh ,d thok 20 cm gSA y?kq pki dh yEckbZ gS --------- lseh A 1
In a circle of diameter 40 cm, the length of a chord is 20 cm. The length
of minor arc of chord is …………. cm.

(8) ;fn tan x = − 5 , x f}rh; prqFkk±'k esa gS] rks sin x dk eku gS % 1
12

5 5
(A) (B) −
13 13

12 12
(C) (D) −
13 13

5
If tan x = − , x lies in 2nd quadrant, then the value of sin x is :
12

5 5
(A) (B) −
13 13

12 12
(C) (D) −
13 13

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(5) 1531

(9) ;fn tan x = 3 , rks cos 2x dk eku gS % 1
4

4 8
(A) (B)
5 5

7
(C) (D) buesa ls dksbZ ugha
25

3
If tan x = , then the value of cos 2x is :
4

4 8
(A) (B)
5 5

7
(C) (D) None of these
25

sin 3x + sin 5x
(10) dk x = π ij eku gS % 1
cos 3x + cos 5x 16

(A) ∞ (B) 0

(C) 1 (D) buesa ls dksbZ ugha

sin 3x + sin 5x π
The value of at x = is :
cos 3x + cos 5x 16

(A) ∞ (B) 0

(C) 1 (D) None of these

1531 P. T. O.

(6) 1531
(11) cos 75° dk eku gS % 1

3 +1 3 −1
(A) (B)
2 2 2 2

3 +1
(C) (D) buesa ls dksbZ ugha
2

The value of cos 75° is :

3 +1 3 −1
(A) (B)
2 2 2 2

3 +1
(C) (D) None of these
2

 3π   3π 
(12) cos + x  − cos −x dk eku cjkcj gS % 1
 4   4 

(A) − 2 sin x (B) 2 sin x

(C) cos 2x (D) buesa ls dksbZ ugha

 3π   3π 
cos + x  − cos − x  is equal to :
 4   4 

(A) − 2 sin x (B) 2 sin x

(C) cos 2x (D) None of these

(13) ;fn 4x + i(3x − y) = 3 − 6i, rks Øe'k% x vkSj y dk eku gS ………….., …………..A 1

If 4x + i(3x − y) = 3 − 6i, then the value of x and y are ………….., …………..
respectively.

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(7) 1531
(14) ;fn 3(2 − x) ≥ 2(1 − x), rks x dk eku ftl varjky esa gS] og gS % 1

(A) (−∞, − 4) (B) (−∞, 4]

(C) [4, ∞) (D) [−4, ∞)

If 3(2 − x) ≥ 2(1 − x), then the value of x lies in the interval :

(A) (−∞, − 4) (B) (−∞, 4]

(C) [4, ∞) (D) [−4, ∞)

1 1 x
(15) x dk eku ftlds fy, + = gS] og gS --------------A 1
6! 7! 8!

1 1 x
The value of x for which + = is …………. .
6! 7! 8!

(16) ;fn fdlh xq.kksÙkj Js<+h (G.P.) dk nok¡ in 3(2)n −1 ] rks mldk lkoZ vuqikr gS -----------A 1

If nth term of a G.P. is 3(2)n −1 , then its common ratio is ………….. .

1
(17) vkSj 729 ds chp xq.kksÙkj ek/; gS ---------------A 1
9

1
The geometric mean between and 729 is …………. .
9

(18) dkWEIysDl uEcj (2 + 3i )2 dk ekikad Kkr djsaA 1

Find the modulus of complex number (2 + 3i )2 .

(19) ;fn n C 5 = n C 7 ] rks n dk eku gS --------------A 1

If n C 5 = n C 7 , then the value of n is ………….. .

1531 P. T. O.

(8) 1531
(20) 5 vkSj 25 ds chp 3 lekUrj ek/; gSa Øe'k% --------------] --------------] --------------A 1

Three arithmetic means between 5 and 25 are …………., ………….,
………….. respectively.

(21) ;fn 3 − 4i dk xq.kkRed çfrykse x + iy gS] rks x vkSj y ds eku gSa ------------] -----------A 1

If multiplicative inverse of 3 − 4i is x + iy, then the values of x and y
are ………….., ………….. .

(22) ,d "kV~dks.k (Hexagon) ds fod.kks± dh la[;k gS ---------------A 1

The number of diagonals in an hexagon is ………….. .

(23) ;fn a, b, c lekarj Js<+h A. P. esa gSa] rks fuEu esa dkSu-lk lR; ugha gS \ 1

a +c
(A) b 2 = ac (B) b=
2
(C) b−a=c−b (D) a − b = b − c
If a, b, c are in A. P., which of the following is not true ?

a +c
(A) b 2 = ac (B) b=
2

(C) b−a=c−b (D) a − b = b − c

(24) ;fn a vkSj b nks fHkUu /ku la[;k,¡ gSa] rks fuEu esa ls dkSu-lk lR; gS \ 1

(A) A=G (B) A<G

(C) A>G (D) A = 2G

If a and b are two distinct positive numbers, then which of the following is
true ?

(A) A=G (B) A<G

(C) A>G (D) A = 2G

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(9) 1531
(25) ;fn ,d js[kk fcUnq (1, 2) vkSj (3, 5) ls xqtjrh gS] rks bldh ço.krk gS % 1

2 3
(A) (B)
3 2

2 3
(C) − (D) −
3 2
If a straight line passes through the points (1, 2) and (3, 5) then its slope
is :
2 3
(A) (B)
3 2
2 3
(C) − (D) −
3 2

(26) ijoy; x 2 = −8y dh ukfHk ds funsZ'kkad gSa % 1

(A) (2, 0) (B) (0, 2)
(C) (−2, 0) (D) (0, −2)
The coordinates of the focus of the parabola x 2 = −8y is :

(A) (2, 0) (B) (0, 2)

(C) (−2, 0) (D) (0, −2)

(27) o`Ùk x 2 + y 2 − 8x + 12y − 12 = 0 ds dsUæ ds funsZ'kkad Kkr dhft,A 1

Find the coordinates of the centre of the circle x 2 + y 2 − 8x + 12y − 12 = 0.

(28) nh?kZo`Ùk 4x 2 + y 2 = 400 dh nh?kZv{k dh yEckbZ gS % 1

(A) 10 (B) 20

(C) 40 (D) 400

The length of major axis of the ellipse 4x 2 + y 2 = 400 is :

(A) 10 (B) 20

(C) 40 (D) 400

1531 P. T. O.

( 10 ) 1531
(29) fcUnq (2, 3) ls tkus okyh vkSj /ku x-v{k ls 45° dk dks.k cukus okyh js[kk dk lehdj.k gS % 1

(A) x−y+1=0 (B) x+y−5=0

(C) x+y−1=0 (D) buesa ls dksbZ ugha

The equation of line passing through (2, 3) and making an angle 45° with
positive x-axis is :

(A) x−y+1=0 (B) x+y−5=0

(C) x+y−1=0 (D) None of these

(30) js[kk 4x + 3y = 12 x-v{k dks ftl fcUnq ij feyrh gS] og gS --------------A 1

The line 4x + 3y = 12 meets x-axis at the point …………. .

(31) fcUnq (1, 1) ls 5x + 12y + 9 = 0 ij Mkys x;s yEc dh yEckbZ gS -------------- A 1

The length of perpendicular from (1, 1) to the line 5x + 12y + 9 = 0
is …………. .

(32) nh?kZo`Ùk 9x 2 + y 2 = 225 dh mRdsUærk Kkr dhft,A 1

Find the eccentricity of the ellipse 9x 2 + y 2 = 225 .
tan x
(33) lim = .......... tgk¡ x jsfM;u eki esa gSA 1
x →0 x

tan x
lim = .......... where x is in radians.
x →0 x

1 + x −1
(34) lim dk eku gS -------------- A 1
x →0 x

1 + x −1
lim is …………. .
x →0 x

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( 11 ) 1531
(35) x 5 (3 − 6x 9 ) dk x ds lkis{k vodyt Kkr dhft,A 1

Find derivative of x 5 (3 − 6x 9 ) w.r.t. x

(36) 3 cot x + 5 cosec x dk x ds lkis{k vodyt gS % 1

(A) 3 cos ec 2 x − 5 cosec x cot x

(B) − 3 cos ec 2 x − 5 cosec x cot x

(C) − 3 cos ec 2 x + 5 cosec x cot x

(D) 3 cos ec 2 x + 5 cosec x cot x

The derivative of 3 cot x + 5 cosec x w. r. t. x is :

(A) 3 cos ec 2 x − 5 cosec x cot x

(B) − 3 cos ec 2 x − 5 cosec x cot x

(C) − 3 cos ec 2 x + 5 cosec x cot x

(D) 3 cos ec 2 x + 5 cosec x cot x

(37) 9, 5, 3, 12, 10, 18, 4, 7, 19 dk ekf/;dk (Median) ds lkis{k ek/; fopyu
gS -------------A 1

The mean deviation of 9, 5, 3, 12, 10, 18, 4, 7, 19 about Median
is ……………. .

(38) ;fn A vkSj B nks ?kVuk,¡ gSa] rks fuEu esa ls dkSu-lk lR; ugha gS \ 1

(A) P(A ∩ B) ≤ P(A ∪ B) (B) P(A ∩ B) ≤ P(A)

(C) P(A) ≤ P(A ∩ B) (D) P(B) ≤ P(A ∪ B)

1531 P. T. O.

( 12 ) 1531
If A and B are any two events, then which of the following is not true ?

(A) P(A ∩ B) ≤ P(A ∪ B) (B) P(A ∩ B) ≤ P(A)

(C) P(A) ≤ P(A ∩ B) (D) P(B) ≤ P(A ∪ B)

(39) ;fn A vkSj B nks ?kVuk,¡ gSa ftlesa P (A ) =
1
] P (B ) = 7 vkSj P (A ∩ B ) = 3 ] rks
2 10 5
P ( A ∪ B ) Kkr dhft,A 1

1 7
If A and B are two events such that P (A ) = ] P (B ) = and
2 10
3
P (A ∩ B ) = , then find P ( A ∪ B ) .
5
2
(40) ;fn fdlh ?kVuk ds gksus dh çkf;drk gS] rks ml ?kVuk ds ^u gksu*s dh çkf;drk gS % 1
11

2
(A) 0 (B)
11

9 −2
(C) (D)
11 11

2
If is the probability of an event then the probability of the event
11
"not A" is :
2
(A) 0 (B)
11
9 −2
(C) (D)
11 11

SECTION – B

[k.M – c

2. fl) dhft, % 2

sin x + sin 2x + sin 3x
= tan 2x
cos x + cos 2x + cos 3x

1531

( 13 ) 1531
Prove that :

sin x + sin 2x + sin 3x
= tan 2x
cos x + cos 2x + cos 3x

 19π 
3. tan  dk eku Kkr dhft,A 2
 3 

 19π 
Find the value of tan .
 3 

4. ;fn x + iy = 1 + 2i ] rks fl) djsa fd x 2 + y 2 = 1 A 2
2+i

1 + 2i
If x + iy = , prove that x 2 + y 2 = 1 .
2+i

5. xq.kksÙkj Js<+h (G. P.) 2, 2 2 , 4, …… dk dkSu-lk in 128 gS \ 2

Which term of the G. P. 2, 2 2 , 4, …… is 128 ?

6. js[kkvksa x − 2y + 5 = 0 vkSj x + 3y − 5 = 0 ds chp dk dks.k Kkr dhft,A 2

Find the angle between the lines x − 2y + 5 = 0 and x + 3y − 5 = 0.

sin x
7. ;fn f (x ) = , rks f ′(x ) Kkr dhft,A 2
1 + cos x

sin x
If f (x ) = , find f ′(x ) .
1 + cos x

1531 P. T. O.

( 14 ) 1531
SECTION – C

[k.M – l

8. fl) dhft, % 4

cot 4x (sin 5x + sin 3x )
=1
cot x (sin 5x − sin 3x )

Prove that :

cot 4x (sin 5x + sin 3x )
=1
cot x (sin 5x − sin 3x )

2x + 3 dy
9. ;fn y = 2
, rks Kkr dhft,A 4
4x + 5 x + 6 dx

2x + 3 dy
If y = , find .
4x 2 + 5 x + 6 dx

10. fuEufyf[kr vk¡dM+ksa dk çeki fopyu (S.D.) Kkr dhft, % 4

x 3 8 13 18 23 28

f 7 10 15 10 6 2

Find Standard Deviation of the following :

x 3 8 13 18 23 28

f 7 10 15 10 6 2

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( 15 ) 1531
11. ,d ijh{kk nks ç'ui=ksa A vkSj B ij vk/kkfjr gSA fdlh ;kn`PN;k pqus x;s fo|kFkhZ ds A esa ikl gksus
dh çkf;drk 80% vkSj B esa ikl gksus dh 70% gSA ;fn mlds fdlh A ;k B esa ikl gksus dh
çkf;drk 95% gS] rks mlds nksuksa esa ikl gksus dh çkf;drk Kkr dhft,A 4

An entrance exam is based on two papers A and B. The probability of passing
one paper A by a randomly selected student is 80% and passing paper B is
70%. The passing at least A or B is 95%. Find the probability that the student
passes both the papers.

SECTION – D

[k.M – n

12. ;fn fdlh xq.kksÙkj Js<+h ds igys rhu inksa dk ;ksx 49 vkSj mudk xq.kuQy 1 gks] rks G. P. dk
15
lkoZ vuqikr vkSj os rhuksa in Kkr dhft,A 6

49
The sum of first three terms of a G. P. is and their product is 1, then find
15
the common ratio and the terms of G. P.

vFkok

OR

;fn a, b, c, d xq.kksÙkj Js<+h G. P. esa gks]a rks fl) dhft, fd (a n + b n ) ] (b n + c n ) ]
(c n + d n ) Hkh G. P. ¼xq.kksÙkj Js<+h½ esa gksaxsA

If a, b, c, d are in G. P., then prove that (a n + b n ) ] (b n + c n ) ] (c n + d n ) are also
in G. P.

13. fcUnq (1, 2) ls js[kk x − 3y + 4 = 0 ij Mkys x;s yEc ds ikn fcUnq ds funsZ'kkad Kkr dhft,A 6

Find the foot of the perpendicular from (1, 2) to the line x − 3y + 4 = 0 .

1531 P. T. O.

( 16 ) 1531
vFkok
OR

ml nh?kZo`Ùk dk lehdj.k Kkr djsa ftldk 'kh"kZ (0, ±13) ij vkSj ukfHk (0, ±5) ij gksA
Find the equation of the ellipse whose vertices are (0, ±13) and foci (0, ±5).

S

1531