Assam Board Class 11 Question Paper 2022 Maths

ASSAM BOARD

QUESTION
PAPER
CLASS 11

Total No. of Printed Pages-12

22E-MATH

2022

MATHEMATICS

Full Marks : 100
Pass Marks : 30

Time : 3 hours
The figures in the margin indicate full marks for the questions

ALLOTMENT OF .MARKS

Q. No. 1 carries 1 mark each lxl0 = 10

Q. No. 2 carries 2 marks each 2xl0 = 20

Q. No. 3 carries 3 marks each 3xl0 = 30

Q. No. 4 carries 4 marks each 4x5 = 20

Q. Nos. 5-8 carry 5 marks each 5x4 = 20

Total= 100

/133 [ Contd.

( 2 )

1xlO==lO
1. Answer the following questions :

(a) Let A= { x Ix is an odd natural number}. Talcing
th e set
' of natural numbers as universal set, write down th e
complement of set A.
~ ~'G'J A= { x Ix uim ~'ill ~1'!,1R11 ~\~ }. ~1,-:,,RJ<fS 'l\~ ' l \ ~
>il<f~;t)~ ~\~ ~'1 ~ A Jf\~Wl1 ~ ~'8~ I

(R) Let A= { a, b, c} and B = { -1, 0, 1}. Find the number of
relations from A to B .
~ ~'G'J A= { a, b, c} ~ B = { -1, 0, 1}. A~ ~ B ~ ~ ~
Jf\~ ~'8~ I

(c) Draw the graph of the trigonometric function sin x for
the interval -2n ~ x ~ 2n.
-2n ~ x ~ 2n '5l~11c1l~ ~~ <fc'R sinx~ car~ '5f\<R ~ 1

37
(d) Find the real part of the complex number (i)- .

(e) Findthe multiplicative inverse of the complex
number -i.

(f) Evaluate :

~f.1"fu~:
8!-5!

/133

( 3 )

(g} What is the 21st term of the sequence defined by
an = (n -1)(20 - n )(3 + n)?
an = (n - 1)(20- n )(3 + n) C<l Jf\~ '51~JJ!i~CUl<I 21~ 91ml ~
~'<:l '?

{h) Find the common ratio of the geometric progression
3 3
3, - ' - ' ....
2 4
3 3
3, - , - , ... ~~~ ~~ J{l~'f ~?flG ~~ I
2 4

(i) If A= { $ }, then find the number of elements in the
power set of A .
~A={$}~,~ A~~~,~~~~~\~~~ I

UJ Find the equation of the line, which makes intercepts
-3 and 2 on the x-axis and y-axis respe_ctively.
x-~ ~ y-~ <l~ -3 ~ 2 ~\icr ~~'1if ~ ~
~'1~'8~1

2. Answer the following questions : 2xl0=20

(a) List all the subsets of the set {-1, 0, 1}.

{ - 1, o, 1} Jf, ~ct1<1 1511t~c<11<1 ;~\~ fat~

1

/133 [ Contd.

( 4 )

(b) Given two sets A and B, draw appropriate Venn
~ diagram for each of the following :

A ~ B ~ ~,~ ffiIT ~'af I ~0-1<1 ~ ~ ~~~ ~ ~ ~ :
(i) (Au B)'
(ii) A' n B'

(c) Prove that

~9<p<{T~

. 2tanx
Sill 2 X =---
l+tan2 x

(d) Convert the complex number i into polar form.

i ~ ~,~ m '511<1>1<1~ ~ ~ I

(e) If nc8 = nc3, then find nc2.

~ nc8 = nC3 ~, ~ nc2 ~1$~ I

(j) Find the value of

iooco - rnoc1 + rnoc2 - rnoc3 + .. . - rnoC99 + rnoc100

100c _ 100c + 100c _ 100c . + _ 100c 100c
0 1 2 3 .. · 99 + 100

(g) Find the coefficient of x 6 in (x +3) 8 .

(x + 3) ¾ x 6<l ~'>I ~1$~ 1

/1 33

( 5 )

(h) In an arithmetic progression (AP), the first term is 2
and the sum of the first two terms is one-fourth of the
sum of the next two terms. Find the 20th term of
the AP.

~tr ~ ~~ ~~ ?fti 2 ~ ~~ 2m ~ • f?~ 2tr m
~ ~~ -~~,Xf I~~~ 2~ ~~~I

(i) Find the equation of the parabola with focus (2, 0) and
directrix x = -2.

~ (2, 0) ~ f.l~l~<PM ~ ' l x = -2 ~'~, ~1'8Ctil<1 ~ ' l
~'6~1

U) Evaluate :
~Rcfu~:
. (x +1) 5 - 1
11m - - -
x➔O X

~- Answer any ten questions : 3xl0=30

Jg) The following figure shows a relationship between the
sets A and B . Write this relation in roster form . Find
the domain and range of the relation :

~ IB~c'G1c~ A ~ B ~,$ ~ ~ ~tr ~ <JiSf~c~ >i~~c'G1 1

<i'm ~ ~~ ~~ >i~~c'G11 '5l1Rc11>~ ~ ~ ~'6-m :
1

A B

/133 [ Contd.

( 6 )

(b) Pro ve tha t

~'l< t>< ll 01

COS ( : + X) + COS ( : - x) = "'2 COS X

(c) Fin d the rea l 0 suc h tha t 3
+ 2is in0 is pu rel y rea l.
l-2 isi n0
3 + 2is in0 ,
1 - 2· . e f~~i~~~~,~e~
I sin ~'

(d) Pro ve tha t

~'t <A l~

m
~ m m- r r
~ Cr · 2 · 5 == 7m
r=O

(e) Fin d the su m up to n ter
ms of the ser ies , wh ere
nth ter m is n (n + l)(n + 4).
~t1 ~~ n~ ~ n (n + l)(n + 4) ~'~ ,
C!l?fl<.61<1 n~ ~
~~ °f. l'fu <A "t I

{f) Fin d the eq ua tio n of the lin e pe
rpe nd icu lar to the lin e
x - 7 y + 5 = 0 an d ha vin g x-i nte
rce pt 3 .
7y + 5 = 0 ~~ cii~~l(.(1 ~ ~ X - ~
X -
3 ~,-ict ~~9 \1'{ <R\
C<t'<-rt 5 WI <1 >1~ ~ <1 "1 tr;faf-,s~ I

/13 3

( 7 )

(g) Find the coordinate of the foci, the leng
th of maj or axis
2 2
and eccentricity of the ellipse ~ + L. = l.
49 36
x2 2
36 = 1 t ~ ~ 'Qr.TI~<fi ii~ ~ ~ ~
-49 + JL
«_ 1·11 ' J,
~~~
~'nl <RJ 1

{h) Find the coordinate of the point which
divides the line
segment joining the points (-2, 3, 5) and (1, -
4, 6) in the
ratio {i) 2 : 3 internally and (ii) 2 : 3 external
ly•
(-2, 3, 5) ~ (1, -4, 6) ~ jj,VTT~ ~~~~~ 2:
3 ~9~
(i) '5ltSR'-"'Bi *
(ii) ~~'-"'Gi ~ ~ ffl ~ ~~ I

(i) Check whe ther the following stat eme nt
is true or not :
"If x, y E 7l are suc h tha t x and y are odd, the
n xy is
odd."

'!la\ '!l mn ~~~Ct:{~~~ :
'~ x, yE 'll ~ x~ y~' ili, ~ xy~ 'ili 1"

lj) Find the mea n deviation abo ut the
med ian for the
following dat a :

X I· 15 21 27 30 35
Ii 3 5 6 7 8

/ 133 [ Contd.

( 8 )

(~) Find the dom ain and ran ge of
the following rea l
function : 1 ½+ 1½ =3

'0cif~ -~ <ff~ ~W 1 i.S ll~ ~ 9frP1<f
~'8 ~ :

f (x) = ✓x 2 ~9

m Find the cen tre and rad ius of the circ le
2x 2 + 2y 2 - X = 0.
1 ½+ l %=3
2x 2 +2y 2 -X = 0 ~ ~ ~ ~~ ~'5 ijl
I

4. Answer any five que stio ns :
4x5 =20

(f3)/ In a gro up of 65 people, 40 like cric
ket , 10 like bot h
cric ket and ten nis . How ma ny like ten
nis ? How ma ny
like ten nis only and not cricket?
2+2 =4
65 ~ \!)tr ffl 40 ~ ~ iSM 9ml, 10
~ ~ ~
~ ~~ iSM 9ml I f<t>~HIStC.i CWPf iSM 9ml
? f<t>~l~IStC--1 m ~
i5M 9ml, m
~ '5Taf .:n rro 7··
9

{b) Define the fun ctio n f: JR ➔ JR by
f (x) = 3 \;/ x ER .
Dra w the gra ph of the fun ctio n f and
find the dom ain
and ran ge of f.
2+ 1+ 1=4
f :iR ➔ JR -~~ ~~ l!lt ~ wr ~ / (x) = 3, ~
x E iR ~ <T1Vl I f14 (?i!'Q[ ~<fi1 ~l<f ~~ ~ ff

l<t fi'fiJ
~ I

/13 3

{ 10 )

if; If

X.< 0
X =O
x.. >0

then for vrha t vah.1 e{s ) of. o.. does 1i:m f (x 4
) eYJS't?
z ~a

p x t +l,, x<O
f {X } = t O > X =0
\_t x ( - 1 ; X > 0

a<t~ -t\-"'kt ~ - lim f ( x ) ~ ~ ?
x--;-a

5. Find the gen eral s olut ion of the follo wing
equa tion 5

cos3 x + cos x - cos 2 x = 0

3.
If tan x = - -rr < x < -3 :ri; , then find the valu e of s in.:_
X: X
4' 2 " cos.-=- ..
2 - 2 -
X
tan -.
2 2 -::-2+ 1. =5

3
°W tan X = -~ 3n . X
rt < X < - ~ ~ C:~ <.~ sm- ,. cosX-. tan
. X
-~ ~,'""\.
4 '2 2 · ? 2

/ 133

( 11 )

6. So lve the fol low ing sys tem of
ine qu ali tie s gra ph ica lly 5
~ '5l> i~~ 2! ~ ~ ~~ <fl<TI :

3x +2 y ~ 12
X ~ 1

y~ 2

OR /i5 f~
So lve the fol low ing sys tem of ine
qu ali tie s gra ph ica lly 5
~ '5Pi~<:fi1 Zi ~ ~ ~~ ~
:

X +2 y ~ 8

2x + y ~ 8
x2' .:0
y 2'.: 0

7. Fin d the der iva tiv es of the fol
low ing fun cti on s w. r.t . x :
2+ 3= 5

1
(a) -
x2

(b) sin2 x

OR /i5 T~

Fin d the der iva tiv e of f (x) = x +~ fro
m the fir st pri nci ple . 5
X

/13 3
[ Co ntd .

( 12)

8. Find the mean and variance for the following data :
2½+2½ =5

X t· 92 93 97 98 102 104 109
Ji 3 2 3 2 6 3 3

OR/~ ~

The mean and variance of seven observations are 8 and 16
respectively. If five of the observations are 2, 4, 10, 12 and
14, then find the remaining two observations. 5

~ ~~ 111~ ~ ~q ~ 8 ~ 16. ~ ~ ~~ ifR
2, 4, 10, 12 ~ 14 ~'~ ~ ~ ~~ 1fR ~'8~ I

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