Assam Board Class 11 Question Paper 2023 Maths

ASSAM BOARD
QUESTION
PAPER
2023

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Total No. of Printed
Pages-12 23E -MATH

2023

MATHEMATICS

Full Marks: 100
Pass Marks : 30

Time: 3 hours

The figures in the margin indicate full marks for the questions
ALLOTMENT OF MARKS

0. No. 1carries 1 mark each 1×10 = 10

Q. No. 2carries 2marks each 2x10 = 20

0. No.3 carries 3 marks each 3x10 = 30

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

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

Total = 100

/136 [Contd.

|2 )
1x10=10
1. Answer the following questions :

(a) Let A={x|x is a letter in the word FOLLOW },
B={y|y is a letter in the word WOLF}. Is A=B?
I 7 A={x| FOLLOW *A x qbi }, B={yl WOLF
* y QDI }. A= B AA?

(b) If A={0}, write P(A).
ÍA A={ }4, P(A) fa1 |

(c) Write the general solution of cosx = 0.

(d) Express (022 in a +ib form.
(j2022 a+ib S |I

(e) What is the number of permutations of n objects
with pobjects of same kind and rest all different?

2
() For what values of x are the numbers -=, x, -7 in GP?
2

2 7

/136

(3 )
(g) Fill in the blank :

The value of "Co +"C, + *. +"Cn 18

(h) Define ellipse.

(9 Write the standard equation of a circle with centre
(h, k) and radius r.

(i) If Ais an event such that P(A) = then find P (not A),
10'

10
P(Aa2) feIA?

2. Answer the following questions : 2x10=20

(a) Write the domain and range of the function
fx)=|x-1,

(b) If A={(1, -1, then find AxAxA.

/136 |Contd.

(4 )

Venn diagram :
() Prove by using

) =(An B)u (A-B)
A
(i) AUB- A)= AUB
(d) Let A={1, 2, (3, 4},
5). Which of the following
statements are incorrect and whv?
13' A=(1, 2, {3, 4}, S}. ONAR GS qO q fA?

() (3, 4) cA
(i) {1, 2, 5} eA
(i) e A
(iv) c A
(1+i)
(e) =1, then find the least positive integral value
of m.

lo
() Write the 4th term in the
expansion of
10

(g) In how many of the distinct
in MISSISSIPPI do the four permutations
of the letters
I's not come together?

/136

(5 )
instalment as
(n) A man starts repaying a loan with first
1,000. If he increases the instalment by 5 every
month, what amount wil1 he pay in the 30th
instalment?

() If three points (h, 0), (a., b) and (o, k) lie on a line, then
b
show that +=1,.
h k

a b
=1.
h k

G) Find dy where
dx

dy
dx

-COS X
y=
sinx

3. Answer the following questions (any ten): 3x10=30

(a) Draw the graph of the function f, where

|1-x, x<0
f<) =1+x, x>0
|1 , x=0

/136 [Contd.

(6)

example each of empty set, finite set and
(b) Give one
infinite set.

(c) Prove that

3x
sin 3x + sin 2x - Sin x = 4 sin xc0S.2 COS

(d) () What do you mean by principal solutions of a
trigonometric equation? 1

(ü) Find the general solution of tan 2x= -cot x+ 2

T
tan 2x=-cot: 3

(e) Find the modulus and argument of the complex
1
number
1+i

1
1+i

) How many numbers greater than 100000 can be
formed by the digits 1, 2, 0, 2, 4, 2?
1, 2, 0, 2, 4, 2yODI IRK R 100000 G8 fAOI

/136

(7)

(g) Show that the middle term in the expansion of (1 + x)n
is 13.5. .... (2n-n,n where n is a positive
n! integer.

13.5. .... (2n-)nn
n!

(R) The sum of two numbers is 6 times their geometric
mean. Show that the numbers are in the ratio
(3 +2V2) : (3 -2/2),

FDNaq (3 +2/2) :(3-2/2)
() () Find the equation of the parabola which is
symmetric about X-axis and passes through the
point (-2, - 3). The vertex of the parabola is the
origin. 2

(ü) Find the coordinates of the foci and the length of
the latus rectum of the hyperbola 92-4x =36. 1

) If the origin is the centroid of the triangle ABC with
vertices A(2a, 2, 6), B(-4, 3b, -10) and C(8, 14, 2c),
then fnd the values of a, b and c.

A(2a, 2, 6), B(-4, 3b, -10) C(8, 14, 2c) -E

/136 | Contd.

(8)

the following statement is true by the
(k) Show that
contrapositive :
method of
integer and x2 1S even, then x is
P:If x is an also even.

P:.
Z + +1
=1+i then find
(9 If z =2-i z, |Z1 -Z +1

ZË +Z +1|
Z =2-i, z, =1+i, |Z1 - +1

4x5-20
(any fue):
4. Answer the following questions

need not imply B=C.
1
that AnB= AnC
(a) () Show
B=CbI
CRSA1 AnB=AnCa
of 60 people, it was found that 25
(ü) In a survey read newspaper T
people read newspaper H, 26
newspaper I, 9 read both HandI 11 read
26 read
H and T, 8 read both T and I. 3read all the
both
number of people who
three newspapers. Find the 3
read exactly one newspaper.

9A H YI* TYRA 9,
C9, 9 GA H IF IGA \C5, 11

/136

(9 )

(b) Solve the following system of inequalities graphically : 4

X+ysl0
X+y21
X-ys0
x>0, y>0
(c) () Find the limits (if exist) : 2

lim tan 2x
X
2

(ü) If the function f(x) satisfies lim flx)-2 = T, then
x’1 x-1
evaluate lim
X’1
f(). 2

f) PaAOA lim f)-2
x’1 x²-1
lim f(x3 A4 tasqII
X’1

(d) Two students Anil and Ashim appeared in an
examination. The probability that Anil will qualify the
examination is 0-05 and that Ashim will qualify the
examination is 0-10. The probability that both will
qualify the examination is 0-02. Find the probability
that
(i) both Anil and Ashim will not qualify the
examination;
(ü) at least one of themn will not qualify the
examination. 3+1=4

/136 [Contd.

( 10 )

(e) If the 4-digit numbers greater than 5000 are
randomly
formed from the digits 0, 1, 3, 5 and 7, what is the
probability of forming a number divisible by 5, when
() the digits are repeated;
(ü) the repetition of the digits is not allowed? 4
0, 1, 3, 5 F 7 RAK I43 5000t$ yET (II

() Find the sum up to n
terms of the series
5+11+19+29 +41+ 4

5+11+19+29 +41+ AcoR n ota ISja tsq |
5. (a) If in two circles, arcs of the
same length
angles 60° and 75° at the centre, then find thesubtend
ratio of
their radii.
3

/136

| 11 )
(b) Find the
degree measure corresponding to the radian
measure 4. (Use = 2

22
7

O. PTove that 2.7" +35"-5 is diiaible by 24 for all neN, 5

Or/qeI
Using the principle of mathematical induction for all neN,
prove that

1,1 1 1
14 47 710 (3n-2)(3n +1) 3n +1

11. 1 1 n

14 47 710 (3n -2)(3n +1) 3n +1

7. (a) If pand qare the lengths of perpendiculars from
the origin to the lines xcos -y sin = kcos 20 and
x sec® + ycosec® =k respectively, then prove that
p +4q =k2. 3

xCOs- ysin = kcos 20
xsec® + ycosect =k aig G2 p Fq G19

/136 [Contd.

( 12 )

quantifier in the following statement and
(b) Identify the
write the
negation of the statemnent : 2
There exists a number which is equal to its square.

deviation for
8. Calculate the mean, variance and standard
the following frequency distribution
5

Class 30-40 40-50 | 50-60 60-70 70-8080-9090-100

Frequency 3 7 12 15 3 2

Or/ RAI

Calculate the mean deviation about median age for the age
distribution of 100 persons given below :

Age 16-2021-25 26-3031-35|36-4041-45|46-50|51-55
Number
5 12 14 26 12 16 9

***

/136 C23