MBOSE Class 11 Question Paper 2022 for Maths

Total No. of Printed Pages ––8 (2)
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3. If A = { 3, 6, 9, 12, 15, 18, 21 }
2022 B = { 4, 8, 12, 16, 20 }
find (i) A  B and (ii) A – B.
MATHEMATICS

Full Marks : 80
4. Find the modulus of the complex number  2  5i
Time : 3 hours

General Instructions :
1. All questions are compulsory. 5. Solve 3x  8  2 when x is an integer.

2. The question paper consists of 36 questions divided into
four Sections A, B, C and D. n n n
6. If C 8  C 2 , Find C 2 .
Section A consists of 20 questions of 1 mark each.
Section B consists of 6 questions of 2 marks each.
Section C consists of 6 questions of 4 marks each. 7. Find the slope of the straight line parallel to the
Section D consists of 4 questions of 6 marks each. straight line passing through the points (–2, 3) and
(8, –5).
3. There is no overall choice. However there will be internal
choices for 4 marks questions and 6 marks questions.
8. Find the equation of a circle with centre (–2, 3) and
4. Use of calculator is not permitted. radius 4.

SECTION – A 9. If the set of natural numbers is the universal set, then
find the complement of the set
{ x : x is a prime number }
1. Write the set in the set -builder form {1, 4, 9, ......,100}.

2. Write the set { x : x  R,  4  x  6 } as interval. 10. Find the radian measure of 240o

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11. Write the contrapositive and converse of the statement.
x3  8
18. Evaluate lim
“If x is a prime number, then x is odd.” x 2 x  2

19. How many 3 digit numbers can be formed from the
12. Write the following statement in the form “if–then” digits 1, 2, 3, 4 and 5 assuming the repetition of the
digits is allowed?
“A quadrilateral is a parallelogram if its diagonals
bisect each other.”
1
20. If E and F are events such that P(E)  1 , P(F)  and
4 2
1
P(E  F)  find P(E or F).
13. Find the median of the data 6, 7, 10, 12, 13, 4, 8, 12. 8

SECTION – B
2 6
14. Write the general term in the expansion of ( x  y ) .

21. Prove that
       
15. If the set A has 3 elements and the set B = { 3, 4, 5 }, cos   x  cos   y   sin  x  sin  y   sin( x  y )
4  4  4  4 
then find the number of elements in A  B .

22. Express the complex number
16. Find the domain and range of the relation R defined by 3
1 
R = {(x, x + 5) : x  { 0, 1, 2, 3, 4, 5 }}   3i  in the form a  ib .
3 

17. Find the nth term of the series 23. Show that the points P(–2, 3, 5), Q(1, 2, 3) and
R (7, 0, –1) are collinear.
3  12  5  22  7  32  ....................

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24. Find the sum of odd integers from 1 to 2001. 28. The sum of first three terms of a G.P. is 16 and the
sum of next three terms is 128. Determine the first
term and the sum of n terms of the G.P.

25. Find the co-ordinates of the focus, the vertex, the axis Or
and the length of the latus rectum of the parabola Find the sum to n terms of the series whose nth term
y 2  12x . is given by n2 + 2n.

29. Convert the complex number –1–i into polar form.
26. One card is drawn from a well shuffled deck of 52
cards. If each outcome is equally likely, calculate the Or
probability that the card will be In how many ways one can select a cricket team of
eleven players from 17 players in which only 5 bowlers
(i) not an ace
can bowl if each cricket team of 11 must include
(ii) not a black card. exactly 4 bowlers.

30. Find the equation of the hyperbola whose foci are
SECTION – C (5, 0 ) and the transverse axis is of lenght 8 units.

Or
27. Prove that Find the equation of the ellipse with foci (5, 0 ) and
 9 3 5 the lenght of major axis is 26 units.
2 cos cos  cos  cos 0
13 13 13 13

Or 31. Find the general solution of the equation
cos 4x  cos 2x.
Prove that
cos 4x  cos 3x  cos 2x
 cot 3x
sin 4x  sin 3x  sin 2x
sin x  cos x
32. Find the derivative of .
sin x  cos x

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SECTION – D Or
The diameters of circles (in mm) drawn in a design
33. Using the principle of mathematical induction prove are given below
1 1 1 1 1
that    ............  n  1  n . Diameters 33–36 37–40 41–44 45–48 49–52
2 4 8 2 2
No of Circles 15 17 21 22 25

34. Solve the system of inequalities graphically Calculate the standard deviation and the mean
diameter of the circle.
3x  4y  60, x  3y  30, x  0, y  0.

Or

Find (x  1)6  (x  1)6 . Hence or otherwise evaluate
 2  1   2  1
6 6

35. In a survey it was found that 21 people liked product
A, 26 liked product B and 29 liked product C. If 14
people liked products A and B, 12 people liked
products C and A, 14 people liked products B and C
and 8 liked all the three products. Find how many
liked products C only.

36. Calculate the mean, variance and standard deviation
for the following distribution

Class 30–40 40–50 50–60 60–70 70–80 80–90 90-100
Frequency 3 7 12 15 8 3 2

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