MBOSE Class 11 Question Paper 2023 for Mathematic

Total No. of Printed Pages ––8 (2)
HS/XI/A. Sc. Com/M/23

x 2 5 1
2023 3. If   1, y     ,  , find the values of x and y. 1
3 3 3 3

MATHEMATICS

Full Marks : 80 4. Find the degree measure corresponding to the radian
11  22 
Time : 3 hours measure : . use   . 1
16  7 

General Instructions :
1. All questions are compulsory. 5. Find the value of cos (–1410o). 1
2. The question paper consists of 36 questions divided into
four Sections A, B, C and D.
6. Express the complex number i 19 in the form (a  ib ) . 1
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. Solve the equation x 2  3x  9  0 . 1
Section D consists of 4 questions of 6 marks each.

3. There is no overall choice. However there will be internal 8. Solve : 24x<100, when x is an integer. 1
choices for 4 marks questions and 6 marks questions.

4. Use of calculator is not permitted. 9. Write the first five terms of the sequence whose nth
2n  3
term is a n  . 1
6
SECTION – A

1. If R is the set of real numbers and Q is the set of
2 7
rational numbers, then what is R – Q? 1 10. If , x, are in Geometric Progression, find the value
7 2
2. Write the power set of A = {1, 2, 3}. 1 of x. 1

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11. Find the equation of the line through (–2, 3) with 17. Write down the sample space when a coin is tossed
slope – 4. 1 three times. 1

18. One card is drawn from a well shuffled deck of 52
cards. If each outcome is equally likely, calculate the
12. Find the equation of the line through the points
probability that the card will be a diamond. 1
(3, –2) and (–1, 4). 1

19. Find the number of words that could be formed with
13. Find the intercepts cutoff by the straight line the letters of the word “COLLEGE”. 1
3x  2y  6 from the co-ordinate axes. 1

1 1 x
20. If   , find x. 1
6! 7! 8!
1 1
14. Find the equation of the circle with centre  ,  and
2 4
SECTION – B
1
radius . 1
12
21. Find the value of tan 15o. 2

 sin ax 
15. Evaluate : lim  ; a, b  0.
x 0 sin bx 
1 22. Find the multiplicative inverse of  5  3i . 2

23. Find r, if 5 4 Pr = 6 5 Pr 1 . 2

(x  1)5  1
16. Evaluate : lim . 1
x 0
 x  24. Find the Co-efficient of x 5 in (x  3)8 . 2

HS/XI/A. Sc. Com/M/23 HS/XI/A. Sc. Com/M/23

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25. Using binomial theorem, evaluate (99)5. 2 Find the equation of the ellipse whose major axis on
the x–axis and passes through the points (4, 3) and
(6, 2).
1
26. Find the derivative of . 2
x2
30. Find the co-ordinates of the points which trisect
the line segment joining the points P(4,2, – 6) and
Q(10, –16, 6). 4
SECTION – C Or
If the origin is the centroid of the triangle PQR with
vertices P(2a, 2, 6), Q(– 4,3b, –10) and R(8, 14, 2c),
27. The relation f is defined by then find the values of a, b and c.
2
f (x )  x , 0  x  3
3x , 3  x  10
The relation g is defined by 31. Find the derivative from first principle of sin x 4
2
g (x )  x , 0  x  2 Or
3x , 2  x  10
Show that f is a function and g is not a function. 4 Find the derivatives of
2
(i) (x  1) (ii) log sin x

28. Solve the following system of inequalities graphically:
x  2y  10 , x  y  1 , x  y  0 , x  0 , y  0 . 4 32. In class XI of a school 40% of the students study
Mathematics and 30% study Biology. 10% of the class
study both Mathematics and Biology. If a student is
selected at random from the class, find the probability
29. Find the co-ordinates of the foci, the vertices, the that he will be studying Mathematics or Biology. 4
eccentricity and the length of the latus rectum of the Or
hyperbola 49y 2  16x 2  784 . 4 Three coins are tossed once. Find the probability of
Or getting (i) 3 heads (ii) at least 2 heads.

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SECTION – D 36. Find the mean deviation about the mean for the
following data: 6

Marks 10–20 20–30 30–40 40–50 50–60 60–70 70-80
33. A college awarded 38 medals in football, 15 in obtained
basketball and 20 in cricket. If these medals went to a Number of 2 3 8 14 8 3 2
total of 58 men and only three men got medals in all Students
the three sports, how many received medals in exactly
two of the three sports. Or
6
Find the mean deviation about the median for the
following data:

Marks 0–10 10–20 20–30 30–40 40–50 50–60
34. The ratio of the A.M. and G.M. of two positive numbers
a and b is m : n. Number of 6 8 14 16 4 2
girls
 
Show that a : b  m  m 2  n 2 : m  m 2  n 2 .  6

Or

Insert five numbers between 8 and 26 such that the
resulting sequence is an A.P.

35. Prove that 6

(i) cot 4x (sin 5x  sin 3x )  cot x (sin 5x  sin 3x )

4 tan x (1  tan2 x )
(ii) tan 4x 
1  6 tan2 x  tan4 x

HS/XI/A. Sc. Com/M/23 HS/XI/A. Sc. Com/M/23