MBOSE Class 11 Question Paper 2019 for Mathematics

Total No. of Printed Pages ––6 (2)
HS/XI/A. Sc. Com/M/19

2. Find the domain of the function f(x) = 9  x 2
2019

MATHEMATICS 3. Solve: 24 x  100 when x is a natural number.

Full Marks : 100
sin 4x
4. Evaluate lim
Time : 3 hours x 0 sin 2x

General Instructions :
SECTION – B
1. All questions are compulsory.
5. Find the multiplicative inverse of 2 – 3i.
2. The question paper consists of 29 questions divided into
four Sections A, B, C and D.
6. Find the co-efficient of x 5 in the expansion of ( x  3)8 .
Section A consists of 4 questions of 1 mark each.
Section B consists of 8 questions of 2 marks each.
Section C consists of 11 questions of 4 marks each. 7. Solve: 2 cos 2 x  3 sin x  0
Section D consists of 6 questions of 6 marks each.
8. Given below are two statements
3. There is no overall choice. However internal choice has been
provided in 4 questions of 4 marks each and 2 questions of p : 25 is a multiple of 5
6 marks each. q : 25 is a multiple of 8.
Write the compound statements connecting
4. Use of calculator is not permitted.
these 2 statements with ‘AND’ and ‘OR’. In both cases,
check the validity of the compound statement.

SECTION –– A
9. Find r if 5 4Pr  6 5Pr 1
1. Write the solution set of the equation x 2  x  2  0 in
roster form. 2 x2
10. Find the derivative of 
x 1 3x 1

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11. A die is rolled. If E be the event ‘die shows 4’ and F be 17. By principle of mathematical induction prove that
the event ‘die shows even number’, then are E and F 2
mutually exclusive? n (n  1)
1  2  3  ...... n  
3 3 3 3

 2 
12. If A = set of rational numbers
Or

B = x I x2  4x  2  0 
Find A – B and B – A. For every positive integer n, prove that 7n – 3n is divisible
by 4.

SECTION –– C
3  2i sin 
18. Find real  , such that is purely real.
13. State whether the following sets are equal or not 1  2i sin 
I=  x : x 2  5x  7  0, x  R  and J  
19. Find the derivative of cosx from 1st principle.

14. Find the value of tan .
8

15. PQR is a triangle with vertices P(2a, 2, 6), 20. Find the equation of circle passing through (0,0) and
Q( –4, 3b, –10 ) and R( 8, 14, 2c ). If the centroid lies at making intercepts ‘a’ and ‘b’ on the co-ordinate axes.
the origin, calculate the values of a, b, c.
Or
Or
Find the ratio in which the line segment joining the
Show that the points (–2, 3, 5), (1, 2, 3) and (7, 0, –1) points (4, 8, 10) and (6, 10, –8) is divided by the
are collinear. yz - plane.

16. How many numbers can be formed with digits 1, 2, 3, 21. Find the sum of the sequence 7, 77, 777, 7777, .........to
4, 3, 2, 1 so that odd digits always occupy the odd n terms.
places?

Or 22. In a class of 35 students, 24 like to play cricket and
16 like to play football. Also each student likes to play
Solve the following system of inequalities graphically : at least one of the two games. How many students
3x  4y  60, x  3y  30, x  0, y  0 like to play both games?

HS/XI/A. Sc. Com/M/19 HS/XI/A. Sc. Com/M/19

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23. In class XI of a School, 40% students study
Mathematics and 30% study Biology. 10% of the class
e x  e x  2
28. Evaluate lim
study both Mathematics and Biology. If a student is x 0 x2
selected at random from the class, find the probability
that he will be studying Mathematics or Biology.
29. The variance of 20 observations is 5. If each observation
is multiplied by 2, find the new variance of the
SECTION – D resulting observations.

Or
24. Prove that
x 9x 5x Find the mean deviation about the mean for the
cos 2x cos  cos 3x cos  sin 5x sin .
2 2 2 following data:

25. Find the equation of the circle passing through the Marks 10–20 20–30 30–40 40–50 50–60 60–70 70–80
points (4, 1) and (6,5) and whose centre is on the line Obtained
4x + y = 16.
No. of 2 3 8 14 8 3 2
Or Students

Find the co-ordinates of the foci and the vertices, the
eccentricity and length of latus rectum of the hyperbola
y2 x 2 
 1
9 27

26. If the sum of n terms of an A.P. is 3n 2  5n and its mth
term is 164, find the value of m.

18
 2 2
27. Determine whether the expansion of  x   will
 x
contain a term containing x10.