MBOSE Class 11 Question Paper 2018 for Mathemarics

Total No. of Printed Pages ––6 (2)
HS/XI/A. Sc. Com/M/18
4. Insert two numbers between 3 and 81 so that the
2018 resulting sequence is GP. 2

MATHEMATICS
5.
o
Prove that Sin75 
 6  2. 2
Full Marks : 100 4

Time : 3 hours
6. If the three points A(a,o), B(o,b) and P(x, y) are collinear,
General Instructions : x y
using slopes, prove that   1. 2
a b
(i) Write all the answers in the Answer Script.

(ii) The question paper consists of three Sections –– A, B
7. Find the equation of a circle with centre (2, 4) and
and C.
radius 5. 2
(iii) Section –– A consists of 15 questions, carrying 2 marks each.

(iv) Section –– B consists of 10 questions, carrying 4 marks 8. Find the domain of the real – valued function
each, out of which 2 questions have internal choices. x 2  2x  3
f (x )  . 2
(v) Section –– C consists of 5 questions, carrying 6 marks each, x 2  5x  6
out of which 2 questions have internal choices.

9. Evaluate lim
sec 2 x  2. 2
SECTION –– A x tan x  1
4
( Answer all the 15 Questions )

1. If A = {2, 5, 7}, find P(A) and n[P(A)] 2 1o 1o 1
10. Prove that 2 sin 22 cos 22  . 2
2 2 2

2. Prove that log(1  2  3)  log 1  log 2  log 3 2
11. In a single throw of two dice, find the probability of
n
3. If C 7 n C 5 , find n . 2 obtaining “a total of 10”. 2

HS/XI/A. Sc. Com/M/18 HS/XI/A. Sc. Com/M/18

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1  i  18. Prove that
12. Express   in the form a  ib . 2
1  i  cos6 x  32cos 6 x  48cos 4 x  18cos 2 x  1 4

19. Find the general solution of 3 cos x  sin x  1 4
n n
13. If Pr  720 and Cr  120 , find value of r. 2
Or

Prove that cos x cos 2x cos 4x cos 8x  sin16 x
14. Write the negation of the following statements: 16sin x

(i) Shillong is the capital of Kerela. 2

(ii) 3 is greater than 5 20. Find the equation of the line passing through the point
(–2, –4) and perpendicular to the line 4x  5y  7  0 . 4

15. Find the middle term in the expansion of 3  x 6 2 21. The probability that a person will get an electrification
2
contract is   and the probability that he will not get
5
SECTION –– B 4
a plumbing contract is   . If the probability of getting
7
( Answer all the Questions ) 2
at least one contract is   , what is the probability
3
that he will get both? 4
16. In an examination, 56% of the candidates failed in
English and 48% failed in Science. If 18% failed in both
English and Science, find the percentage of those who
22. Prove that n Cr n Cr 1  n 1Cr 4
passed in both the subjects. 4
Or
17. Using the principle of mathematical induction, prove
(i) How many permutations can be made of the
1 letters of the word “SERIES”?
that 1  2  3  ......  n  n (n  1) 4
2
(ii) How many of these start with S and end with S?

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23. Solve the following systems of inequations graphically: 28. (i) Using Binomial theorem, find the value of (999)4 3
3x  2y  18, x  2y  10, x  0, y  0. 4
(ii) Find the coefficient of x 6 in the expansion of
9
24. Find from first principle the derivative of sin2x  3 4  2 1  3
 3x  
 3x 

 
25. Represent the complex number  1  i 3 in the polar
form. 4
29. Find the (i) lengths of major and minor axes,
(ii) coordinates of the vertices, (iii) eccentricity,
(iv) coordinates of the foci and (v) length of the latus
SECTION –– C rectum of the ellipse 6
2 2
9x  16y  144 .
( Answer all the Questions )

30. Find the mean deviation about the median for the data: 6
26. Prove that
3 Class 0–10 10–20 20–30 30–40 40–50 50–60
cos 10o cos 30o cos 50o cos 70o  6
16 Frequency 6 8 11 18 5 2

27. If S be the sum, P the product and R the sum of the Or
reciprocals of n terms in a GP, Prove that 6
n Find the mean, variance and standard deviation of first
2S 
P   . n natural numbers.
R 

Or


Find the sum of the series 7  77  777  ... to n terms 6

HS/XI/A. Sc. Com/M/18 HS/XI/A. Sc. Com/M/18