SSM CENTRAL SCHOOL – SENIOR SECONDARY
KUPPANDAPALAYAM
CLASS : XI MARKS : 80
SUBJECT : MATHEMATICS DURATION: 3 Hrs
SECTION – A
I Choose the correct answer 20 x 1 = 20
1. Two finite sets have m and n elements. The number of subsets of the first set is
112 more than that of the second set. The values of m and n are respectively is
(a) 8,4 (b) 7, 4 (c) 4,4 (d) 7,7
2. If A and B are two sets then A ∩ 𝐴 ∪ 𝐵 is
(a) A (b) B (c) ∅ (d) A∩B
3. Let S = {x/x is a +ve multiple of 3 < 100} P = {x/x is a prime number < 20} then
n(S)+n(P) is
(a) 44 (b) 41 (c) 40 (d) 43
4. Let A and B be any two sets such that n(B) = P, n(A) =q then the total number of
functions F: A→B is
(a) pq (b) qp (c) pq (d) none
𝑥 2 +2𝑥+1
5. The domain of the function f given by f(x) = is
𝑥 2 −𝑥−6
(a) R – {3,-2} (b) R – {-3,2} (c) R – {-3,-2} (d) R – {3,2}
6. The domain of 𝑎2 − 𝑥 2 𝑎 > 0 is
(a) (-a, a ) (b)[-a,a] (c)[0,a) (d)( -a.0]
7. The equivalent degree measure of 6 radians is
(a) 343037’11”(b) 343038’11” (c) 343038’10” (d) 343037’11”
31𝜋
8. The value of sin is
3
(a) ½ (b) 1/ 2 (c) 3/2 (d) 1
9. If A+B+C = n𝜋 then tanA + tanB + tanC =
(a) tan (A+B+C) (b) tanAtanBtanC (c) tan(ABC) (d) A+B+C = 0
10. The maximum and minimum value of the expression Acos𝜃 + 𝐵𝑠𝑖𝑛𝜃 are
(a) 𝐴2 − 𝐵2 , 𝐴2 + 𝐵2 (b) 𝐴1 + 𝐵1 , 𝐴1 − 𝐵1
(c) 𝐴2 + 𝐵2 , 𝐴2 − 𝐵2 (d) 𝐴3 − 𝐵3 , 𝐴3 + 𝐵3
11. The value of 3𝑐𝑜𝑠𝑒𝑐20° − 𝑠𝑒𝑐20° is
(a) 1 (b) 2 (c) 3 (d)4
12. 1+3+5+……+(2n+1) is
(a) n ( b) n2 (c) 2n (d) 2n+1
13. Let P(n) = 2n < (1x2x3…….n) Then the smallest positive integer for which P(n) is
true is
(a) 1 (b) 2 (c) 3 (d) 4
14. If P(n) = 49n+16n+k is divisible by 64, for n ∈N is true then the least negative
value of k is
(a) 1 (b) -1 (c) -2 (d) -3
1−𝑖
15. The conjugate of the complex number is
1+𝑖
(a) i (b) -1 (c) -i (d) 1
𝑖 4𝑛 +1 −𝑖 4𝑛 −1
16. The value of is
2
(a) i (b) -1 (c) -i (d) 1
17. What is the reciprocal of Z ?
1 1 𝑧 𝑧
(a) (b) (c) (d)
𝑧 𝑧 𝑧 𝑧2
18. The sum of the series 𝑖 + 𝑖 2 + 𝑖 3 + ⋯ …. upto 1000 terms is
(a) 0 (b) 1 (c) 2 (d) 3
19. Solve 4x+3 < 6x+7
(a)(2,∞) (b)(-∞, 2) (c)(-2,∞) (d)[-2,∞]
8
20. The coefficient of x5 in 𝑥 + 3 is
(a) -1512 (b) 1512 (c) 5121 (d)5112
SECTION – B
II Answer all the questions 6x2 = 12
21. Write down all the subsets of {1,2,3}
22. Let A = {-1,2,3} and B ={1,3} determine AXB and BXA
𝑝+𝑞
23. If tan(A+B) = p and tan(A-B) = q then show that tan2A =
1−𝑝𝑞
3𝑥−4 𝑥+1
24. Solve ≥ − 1. Show the graph of the solution on number line.
2 4
25. Find the sum of odd integers from 1 to 2001
26. Find the 20th and nth terms of the G.P 5/2,5/4,5/8,……
SECTION – C
III Answer all the questions 8 x 3 = 24
27. From 50 students taking examinations in mathematics, physics and chemistry
each of the student has passed in at least one of the subject, 37 passed
mathematics,24 physics and 43 chemistry. At most 19 passed mathematics and
physics at most 29 mathematics and chemistry and at most 20 physics and
chemistry. What is the largest possible number that could have passed all 3 exam.
28. Find the domain and range of the relation R given by R = {(x,y): y = x + 6/x
where x,y belongs to N and x < 6}
1−𝑚
29. If cos(𝜃 + 𝜑) = mcos(𝜃 − 𝜑) prove that tan𝜃 = 𝑐𝑜𝑡𝜑
1+𝑚
30. Prove by the principal of mathematical induction 2+4+6+…+2n = n2+n for all n
belongs to N.
50
31. Find a , if the 17th and 18th terms of the expansion 2 + 𝑎 are equal.
𝑎 𝑛 +𝑏 𝑛
32. If is the A.M between a and b then find the value of n.
𝑎 𝑛 −1 +𝑏 𝑛 −1
33. Insert two numbers between 3 and 81 so that the resulting sequence is a G.P
34. Find the sum to n terms of the series n2+2n
SECTION – D
IV Answer all the questions 6x4 = 24
35. Match the following
A B
′
i. 𝐴′ ∪ 𝐵′ − 𝐴 a. B
ii. 𝐵′ ∪ 𝐵′ − 𝐴 ′ b. A ∩C – B
Iii (A-B) - (B-C) c. A
iv. (A-B) ∩(C - B) d. A – B
36. Find the general solution of 5cos 𝜃 + 7 sin2𝜃 - 6 = 0.
2
37. Prove by the principle of mathematical induction
𝑛 2𝑛 −1 (2𝑛 +1)
12+32+52+………+ (2n-1)2 =
3
1 1 1
38. Find the sum to n terms of + + + ⋯…
1𝑥2 2𝑥3 3𝑥4
39. Find the sum to n terms of the sequence 8,88,888,8888,….
40. Find a positive value of m for which the coefficient of x2 in the expansion of
(1+x)m is 6.
