Subject: Mathematics
Class XI
Time Allowed: 3 hours
Max. Marks: 80
General Instructions:
1. All questions are compulsory.
2. Section A contains 20 questions each carries 1 mark.
3. Section B contains 5 questions each carries 2 marks.
4. Section C contains 6 questions each carries 3 marks.
5. Section D contains 3 case based questions of 4 marks each.
6. Section E contains 4 questions each carries 5 mark.
7. There are some internal choice questions in Sections B, C and E.
Section A
1. If A = {x : x is a multiple of 4} and B = {x : x is a multiple of 6}, then A ∩ B consists of all multiples of
a) 8 b) 16 c) 4 d) 12
2. Sets A and B have 3 and 6 elements respectively. What can be the maximum number of elements in A∪B.
a) 3 b) 9 c) 18 d) 6
3. If A = {1, 2, 3, 4, 5, 6} then the number of proper subsets is
a) 63 b) 36 c) 64 d) 25
4. The range of the function
a) None of these b) R – {-1, 1} c) R -{0} d) {-1, 1}
5. If [x] denotes the greatest integer ≤ x, then
a) 99 b) 66 c) 98 d) 65
6. Let R be the relation on N defined as by x + 2 y = 8. The domain of R is
a) {2, 4, 6, 8} b) {2, 4, 8} c) {1, 2, 3, 4} d) {2, 4, 6}
7. The value of
a) 1/10 b) 10 c) 1 d) 0
10. Two circles of radii 2 units have their centre 2 units apart. If S and p represent the area and perimeter of the common portion of two circles, then p – S equals:
a) -4 b) 4 c) 2 – 8 d) 8 – 2π
11. If z = (2 + √−5) then |z| = ?
a) None of these b) 9 c) 3 d) 7
12. If z = z¯, then
a) none of these b) z is a complex number c) z is purely real d) z is purely imaginary
13. Mark the correct answer for: i-38 = ?
a) i b) –i c) -1 d) 1
14. Solution of a linear inequality in variable x is represented on the number line as follow:
a) x ∈ (7/2, ∞) b) x ∈ (-∞, 7/2) c) x ∈ (-∞, 7/2] d) x ∈ (7/2, -∞)
15. The solution set of 6x – 1 > 5 is:
a) none of these b) {x : x > 1, x R} c) {x : x < 1, x N} d) {x : x < 1, x W}
16. The solution set of the inequation |x + 2| ≤ 5 is
a) (-7, 5) b) [-7, 3] c) (-7, 3) d) [-5, 5]
17. For what values of x are the numbers, -2/7, x, -7/2 in G.P?
a) -1 and 1 b) -2 and 2 c) -2 and 1 d) -1 and 2
18. GM between 0.15 and 0.0015 is
a) 1.5 b) None of these c) 0.015 d) 0.15
19. The 4th, 7th and 10th terms of a GP are in
a) AP b) GP c) HP d) None of these
20. The sum of the infinite GP
a) 3/2 b) 4/9 c) 5/9 d) 2/3
Section B
21. If A = {1, 2, 3, 4, 5} and B = {2, 4, 6}, then find the sets A – B and B – A.
22. Convert 6 radian into degree measure.
OR
Reduce √3 sin x + cos x as a single term consisting sine only
23. If sin x = 3/5, cos y = -12/13, where x and y both lie in second quadrant, find the value of sin (x + y)
OR
Prove that:
24. Find the real values of x and y for which: x + 4yi = ix + y + 3
25. Solve the inequality 2 (2x + 3) – 10 < 6 (x – 2) for real x
Section – C
26. Let A = {1, 2, 4, 5} B = {2, 3, 5, 6} C = {4, 5, 6, 7}.
Verify: A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩C).
27. Let A = {1,2,3,4} and B = {1,4,9,16,25} and R be a relation defined from A to B as
R = {(x, y):x A, y B and y = x2 }.
i. Depict this relation using arrow diagram.
ii. Find the domain of R.
iii. Find the range of R.
iv. Find the codomain of R.
28. If sin x = -1/2 and x lies in Quadrant IV, find the values of
i. sin x/2
ii. cos x/2
iii. tan x/2
29. Express the complex number (-2 – 1/3 i)3 in the form of a + ib
OR
Evaluate to the standard form:
30. Solve 3x + 8 > 2 when
(i) x is integer
(ii) x is a real number
31. Evaluate:
OR
Insert 5 numbers between 8 and 26 such that the resulting sequence is an A.P.
Section – D
32. Read the text carefully and answer the questions that follow:
A class teacher, Mamta Sharma of class XI, writes three sets A, B, and C, such that A= {1, 3, 5, 7, 9}, B = {2, 4, 6, 8}, and C = {2, 3, 5, 7, 11}.
(i) Write the number of subsets of set B.
a) 12 b) 16 c) 8 d) 4
(ii) Which of the following is correct for the two sets A and C to intersect?
a) A ∪ C ≠ ϕ b) A ∩ C ≠ ϕ c) A ∪ C = ϕ d) A ∩ C = ϕ
(iii) Which of the following is correct for two sets A and B to be disjoint?
a) A ∪ B ≠ ϕ b) A ∩ B = ϕ c) A ∪ B = ϕ d) A ∩ B ≠ ϕ
(iv) Find A ∩ C.
a) {3, 5, 7} b) ϕ c) {3, 4, 7} d) {1, 5, 7}
33. Read the text carefully and answer the questions that follow:
Function as a Relation A relation f from a non-empty set A to a non-empty set B is said to be a function, if every element of set A has one and only one image in set B. In other words, we can say that a function f is a relation from a non-empty set A to a nonempty set B such that the domain of f is A and no two distinct ordered pairs in f have the same first element or component.
If f is a function from a set A to a set B, then we write
and it is read as f is a function from A to B or f maps A to B.
(i) If f(x) = 1/(2 – sin x), then range (f) is equal to
a) [1/3, 1] b) [-1, -1/3] c) [-1/3, 1/3] d) [-1, 1]
(ii) If f (1 + x) = x2 + 1, then f (2 – h) is:
a) h2 − 2h + 2 b) h2 − 2h + 1 c) h2 − 2h – 2 d) h2 + 2h + 2
(iii) If f(x) = x2 + 2x + 3, then among f(1), f(2) and f(3), which one gives the maximum value.
a) f(1) = f(2) = f(3) b) f(1) c) f(2) d) f(3)
(iv)The given curve is a:
a) Data not sufficient b) Function c) Can’t say anything d) Relation
34. Read the text carefully and answer the questions that follow:
A sequence of non-zero numbers is said to be a geometric progression if the ratio of each term, except the first one, to its preceding term is always constant. Rahul, being a plant lover, decides to open a nursery, and he buys a few plants with pots. He wants to place pots in such a way that the number of pots in the first row is 2, in the second row is 4, in the third row is 8, and so on …
(i) If Rahul wants to place 510 pots in total, then the total number of rows formed in this arrangement is:
a) 7 b) 5 c) 9 d) 8
(ii) Total number of pots upto 10th row is :
a) 2046 b) 1046 c) 1023 d) 1024
(iii) The difference in number of pots placed in 7th row and 5th row is :
a) 90 b) 96 c) 86 d) 50
(iv)The number of pots in 8th row is :
a) 156 b) 300 c) 456 d) 256
Section – E
35. i. Find the domain and range of the function:
ii. Find the domain of the function:
36. Prove that: 4 sin A sin (60o – A) sin (60o + A) = sin 3A.
Hence deduce that: sin 20o x sin 40o x sin 60o x sin 80o = 3/16
OR
37. Express [(√5 + i/2) (√5 − 2i)] ÷ (6 + 5 i) in the form of a + ib.
38. Solve the following system of linear inequalities:
OR
Solve the following system of linear inequalities
