R.
P classes
PAPER-1-11-24
Class 11 - Mathematics
Time Allowed: 3 hours Maximum Marks: 80
General Instructions:
1. This Question paper contains - five sections A, B, C, D, and E. Each section is
compulsory. However, there are internal choices in some questions.
2. Section A has 18 MCQs and 02 Assertion-Reason-based questions of 1 mark each.
3. Section B has 5 Very Short Answer (VSA)-type questions of 2 marks each.
4. Section C has 6 Short Answer (SA)-type questions of 3 marks each.
5. Section D has 4 Long Answer (LA)-type questions of 5 marks each.
6. Section E has 3 source-based/case-based/passage-based/integrated units of
assessment (4 marks each) with sub-parts
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7. All Questions are compulsory. However, an internal choice in 2 Questions of 2 marks, 3
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Questions of 3 marks and 2 Questions of 5 marks have been provided. An internal choice has been
provided in the 2-mark questions of Section E.
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8. Draw neat figures wherever required. Take π = 227 wherever required if not stated.
Section A
1. Let A and B be two sets containing four and two elements respectively.Then,the number of subsets of A×B,each having
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at least three elements is:
a) 256 b) 219
c) 510 d) 275
2. If x is an acute angle and tan x = , then the value of is
a) b)
c) 2 d)
3. The solution set of the inequation: is:
a) none of these b) x N
c) null set d) x W
4. How many different teams of 7 players can be chosen out of 10 players?
a) 70 b) 120
c) 720 d) None of these
5. is equal to
a) 6n b) 5-n
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All the very best
c) 4n d) 5n
6. The distance of the point P (1, – 3) from the line 2y – 3x = 4 is
a) 13 b) None of these
c) d)
7. If the major axis of an ellipse is three times the minor axis, then its eccentricity is equal to
a) b)
c) d)
8. How many terms of the GP 2, 6, 18, ... will make the sum 728?
a) 7 b) 8
c) 6 d) 9
9. L is the foot of the perpendicular drawn from a point (3, 4, 5) on x-axis. The coordinates of L are
a) (0, 0, 5) b) (0, 4, 0)
c) none of these d) (3, 0, 0)
10. is equal to:
a) 1 b) R
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c) None of these d)
11. Mean deviation for n observations x1, x2, ..., xn from their mean is given by
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a) b)
c) d)
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12. Three squares of chess board are selected at random. The probability of getting 2 squares of one colour and other of a
different colour is
a) b)
c) d)
13. sin 18° = ?
a) b)
c) d)
14. A man wants to cut three lengths from a single piece of board of length 91 cm. The second length is to be 3 cm longer
than the shortest and third length is to be twice as long as the shortest. What are the possible lengths for the shortest
board if the third piece is to be at least 5 cm longer than the second?
a) 3 x 91 b) 3 x 5
c) 5 x 91 d) 8 x 22
15. The number of ways, in which a student can choose 5 courses out of 8 courses, when 2 courses are compulsory, is
a) none of these b) 20
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All the very best
c) 120 d) 63
16. The sum of the infinite GP is:
a) b)
c) d)
17. The distance of a point P(a, b, c) from x-axis is
a) b2 + c2 b)
c) d)
18. is equal to
a) for |x| > 1 b) for |x| > 1
c) for |x| > 1 d) for |x| > 1
19. Assertion (A): Equation of line passing through (0, 0) with slope m is y = mx.
Reason (R): The equation of a straight line whose slope is m and parses through the point P(x, y) is y - y1 = m(x - x1).
a) Both A and R are true and R is the correct b) Both A and R are true but R is not the
explanation of A.
c) A is true but R is false. R
correct explanation of A.
d) A is false but R is true.
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20. A card is selected from a pack of 52 cards. Calculate the probability that the card is an ace of spades.
Section B
21. Prove that = tan A.
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22. If a point P(x, y) is equidistant from the points A (6, -1) and B(2, 3), find the relation between x and y.
23. Let f(x)= If f(x) exists then find the value of a.
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OR
Differentiate ex cos x.
24. Find the number of words formed by permuting all the letters of the word: INDEPENDENCE.
25. Three unbiased coins are tossed once. What is the probability of getting at least 2 heads?
OR
If A and B are mutually exclusive event, P(A) = 0.35 and P (B) = 0.45, find P (A B′)
Section C
26. Find the domain and range of the function
27. Solve the system of linear inequation: 3x - x >
OR
To receive grade A in a course one must obtain an average of 90 marks or more in five papers, each of 100 marks. If
Tanvy scored 89, 93, 95 and 91 marks in first four papers, find the minimum marks that she must score in the last
paper to get grade A in the course.
28. Using binomial theorem, prove that (23n - 7n - 1) is divisible by 49, where
OR
Expand the given expression (2x - 3)6
29. Find the equation of hyperbola having Foci ( 4, 0) and the latus rectum is of length 12.
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All the very best
OR
Find the centre and radius of the circles: x2 + y2 - 4x + 6y = 5.
30. Show that the points (-2, 3, 5), (1, 2, 3) and (7, 0, -1) are collinear.
31. Find a G.P. for which sum of the first two terms is -4 and the fifth term is 4 times the third term.
Section D
32. Prove that: cos 40° cos 80° cos 160° = .
OR
If sin x = and x lies in the 2nd quadrant, find the values of cos , sin and tan .
33. Calculate the mean deviation about the median for the following data:
Height (in cm) 95 - 105 105 - 115 115 - 125 125 - 135 135 - 145 145 - 155
Number of boys 9 13 25 30 13 10
OR
The mean and standard deviation of 100 observations were calculated as 40 and 5.1, respectively by a student who
took by mistake 50 instead of 40 for one observation. What are the correct mean and standard deviation?
34. Find the equations of the altitudes of a ABC, whose vertices are A (2, -2), B(1, 1) and C (-1, 0).
35. Find the differential coefficient of sec x, using first principle.
36. R
Section E
A permutation is an act of arranging the objects or numbers in order. Combinations are the way of selecting the
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objects or numbers from a group of objects or collections, in such a way that the order of the objects does not matter.
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How many words, with or without meaning can be made from the letters of the word, MONDAY, assuming that no
letter is repeated if
(i) 4 letters are used at a time
(ii) all letters are used at a time
OR
From 4 officers and 8 jawans in how many ways can 6 be chosen to include at least one officer?
37. A rod of length 12 cm moves with its ends always touching the coordinate axes. Determine the equation of the locus of a
point P on the rod, which is 3 cm from the end in contact with the x-axis.
38. In a hostel 60% of the students read Hindi news paper, 40% read English news paper and 20% read both Hindi and
English news papers.
A student is selected at random.
a. Find the probability that she read neither Hindi nor English news papers.
b. If she reads Hindi news paper, find the probability that she reads English news paper.
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All the very best
