This document contains 53 short questions related to mathematics covering topics like sets, relations, trigonometry, limits, probability, and derivatives. The questions range from writing sets in roster form to finding derivatives of trigonometric and logarithmic functions to problems involving probabilities of combinations and permutations.

1. CLASS XI MATHEMATICS SHORT QUESTIONS
1. Write the set A = { 𝒙 𝒙 ∈ 𝒁, 𝒙 𝟐
< 20} in the roster form.
2. What is the total number of proper subsets of a set consisting of n elements?
3. Find sets A, B and C such that A ∩ B, A ∩ C and B ∩ C are non- empty sets and A ∩ B ∩ C = ∅ .
4. Write the relation R = {(x, x3
) : x is a prime number less than 10} in roaster form.
5. If A = {1, 2}, form the set A × A× A.
6. Find the domain of f(x) =
𝒙 𝟐+𝟑𝒙+𝟓
𝒙 𝟐−𝟓𝒙+𝟒
7. Prove that : sin(n + 1) A (n + 2) A + cos (n + 1) A cos (n + 2) A = cos A
8. Find the maximum and minimum values of 7 cos 𝜽 + 𝟐𝟒 𝒔𝒊𝒏 𝜽.
9. If (a + b) – i (3a + 2b) = 5 + 2i, find a and b.
10. Find the multiplication inverse of z = 3 – 2i.
11. Find the conjugate of
1
3+4𝑖
.
12. Find non – zero integral solutions of 1 − 𝑖 x
= 2x
.
13. 3𝑥 − 2 ≤
1
2
.
14. In how many ways can 9 examination papers be arranged so that the best and the worst papers are never
together?
15. How many three letter words can be made using the letters of the word ‘ORIENTAL’?
16. How many chords can be drawn through 21 points on a circle?
17. A polygon has 44 diagonals. Find the number if its sides.
18. Which is larger 1.01 1000000
or 10,000?
19. Show that the sum (m + n)th
and (m - n)th
term of an A.P. is equal to twice the mth
term.
20. Find the sum of first 24 terms of the A.P. a1 , a2, a3, ......., if it is known that
a1 + a5 + a10+ a15 + a20 + a24 = 225.
21. Find the sum of infinity of the G.P. -
5
4
,
5
16
, −
5
64
, … … … ….
22. Prove that 61/2
. 61/4
. 61/8
............ ∞ = 6.
23. If A (-2, 1), B (2, 3) and C (-2, -4) are three points, find the angle between BA and BC.
24. If three points A (h, 0), P(a, b) and B (0, k) lie on a line, show that :
𝑎
ℎ
+
𝑏
𝑘
= 1 .
25. Line through the points (-2, 6) and (4, 8) is perpendicular to the line through the points (8, 12) and (x,24) . find
the value of x.
26. Find the value of θ and p, if the equation x cos θ + y sin θ = p is the normal form of the line
3 x + y + 2 = 0
27. Find the value of λ, if the lines 3x – 4y – 13 = 0, 8x – 11y – 33 = 0 and 2x – 3y + λ = 0 are concurrent.
28. The line through (h, 3) and (4, 1) intersects the line 7x – 9y – 19 = 0 at right angle. Find the value of h.
29. Find the number of terms in (x3
+3x2
+3x+1)25
.

2. 30. Find the equation of the circle which passes through the point of intersection of the lines
3x – 2y – 1 = 0 and 4x + y – 27 = 0 and whose centre is (2, -3).
31. Find the centre and radius of the circle given by the equation 2x2
+ 2y2
+ 3x + 4y +
9
8
= 0.
32. Find the equation of the ellipse whose axes are along the coordinate axes, vertices are (±5, 0) and foci at
(± 4, 0) .
33. Find the axes, eccentricity, latus – rectum and the coordinates of the foci of the hyperbola
25x2
- 36y2
= 225.
34. Find the points on z –axis which are at a distance 21 from the point (1, 2, 3).
35. Three vertices of a parallelogram ABCD are A (3, -1, 2), B (1, 2, -4) and C (-1, 1, 2). Find the coordinates of
the fourth vertex.
36. If the origin is the centroid of the triangle with vertices P(2a, 2, 6), Q (-4, 3b, -10) and
R (8, 14, 2c) , find the values of a, b and c.
37. Find the ratio in which the line segment joining the points (4, 8, 10) and (6, 10, -8) is divided by the yz – plane.
38. Evaluate : lim 𝑥→2
𝑥2−5𝑥+6
𝑥2−4
.
39. Evaluate : lim 𝑥→0
𝑎2+𝑥2− 𝑎2−𝑥2
𝑥2 .
40. Evaluate: lim 𝑥→5
𝑒 𝑥 −𝑒5
𝑥−5
41. A coin is tossed and then a die is rolled only in case a head is shown on the coin. Describe the sample space to
this experiment.
42. Three dice are thrown together. Find the probability of getting a total of at least 6.
43. Three letters are dictated to three persons and an envelop is addressed to each of them the letters are inserted
into the envelopes at random so that each envelope contains exactly one letter. Find the probability that at least
one letter is in its proper envelop.
44. A word consists of 9 letters; 5 consonants and 4 vowels. Three letters are chosen at random. What is the
probability that more than one vowel will be selected?
45. A and B are two non- mutually exclusive events. If P(A) =
1
4
, P(B) =
2
5
and P (A ∪ 𝐵) =
1
2
, find the values of
P(A ∩ B) and P (A ∩ 𝐵 ).
46. Find the derivative of
𝑎+𝑏 𝑠𝑖𝑛 𝑥
𝑐+𝑑 𝑐𝑜𝑠 𝑥
47. If y =
1−𝑐𝑜𝑠 2𝑥
1+𝑐𝑜𝑠 2𝑥
, then find
𝑑𝑦
𝑑𝑥
.
48. How many 3- digit even numbers can be formed from the digits 1, 2, 3, 4, 5, 6, if the digits can be repeated?
49. Let A = {1, 2} B = {3, 4}. How many subsets will A X B have?
50. Let R be a relation on N defined by R = {(a, b): a, b ∈ N and a = b2
}. Is (a, a) ∈ R ∀ a ∈ 𝑁. Give example.
51. Find principal solution of cot x = -1.
52. Find the derivative of f(x)= log(cosecx - cotx)
53. Find the value of tan
13𝜋
12