MATHEMATICS class 11

byMahanand Tudu -
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INTRODUCTION

Mathematics in Class 11 marks a crucial transition from basic concepts to more advanced and analytical thinking. A clear understanding of the syllabus is essential for building a strong foundation for higher studies and competitive exams. This article provides a structured overview of the complete Class 11 Mathematics syllabus, along with carefully designed self-evaluation question sets.

To help students assess their understanding effectively, four sets of practice questions have been included. Each set is progressively structured, containing 8, 10, 30, and 40 questions respectively, allowing learners to gradually test their knowledge, improve problem-solving skills, and build confidence. Whether you are revising concepts or preparing for exams, these question sets will serve as a valuable resource for systematic practice and self-assessment.

CLASS XI : Syllabus of Mathematics

1.Sets

2. Relations and functions

3.Trigonometric functions

4. Complx number and Quadratic equations

5. Linear Inequalities

6. Permutations & combinations

7. Binomial theorem

8. Sequences and series

9. Straight lines

10.Conic sections

11. Introduction to three dimensional geometry

12.Limits and Derivatives

13. Statistics

14. Probability

SELF EVALUATION -1


1. SETS


If A = {1, 2, 3, 4} and B = {3, 4, 5, 6}, then A ∩ B is: 
 A) {1, 2} 
 B) {3, 4} 
 C) {5, 6} 
 D) {1, 6} 

 

2. Relations & Functions


 If f(x) = 2 x + 3, then f(4) is: 
 A) 8 
 B) 10 
 C) 11
 D) 12 

 

3. Trigonometric Identities

 

 The value of sin²θ + cos²θ is: 
 A) 0 
 B) 1
 C) 2
 D) –1

 

4. Complex Numbers


 i² equals:
 A) 1
 B) –1
 C) 0 
 D) i 

 

5. Quadratic Equations

 

 The nature of roots of ax² + bx + c = 0 depends on: 
 A) b² – 4 ac 
 B) a + b + c 
 C) a – b 
 D) c² 

 

6. Permutations & Combinations

 

 The value of 5P2 is: 
 A) 10
 B) 20 
 C) 5 
 D) 25

 

7. Statistics

 

 Mean of first 5 natural numbers is: 
 A) 2 
 B) 2.5 
 C) 3 
 D) 4 

 

8. Straight Lines

 

 Slope of the line 2 x + 3 y = 6 is:
 A) 2/3 
 B) –2/3 
 C) 3/2 
 D) –3/2 

SELF EVALUATION -2

1. Sets


If A = {x : x is a prime number less than 10}, then A is: 
A) {1, 2, 3, 5, 7}
B) {2, 3, 5, 7}
C) {2, 4, 6, 8}
D) {1, 3, 5, 7}

2. Relations


If A = {1, 2, 3}, then the total number of relations on A is: 
A) 3
B) 6
C) 9
D) 512


3. Functions


If f(x) = x² – 1, then f(–2) is: 
A) 3
B) –3
C) 5
D) –5

4. Trigonometry


The value of tan 45° is: 
A) 0
B) 1
C) √3
D) –1

5. Complex Numbers


If z = 3 + 4 i, then |z| is: 
A) 5
B) 7
C) 25
D) 1

6. Permutations


The number of ways to arrange the letters of the word “MATH” is: 
A) 4
B) 12
C) 24
D) 16

7. Binomial Theorem


The coefficient of x² in (1 + x)⁴ is: 
A) 4
B) 6
C) 12
D) 24

8. Straight Line


Distance between points (1,2) and (4,6) is: 
A) 5
B) 4
C) √13
D) 6


9. Limits


lim x→0 (sin x)/x equals: 
A) 0
B) 1
C) ∞
D) –1

10. Statistics


If the mean of 10 numbers is 20, then their total sum is: 
A) 200
B) 20
C) 100
D) 10

SELF EVALUATION -3

1. If A = {1,2,3} and B = {2,3,4}, then A ∪ B is:


A) {1,2,3}
B) {2,3}
C) {1,2,3,4}
D) {4}


2. Number of subsets of a set containing 4 elements is:


A) 4
B) 8
C) 16
D) 32


3. If n(A) = 3, then number of relations on A is:


A) 9
B) 27
C) 512
D) 64


4. If f(x) = x³, then f(2) equals:


A) 6
B) 8
C) 4
D) 10


5. Value of sin 90° is:


A) 0
B) 1
C) –1
D) √3


6. sin²θ + cos²θ =


A) 0
B) 1
C) 2
D) –1


7. If i² =


A) 1
B) –1
C) i
D) 0


8. Modulus of 1 + i is:


A) 1
B) √2
C) 2
D) 0


9. Discriminant of 2 x² + 3 x + 1 = 0 is:


A) 1
B) –1
C) 5
D) 0


10. Roots of x² – 4 = 0 are:


A) ±2
B) ±4
C) 2
D) –2


11. Value of 5! is:


A) 20
B) 60
C) 120
D) 720


12. ⁶C₂ equals:


A) 12
B) 15
C) 30
D) 6


13. Coefficient of x² in (1 + x)³ is:


A) 3
B) 6
C) 9
D) 1


14. Distance between (0,0) and (3,4) is:


A) 5
B) 4
C) 7
D) 3


15. Slope of line y = 3 x + 2 is:


A) 2
B) 3
C) –3
D) 1


16. If mean of 5 numbers is 10, their sum is:


A) 50
B) 15
C) 5
D) 10


17. lim x→0 (sin x)/x equals:


A) 0
B) 1
C) ∞
D) –1


18. If tan θ = 1, then θ =


A) 30°
B) 45°
C) 60°
D) 90°


19. Domain of f(x) = 1/x is:


A) All real numbers
B) x ≠ 0
C) x = 0
D) x > 0


20. (a + b)² equals:


A) a² + b²
B) a² + 2ab + b²
C) a² – b²
D) 2ab


21. If A = {1,2} and B = {3,4}, number of elements in A × B is:


A) 2
B) 4
C) 6
D) 8


22. Equation of x-axis is:


A) x = 0
B) y = 0
C) x = y
D) y = 1


23. Value of cos 0° is:


A) 0
B) 1
C) –1
D) 1/2


24. If |z| = 0, then z is:


A) 1
B) i
C) 0
D) –1


25. Number of diagonals in a quadrilateral is:


A) 2
B) 4
C) 6
D) 1


26. 7P2 equals:


A) 14
B) 42
C) 21
D) 49


27. If variance = 9, then standard deviation is:


A) 9
B) 3
C) 81
D) 6


28. Solution of 2 x – 4 = 0 is:


A) 2
B) –2
C) 4
D) 0


29. If n(A) = 5, number of proper subsets is:


A) 31
B) 32
C) 30
D) 25


30. Value of sec 60° is:


A) 1
B) 2
C) √3
D) 1/2


SELF EVALUATION -4

  1. All possible subsets of set A = {2,3,4} are


    2. (A) P(A) = {2},{3}, {4}

    (B) P(A) = {{2},{3}, {4}, {2,3,4}}

    (C) P(A) = {ϕ,{2},{3}, {4},{2,3},{3,4},{4,2} ,{2,3,4}}

    (D) none of these



  2. If A' is the complement of set A, then


    3. (A) A' = U - A

    (B) A' = U + A

    (C) A' - A = U

    (D) A' = A



  3. If A and B are two sets such that n(A)= 27, n(B) = 35 and n(A ∪ B) = 50, then find n(A ∩ B).


    4. (A) 10

    (B) 12

    (C) 14

    (D) 16



  4. Find a and b when (a - 2 b, 13) = (7,2a - 3 b).


    5. (A) a = 4, b = 1

    (B) a = 5, b = 2

    (C) a = 5, b = -1

    (D) a = 6, b = 7



  5. If f:R→R : f(x) = x² + 3 = 19, then find the pre-image of the function.


    6. (A) 4

    (B) -4

    (C) ±4

    (D) 0



  6. Find the domain of the function f(x) = ( x² + 1)/(x² - 1)


    7. (A) R - {1}

    (B) R - {-1,1}

    (C) R - {-1}

    (D) R



  7. Range of the modulus function f(x)= |x| is


    8. (A) Range(f) = [0,∞)

    (B) Range(f) = (0,∞)

    (C) Range(f) = (-∞,∞)

    (D) none of these



  8. The value of 1+ i² + i⁴ + i⁶ is


    9. (A) 1

    (B) -1

    (C) 0

    (D) -2



  9. Conjugate of z = 5 - 2 i is


    10. (A) -5 - 2 i

    (B) 5 + 2 i

    (C) -5 + 2 i

    (D) 5 + i



  10. If 2 y + (3 x - y)i = (5 - 2 i) then find the value of x and y.


    11. (A) x = 3/2, y = 5/2

    (B) x = 1/6, y = 5/2

    (C) x = 3/2, y = 4/3

    (D) x = 5/3, y = 1/6



  11. If z = 4 - 3 i  then the multiplicative inverse of z is


    12. (A) 4/25 + 3 i/25

    (B) 3/25 + 4 i/25

    (C) -4/25 - 3 i/25

    (D) 4/25 - 3 i/25



  12. Polar form of Z = (-√3 - i) is


    13. (A) 2(Cos 5 π/6 - i sin 5 π/6)

    (B) 2(- Cos 5 π/6 + i sin 5 π/6)

    (C) 2(Cos 5 π/6 + isin 5 π/6)

    (D) none of these



  13. Imaginary roots of the equation x² + 3 x + 9 = 0 are


    14. (A) x = (-3 ± i3√3)/2

    (B) x = (3 ± i3√3)/2

    (C) x = (-3 - i3√3)/2

    (D) x = (-3 + i3√3)/2



  14. Let a is a positive integer then |x| > a is


    15. (A) x < -a or x > a

    (B) x > -a or x < a

    (C) x < -a or x > -a

    (D) none of these



  15. ⁿP₅ = 42 × ⁿP₃ , n > 4 find n.


    16. (A) 12

    (B) 10

    (C) 14

    (D) 16



  16. If 1/4! + 1/5! = x/6!, then value of x is


    17. (A) 40

    (B) 36

    (C) 38

    (D) 32



  17. ⁿCᵣ + ⁿCᵣ₋₁ = ?


    18. (A) ⁿ⁺¹Cᵣ

    (B) ⁿ⁻¹Cᵣ

    (C) ⁿ⁺¹Cᵣ₊₁

    (D) none of these



  18. Relation between permutation and combination is


    19. (A) ⁿCᵣ = ⁿPᵣ/r!

    (B) ⁿCᵣ × r! = 1

    (C) ⁿCᵣ/r! = ⁿPᵣ

    (D) none of these



  19. If ⁿC₈ = ⁿC₆ then the value of ⁿC₃ is


    20. (A) 350

    (B) 346

    (C) 364

    (D) 580



  20. Find the 6th term of the expansion (4x/5 − 5/2x)⁹


    21. (A) 5040/x

    (B) 4050/x

    (C) -5040/x

    (D) -4050/x



  21. Which term of the A.P. 9, 14, 19, 24, 29, ... is 379 ?


    22. (A) 80 th

    (B) 78 th

    (C) 75 th

    (D) 60 th



  22. What will be the sum of all natural numbers between 100 and 1000 which are divisible by 5?


    23. (A) 94850

    (B) 98450

    (C) 99450

    (D) 94950



  23. For what value of x are the numbers -2/7, x , -7/2 are in G.P. ?


    24. (A) x = 1, x = - 1

    (B) x = -1, x = 3

    (C) x = 0, x = 2

    (D) none of these



  24. Degree measure of (3/4)ᶜ is


    25. (A) 42°50"

    (B) 42°57'16"

    (C) 49°61'

    (D) 41°57'18"



  25. Find the degree of the angle subtended at the centre of a circle of diameter 50 cm by an arc of length 11 cm.


    26. (A) 30°

    (B) 22°17'

    (C) 25°12'

    (D) none of these



  26. Value of Cos 15 π is


    27. (A) 1

    (B) 0

    (C) -1

    (D) 2



  27. Cosec(-41 π/4) is


    28. (A) √2

    (B) -√2

    (C) 1/2

    (D) -1/2



  28. tan(x + y) is equal to


    29. (A) (tan x + tan y) / (1 - tan x • tan y)

    (B) (tan x - tan y) / (1 + tan x • tan y)

    (C) (1-tan x • tany) / (tan x + tan y)

    (D) (1 + tan x • tan y) / (tan x - tan y)



  29. The value of tan(13 π/12) is


    30. (A) (2 + √3)

    (B) (2 - √3)

    (C) (2 ± √3)

    (D) (2 ∓ √3)



  30. If Cos²θ = Cos²α then general solution is


    31. (A) θ = n π + α

    (B) θ = n π - α

    (C) θ = n π ± α

    (D) none of these



  31. When two lines L₁ and L₂ are perpendicular to each other then their slopes m₁ and m₂ are related as


    32. (A) m₁ × m₂ = 1

    (B) m₁ × m₂ = -1

    (C) m₁/m₂ = ∞

    (D) m₂/m₁= ∞



  32. Intercept form of a straight line is


  33. (A) (A) x/a + y/b = 1
  34. (B) (B) x/a - y/b = 1
  35. (C) (C) x/a + y/b = -1
  36. (D) (D) none of these


  37. A circle passes through the points A(2,-4), B(5,-8) and C(2,1). The centre of the circle is


    38. (A) (2,-4)

    (B) (-3,4)

    (C) (3,-16/3)

    (D) none of these



  38. For the parabola x² = 6 y , the focus and the equation of directrix are respectively


    39. (A) F(0, -3/2), y = 3/2

    (B) F(0, 3/2), y = 3/2

    (C) F(0, 3/2), y = -3/2

    (D) none of these



  39. The vertices of an ellipse are (±5,0) and its foci are (±4,0). The equation of the ellipse is


    40. (A) x² /25 + y² /16 = 1

    (B) x² /9 + y² /25 = 1

    (C) x² /25 + y² /9 = 1

    (D) x² /16 + y² /25 = 1



  40. lim x→0 (Sin ax / Sin bx) is equal to


    41. (A) b/a

    (B) a/b

    (C) -a/b

    (D) -b/a



  41. lim x→0 [(3²ˣ − 1)/(2³ˣ − 1) ] is equal to


    42. (A) log 9/log 8

    (B) log 8/log 9

    (C) log 2/log 3

    (D) log 3/log2



  42. If y = tan√x then dy/dx = ?


    43. (A) (sec√x)/2√x

    (B) (secx)/2√x

    (C) (sec²√x)/2√x

    (D) (sec²√x)/√x



  43. If y = x²sinx then dy/dx =?


    44. (A) 2 x •sinx +x² cos x

    (B) x² sinx + 2 x•cos x

    (C) 2 x •sinx - x² cos x

    (D) none of these



  44. Probability of the event is defined as


    45. (A) P(E) = n(E)/n(S)

    (B) P(E) = [n(E)+n(S)]/n(S)

    (C) P(E) = [P(S)+P(E)]/P(E)

    (D) none of these



CONCLUSION

In conclusion, a clear understanding of the Class 11 Mathematics syllabus combined with consistent practice is key to achieving success. The self-evaluation question sets provided in this article are designed to help students gradually strengthen their concepts and improve problem-solving skills.

By working through each set—ranging from 8 to 30 questions—students can effectively track their progress, identify areas that need improvement, and build confidence over time. Regular self-assessment not only enhances accuracy but also prepares learners for exams in a structured and systematic way.



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