Class 11 Mathematics

1. If (x + 1, y - 2) = (3, 1), then the values of x and y are:

• A. x = 2, y = 3
• B. x = 3, y = 2
• C. x = 1, y = 3
• D. x = 2, y = 1

2. If set A has 3 elements and set B = {3, 4, 5}, then the number of elements in A × B is:

• A. 9
• B. 6
• C. 3
• D. 12

3. If A = {1, 2} and B = {3, 4}, then the number of relations from A to B is:

• A. 16
• B. 4
• C. 8
• D. 2

4. The domain of the relation R = {(x, x²) : x is a prime number less than 10} is:

• A. {2, 3, 5, 7}
• B. {4, 9, 25, 49}
• C. {2, 3, 5, 7, 9}
• D. {1, 2, 3, 5, 7}

5. The range of the relation R = {(x, x²) : x is a prime number less than 10} is:

• A. {4, 9, 25, 49}
• B. {2, 3, 5, 7}
• C. {1, 4, 9, 25}
• D. {4, 9, 16, 25}

6. The domain of the real function f(x) = √(x - 2) is:

• A. [2, ∞)
• B. (2, ∞)
• C. (-∞, 2]
• D. R

7. The domain of the function f(x) = 1 / (x - 3) is:

• A. R - {3}
• B. R
• C. (3, ∞)
• D. (-∞, 3)

8. The range of the function f(x) = |x| for all x ∈ R is:

• A. [0, ∞)
• B. (-∞, 0]
• C. R
• D. (0, ∞)

9. If f(x) = x² + 2x + 1, then the value of f(-1) is:

• A. 0
• B. 1
• C. 2
• D. 4

10. Which of the following relations is a function?

• A. {(2, 1), (3, 1), (4, 2)}
• B. {(2, 1), (2, 2), (3, 3)}
• C. {(1, 2), (1, 3), (1, 4)}
• D. {(3, 2), (3, 4), (5, 1)}

11. A relation R from a non-empty set A to a non-empty set B is a subset of:

• A. A × B
• B. B × A
• C. A ∪ B
• D. A ∩ B

12. The identity function f: R → R is defined by:

• A. f(x) = x for all x ∈ R
• B. f(x) = c (constant)
• C. f(x) = x²
• D. f(x) = |x|

13. The range of the constant function f(x) = 5 for all x ∈ R is:

• A. {5}
• B. R
• C. [0, 5]
• D. (0, 5)

14. If f(x) = x³ and g(x) = x + 1, then (f + g)(2) is:

• A. 11
• B. 10
• C. 8
• D. 9

15. If f(x) = 2x - 5, then the value of x for which f(x) = 0 is:

• A. 5/2
• B. -5/2
• C. 2/5
• D. -2/5

16. The signum function f: R → R is defined as f(x) = 1 if x > 0, 0 if x = 0, and -1 if x < 0. Its range is:

• A. {-1, 0, 1}
• B. [-1, 1]
• C. R
• D. {0, 1}

17. The domain of the function f(x) = √(9 - x²) is:

• A. [-3, 3]
• B. (-3, 3)
• C. [0, 3]
• D. (-∞, -3] ∪ [3, ∞)

18. The range of the function f(x) = √(9 - x²) is:

• A. [0, 3]
• B. [-3, 3]
• C. (0, 3)
• D. [0, 9]

19. The greatest integer function f(x) = [x] takes values in which set?

• A. Set of all Integers (Z)
• B. Set of Real Numbers (R)
• C. Set of Natural Numbers (N)
• D. Set of Rational Numbers (Q)

20. If f(x) = x² and g(x) = 2x + 1, then (fg)(3) is equal to:

• A. 63
• B. 54
• C. 42
• D. 27

21. If A = {1, 2} and B = {a, b}, then A × B is equal to:

• A. {(1, a), (1, b), (2, a), (2, b)}
• B. {(a, 1), (b, 1), (a, 2), (b, 2)}
• C. {(1, 1), (2, 2), (a, a), (b, b)}
• D. {(1, a), (2, b)}

22. If A × B = {(a, x), (a, y), (b, x), (b, y)}, then set A is:

• A. {a, b}
• B. {x, y}
• C. {a, x}
• D. {b, y}

23. If n(A) = p and n(B) = q, then total number of non-empty relations from A to B is:

• A. 2ᵖ𝑞 - 1
• B. 2ᵖ𝑞
• C. p × q
• D. 2ᵖ⁺𝑞

24. The domain of the function f(x) = 1 / √(x² - 1) is:

• A. (-∞, -1) ∪ (1, ∞)
• B. [-1, 1]
• C. (-1, 1)
• D. (-∞, -1] ∪ [1, ∞)

25. If f(x) = x³ - 1/x³, then f(x) + f(1/x) equals:

• A. 0
• B. 2x³
• C. -2/x³
• D. 1

26. If A × B = Ø, then which of the following must be true?

• A. Either A = Ø or B = Ø
• B. Both A ≠ Ø and B ≠ Ø
• C. A = B
• D. A ∩ B = Ø

27. If f(x) = log(x), then its domain is:

• A. (0, ∞)
• B. [0, ∞)
• C. R
• D. R - {0}

28. If f(x) = [x], then value of f(2.7) - f(-2.3) is:

• A. 5
• B. 4
• C. 1
• D. 0

29. If f: R → R is given by f(x) = (3 - x³)¹/³, then f(f(x)) is equal to:

• A. x
• B. x³
• C. 3 - x³
• D. (3 - x³)³

30. The range of the function f(x) = x² + 2 for all x ∈ R is:

• A. [2, ∞)
• B. (2, ∞)
• C. [0, ∞)
• D. R