Assignments Class 11 Mathematics Relations and Functions

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Relations and Functions Assignments Class 11 Mathematics

Question. The domain of the definition of the function f(x) = 1/4-x2 + log10(x3-x)
(a) (–1, 0) ∪ (1, 2) ∪ (3, ∞)
(b) (–2, –1) ∪ (–1, 0) ∪ (2, ∞)
(c) (–1, 0) ∪ (1, 2) ∪ (2, ∞)
(d) (1, 2) ∪ (2, ∞)

Question. Let ƒ(n) = [1/3 + 3n/100]n, where [n] denotes the greatest integer less than or equal to n. Then

 is equal to:
(a) 56
(b) 689
(c) 1287
(d) 1399

Question. Let f be an odd function defined on the set of real numbers such that for x ≥ 0, f(x) = 3 sin x + 4 cos x. Then f(x) at x = −(11Π/6) is equal to:
(a) 3/2 + 2√3
(b) −3/2 + 2√3
(c) 3/2 − 2√3
(d) −3/2 − 2√3

Question. Domain of definition of the function f(x) = 3/4-x2 + log10(x3-x) is
(a) (-1,0)∪(1,2)∪(2,∞)
(b) (a,2)
(c) (-1,0)∪(a,2)
(d) (1,2)∪(2,∞)

Question. Let [t] denote the greatest integer ≤ t. Then the equation in x, [x]² + 2[x + 2] – 7 = 0 has :
(a) exactly two solutions
(b) exactly four integral solutions
(c) no integral solution
(d) infinitely many solutions

Question. Let R₁ and R₂ be two relations defined as follows :
R₁= {(a, b) ∈ R² : a² + b² ∈ Q} and R₂ ={(a, b) ∈ R² : a² + b² ∉ Q}, where Q is the set of all rational numbers. Then :
(a) Neither R₁ nor R₂ is transitive.
(b) R₂ is transitive but R₁is not transitive.
(c) R₁ is transitive but R₂ is not transitive.
(d) R₁ and R₂ are both transitive.

Question. Let ƒ(x) be a quadratic polynomial such that ƒ(–1) + ƒ(2) = 0. If one of the roots of ƒ(x) = 0 is 3, then its other root lies in :
(a) (–1, 0)
(b) (1, 3)
(c) (–3, –1)
(d) (0, 1)

Question. Let f : R → R be defined by f(x) = x/1+x² xÎR. Then the range of f is :
(a) [-1/2 ,1/2]
(b) R – [–1, 1]
(c) R-[-1/2 ,1/2]
(d) (–1, 1) – {0}

Question. Let ƒ(1, 3) → R be a function defined by ƒ(x) = x[x] / 1 + x² , where [x] denotes the greatest integer ≤ x. Then the range ofƒ is:
(a) (2/5 , 3/5)∪(3/4 , 4/5)
(b) (2/5 , 1/2)∪(3/5 , 4/5)
(c) (2/5 , 4/5)
(d) (3/5 , 4/5)

Question. If f(x) = loge (1−x / 1+x), |x|<1, then ƒ(2x / 1 + x²) is equal to :
(a) 2ƒ(x)
(b) 2ƒ(x²)
(c) (ƒ(x))²
(d) –2ƒ(x)

Question. Let ƒ(x) = ax (a > 0) be written as f(x) = ƒ₁(x) + ƒ₂(x), where ƒ₁(x) is an even function and ƒ₂(x) is an odd function. Then ƒ₁(x + y) + ƒ₁(x – y) equals :
(a) 2ƒ₁(x) ƒ₁(y)
(b) 2ƒ₁(x + y) ƒ₁(x – y)
(c) 2ƒ₁(x)ƒ₂(y)
(d) 2ƒ₁(x + y) ƒ₂(x – y)

Question. A real valued function f(x) satisfies the functional equation
f(x – y) = f(x) f(y) – f(a – x) f(a + y)
where a is a given constant and f(0) = 0, f(2a – x) is equal to
(a) – f (x)
(b) f (x)
(c) f (a) + f (a – x)
(d) f (– x)

Question. The domain of the function f(x) =

 is (-∞, – a] ∪ [a, ∞]. Then a is equal to :
(a) √17/2
(b) √17–1/2
(c) 1+√17/2
(d) √17/2 + 1

Question. If R = {(x, y) : x, y ε Z, x +3y ≤ 8} is a relation on the set of integers Z, then the domain of R^–1 is :
(a) {–2, –1, 1, 2}
(b) {0, 1}
(c) {–2, –1, 0, 1, 2}
(d) {–1, 0, 1}

Question. The graph of the function y = f(x) is symmetrical about the line x = 2, then
(a) f (x) = – f (-x)
(b) f (2 + x) = f (2 – x)
(c) f (x) = f (-x)
(d) f (x + 2) = f (x – 2)

Question. The range of the function

(a) R
(b) (– 1, 1)
(c) R – {0}
(d) [– 1, 1]

Question. The domain of the function f(x) =

(a) (0, ∞ )
(b) (– ∞ , 0)
(c) (– ∞ , ∞ ) – {0}
(d) (– ∞ , ∞ )

Question. If f : R → R satisfies f (x + y) = f (x) + f ( y) , for all x, y ∈ R and f(1) = 7, then

(a) 7n(n+1) / 2
(b) 7n/2
(c) 7(n+1) / 2
(d) 7n+(n +1)