# Assignments Class 11 Mathematics Relations and Functions

Please refer to Assignments Class 11 Mathematics Relations and Functions Chapter 2 with solved questions and answers. We have provided Class 11 Mathematics Assignments for all chapters on our website. These problems and solutions for Chapter 2 Relations and Functions Class 11 Mathematics have been prepared as per the latest syllabus and books issued for the current academic year. Learn these solved important questions to get more marks in your class tests and examinations.

## 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, ∞)

Answer

C

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

Answer

D

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

Answer

C

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,∞)

Answer

A

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

Answer

D

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.

Answer

A

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)

Answer

A

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}

Answer

A

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)

Answer

B

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)

Answer

B

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)

Answer

A

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)

Answer

A

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

Answer

C

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}

Answer

D

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)

Answer

B

Question. The range of the function

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

Answer

B

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

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

Answer

B

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)

Answer

A