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All questions of Relations & Functions for Year 10 Exam
If A = {1, 2, 3 }, B = {4, 5, 6 }, which of the following is not a relation from A to Ba) R1 = {(1, 4), (1, 5),(1, 6)}b) R2 = {(1, 5), (2, 4), (3, 6)}c) R3 = {(4, 2), (2, 6), (5, 1), (2, 4)}d) R4 = {(1, 4), (1, 5), (3, 6), (2, 6), (3, 4)}Correct answer is option 'C'. Can you explain this answer?
|
Poonam Reddy answered |
A × B = {(1, 4), (1, 5), (1, 6), (2, 4), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6)}
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If f(x) = x2 and g(x) = cosx, which of the following is true?- a)f + g is even function
- b)f – g is an odd function
- c)f + g is not defined
- d)f + g is an odd function
Correct answer is option 'A'. Can you explain this answer?
If f(x) = x2 and g(x) = cosx, which of the following is true?
a)
f + g is even function
b)
f – g is an odd function
c)
f + g is not defined
d)
f + g is an odd function
|
Raghav Bansal answered |
if f(x) is an odd function
So, f(−x)=−f(x)
F(−x)=cos(f(−x))
=cos(−f(x))
=cos(f(x))
=F(x)
So cos(f(x)) is an even function
So, f(x) and g(x) is an even function
If n(A) = p and n(B) = q, then how many relations are there from A to B.- a)pq
- b)3pq
- c)2pq
- d)(pq)2
Correct answer is option 'C'. Can you explain this answer?
If n(A) = p and n(B) = q, then how many relations are there from A to B.
a)
pq
b)
3pq
c)
2pq
d)
(pq)2
|
|
Preeti Khanna answered |
Number of relation from A to B = 2n(A)×n(B)
n(A) = p, n(B) = q
⇒ Number of relation from A to B = 2pq
⇒ Number of relation from A to B = 2pq
Which of the following statement is false?- a)If R is a relation from A to B, then domain of R is a subset of A and range of R is a subset of B.
- b)If A = {1, 2, 3, 4} and B = {5, 6}, then the number of relations from A to B is 256.
- c)A subset of A × B is called a relation from the set A to set B.
- d)If A = {x, y, z} and B = {1, 2} then the number of relations from A to B is 22.
Correct answer is option 'D'. Can you explain this answer?
Which of the following statement is false?
a)
If R is a relation from A to B, then domain of R is a subset of A and range of R is a subset of B.
b)
If A = {1, 2, 3, 4} and B = {5, 6}, then the number of relations from A to B is 256.
c)
A subset of A × B is called a relation from the set A to set B.
d)
If A = {x, y, z} and B = {1, 2} then the number of relations from A to B is 22.
|
|
Riya Banerjee answered |
Option D: The number of relations from A to B is 23*2= 26
Let R be a relation defined on the set of N natural numbers as R = {(x, y): y is a factor of x, x, y∈ N} then,- a)(2, 4) ∈ R
- b)(9, 5) ∈ R
- c)(4, 2) ∈ R
- d)(3, 9) ∈ R
Correct answer is option 'C'. Can you explain this answer?
Let R be a relation defined on the set of N natural numbers as R = {(x, y): y is a factor of x, x, y∈ N} then,
a)
(2, 4) ∈ R
b)
(9, 5) ∈ R
c)
(4, 2) ∈ R
d)
(3, 9) ∈ R
|
Om Desai answered |
R = {(x, y): y is a factor of x, x, y∈ N}
As we know that 2 is a factor of 4
So, according to the options (4, 2) ϵ R
As we know that 2 is a factor of 4
So, according to the options (4, 2) ϵ R
The relation shown in the arrow diagram in set builder form is
- a){(x, y): x is the square of y, x ∈ P, y ∈ Q}
- b){(x, y), x = 4, 1, y = 2, 1, -1, -2}
- c){(x, y): y is the square of x, x ∈ P, y ∈ Q }
- d){(4, 2), (4, -2), (1, 1), (1, -1)}
Correct answer is option 'A'. Can you explain this answer?
The relation shown in the arrow diagram in set builder form is
a)
{(x, y): x is the square of y, x ∈ P, y ∈ Q}
b)
{(x, y), x = 4, 1, y = 2, 1, -1, -2}
c)
{(x, y): y is the square of x, x ∈ P, y ∈ Q }
d)
{(4, 2), (4, -2), (1, 1), (1, -1)}
|
Geetika Shah answered |
Set P is square of the element of set Q.
{(x, y): x is the square of y, x ∈ P, y ∈ Q}
{(x, y): x is the square of y, x ∈ P, y ∈ Q}
If A = {1, 2, 3}, and B = {3, 6} then the number of relations from A to B is
- a)32
- b)23
- c)23
- d)26
Correct answer is option 'D'. Can you explain this answer?
If A = {1, 2, 3}, and B = {3, 6} then the number of relations from A to B is
a)
32
b)
23
c)
23
d)
26
|
|
Preeti Iyer answered |
The number of relations between sets can be calculated using 2mn where m and n represent the number of members in each set.
So, number of relations from A to B is 26.
So, number of relations from A to B is 26.
Let A = {1, 2, 3, …, 50} and R be the relation “is square of” on A. Then R as a subset of A x A is written as:
- a){(1, 1), (2, 2), (3, 3), (4, 4) (5, 5), (6, 6), (7, 7)}
- b){(1, 1), (2, 5), (3, 9), (4, 15) (5, 25), (6, 36), (7, 49)}
- c){(1, 1), (4, 4), (9, 9), (16, 16) (25, 25), (36, 36), (49, 49)}
- d){(1, 1), (4, 2), (9, 3), (16, 4) (25, 5), (36, 6), (49, 7)}
Correct answer is option 'D'. Can you explain this answer?
Let A = {1, 2, 3, …, 50} and R be the relation “is square of” on A. Then R as a subset of A x A is written as:
a)
{(1, 1), (2, 2), (3, 3), (4, 4) (5, 5), (6, 6), (7, 7)}
b)
{(1, 1), (2, 5), (3, 9), (4, 15) (5, 25), (6, 36), (7, 49)}
c)
{(1, 1), (4, 4), (9, 9), (16, 16) (25, 25), (36, 36), (49, 49)}
d)
{(1, 1), (4, 2), (9, 3), (16, 4) (25, 5), (36, 6), (49, 7)}
|
Tejas Verma answered |
Since x is the square of y in relation R.
i.e. option D is correct.
i.e. option D is correct.
Which of the following relations is not a function?- a)R= {(1,2), (3,4),(2,1),(5,1)}
- b)R={(1,2), (1,4)(3,1),(5,1)}
- c)R= {(1,2), (3,4)(2,1),(5,2)}
- d)R= {(2,1), (4,4)(3,1),(5,1)}
Correct answer is option 'B'. Can you explain this answer?
Which of the following relations is not a function?
a)
R= {(1,2), (3,4),(2,1),(5,1)}
b)
R={(1,2), (1,4)(3,1),(5,1)}
c)
R= {(1,2), (3,4)(2,1),(5,2)}
d)
R= {(2,1), (4,4)(3,1),(5,1)}
|
|
Gaurav Kumar answered |
A function is a relation in which no two ordered pairs have the same first element. A function associates each element in its domain with one and only one element in its range. R={(1,2), (1,4)(3,1),(5,1)} is not a function because all the first elements are not different.
If X = {1, 2, 3, 4}, Y = {1, 2, 3,…., 20}, and f: X –> Y be the correspondence which assigns each element in X the value equal to its square, then the domain, co-domain and range of f is- a)Domain = {1, 2, …, 20}, Range = {1, 2, 3, 4}, Co domain = {1, 2, 3, 4}
- b)Domain = {1, 4, 9, 16}, Range = {1, 2, 3, 4}, Co domain = {1, 2, 3, …, 16}
- c)Domain = {1, 2, 3, 4}, Range = {1, 4, 9, 16}, Co domain = {1, 2, 3, …, 20}
- d)Domain = {1, 2, 3, 4}, Range = {1, 4, 9, 16}, Co domain = {1, 2, 3, …, 16}
Correct answer is option 'B'. Can you explain this answer?
If X = {1, 2, 3, 4}, Y = {1, 2, 3,…., 20}, and f: X –> Y be the correspondence which assigns each element in X the value equal to its square, then the domain, co-domain and range of f is
a)
Domain = {1, 2, …, 20}, Range = {1, 2, 3, 4}, Co domain = {1, 2, 3, 4}
b)
Domain = {1, 4, 9, 16}, Range = {1, 2, 3, 4}, Co domain = {1, 2, 3, …, 16}
c)
Domain = {1, 2, 3, 4}, Range = {1, 4, 9, 16}, Co domain = {1, 2, 3, …, 20}
d)
Domain = {1, 2, 3, 4}, Range = {1, 4, 9, 16}, Co domain = {1, 2, 3, …, 16}
|
|
Raghav Bansal answered |
The correct option is B
Since the function is defined from
XY.So the domain will be the set X which is {1,2,3,4}. Codomain is what may possibly come out of a function. So codomain is the whole set Y which is {1,2,3,...,20}. Range is The range is the set of possible output values which will be the values in the set of Y which have a pre-image. That is, the value of squares. So the range is {1,4,,9,16}.
Let X = {1, 2, 3, 4}, Y = {1, 2, …, 10} and f : X –> Y be defined by f(x) = 2x + 1, x ∈ X. Then the range of f is- a){1, 2,…., 10}
- b){5, 6, 7, 8, 9, 10}
- c){3, 5, 7, 9}
- d){1, 2, 3, 4}
Correct answer is option 'C'. Can you explain this answer?
Let X = {1, 2, 3, 4}, Y = {1, 2, …, 10} and f : X –> Y be defined by f(x) = 2x + 1, x ∈ X. Then the range of f is
a)
{1, 2,…., 10}
b)
{5, 6, 7, 8, 9, 10}
c)
{3, 5, 7, 9}
d)
{1, 2, 3, 4}
|
Krishna Iyer answered |
X = {1, 2, 3, 4}
Y = {1, 2, …, 10}
f: X→ Y be defined by
f(x) = 2x + 1
f (1) = 3
f (2) = 5
f (3) = 7
f (4) = 9
Range(f) = {3, 5, 7, 9}
Y = {1, 2, …, 10}
f: X→ Y be defined by
f(x) = 2x + 1
f (1) = 3
f (2) = 5
f (3) = 7
f (4) = 9
Range(f) = {3, 5, 7, 9}
Which of the following is not an example of polynomial function ?- a)g(x) = 8x2 + 5x – 2
- b)p(x) =5x3 + 3x2 + x – 2
- c)h(x) =3 root of x minus 1 over x
- d)f(x) = 3x2 + x – 2
Correct answer is option 'C'. Can you explain this answer?
Which of the following is not an example of polynomial function ?
a)
g(x) = 8x2 + 5x – 2
b)
p(x) =5x3 + 3x2 + x – 2
c)
h(x) =3 root of x minus 1 over x
d)
f(x) = 3x2 + x – 2
|
Lavanya Menon answered |
A polynomial function is a function which involves only non-negative integer powers or only positive integer exponents of a variable in an equation.
In option C, powers of x are negative and fractional.
In option C, powers of x are negative and fractional.
Let R be a relation defined as
R = {(x, y): y = 2x, x is natural number < 5} then Range of R is given as ,- a){2, 4, 6, 8}
- b){2, 4, 6, 8, 10}
- c){1, 2, 3, 4}
- d)N
Correct answer is option 'A'. Can you explain this answer?
Let R be a relation defined as
R = {(x, y): y = 2x, x is natural number < 5} then Range of R is given as ,
R = {(x, y): y = 2x, x is natural number < 5} then Range of R is given as ,
a)
{2, 4, 6, 8}
b)
{2, 4, 6, 8, 10}
c)
{1, 2, 3, 4}
d)
N
|
|
Gaurav Kumar answered |
X is a natural number and x < 5, the number is 1, 2, 3, 4
y = 2x
y = 2x
► x(1), y = 2 × 1 = 2
► x(2), y = 2 × 2 = 4
► x(3), y = 2 × 3 = 6
► x(4), y = 2 × 4 = 8
► x(2), y = 2 × 2 = 4
► x(3), y = 2 × 3 = 6
► x(4), y = 2 × 4 = 8
Range = {2, 4, 6, 8}
Number of subsets of a set of order three is- a)2
- b)4
- c)6
- d)8
Correct answer is option 'D'. Can you explain this answer?
Number of subsets of a set of order three is
a)
2
b)
4
c)
6
d)
8
|
Raj Ghoshal answered |
Number of Subsets of a Set of Order Three
To find the number of subsets of a set of order three, we need to consider all possible combinations of elements in the set.
Let's say we have a set S = {a, b, c}. We can represent each element of the set as a binary digit, where 0 represents the absence of the element and 1 represents the presence of the element.
- Empty Set: The empty set is a subset of every set, so it is included.
- Single Element Subsets: There are three single element subsets - {a}, {b}, and {c}.
- Two Element Subsets: There are three possible two-element subsets - {a, b}, {a, c}, and {b, c}.
- Three Element Subset: There is only one three-element subset - {a, b, c}.
Therefore, the total number of subsets of the set S = {a, b, c} is 1 (empty set) + 3 (single element subsets) + 3 (two-element subsets) + 1 (three-element subset) = 8.
Hence, the correct answer is option 'D' - 8.
In summary, to find the number of subsets of a set of order three, we consider all possible combinations of elements, including the empty set and subsets of different sizes. By applying this approach to the given set S = {a, b, c}, we find that there are 8 subsets in total.
To find the number of subsets of a set of order three, we need to consider all possible combinations of elements in the set.
Let's say we have a set S = {a, b, c}. We can represent each element of the set as a binary digit, where 0 represents the absence of the element and 1 represents the presence of the element.
- Empty Set: The empty set is a subset of every set, so it is included.
- Single Element Subsets: There are three single element subsets - {a}, {b}, and {c}.
- Two Element Subsets: There are three possible two-element subsets - {a, b}, {a, c}, and {b, c}.
- Three Element Subset: There is only one three-element subset - {a, b, c}.
Therefore, the total number of subsets of the set S = {a, b, c} is 1 (empty set) + 3 (single element subsets) + 3 (two-element subsets) + 1 (three-element subset) = 8.
Hence, the correct answer is option 'D' - 8.
In summary, to find the number of subsets of a set of order three, we consider all possible combinations of elements, including the empty set and subsets of different sizes. By applying this approach to the given set S = {a, b, c}, we find that there are 8 subsets in total.
Which of the following is incorrect?- a)Modulus function, Domain: R; Range: [0, infinity)
- b)Signum function, Domain: R; Range: {-1, 0,1}
- c)Constant function, Domain: R; Range: R
- d)Identity function, Domain: R; Range: R
Correct answer is option 'C'. Can you explain this answer?
Which of the following is incorrect?
a)
Modulus function, Domain: R; Range: [0, infinity)
b)
Signum function, Domain: R; Range: {-1, 0,1}
c)
Constant function, Domain: R; Range: R
d)
Identity function, Domain: R; Range: R
|
|
Preeti Khanna answered |
Constant Function is defined as the real valued function.
f : R→R, y = f(x) = c for each x∈R and c is a constant.
f : R→R, y = f(x) = c for each x∈R and c is a constant.
So, this function basically associate each real number to a constant value.
It is a linear function where f(x1) = f(x2) for all x1,x2 ∈ R
For f : R→R, y = f(x) = c for each x ∈ R
Domain = R
Range = {c}
The value of c can be any real number.
Domain = R
Range = {c}
The value of c can be any real number.
If f and g are two functions over real numbers defined as f(x) = 3x + 1, g(x) = x2 + 2, then find f-g- a)x2+1
- b)3x + x2
- c)3x – x2-1
- d)x2+1-3x
Correct answer is option 'C'. Can you explain this answer?
If f and g are two functions over real numbers defined as f(x) = 3x + 1, g(x) = x2 + 2, then find f-g
a)
x2+1
b)
3x + x2
c)
3x – x2-1
d)
x2+1-3x
|
|
Karthikeyeni Baskaran answered |
It is just a simple subtraction...subtract g from f
If f(x) = x2 and g(x) = x are two functions from R to R then f(g(2)) is
- a)8
- b)4
- c)1
- d)2
Correct answer is option 'B'. Can you explain this answer?
If f(x) = x2 and g(x) = x are two functions from R to R then f(g(2)) is
a)
8
b)
4
c)
1
d)
2
|
|
Raghav Bansal answered |
f(g(2)) compare f(gx) x=2
on comparing g(x)=x, g(2)=2
f(g(x)) = f(2) = x2 = 22= 4
on comparing g(x)=x, g(2)=2
f(g(x)) = f(2) = x2 = 22= 4
The domain and range of the function f: R → R defined by: f = {(x+1, x+5): x ∈ {0, 1, 2, 3, 4, 5}}
- a)Domain = {2, 3, 4, 5, 6}; Range = {6, 7, 8, 9, 10}
- b)Domain = R ; Range = R
- c)Domain = {1, 2, 3, 4, 5, 6}; Range = {5, 6, 7, 8, 9, 10}
- d)Domain = {1, 2, 3, 4, 5}; Range = {5, 6, 7, 8, 9}
Correct answer is option 'C'. Can you explain this answer?
The domain and range of the function f: R → R defined by: f = {(x+1, x+5): x ∈ {0, 1, 2, 3, 4, 5}}
a)
Domain = {2, 3, 4, 5, 6}; Range = {6, 7, 8, 9, 10}
b)
Domain = R ; Range = R
c)
Domain = {1, 2, 3, 4, 5, 6}; Range = {5, 6, 7, 8, 9, 10}
d)
Domain = {1, 2, 3, 4, 5}; Range = {5, 6, 7, 8, 9}
|
Tejas Chawla answered |
Correct answer is C.
If f(x) = x2 – x + 1; g(x) = 7x – 3, be two real functions then (f + g)(3) is- a)25
- b)3
- c)7
- d)18
Correct answer is option 'A'. Can you explain this answer?
If f(x) = x2 – x + 1; g(x) = 7x – 3, be two real functions then (f + g)(3) is
a)
25
b)
3
c)
7
d)
18
|
|
Riya Banerjee answered |
f(x) = x2 – x + 1; g(x) = 7x – 3
(f+g)(x) = (x2 - x + 1 + 7x - 3)
=(x2 - x + 7x + 1 - 3)
= x2 + 6x - 2
(f+g)(3) = x2 + 6x - 2
= (3)2 + 6(3) - 2
= 9 + 18 - 2
= 25
(f+g)(x) = (x2 - x + 1 + 7x - 3)
=(x2 - x + 7x + 1 - 3)
= x2 + 6x - 2
(f+g)(3) = x2 + 6x - 2
= (3)2 + 6(3) - 2
= 9 + 18 - 2
= 25
Which is not true for the graph of the real function y = x2:- a)The least value of x2 is one and will be so when x = 1.
- b)For this function domain = Real numbers
- c)The parabola will open upward.
- d)The graph of the given function is a parabola.
Correct answer is option 'A'. Can you explain this answer?
Which is not true for the graph of the real function y = x2:
a)
The least value of x2 is one and will be so when x = 1.
b)
For this function domain = Real numbers
c)
The parabola will open upward.
d)
The graph of the given function is a parabola.
|
|
Om Desai answered |
For the graph y=x2
The least value of x2 is zero and square of any number will also be zero.
The least value of x2 is zero and square of any number will also be zero.
Which of the following is not true?- a)Every relation from the set A to the set B is a function from the set A to the set B.
- b)If f is a function from A to B and (a, b) ∈ f, then f(a) = b, where a is called the pre-image of b under f.
- c)Every function from the set A to the set B is a relation from the set A to the set B
- d)If f is a function from A to B and (a, b) ∈ f, then f(a) = b, where b is called the image of a under f.
Correct answer is option 'A'. Can you explain this answer?
Which of the following is not true?
a)
Every relation from the set A to the set B is a function from the set A to the set B.
b)
If f is a function from A to B and (a, b) ∈ f, then f(a) = b, where a is called the pre-image of b under f.
c)
Every function from the set A to the set B is a relation from the set A to the set B
d)
If f is a function from A to B and (a, b) ∈ f, then f(a) = b, where b is called the image of a under f.
|
|
Pooja Shah answered |
A relation f from a set A to a set B is said to be function if every element of set A has one and only one image in set B. In other words, a function f is a relation such that no two pairs in the relation has the same first element. The notation f : X →Y means that f is a function from X to Y.
The function f : R → R defined by y = f(x) = 5 for each x ∈ R is- a)Modulus function
- b)Signum function
- c)Identity function
- d)Constant function
Correct answer is option 'D'. Can you explain this answer?
The function f : R → R defined by y = f(x) = 5 for each x ∈ R is
a)
Modulus function
b)
Signum function
c)
Identity function
d)
Constant function
|
Swathi Raj answered |
Because let whatever the value of x be f(x) is always constant
The domain of the function f(x)= 
is all real x such that- a)x<2
- b)-2
- c)-2 ≤ x ≤ 2
- d)x>-2
Correct answer is option 'C'. Can you explain this answer?
The domain of the function f(x)= is all real x such that
is all real x such thata)
x<2
b)
-2
c)
-2 ≤ x ≤ 2
d)
x>-2
|
|
Geetika Shah answered |
4 - x2 = 0
=> (2+x)(2-x) = 0
x = +-2
Now select a test point, let it be x = 0. Then y = (4 - (0)2)1/2 = 2, so the function is defined on [-2,2]
Thus, the graph of y = (4 - x2)1/2 is a semicircle with radius 2 and domain is [-2,2]
=> (2+x)(2-x) = 0
x = +-2
Now select a test point, let it be x = 0. Then y = (4 - (0)2)1/2 = 2, so the function is defined on [-2,2]
Thus, the graph of y = (4 - x2)1/2 is a semicircle with radius 2 and domain is [-2,2]
A relation R defined on the set A = {1,2,3,5} as {(x, y): x+y >10: x,y ∈ A} is- a)Empty relation
- b)Universal relation
- c)Zero relation
- d)Identity relation
Correct answer is option 'A'. Can you explain this answer?
A relation R defined on the set A = {1,2,3,5} as {(x, y): x+y >10: x,y ∈ A} is
a)
Empty relation
b)
Universal relation
c)
Zero relation
d)
Identity relation
|
|
Gayatri Kumar answered |
This relation R is not transitive.
To show this, we need to find a counterexample where the relation fails to hold for three elements in A.
Let's consider (1,2), (2,5), and (1,5). We know that (1,2) and (2,5) are in R, since 1 is less than 2 and 2 is less than 5. Similarly, (2,5) is in R because 2 is less than 5.
However, (1,5) is not in R since 1 is less than 5. Therefore, we have a counterexample where (1,2) and (2,5) are in R, but (1,5) is not. This shows that R is not transitive.
To show this, we need to find a counterexample where the relation fails to hold for three elements in A.
Let's consider (1,2), (2,5), and (1,5). We know that (1,2) and (2,5) are in R, since 1 is less than 2 and 2 is less than 5. Similarly, (2,5) is in R because 2 is less than 5.
However, (1,5) is not in R since 1 is less than 5. Therefore, we have a counterexample where (1,2) and (2,5) are in R, but (1,5) is not. This shows that R is not transitive.
f(x) = x is called- a)an identity function
- b)a constant function
- c)inverse function
- d)step function
Correct answer is option 'A'. Can you explain this answer?
f(x) = x is called
a)
an identity function
b)
a constant function
c)
inverse function
d)
step function
|
Mira Sharma answered |
In mathematics, an identity function, also called an identity relation or identity map or identity transformation, is a function that always returns the same value that was used as its argument. In equations, the function is given by f(x) = x.
Which of the relations is not a function?- a)one many
- b)domain = codomain
- c)many one
- d)one-one
Correct answer is option 'A'. Can you explain this answer?
Which of the relations is not a function?
a)
one many
b)
domain = codomain
c)
many one
d)
one-one
|
|
Rohan Singh answered |
One-to-one and many-to-one functions. A function is said to be one-to-one if every y value has exactly one x value mapped onto it, and many-to-one if there are y values that have more than one x value mapped onto them. This graph shows a many-to-one function.
A Relation R from A to B can be depicted pictorially using arrow diagram. In arrow diagram, we write down the elements of two sets A and B in two disjoint circles. Then we draw arrow from set A to set B whenever (a, b) ∈ R. An example of information depicted through an arrow diagram is shown below. For example:A company has four categories of employees given by Assistants (A), Clerks (C), Managers (M) and an Executive Officer (E). The company provides ₹10,000, ₹25,000, ₹50,000 and ₹1,00,000 as salaries to the people who work in the categories A, C, M and E respectively. Here A1, A2, A3, A4 and A5 are Assistants; C1, C2, C3, C4 are Clerks; M1, M2, M3 are Managers and E1, E2 are Executive Officers then the relation R is defined by xRy, where x is the salary given to person y.
The relation defined in the above arrow diagram from set P to set Q is- a)“x is a square of y”
- b)“x is a square root of y”
- c)“x is a cube root of y”
- d)None
Correct answer is option 'A'. Can you explain this answer?
A Relation R from A to B can be depicted pictorially using arrow diagram. In arrow diagram, we write down the elements of two sets A and B in two disjoint circles. Then we draw arrow from set A to set B whenever (a, b) ∈ R. An example of information depicted through an arrow diagram is shown below. For example:
A company has four categories of employees given by Assistants (A), Clerks (C), Managers (M) and an Executive Officer (E). The company provides ₹10,000, ₹25,000, ₹50,000 and ₹1,00,000 as salaries to the people who work in the categories A, C, M and E respectively. Here A1, A2, A3, A4 and A5 are Assistants; C1, C2, C3, C4 are Clerks; M1, M2, M3 are Managers and E1, E2 are Executive Officers then the relation R is defined by xRy, where x is the salary given to person y.
The relation defined in the above arrow diagram from set P to set Q is
a)
“x is a square of y”
b)
“x is a square root of y”
c)
“x is a cube root of y”
d)
None
|
Nandini Iyer answered |
When x = 9, y = ±3
When x = 4, y = ±2
When x = 25, y = ±5
∴ x is a square of y.
If monthly pay of salesman is 'y' and includes basic pay $200 plus a commission of $5 for every unit he sales then function for this can be written as- a)x = 205 + 5y
- b)200 + 5xy
- c)x = 387 + 5y
- d)y = 200 + 5x
Correct answer is option 'D'. Can you explain this answer?
If monthly pay of salesman is 'y' and includes basic pay $200 plus a commission of $5 for every unit he sales then function for this can be written as
a)
x = 205 + 5y
b)
200 + 5xy
c)
x = 387 + 5y
d)
y = 200 + 5x
|
Harshitha Chopra answered |
Let the no. of units sold be x.
Monthly pay: y = 200 + 5x
Monthly pay: y = 200 + 5x
Find the domain of the function f(x) = 
- a)R – {-4}
- b)R
- c)R – {4}
- d)R+
Correct answer is option 'C'. Can you explain this answer?
Find the domain of the function f(x) =
a)
R – {-4}
b)
R
c)
R – {4}
d)
R+
|
|
Lavanya Menon answered |
f(x) = 3x/2x-8
denominator can't be zero so
2x - 8 not equal to 0
x should not equal to 4
we have domain R - {4}
denominator can't be zero so
2x - 8 not equal to 0
x should not equal to 4
we have domain R - {4}
If A = {1,2,3}, B = {a,b,c}, which of the following is a function?- a)R = {(1, c), (2, b), (2, c)}
- b)R = {(1, b), (2, c), (3, a)}
- c)R = {(1,b), (1, c), (3, a)}
- d)R = {1,,a), (2, a), (1, c)}
Correct answer is option 'B'. Can you explain this answer?
If A = {1,2,3}, B = {a,b,c}, which of the following is a function?
a)
R = {(1, c), (2, b), (2, c)}
b)
R = {(1, b), (2, c), (3, a)}
c)
R = {(1,b), (1, c), (3, a)}
d)
R = {1,,a), (2, a), (1, c)}
|
|
Tanvi Kulkarni answered |
Option A has value b & c for 2.
Option C has value b & c for 1.
Option D has value a & c for 1.
Option C has value b & c for 1.
Option D has value a & c for 1.
If n(A) = 2, n(B) = 2. What is the total number of relations from A to B?- a)4
- b)32
- c)12
- d)16
Correct answer is option 'D'. Can you explain this answer?
If n(A) = 2, n(B) = 2. What is the total number of relations from A to B?
a)
4
b)
32
c)
12
d)
16
|
Varun Kapoor answered |
Hint: To solve this problem you don’t need to count the number of relations by assuming it on your own. Use the formula of the number of relations from set A to set B.
Complete step-by-step answer:
It is given that A = {1, 2} and B = {3, 4}
The number of elements in A is n(A)=2 and that of B is n(B) = 2.
The formula for the number of relations from one set to another is:
⇒2(number of elements in the first set) x (number of elements of the second set)
Therefore, we can write it as follows.
No. of relations from set A to set B = 2n(A)n(B) = 2(2*2) = 16
Hence, the number of relations from A to B is 16.
Complete step-by-step answer:
It is given that A = {1, 2} and B = {3, 4}
The number of elements in A is n(A)=2 and that of B is n(B) = 2.
The formula for the number of relations from one set to another is:
⇒2(number of elements in the first set) x (number of elements of the second set)
Therefore, we can write it as follows.
No. of relations from set A to set B = 2n(A)n(B) = 2(2*2) = 16
Hence, the number of relations from A to B is 16.
A Relation R from A to B can be depicted pictorially using arrow diagram. In arrow diagram, we write down the elements of two sets A and B in two disjoint circles. Then we draw arrow from set A to set B whenever (a, b) ∈ R. An example of information depicted through an arrow diagram is shown below. For example:A company has four categories of employees given by Assistants (A), Clerks (C), Managers (M) and an Executive Officer (E). The company provides ₹10,000, ₹25,000, ₹50,000 and ₹1,00,000 as salaries to the people who work in the categories A, C, M and E respectively. Here A1, A2, A3, A4 and A5 are Assistants; C1, C2, C3, C4 are Clerks; M1, M2, M3 are Managers and E1, E2 are Executive Officers then the relation R is defined by xRy, where x is the salary given to person y.
The relation defined in the above arrow diagram from set A to set B is- a)“x = 2y”
- b)“x is a square of y”
- c)“x is a factor of y”
- d)None
Correct answer is option 'C'. Can you explain this answer?
A Relation R from A to B can be depicted pictorially using arrow diagram. In arrow diagram, we write down the elements of two sets A and B in two disjoint circles. Then we draw arrow from set A to set B whenever (a, b) ∈ R. An example of information depicted through an arrow diagram is shown below. For example:
A company has four categories of employees given by Assistants (A), Clerks (C), Managers (M) and an Executive Officer (E). The company provides ₹10,000, ₹25,000, ₹50,000 and ₹1,00,000 as salaries to the people who work in the categories A, C, M and E respectively. Here A1, A2, A3, A4 and A5 are Assistants; C1, C2, C3, C4 are Clerks; M1, M2, M3 are Managers and E1, E2 are Executive Officers then the relation R is defined by xRy, where x is the salary given to person y.
The relation defined in the above arrow diagram from set A to set B is
a)
“x = 2y”
b)
“x is a square of y”
c)
“x is a factor of y”
d)
None
|
|
Preeti Iyer answered |
1,2,4 and 8 are factors of 8.
Consider the graphs of the functions f(x), h(x) and g(x).
The range of g(x) is ................- a)R
- b)[–1, 1]
- c){–1, 0, 1}
- d)Z
Correct answer is option 'C'. Can you explain this answer?
Consider the graphs of the functions f(x), h(x) and g(x).
The range of g(x) is ................
a)
R
b)
[–1, 1]
c)
{–1, 0, 1}
d)
Z
|
|
Preeti Iyer answered |
g(x) is the signum function. Its range is {–1, 0, 1}.
Consider the graphs of the functions f(x), h(x) and g(x).
The range of h(x) is .......................- a)R
- b)[–1, 1]
- c){–1, 0, 1}
- d)Z
Correct answer is option 'D'. Can you explain this answer?
Consider the graphs of the functions f(x), h(x) and g(x).
The range of h(x) is .......................
a)
R
b)
[–1, 1]
c)
{–1, 0, 1}
d)
Z
|
|
Preeti Iyer answered |
h(x) = [x] is the greatest integer function. Its range is Z (set of integers)
If A = {2, 4, 6, 8} and B = {2, 3, 5, 7, 9}. Which of the following is a function from A to B?- a)f : A → B defined by f(2) = 2, f(4) = 3, f(2) = 3
- b)f : A → B defined by f(2) = 2, f(4) = 3, f(4) = 2
- c)f : A → B defined by f(2) = 2, f(4) = 3, f(6) = 5, f(8) = 7
- d)f : A → B defined by f(2) = 2, f(4) = 2, f(2) = 3, f(8) = 9
Correct answer is option 'C'. Can you explain this answer?
If A = {2, 4, 6, 8} and B = {2, 3, 5, 7, 9}. Which of the following is a function from A to B?
a)
f : A → B defined by f(2) = 2, f(4) = 3, f(2) = 3
b)
f : A → B defined by f(2) = 2, f(4) = 3, f(4) = 2
c)
f : A → B defined by f(2) = 2, f(4) = 3, f(6) = 5, f(8) = 7
d)
f : A → B defined by f(2) = 2, f(4) = 2, f(2) = 3, f(8) = 9
|
Uday Kiran Pailu answered |
C . Because function from Ato B means functional value of A should be equal to values in B
A Relation R from A to B can be depicted pictorially using arrow diagram. In arrow diagram, we write down the elements of two sets A and B in two disjoint circles. Then we draw arrow from set A to set B whenever (a, b) ∈ R. An example of information depicted through an arrow diagram is shown below. For example:A company has four categories of employees given by Assistants (A), Clerks (C), Managers (M) and an Executive Officer (E). The company provides ₹10,000, ₹25,000, ₹50,000 and ₹1,00,000 as salaries to the people who work in the categories A, C, M and E respectively. Here A1, A2, A3, A4 and A5 are Assistants; C1, C2, C3, C4 are Clerks; M1, M2, M3 are Managers and E1, E2 are Executive Officers then the relation R is defined by xRy, where x is the salary given to person y.
Which among the above figures shows a Relation between the two non - empty sets?- a)A, C
- b)B, C
- c)A, B
- d)A, B, C
Correct answer is option 'C'. Can you explain this answer?
A Relation R from A to B can be depicted pictorially using arrow diagram. In arrow diagram, we write down the elements of two sets A and B in two disjoint circles. Then we draw arrow from set A to set B whenever (a, b) ∈ R. An example of information depicted through an arrow diagram is shown below. For example:
A company has four categories of employees given by Assistants (A), Clerks (C), Managers (M) and an Executive Officer (E). The company provides ₹10,000, ₹25,000, ₹50,000 and ₹1,00,000 as salaries to the people who work in the categories A, C, M and E respectively. Here A1, A2, A3, A4 and A5 are Assistants; C1, C2, C3, C4 are Clerks; M1, M2, M3 are Managers and E1, E2 are Executive Officers then the relation R is defined by xRy, where x is the salary given to person y.
Which among the above figures shows a Relation between the two non - empty sets?
a)
A, C
b)
B, C
c)
A, B
d)
A, B, C
|
|
Preeti Iyer answered |
Figures A and B show relations. Figure C shows a function but not a relation.
The following arrow diagram of the function f : A → A be defined as
- a)f (1) = 1, f (2) = 2, f(3) = 3, f(4) = 4, f(5) = 5
- b)f (1) = 2, f(2) = 2, f(3) = 5, f(4) = 1, f(5) = 4
- c)f (1) = 2, f (3) = 5, f(4) = 1, f(5) = 4
- d)f(1) = 4, f (2) = 1, f(3) = 2, f(4) = 5, f(5) = 3
Correct answer is option 'B'. Can you explain this answer?
The following arrow diagram of the function f : A → A be defined as
a)
f (1) = 1, f (2) = 2, f(3) = 3, f(4) = 4, f(5) = 5
b)
f (1) = 2, f(2) = 2, f(3) = 5, f(4) = 1, f(5) = 4
c)
f (1) = 2, f (3) = 5, f(4) = 1, f(5) = 4
d)
f(1) = 4, f (2) = 1, f(3) = 2, f(4) = 5, f(5) = 3
|
Arvind Kumar answered |
B
A Relation R from A to B can be depicted pictorially using arrow diagram. In arrow diagram, we write down the elements of two sets A and B in two disjoint circles. Then we draw arrow from set A to set B whenever (a, b) ∈ R. An example of information depicted through an arrow diagram is shown below. For example:A company has four categories of employees given by Assistants (A), Clerks (C), Managers (M) and an Executive Officer (E). The company provides ₹10,000, ₹25,000, ₹50,000 and ₹1,00,000 as salaries to the people who work in the categories A, C, M and E respectively. Here A1, A2, A3, A4 and A5 are Assistants; C1, C2, C3, C4 are Clerks; M1, M2, M3 are Managers and E1, E2 are Executive Officers then the relation R is defined by xRy, where x is the salary given to person y.
If the number of elements in set A and set B are p and q, then the number of relations from A to B are- a)2pq – 1
- b)2pq + 1
- c)2p2
- d)2pq
Correct answer is option 'D'. Can you explain this answer?
A Relation R from A to B can be depicted pictorially using arrow diagram. In arrow diagram, we write down the elements of two sets A and B in two disjoint circles. Then we draw arrow from set A to set B whenever (a, b) ∈ R. An example of information depicted through an arrow diagram is shown below. For example:
A company has four categories of employees given by Assistants (A), Clerks (C), Managers (M) and an Executive Officer (E). The company provides ₹10,000, ₹25,000, ₹50,000 and ₹1,00,000 as salaries to the people who work in the categories A, C, M and E respectively. Here A1, A2, A3, A4 and A5 are Assistants; C1, C2, C3, C4 are Clerks; M1, M2, M3 are Managers and E1, E2 are Executive Officers then the relation R is defined by xRy, where x is the salary given to person y.
If the number of elements in set A and set B are p and q, then the number of relations from A to B are
a)
2pq – 1
b)
2pq + 1
c)
2p2
d)
2pq
|
|
Preeti Iyer answered |
Number of relations from A to B is 2n(A)n(B) =2pq.
A Relation R from A to B can be depicted pictorially using arrow diagram. In arrow diagram, we write down the elements of two sets A and B in two disjoint circles. Then we draw arrow from set A to set B whenever (a, b) ∈ R. An example of information depicted through an arrow diagram is shown below. For example:A company has four categories of employees given by Assistants (A), Clerks (C), Managers (M) and an Executive Officer (E). The company provides ₹10,000, ₹25,000, ₹50,000 and ₹1,00,000 as salaries to the people who work in the categories A, C, M and E respectively. Here A1, A2, A3, A4 and A5 are Assistants; C1, C2, C3, C4 are Clerks; M1, M2, M3 are Managers and E1, E2 are Executive Officers then the relation R is defined by xRy, where x is the salary given to person y.
If the number of elements in set A and set B are p and q then the number of functions from A to B are- a)2pq – 1
- b)pq
- c)2pq
- d)qp
Correct answer is option 'D'. Can you explain this answer?
A Relation R from A to B can be depicted pictorially using arrow diagram. In arrow diagram, we write down the elements of two sets A and B in two disjoint circles. Then we draw arrow from set A to set B whenever (a, b) ∈ R. An example of information depicted through an arrow diagram is shown below. For example:
A company has four categories of employees given by Assistants (A), Clerks (C), Managers (M) and an Executive Officer (E). The company provides ₹10,000, ₹25,000, ₹50,000 and ₹1,00,000 as salaries to the people who work in the categories A, C, M and E respectively. Here A1, A2, A3, A4 and A5 are Assistants; C1, C2, C3, C4 are Clerks; M1, M2, M3 are Managers and E1, E2 are Executive Officers then the relation R is defined by xRy, where x is the salary given to person y.
If the number of elements in set A and set B are p and q then the number of functions from A to B are
a)
2pq – 1
b)
pq
c)
2pq
d)
qp
|
|
Preeti Iyer answered |
Number of functions from A to B n(B)n(A) = qp
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