11th Maths Monthly Test-3 ( Sets, Relations and Functions )

St. Britto Hr. Sec. School - Madurai

11th Maths Monthly Test-3 ( Sets, Relations and Functions )-Aug 2020

Time : 2.30 Hours

Part - A

Generic 2 - Answer All Question

If the function f:R➝R be given by f(x)=x²+2 and g(x)=2x, find fog and gof

If f: R ⟶ R is an bijection given by f(x)= x³+3, then find f^-1(x)

On the set of natural number let R be the relation defined by aRb if a + b \(\le\) 6. Write down the relation by listing all the pairs. Check whether it is equivalence.

Let A = {0,1, 2, 3}. Construct relations on A of the following types:
(i) not reflexive, symmetric, not transitive.
(ii) not reflexive, symmetric, transitive.

Find the domain and range of \({1 \over 1-cos\ x}.\)

Find the domain of \(d(x)={1\over 1-3cosx}\)

On the set of natural number let R be the relation defined by aRb if a + b \(\le\) 6. Write down the relation by listing all the pairs. Check whether it is transitive

For n, m\(\in \)N, n/m means that n is a factor of n & m. Then find whether the given relation is an equivalence relation.

The weight of the muscles of a man is a function of his body weight x and can be expressed as W(x)=0.35x. Determine the domain of this function.

Let X = {a, b, c, d}, and R = {(a, a) (b, b) (a, c)}. Write down the minimum number of ordered pairs to be included to R to make it
Reflexive

this is demo

State whether the following sets are finite or infinite.
{x \(\in \) R:x is a rational number}

Write the following sets in roster form, {The set of positive roots of the equation (x²-4)(x³-27)=0}.

Let A={1,2,3,4} and B = {a,b,c,d}. Give a function from A\(\rightarrow\)B for each of the following:
neither one- to -one and nor onto.

Part - B

Generic 3 - Answer All Question

Draw venn diagram of three sets A, B and C which illustrates the following:
A ∩ B ∩ C

If f,g,h are real valued functions defined on R, then prove that (f+g) oh=foh+goh. What can you say about fo(g+h)? Justify your answer.

Consider the functions:
(i) y = x²; (ii) y = -x²

By taking suitable sets A, B, C, verify the following results:
A \(\times\) (B\(\cap \)C)=(A\(\times\)B) \(\cap \) (A\(\times\)C)

If n (p(A)) = 1024, n(A\(\cup\)B)=15 and n(p(B))=32, then find n(A\(\cap\)B).

Let us now draw the graph of y = 2 sin ( x - 1 ) + 3.

By using the same concept applied in previous example, graphs of y = sin x and y = sin 2x, and also their combined graphs are given figures (a), (b) and (c). The minimum and maximum values of sin x and sin 2x are the same. But they have different x-intercepts. The x-intercepts for y = sin x are \(\pm n\pi\) and for y = sin 2x are \(\pm{1\over 2}n\pi,\ n\in Z.\)

Consider the positive branches y² = x and y² = -x.

In a survey of 5000 persons in a town, it was found that 45% of the persons know Language A, 25% know Language B, 10% know Language C,5% know Languages A and B, 4% know Languages B and C, and 4% know Languages A and C. If 3% of the persons know all the three Languages, find the number of persons who knows only Language A.

By taking suitable sets A, B, C, verify the following results:
C-(B-A) = (C\(\cap \) A) \(\cup \) (C\(\cap \)B')

If the function f and g are given by f = {(1, 2), (3,5), (4, 1)} g = {(2, 3), (5, 1), (1, 3)} find range of fand g. Also write down fog.

By taking suitable sets A, B, C, verify the following results:
(B-A)\(\cap \)C = (B\(\cap \)C)-A = B\(\cap \)(C-A)

Compare and contrast the graph y = x² - 1, y = 4(x² - 1) and y = (4x)² = 1.

Which of the following sets are finite and which are infinite?
Set of concentric circles in a plane.

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11th Maths Monthly Test-3 ( Sets, Relations and Functions )

St. Britto Hr. Sec. School - Madurai

11th Maths Monthly Test-3 ( Sets, Relations and Functions )-Aug 2020

Part - A

Generic 2 - Answer All Question

If the function f:R➝R be given by f(x)=x2+2 and g(x)=2x, find fog and gof

If f: R ⟶ R is an bijection given by f(x)= x3+3, then find f-1(x)

On the set of natural number let R be the relation defined by aRb if a + b \(\le\) 6. Write down the relation by listing all the pairs. Check whether it is equivalence.

Let A = {0,1, 2, 3}. Construct relations on A of the following types: (i) not reflexive, symmetric, not transitive. (ii) not reflexive, symmetric, transitive.

Find the domain and range of \({1 \over 1-cos\ x}.\)

Find the domain of \(d(x)={1\over 1-3cosx}\)

On the set of natural number let R be the relation defined by aRb if a + b \(\le\) 6. Write down the relation by listing all the pairs. Check whether it is transitive

For n, m\(\in \)N, n/m means that n is a factor of n & m. Then find whether the given relation is an equivalence relation.

The weight of the muscles of a man is a function of his body weight x and can be expressed as W(x)=0.35x. Determine the domain of this function.

Let X = {a, b, c, d}, and R = {(a, a) (b, b) (a, c)}. Write down the minimum number of ordered pairs to be included to R to make it Reflexive

this is demo

State whether the following sets are finite or infinite. {x \(\in \) R:x is a rational number}

Write the following sets in roster form, {The set of positive roots of the equation (x2-4)(x3-27)=0}.

Let A={1,2,3,4} and B = {a,b,c,d}. Give a function from A\(\rightarrow\)B for each of the following: neither one- to -one and nor onto.

Part - B

Generic 3 - Answer All Question

Draw venn diagram of three sets A, B and C which illustrates the following: A ∩ B ∩ C

If f,g,h are real valued functions defined on R, then prove that (f+g) oh=foh+goh. What can you say about fo(g+h)? Justify your answer.

Consider the functions: (i) y = x2; (ii) y = -x2

By taking suitable sets A, B, C, verify the following results: A \(\times\) (B\(\cap \)C)=(A\(\times\)B) \(\cap \) (A\(\times\)C)

If n (p(A)) = 1024, n(A\(\cup\)B)=15 and n(p(B))=32, then find n(A\(\cap\)B).

Let us now draw the graph of y = 2 sin ( x - 1 ) + 3.

Consider the positive branches y2 = x and y2 = -x.

By taking suitable sets A, B, C, verify the following results: C-(B-A) = (C\(\cap \) A) \(\cup \) (C\(\cap \)B')

If the function f and g are given by f = {(1, 2), (3,5), (4, 1)} g = {(2, 3), (5, 1), (1, 3)} find range of fand g. Also write down fog.

By taking suitable sets A, B, C, verify the following results: (B-A)\(\cap \)C = (B\(\cap \)C)-A = B\(\cap \)(C-A)

Compare and contrast the graph y = x2 - 1, y = 4(x2 - 1) and y = (4x)2 = 1.

Which of the following sets are finite and which are infinite? Set of concentric circles in a plane.

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If the function f:R➝R be given by f(x)=x²+2 and g(x)=2x, find fog and gof

If f: R ⟶ R is an bijection given by f(x)= x³+3, then find f^-1(x)

Let A = {0,1, 2, 3}. Construct relations on A of the following types:
(i) not reflexive, symmetric, not transitive.
(ii) not reflexive, symmetric, transitive.

Let X = {a, b, c, d}, and R = {(a, a) (b, b) (a, c)}. Write down the minimum number of ordered pairs to be included to R to make it
Reflexive

State whether the following sets are finite or infinite.
{x \(\in \) R:x is a rational number}

Write the following sets in roster form, {The set of positive roots of the equation (x²-4)(x³-27)=0}.

Let A={1,2,3,4} and B = {a,b,c,d}. Give a function from A\(\rightarrow\)B for each of the following:
neither one- to -one and nor onto.

Draw venn diagram of three sets A, B and C which illustrates the following:
A ∩ B ∩ C

Consider the functions:
(i) y = x²; (ii) y = -x²

By taking suitable sets A, B, C, verify the following results:
A \(\times\) (B\(\cap \)C)=(A\(\times\)B) \(\cap \) (A\(\times\)C)

Consider the positive branches y² = x and y² = -x.

By taking suitable sets A, B, C, verify the following results:
C-(B-A) = (C\(\cap \) A) \(\cup \) (C\(\cap \)B')

By taking suitable sets A, B, C, verify the following results:
(B-A)\(\cap \)C = (B\(\cap \)C)-A = B\(\cap \)(C-A)

Compare and contrast the graph y = x² - 1, y = 4(x² - 1) and y = (4x)² = 1.

Which of the following sets are finite and which are infinite?
Set of concentric circles in a plane.