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Chapter:

Determinants

1. Which of following is not a set of letters of word PRINCIPAL?

{P,R,I,N,C,A,L} {C,A,P,I,N,R,L} {P,R,I,N,C,I,P,A,L} {L,N,I,P,C,A,R}

{P,R,I,N,C,I,P,A,L}

A set has all unique elements. So set which contain all elements of word PRINCIPAL and no letter is repeated. Hence, {P,R,I,N,C,I,P,A,L} cannot be a set.

Hint Answer

2. Write solution set of equation x²-3x+2=0 in roster form.

{1,3} {2,4} {1,4} {1,2}

{1,2}

x²-3x+2=0
=>x²-x-2x-2=0=>x(x-1)-2(x-1)=0
=>(x-1)(x-2)=0=>x=1,2
so, solution set of equation x²-3x+2=0 in roster form is {1,2}.

Hint Answer

3. Write set \({\frac{1}{2}, \frac{2}{3}, \frac{3}{4}, \frac{4}{5}, \frac{5}{6}}\) in set builder form.

{x: \(x=\frac{n}{n+1}\) where n is a natural number less than 6} {x: \(x=\frac{n+1}{n+2}\) where n is a natural number less than 6} {x: \(x=\frac{n+1}{n}\) where n is a natural number less than 6} {x: \(x=\frac{n}{n+1}\) where n is a natural number less than 5}

{x: \(x=\frac{n}{n+1}\) where n is a natural number less than 6}

Since denominator is one more than numerator and only 5 terms are present. So, above set can be written as {x : \(x=\frac{n}{n+1}\) where n is a natural number less than 6}.

Hint Answer

4. Write set {x : x is an integer and x²-9=0} in roster form.

{3} {-3} {3,-3} {9,3}

{3,-3}

Since x is given as integer so x can be positive as well as negative.
x²-9=0 => (x-3)(x+3)=0 => x=3,-3.
So, set {x : x is an integer and x²-9=0} can be written as {3,-3}.

Hint Answer

5. Write set {x : x is a natural number and x²-9=0} in roster form.

{3} {-3} {3,-3} {9,3}

{3}

Since x is given as natural number so x can be positive only. x²-9=0 => (x-3)(x+3)=0 => x=3,-3.
Here, -3 is not a natural number so, set {x : x is a natural number and x²-9=0} can be written as {3}.

Hint Answer

6. Let A={1,2,3,4,5}. Insert appropriate symbol in 2 ____ A.

= < ∈ ∉

∈

Here, 2 is an element of set A.
So, 2 belong to set A. 2∈A.

Hint Answer

7. Let X={1,2,3,4,5,6}. Insert appropriate symbol in 9 ____ X.

= < ∈ ∉

∉

Here, 9 is not an element of set X.
So, 9 does not belongs to set A. 9∉X.

Hint Answer

8. Which of following does not belong to set {x : x is a vowel in English alphabet}?

e b i o

b

There are five vowels in English Alphabet a, e, i, o, u. So, set can be written in roster form as {a, e, i, o, u}. ?b? does not belongs to given set.

Hint Answer

9. Which one of following is correct representation for set {x: x is a positive integer and x³<50} in roster form?

{0,1,2,3,4,5} {-1,1,2,3} {1,2,3} {0,1,2,3}

{1,2,3}

0 is not a positive integer moreover
3³<50 and 4³>50

Hint Answer

10. The number of elements in set {x : x is a letter of word TRIGONOMETRY} is ______

8 7 9 10

9

The above set can be represented as {T,R,I,G,O,N,M,E,Y}. So, number of elements in set is 9.

Hint Answer

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Sets

Relations and Functions

Relations and Functions

Trigonometric Functions

Trigonometric Functions

Principle of Mathematical Induction

Principle of Mathematical Induction

Complex Numbers and Quadratic Equations

Complex Numbers and Quadratic Equations

Linear Inequalities

Linear Inequalities

Permutations and Combinations

Permutations and Combinations

Binomial Theorem

Binomial Theorem

Sequences and Series

Sequences and Series

Straight Lines

Conic Sections

Three Dimensional Geometry

Three Dimensional Geometry

Limits and Derivatives

Limits and Derivatives

Mathematical Reasoning

Mathematical Reasoning

Statistics

Probability

Relations and Functions II

Relations and Functions

Inverse Trigonometric Functions

Inverse Trigonometric Functions

Matrices

Determinants

Continuity and Differentiability

Continuity and Differentiability

Application of Derivatives

Application of Derivatives

Integrals

Application of Integrals

Application of Integrals

Differential Equations

Differential Equations

Vector Algebra

Three Dimensional Geometry

Three Dimensional Geometry

Linear Programming

Linear Programming

Probability

Application of Calculus

Application of Calculus

Topics

This Chapter Determinants consists of the following topics

Sets

Which of following is not a set of letters of word PRINCIPAL?

Write solution set of equation x²-3x+2=0 in roster form.

Write set \({\frac{1}{2}, \frac{2}{3}, \frac{3}{4}, \frac{4}{5}, \frac{5}{6}}\) in set builder form.

Write set {x : x is an integer and x²-9=0} in roster form.

Write set {x : x is a natural number and x²-9=0} in roster form.

Let A={1,2,3,4,5}. Insert appropriate symbol in 2 ____ A.

Let X={1,2,3,4,5,6}. Insert appropriate symbol in 9 ____ X.

Which of following does not belong to set {x : x is a vowel in English alphabet}?

Which one of following is correct representation for set {x: x is a positive integer and x³<50} in roster form?

The number of elements in set {x : x is a letter of word TRIGONOMETRY} is ______

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