Cardinal number of some sets MCQ - Practice Questions & Answers

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If $f(x)=x^{2}+2bx+2c^{2}$ and $g(x)=x^{2}-2cx+b^{2}$ such that $min \hspace{0.2cm}f(x)> \hspace{0.2cm} max\hspace{0.2cm}g(x)$ , then the relation between $b$ and $c$ is.

$\quad|c|>\sqrt{3}|b|$

$\quad|c|>\sqrt{2}|b|$

$\quad|c|>\sqrt{5}|b|$

none of these

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The number of symmetric matrices of order 3, with all the entries from the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, is

$10^{9}$

$10^{6}$

$9^{10}$

$6^{10}$

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Concepts Covered - 1

Cardinal number of some sets

The number of distinct elements in a finite set A is called Cardinal number of set A and it is denoted by n(A).

For example, if set A = {1, 3, 7, 11, 13} then n(A) = 5

Given, any two finite sets A and B, then Number of Elements in the union of set A & B is given by

n (A ∪ B) = n (A) + n (B) – n (A ∩ B)

If (A ∩ B) = φ,then n(A ∪ B) = n (A) + n (B)

Given A, B and C be any finite sets, then Number of Elements in the union of sets A, B & C is given by

$\mathrm{n(A\cup B\cup C)=n(A)+n(B)+n(C)-n(A\cap B)-n(B\cap C)-n(A\cap C)+n(A\cap B\cap C)}$

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Cardinal number of some sets - Practice Questions & MCQ

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