Question

If $$A = \left\{ {1,\,2,\,3,\,4,\,5} \right\},$$     then the number of proper subject of $$A$$ is :

A. $$31$$  
B. $$38$$
C. $$48$$
D. $$54$$
Answer :   $$31$$
Solution :
Note : Number of proper subjects of $$A = {2^n} - 1$$
Given : $$A = \left\{ {1,\,2,\,3,\,4,\,5} \right\}.$$     Here $$n = 5$$
$$\therefore $$  number of proper subjects $$ = {2^5} - 1 = 31$$

Releted MCQ Question on
Calculus >> Sets and Relations

Releted Question 1

If $$X$$ and $$Y$$ are two sets, then $$X \cap {\left( {X \cup Y} \right)^c}$$   equals.

A. $$X$$
B. $$Y$$
C. $$\phi $$
D. None of these
View Answer
Releted Question 2

The expression $$\frac{{12}}{{3 + \sqrt 5 + 2\sqrt 2 }}$$    is equal to

A. $$1 - \sqrt 5 + \sqrt 2 + \sqrt {10} $$
B. $$1 + \sqrt 5 + \sqrt 2 - \sqrt {10} $$
C. $$1 + \sqrt 5 - \sqrt 2 + \sqrt {10} $$
D. $$1 - \sqrt 5 - \sqrt 2 + \sqrt {10} $$
View Answer
Releted Question 3

If $${x_1},{x_2},.....,{x_n}$$    are any real numbers and $$n$$ is any positive integer, then

A. $$n\sum\limits_{i = 1}^n {{x_i}^2 < {{\left( {\sum\limits_{i = 1}^n {{x_i}} } \right)}^2}} $$
B. $$\sum\limits_{i = 1}^n {{x_i}^2 \geqslant {{\left( {\sum\limits_{i = 1}^n {{x_i}} } \right)}^2}} $$
C. $$\sum\limits_{i = 1}^n {{x_i}^2 \geqslant n{{\left( {\sum\limits_{i = 1}^n {{x_i}} } \right)}^2}} $$
D. none of these
View Answer
Releted Question 4

Let $$S$$ = {1, 2, 3, 4}. The total number of unordered pairs of disjoint subsets of $$S$$ is equal to

A. 25
B. 34
C. 42
D. 41
View Answer

Practice More Releted MCQ Question on
Sets and Relations

Practice More MCQ Question on Maths Section

AlgebraSequences and SeriesQuadratic EquationComplex NumberMatrices and DeterminantsPermutation and CombinationBinomial TheoremMathematical InductionMathematical Reasoning
Statistics and ProbabilityStatisticsProbability
CalculusSets and RelationsFunctionLimitsContinuityDifferentiability and DifferentiationApplication of DerivativesDifferential EquationsIndefinite IntegrationDefinite IntegrationApplication of Integration
GeometryStraight LinesCircleParabolaEllipseHyperbolaLocus3D Geometry and VectorsThree Dimensional Geometry
TrigonometryTrigonometric Ratio and IdentitiesTrignometric EquationsProperties and Solutons of TriangleInverse Trigonometry Function