Class 11

Math

JEE Main Questions

Sets

Assume that $P(A)=P(B)$. Show that $A=B$

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Write the set \displaystyle{A}={\left\lbrace{1},{4},{9},{16},{25},\dot{\dot{{\dot}}}\right\rbrace}in setbuilder form.

Statements: All buildings are windows. No toy is building Some tigers are toys. Conclusions: I Some tigers are buildings. II Some window are tigers. III All toys are tigers. IV Some windows are toys.

Directions: In each of the following questions below, a statement is given followed by two conclusions numbered I and II. You have to decide which alternative among the given options follow from the given statement. Statements: Population increase coupled with depleting resources is going to be the scenario of many developing countries in days to come. Conclusions: I. The population of developing countries will not continue to increase in future. II. It will be very difficult for the governments of developing countries to provide its people decent quality of life.

Find sets A, B and C such that $A∩B$, $B∩C$ and $A∩C$ are non empty sets and $A∩B∩C=ϕ$.

Write the following sets in the set-builder form(i) ${3,6,9,12}$ (ii) ${2,4,8,16,32}$ (iii) ${5,25,125,625}$ (iv) ${2,4,6,...}$ (v) ${1,4,9,...,100}$

If $U={1,2,3,4,5,6,7,8,9},A={2,4,6,8}$ and $B={2,3,5,7}.$ Verify that(i) $(A∪B)_{′}=A_{′}∩B_{′}$ (ii) $(A∩B)_{′}=A_{′}∪B_{′}$

How many elements has $P(A)$ , if $A=ϕ$?

Let $U={1,2,3,4,5,6,7,8,9},A={1,2,3,4},B={2,4,6,8}$ and $C={3,4,5,6}$.