Class 11

Math

JEE Main Questions

Sets

Find the pairs of equal sets, if any, give reasons:$A={0},$ $B={x:x>15andx<5},$$C={x:x5=0},$$D={x:x_{2}=25},$\displaystyle{E}={\left\lbrace{x}:{x}{i}{s}{a}{n}\in{t}{e}{g}{r}{a}{l}{p}{o}{s}{i}{t}{i}{v}{e}\right.}

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Directions: In each of the questions below are given two statements followed by two conclusion numbered I and II. You have to take the two given statements to be true even if they seems to be at variance from commonly known facts. Read the conclusions and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts. Statements: Some metals are minerals. All minerals are solids. Conclusions: I All solids are made up of metals and minerals. II some minerals are metals.

If $X$ and $Y$ are two sets such that $X$ has $40$ elements, $X∪Y$ has $60$ elements and $X∩Y$ has $10$ elements, how many elements does $Y$ have?

Looking at the Venn diagram list the elements of the following sets:$C∖B$

With the help of Venn diagram prove that : $(A∪B)_{′}=A_{′}∩B_{′}$

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.

In a group of $70$ people, $37$ like coffee, $52$ like tea and each person likes at least one of the two drinks. How many people like both coffee and tea?

In the Venn diagram, the universal set, $ξ=P∪Q∪R$Which of the four regions labelled A, B, C and D represents the sets $P∩Q∩R$?

Decide, among the following sets, which sets are subsets of one and another: