Class 11

Math

JEE Main Questions

Sets

Write the solution set of the equation $x_{2}+x−2=0$in roster form.

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

Is it true that for any sets A and B, $P(A)∪P(B)=P(A∪B)$? Justify your answer.

Find the intersection of each pair of sets of question 1 above.

In a group of $400$ people, $250$ can speak Hindi and $200$ can speak English. How many people can speak both Hindi and English?

Using properties of sets, show that(i) $A∪(A∩B)=A$ (ii) $A∩(A∪B)=A$.

If $U={a,b,c,d,e,f,g,h}$, find the complements of the following sets:

Which of the following are examples of the null set(i) Set of odd natural numbers divisible by 2(ii) Set of even prime numbers(iii) {x: x is a natural numbers, $x<5$and $x>7$}(iv) {y: y is a point common to any two parallel lines}

Match each of the set on the left in the roster form with the same set on the right described in set builder form: (i) ${1,2,3,6}$ (a) {x : x is a prime number and a divisor of 6} (ii) ${2,3}$ (b) {x : x is an odd natural number less than 10} (iii) {M,A,T,H,E,I,C,S} (c) {x : x is natural number and divisor of 6} (iv) {1, 3, 5, 7, 9} (d) {x : x is a letter of the word MATHEMATICS}.