Class 11

Math

JEE Main Questions

Sets

Let $A={1,2,3,4,5,6}$. Insert the appropriate symbol $∈$or $∈/$in the blank spaces:(i) $5.A˙˙$ (ii) $8…A$ (iii) $0.A˙˙$(iv) $4..A˙$ (v) $2.A˙˙$ (vi) \displaystyle{10}.\dot{}

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Consider the sets X and Y of Example 14. Find $X∩Y$

Make correct statements by filling in the symbols $⊂$ or $⊂$ in blank spaces:(i) ${2,3,4}......{1,2,3,4,5}$ (ii) ${a,b,c}...{b,c,d}$(iii) {$x:x$ is a student of Class XI of your school}. . .{$x:x$ student of your school}(iv) {$x:x$ is a circle in the plane} . . .{$x:x$ is a circle in the same plane with radius 1 unit}(v) {$x:x$ is a triangle in a plane} . . . {$x:x$ is a rectangle in the plane}(vi) {$x:x$ is an equilateral triangle in a plane} . . . {$x:x$ is a triangle in the same plane}(vii) {$x:x$ is an even natural number} . . . {$x:x$ is an integer}

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: All messengers are soliders. All soliders are generals. Conclusions: I All messengers are generals. II All soliders are messengers.

Let $U={1,2,3,4,5,6,7,8,9}$, $A={1,2,3,4}$, $B={2,4,6,8}$and $C={3,4,5,6}$. Find (i) $A_{prime}$(ii) $B_{prime}$ (iii) $(A∪C)_{prime}$ (iv) $(A∪B)_{prime}$ (v) $(A′)′$ (vi) $(B–C)′$

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

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. Statement: In a one day cricket match, the total runs made by a team were 200. Out of these 160 runs were made by spinners. Conclusions: I. 80% of the team consists of spinners. II. The opening batsmen were spinners.

Let $A={a,e,i,o,u}$and $B={a,b,c,d)˙$Is A a subset of B? No.(Why?). Is B a subset of A? No. (Why?)

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: The distance of 900 km by road between Bombay and Jafra will be reduced to 280 km by sea. This will lead to a saving of Rs. 7.92 crores per annum on fuel. Conclusions: I. Transportation by sea is cheaper than that by road. II. Fuel must be saved to the greatest extent.