Class 11

Math

JEE Main Questions

Mathematical Reasoning

Find out weather following sentence is a statement or not. Justify your answer: Is the earth round?

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Given statements in (a) and (b). Identify the statements given below as contrapositive or converse of each other.(a) If you live in Delhi, then you have winter clothes. (i) If you do not have winter clothes, then you do not live in Delhi. (ii) If you have winter clothes, then you live in Delhi.(b) If a quadrilateral is a parallelogram, then its diagonals bisect each other. (i) If the diagonals of a quadrilateral do not bisect each other, then the quadrilateral is not a parallelogram. (ii) If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.

Write the negation of the following statements:(i) Chennai is the capital of Tamil Nadu,(ii) $2 $is not a complex number(iii) All triangles are not equilateral triangle.(iv) The number 2 is greater than 7.(v) Every natural number is

For each of the following statements, determine whether an inclusive OR or exclusive OR is used. Give reasons for your answer: A lady gives birth to a baby boy or a baby girl. To apply for a driving license, you should have a ration card or a passport.

Given below are two pairs of statements. Combine these two statements using if and only if: $p:$ if the sum of the digits of a number is divisible by 3, then the number is divisible by 3. $q:$ if a number is divisible by 3, then the sum of its divisible by 3.

Write the component statements of the following compound statements and check whether the compound statement is true or false: $2 $ is rational number or an irrational number. The school is closed, if there is a holiday or Sunday. A rectangle is a quadrilateral or a 5-sided polygon.

Show that the statement: $p:Ifx$ is a real number such that $x_{3}+4x=0,thexis0$ is true by (i)Direct method(ii). method of contradiction (iii). method of contrapositive.

Find the component of the following compound statement and check whether they are true or not: $2 $ is a rational number or an irrational number.

Check whether the following pair of statements is negation of each other. Give reasons for the answer(i) $x+y=y+x$ is true for every real numbers $x$ and $y$(ii) There exists real number $x$ and $y$ for which $x+y=y+x$