Class 11

Math

JEE Main Questions

Mathematical Reasoning

Write the negation of the following statements: (i)For all positive integer $x,$ we have $x+2>8.$ (ii)Every living person in not 150 years old.

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Write the negation of the following statements and check whether the resulting statements are true: The sum of 2 and 5 is 9.

Determine the contrapositive of each of the following statements: (i)If Mohan is a poet, then he is poor. (ii)If she works, she will earn money. (iii)It never rains when it is cold.

Evaluate the following limit: $(lim)_{x→0}xsinxx_{2}+1−cosx $

Write the component statements of the following compound statements and check whether the compound statement is true or false.(i) A line is straight and extends indefinitely in both directions.(ii) 0 is less than every positive integer and every negative integer.(iii) All living things have two legs and two eyes.

Write the following statements in the form if $p$ then $q:$ You can access the website only if you pay a subscription fee.

Write each of the following statements in the form if $p$ then $q:$ There is traffic jam whenever it rains.

Write the contrapositive of the following statements: (i) If a number is divisible by 9, then it is divisible by 3. (ii) If you are born in India, then you are a citizen of India (iii) If a triangle is equilateral it is isosceles.

For each of eth following statements, determine whether an inclusive OR or exclusive OR is used. Give reasons for your answer: Sun rises or Moon sets. Al integers are positive or negative.