Class 11

Math

JEE Main Questions

Mathematical Reasoning

Find the component statement of the following and check whether they are true or not: 24 is a multiple of 2,4, and 8.

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Write the component statements of each of the following statements. Also, check whether the statements are true or not. (i)If a triangle ABC is equilateral then it is isosceles. (ii)If $aandb$ are integers, then $ab$ is a rational number.

State whether the Or used in the following statements is exclusive of' inclusive. Give reasons for your answer.(i) Sun rises or Moon sets.(ii) To apply for a driving license, you should have a ration card or a passport.(iii) All integers are positive or negative.

Which of the following sentences are statements? Give reasons for your answer(i) There are $35$ days in a month(ii) Mathematics is difficult(iii) The sum of $5$ and $7$ is greater than $10$(iv) The square of a number is an even number(v) The sides of a quadrilateral have equal length(vi) Answer this question(vii) The product of $(−1)$ and $8$ is $8$(viii) The sum of all interior angles of a triangle is $180_{∘}$(ix) Today is a windy day(x) All real numbers are complex numbers

Write the contrapositive of the following statements: (i)If $x$ is prime number then $x$ is odd (ii)If two lines re parallel then they do not intersect in the same plane. (iii)$x$ is even number implies that $x$ is divisible by 4.

Write the negation of each of the following statements: (i)There exists a capital for every state in India. (ii)There exists a number which is equal to its square.

Find out whether the following sentence is a statement or not. Justify your answer: Mathematics is difficult.

Write the converse of the following statements: (i)If two integers $aandb$ are such that $a>b$ then $a−b$ is always a positive integer. (ii)If $x$ is prime number, then $x$ is odd. (iii)If two lines are parallel, then they do not intersect in the same place.

Find the component statements of the following compound statement: The roof is red and the will is white.