Explain, why 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 are composite numbers.

Given numbers are 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 . We know that composite numbers are the numbers which are not prime and having more than two factors. ∴ 7 × 11 × 13 + 13 = 13 7 × 11 + 1 = 13 77 + 1 = 13 × 78 So, it is the product of two integers. Then, it has more than two factors. Hence, 7 × 11 × 13 + 13 is a composite number. ∴ 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 = 5 7 × 6 × 4 × 3 × 2 × 1 + 1 = 5 1 , 008 + 1 = 5 × 1009 So, it is the product of two integers. Then, it has more than two factors. Therefore, 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 is also a composite number.

Explain, why 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 are composite numbers.

Given numbers are 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 . We know that composite numbers are the numbers which are not prime and having more than two factors. ∴ 7 × 11 × 13 + 13 = 13 7 × 11 + 1 = 13 77 + 1 = 13 × 78 So, it is the product of two integers. Then, it has more than two factors. Hence, 7 × 11 × 13 + 13 is a composite number. ∴ 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 = 5 7 × 6 × 4 × 3 × 2 × 1 + 1 = 5 1 , 008 + 1 = 5 × 1009 So, it is the product of two integers. Then, it has more than two factors. Therefore, 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 is also a composite number.

If a number x is chosen at random from the numbers - 3 , - 2 , - 1 , 0 , 1 , 2 , 3 . What is the probability that x 2 ≤ 4 ?

Given numbers are - 3 , - 2 , - 1 , 0 , 1 , 2 , 3 Square of the numbers are 9 , 4 , 1 , 0 , 1 , 4 , 9 Then total number for which x 2 ≤ 4 are 5 Probability = Totalnumbers satisfying the condition Total numbers = 5 7 Therefore, the probability of x 2 ≤ 4 is 5 7 .

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Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 16 - Solved Mathematics Paper-1>Exercise>Q 22

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Explain, why $7 \times 11 \times 13 + 13$ and $7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 + 5$ are composite numbers.

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Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 16 - Solved Mathematics Paper-1>Exercise>Q 23

Find the number of roots, nature of roots and the roots of the graph given below.

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Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 16 - Solved Mathematics Paper-1>Exercise>Q 24

A boy was asked to add 3 to a certain number and to divide the sum by 2, but he subtracted 2 from the number and multiplied the remainder by 3 and got the same result. Find the number and the result.

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Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 16 - Solved Mathematics Paper-1>Exercise>Q 25

The product of Shikha's age five years ago and her age