Integers

Q. Question 6
Simplify $(256{)}^{-\left(4^{-\frac{3}{2}}\right)}$

Q.

Question

Prove that one of every three consecutive integers is divisible by3

Q.

Which of the following statements is correct?

1. 0 is a natural number

2. -1 is a whole number

3. 6.5 is an integer

4. 1 is a whole number

Q. A mother said to her son, the sum of our present ages is twice my age 12years ago and nine years hence, the sum of our ages will be thrice my age 14years ago. What is her sons present age

Q.

Prove that one of any three consecutive positive integers must be divisible by 3

Q. Question 5 (ix)
Find
2.73 $÷$ 1.3

Q. 4. If 4 whole numbers taken at random are multiplied together, then prob that the last digit in the product is 1, 3, 7 or 9 is

Q.

The ages of two friends Ani and Biju differ by 3 years. Ani’s father Dharam is twice as old as Ani and Biju as twice as old as his sister Cathy. The ages of Cathy and Dharam differ by 30 years. Find the ages of Ani and Biju.

Q. 50.If the eight digit number 2575d568 is divisible by 54 and 87 then find the value of the digit d .

Q.

1. Prove that the product of two consecutive positive integers is divisible by 2.

2. Prove that the product of three consecutive integers is divisible by 6.

Q.

Are all integers real numbers?

Q.

The predecessor of the integer $-1$ is

Q. If x and y are two odd primes such that X>y then x^2-y^2 is A. An odd number B. A prime number C.An even number D.An odd prime number

Q.

Question 3 (i)
Prove that $\frac{1}{\sqrt{2}}$ is irrational.

Q.

Write the successor of the number

$-47$

Q. If four positive integers a , b, c and d have a product of 8! and satisfy ab + a + b = 524 bc + b + c = 146 cd + c + d = 104 then the value of a - d is

Q.

Prove that one out of the every three consecutive positive integer is divisible by 3

Q.

Question 1 (i)
Without actually performing the long division, state whether $\frac{13}{3125}$ will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

Q. prime factorization of 7429

Q.

The successor of $-51$ is

1. $-50$

2. $-52$

3. $50$

4. $52$

Q. A six digit number is formed by repeating a three digit number, eg: 256256 or 678678. Any number of this form is divisible by: 1)7 2)1001 3)11 4)all of these

Q.

Write the predecessor and successor of the following integers.

$-5$

Q.

Prove that one of every three consecutive positive integers is divisible by 3

Q.

Find the successor of each of the following integers.

$-1$

Q. Prove that the product of three consecutive positive integer is divisible by 6.(note:its not any three consecutive positive integers.)

Q. 36. If the eight digit number 2575d568 is divisible by 54 and 87 , then the value of the digit d is 1. 4 2. 7 3. 0 4. 8

Q. show that one and only one out of n , n+2, n + 4 is divisible by 3 Where n is any positive integer

Q. If n is a natural number then 9²ⁿ – 5²ⁿ is divisible by --

Q. Prime factors of 609

Q.

Why is $0$ a real number?