Question

Can you please provide me with all the important high grade questions of Real numbers.

Answer 1

LONG ANSWER TYPE QUESTIONS: Real Number

1. Find HCF of 56, 96 and 324 by Euclid’s algorithm
2. Show that the square of any positive integer is either of the form 3m or 3m + 1 for some integer m
3. Show that any positive odd integer is of the form 6q + 1, 6q + 5 where q is some integer.
4. Prove that the square of any positive integer is of the form 5q, 5q + 1, 5q + 4 for some integer, q.
5. Prove that the product of three consecutive positive integers is divisible by 6.
6. Show that one and only one of n, n + 2, n + 4 is divisible by 3.
7. Two milk containers contains 398 l and 436 l of milk. The milk is to be transferred to another container with the help of a drum. While transferring to another container 7 l and 11 l of milk is left in both the containers respectively. What will be the maximum capacity of the drum.
8. Check whether 5 × 6 × 2 × 3 + 3 is a composite number
9. Check whether 14n can end with the digit zero for any natural number, n
10. If a = 4q + r then what are the conditions for a and q. What are the values that r can take?

Using Euclid’s theorem to find the HCF between the following numbers
a) 867 and 225
b) 616 and 32

True or False statement
a) Number of the form 2n +1 where n is any positive integer are always odd number
b) Product of two prime number is always equal to their LCM
c) √3X √12 is a irrational number
d) Every integer is a rational number
e) The HCF of two prime number is always 1
f) There are infinite integers between two integers
g) There are finite rational number between 2 and 3
h) √3 Can be expressed in the form √3/1,so it is a rational number
i) The number 6ⁿ for n in natural number can end in digit zero
j) Any positive odd integer is of the form 6m+1 or 6m+3 or 6m +5 where q is some integer


2+√2 Is a
a)Non terminating repeating
b) Terminating
c)Non terminating non repeating
d) None of these


Find the HCF and LCM of these by factorization technique
a)27,81
b) 120 ,144
c) 29029 ,580


if x2=3,y2=9,z3=27, which of these is true
a) x is a irrational number
b) y is a rational number
c) z is rational number
d) All of the above

Find all the positive integral values of p for which p2+16 is a perfect square?



hope this helps you