REAL NUMBERS

Euclid's division lemma: For any two positive integers 'a' and 'b', there exist unique integers 'q' and 'r' such that a = bq + r. What is the condition that 'r' must satisfy?
1. 0 ≤ r ≤ b
2. 0 < r ≤ b
3. 0 ≤ r < b
4. 0 < r < b
The following are the first and last step in finding the H.C.F. of 36 and 56 using Euclid?s algorithm.
Step 1:56 = 36 × 1 + 20
Step 2: ____________
Step 3: ____________
Step 4:16 = 4 × 4 + 0
Choose the steps 2 and 3.
(i) 36 = 20 × 1 + 16
(ii) 24 = 20 × 1 + 4
(iii) 20 = 16 × 1 + 4
(iv) 56 = 18 × 2 + 20
1. (i) and (ii)
2. (i) and (iii)
3. (ii) and (iii)
4. (iii) and (iv)
Set of natural number is a subset of
1. Set of even numbers
2. Set of odd numbers
3. Set of composite numbers
4. Set of real numbers.
According to the fundamental theorem of arithmetic, if p(a prime number) divides a² and a is positive, then
1. a divides p
2. a² divides p
3. a² divides p²
4. p divides a
The number in the form of 4K + 3 where K is whole number, is always;
1. An odd number
2. An even number
3. A perfect square
4. Divisible by 3
The L.C.M. and H.C. F. of marks scored by Supravin & Kumar in a test are 1489645 and 1 respectively. If Supravin's score is 1145, what is Kumar's score?
1. 68
2. 666
3. 1295
4. 1301
When a number is divided by 19, its remainder is always
1. Greater than 19
2. Lies between 19 and 57
3. Greater or equal to zero but less than 19
4. Less than zero
The factor tree shows the prime factorization of 1020. Then (a, b) is
1. 2, 17
2. 3, 34
3. 34, 3
4. 5, 17
'P' is the remainder obtained when a perfect square is divided by 3. What is the value of 'p'?
1. 1
2. 0
3. Either (a) or (b)
4. Neither (a) or (b)
If 9 divides 6561, which of the following statements is true?
1. 9 divides 81
2. 7 divides 243
3. 7 divides 2178
4. 9 divides 2189
The remainder when a number is divided by 165 is 21. What is the remainder, when the same number is divided by 11?
1. 4
2. 5
3. 11
4. 10
A positive number 'n' when divided by 9 leaves a remainder 6 what is the remainder when 3n + 2 is divided by 3?
1. 0
2. 1
3. 2
4. 3
Which of the following is true for two co-prime numbers?
1. Their H.C.F. is 1.
2. Their L.C.M. is 1.
3. Their H.C.F. is equal to their product.
4. Their L.C.M. is twice their H.C.F.
By what number must 1587 be divided to get a quotient 27 and remainder 21?
1. 58
2. 57
3. 59
4. 63
Find the number which when divided by 87 leaves a remainder 49 and gives a quotient 50.
1. 3997
2. 4399
3. 4301
4. 4019
Choose the terminating decimal.
1. 641/8000
2. 29/66
3. 283/120
4. 617/81
Given a=p−√q and b=p+√q which of the following is correct. Where q is a prime number.
1. a + b is irrational
2. a - b is rational
3. 2ab is rational
4. a/b is rational
1 ∕ (√3 - √2)is not equal to
1. √3+√2
2. √3 ∕ (3-√6)
3. (√3-√2) ∕ (5-2√6)
4. 4 ∕ (√10-√8)
Choose the irrational number
1. 3 - √9
2. (√12)²
3. √625−√576
4. √125−√64
Find the LCM and HCF of the 26 and 91
1. 182,13
2. 162,11
3. 192,14
4. None

REAL NUMBERS

Quiz