Olympiad – Class X – Mathematics - Real Numbers

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Question - 1

The L.CM. and H.C.F. of marks scored by Ajit and Amar in a math test are 5040 and 12 respectively. If Amar's score is 144, what is Ajit's score?

  • A 288
  • B 132
  • C 564
  • D 420

Question - 2

'p' is the remainder obtained when a perfect square is divided by 3.What is the value of 'p'?

  • A 1
  • B 0
  • C Either (A) or (B).
  • D Neither (A) nor (B).

Question - 3

The factor tree shows the prime factorization of 1314.

Find the respective values of 'a' and 'b'

  • A 3,37
  • B 3,73
  • C 73,3
  • D 9,73

Question - 4

The following are the first and last steps in finding the H.CF.of 408 and 1032 using Euclid's algorithm.
Step 1: 1032 = 408 x 2 + 216
Step 2: _________________
Step 3: _________________
Step 4: 192 = 24 x 8 + 0
Choose the steps 2 and 3.
(i) 408 = 216 1 + 192
(ii) 408 = 216 + 180 + 12
(iii) 216 = 192 1 + 24
(iv) 192 = 24 8 + 0

  • A (i) and (ii)
  • B (i) and (iii)
  • C (ii) and (iii)
  • D (iii) and (iv)

Question - 5

For what value of 'x' does 6x end with 5?

  • A 0
  • B 1
  • C 5
  • D Never ends with 5.

Question - 6

If 4 divides 1728, which of the following statements is true?

  • A 4 divides 12
  • B 6 divides 1728
  • C 2 divides 1728
  • D 4 divides 144.

Question - 7

Dimensions of a rectangle are (25 x 7) cm and (2 x 52 x 73) cm. Express the area of the rectangle in prime factorization form.

  • A 2 x 5 x 7 cm2
  • B 2 x 73 cm2
  • C 26 x 52 x 74 cm2 
  • D 25 x 52 x 73 cm2

Question - 8

Choose the irrational number.

  • A 2-\(\sqrt{4}\)
  • B \(\left( \sqrt { 5 } \right) ^{ 2 }\).
  • C \(\sqrt { 9 } -\sqrt { 4 } \).
  • D \(\sqrt { 2 } -\sqrt { 3 } \).

Question - 9

Given a=3-\(\sqrt{2}\) and b=3+\(\sqrt{2}\), which of the following is correct?

  • A a + b is irrational.
  • B a - b is rational
  • C ab is rational.
  • D \(\frac{a}{b}\) is rational.

Question - 10

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?

  • A 0≤r≤b
  • B 0<r≤b
  • C 0≤r<b
  • D 0<r<b