Real Numbers Test

Real Numbers

This is Real Numbers Test-05 for CBSE class 10 Maths.. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
If \(a\) is a non-zero rational and \(\sqrt b \) is irrational, then \(a\sqrt b \) is:
  • A
    an irrational number
    Correct
  • B
    a natural number
  • C
    an integer
  • D
    a rational number
2
The number \({(\sqrt 3 + \sqrt 5 )^2}\) is
  • A
    an irrational number
    Correct
  • B
    not a real number
  • C
    a rational number
  • D
    an integer
3
The number \(\frac{{\sqrt 5 + \sqrt 2 }}{{\sqrt 5 - \sqrt 2 }}\) is
  • A
    a rational number
  • B
    not a real number
  • C
    an irrational number
    Correct
  • D
    an integer
4
If ‘a’ and ‘b’ are both positive rational numbers, then \((\sqrt a + \sqrt b )(\sqrt a - \sqrt b )\) is
  • A
    neither rational nor rational number
  • B
    an irrational number
  • C
    a rational number
    Correct
  • D
    none of these
5
If ‘a’ and ‘b’ are both positive rational numbers, then \((\sqrt a + \sqrt b )(\sqrt a - \sqrt b )\) is
  • A
    an irrational number
  • B
    none of these
  • C
    a rational number
    Correct
  • D
    neither rational nor rational number
6
All non-terminating and non-recurring decimal numbers are
  • A
    natural numbers
  • B
    rational numbers
  • C
    integers
  • D
    irrational numbers
    Correct
7
A rational number can be expressed as a terminating decimal if the denominator has the factors
  • A
    2, 3 or 5 only
  • B
    2 or 3 only
  • C
    2 or 5 only
    Correct
  • D
    2 and 5 only
8
A rational number can be expressed as a non-terminating repeating decimal if the denominator has the factors
  • A
    none of these
  • B
    2 or 3 only
  • C
    other than 2 or 5
    Correct
  • D
    2 or 5 only
9
Let \(\frac{p}{q}\) be a rational number. Then, the condition on \(q\) such that \(\frac{p}{q}\) has a non-terminating but repeating decimal expansion is:
  • A
    \(q = {2^m} \times {3^n};m,n\) are whole numbers
  • B
    \(q = {2^m} \times {5^n};m,n\) are whole numbers
  • C
    \(q \ne {2^m} \times {3^n};m,n\) are whole numbers
  • D
    \(q \ne {2^m} \times {5^n};m,n\) are whole numbers
    Correct
10
Which of the following numbers has terminating decimal expansion?
  • A
    \(\frac{3}{{11}}\)
  • B
    \(\frac{5}{3}\)
  • C
    \(\frac{3}{7}\)
  • D
    \(\frac{3}{5}\)
    Correct
11
Which of the following numbers has non-terminating repeating decimal expansion?
  • A
    \(\frac{{15}}{{1600}}\)
  • B
    \(\frac{{23}}{8}\)
  • C
    \(\frac{{35}}{{50}}\)
  • D
    \(\frac{{17}}{6}\)
    Correct
12
The decimal expansion of ‘\(\pi \)’
  • A
    is terminating
  • B
    is non-terminating and recurring
  • C
    does not exist
  • D
    is non-terminating and non-recurring
    Correct
13
Which of the following numbers has non-terminating repeating decimal expansion?
  • A
    \(\frac{{77}}{{210}}\)
    Correct
  • B
    \(\frac{6}{{15}}\)
  • C
    \(\frac{{21}}{{280}}\)
  • D
    \(\frac{{117}}{{{6^2} \times {5^3}}}\)
14
The decimal expansion of the rational number \(\frac{{14587}}{{1250}}\) will terminate after
  • A
    1 decimal place
  • B
    4 decimal places
    Correct
  • C
    3 decimal places
  • D
    2 decimal places
15
The decimal form of \(\frac{5}{8}\) is
  • A
    0.375
  • B
    0.750
  • C
    0.600
  • D
    0.625
    Correct