Surds And Indices Questions MCQs


surds and indices Questions

Total Questions : 136

Page 1 of 7 pages
Question 1. (17)3.5 × (17)? = 178
  1.    2.29
  2.    2.75
  3.    4.25
  4.    4.5
Answer: Option D
Question 2. Given that 100.48 = x, 100.70 = y and xz = y2, then the value of z is close to:
  1.    1.45
  2.    1.88
  3.    2.9
  4.    3.7
Answer: Option C
Question 3. $${\text{If}}\,{\kern 1pt} {\left( {\frac{a}{b}} \right)^{x - 1}} = {\left( {\frac{b}{a}} \right)^{x - 3}},$$     then the value of x is
  1.    $$\frac{1}{2}$$
  2.    1
  3.    2
  4.    $$\frac{7}{2}$$
Answer: Option C
Question 4. If 5a = 3125, then the value of 5(a - 3) is:
  1.    25
  2.    125
  3.    625
  4.    1625
Answer: Option A
Question 5. If 3(x - y) = 27 and 3(x + y) = 243, then x is equal to:
Answer: Option A
Question 6. (256)0.16 × (256)0.09 = ?
  1.    4
  2.    16
  3.    64
  4.    256.25
  5.    None of these
Answer: Option A
Question 7. The value of [(10)150 ÷ (10)146]
  1.    1000
  2.    10000
  3.    100000
  4.    106
  5.    None of these
Answer: Option B
Question 8. $$\frac{1}{{1 + {x^{\left( {b - a} \right)}} + {x^{\left( {c - a} \right)}}}}$$    $$ + \frac{1}{{1 + {x^{\left( {a - b} \right)}} + {x^{\left( {c - b} \right)}}}}$$    $$ + \frac{1}{{1 + {x^{\left( {b - c} \right)}} + {x^{\left( {a - c} \right)}}}} = ?$$
Answer: Option B
Question 9. (25)7.5 × (5)2.5 ÷ (125)1.5 = 5?
  1.    8.5
  2.    13
  3.    16
  4.    17.5
  5.    None of these
Answer: Option B
Question 10. (0.04)-1.5 = ?
  1.    25
  2.    125
  3.    250
  4.    625
Answer: Option B
Question 11. $$\frac{{{{\left( {243} \right)}^{n/5}} \times {3^{2n + 1}}}}{{{9^n} \times {3^{n - 1}}}} = ?$$
  1.    1
  2.    2
  3.    9
  4.    3n
Answer: Option C
Question 12. $$\frac{1}{{1 + {a^{\left( {n - m} \right)}}}} + \frac{1}{{1 + {a^{\left( {m - n} \right)}}}} = ?$$
Answer: Option C
Question 13. If m and n are whole numbers such that mn = 121, the value of (m - 1)n + 1 is:
  1.    1
  2.    10
  3.    121
  4.    1000
Answer: Option D
Question 14. If $$x = 3 + 2\sqrt 2 ,$$    then the value of $$\left( {\sqrt x - \frac{1}{{\sqrt x }}} \right)$$   is:
  1.    1
  2.    2
  3.    $$2\sqrt 2 $$
  4.    $$3\sqrt 3 $$
Answer: Option B
Question 15. $${\left( {\frac{{{x^b}}}{{{x^c}}}} \right)^{\left( {b + c - a} \right)}}.$$   $${\left( {\frac{{{x^c}}}{{{x^a}}}} \right)^{\left( {c + a - b} \right)}}.$$   $${\left( {\frac{{{x^a}}}{{{x^b}}}} \right)^{\left( {a + b - c} \right)}}$$   = ?
  1.    xabc
  2.    1
  3.    xab + bc + ca
  4.    xa + b + c
Answer: Option B
Question 16. Simplify : $$\left( {\frac{{\frac{3}{{2 + \sqrt 3 }} - \frac{2}{{2 - \sqrt 3 }}}}{{2 - 5\sqrt 3 }}} \right) = ?$$
  1.    $$\frac{1}{2} - 5\sqrt 3 $$
  2.    2 - $$5\sqrt 3 $$
  3.    1
  4.    0
Answer: Option C
Question 17. ($$\sqrt 8$$ - $$\sqrt 4 $$ - $$\sqrt 2 $$) Equals to = ?
  1.    2 - $$\sqrt 2 $$
  2.    $$\sqrt 2 $$ - 2
  3.    2
  4.    -2
Answer: Option B
Question 18. $${\left( {64} \right)^{ - \frac{2}{3}}} \times {\left( {\frac{1}{4}} \right)^{ - 2}}$$    is equal to ?
  1.    1
  2.    2
  3.    $$\frac{1}{2}$$
  4.    $$\frac{1}{{16}}$$
Answer: Option A
Question 19. The value of $$\left( {\frac{{{9^2} \times {{18}^4}}}{{{3^{16}}}}} \right)$$   is = ?
  1.    $$\frac{3}{2}$$
  2.    $$\frac{4}{9}$$
  3.    $$\frac{{16}}{{81}}$$
  4.    $$\frac{{32}}{{243}}$$
Answer: Option C
Question 20. $$\left[ {{4^3} \times {5^4}} \right] \div {4^5} = ?$$
  1.    29.0825
  2.    30.0925
  3.    35.6015
  4.    39.0625
  5.    None of these
Answer: Option D