Surds And Indices MCQ

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• The greatest of $$\sqrt 2 ,$$  $$\root 6 \of 3 ,$$  $$\root 3 \of 4 ,$$  $$\root 4 \of 5 $$   is = ?
  ক

  $$\sqrt 2 $$

  খ

  $$\root 3 \of 4 $$

  গ

  $$\root 4 \of 5 $$

  ঘ

  $$\root 6 \of 3 $$
• The greatest among the numbers $${\left( {2.89} \right)^{0.5}},$$   $$2 - {\left( {0.5} \right)^2},$$   $$1 + \frac{{0.5}}{{1 - \frac{1}{2}}},$$   $$\sqrt 3 $$  is = ?
  ক

  $${\left( {2.89} \right)^{0.5}}$$

  খ

  $${\text{2}} - {\left( {0.5} \right)^2}$$

  গ

  $$1 + \frac{{0.5}}{{1 - \frac{1}{2}}}$$

  ঘ

  $$\sqrt 3 $$
• The greatest one of $$\sqrt 2 ,$$  $$\root 3 \of 3 ,$$  $$\root 6 \of 6 ,$$  $$\root 5 \of 5 $$  is = ?
  ক

  $$\sqrt 2 $$

  খ

  $$\root 3 \of 3 $$

  গ

  $$\root 6 \of 6 $$

  ঘ

  $$\root 5 \of 5 $$
• The least one among $${\text{2}}\sqrt 3 {\text{,}}$$  $${\text{2}}\root 4 \of 5 {\text{,}}$$  $$\sqrt 8 {\text{,}}$$  $${\text{3}}\sqrt 2 $$  is = ?
  ক

  $${\text{2}}\sqrt 3 $$

  খ

  $${\text{2}}\root 4 \of 5 $$

  গ

  $$\sqrt 8 $$

  ঘ

  $${\text{3}}\sqrt 2 $$
• $$2\root 3 \of {32} - 3\root 3 \of 4 + \root 3 \of {500} = ?$$
  ক

  $$4\root 3 \of 6 $$

  খ

  $$3\sqrt {24} $$

  গ

  $$6\root 3 \of 4 $$

  ঘ

  916
• 21^? × 21^6.5 = 21^12.4
  ক

  18.9

  খ

  4.4

  গ

  5.9

  ঘ

  13.4
• The value of $$\frac{1}{{1 + \sqrt 2 + \sqrt 3 }} + $$   $$\frac{1}{{1 - \sqrt 2 + \sqrt 3 }}$$   is = ?
  ক

  $$\sqrt 2 $$

  খ

  $$\sqrt 3 $$

  গ

  1

  ঘ

  $$4\left( {\sqrt 3 + \sqrt 2 } \right)$$
• The quotient when 10¹⁰⁰ is divided by 5⁷⁵ is
  ক

  2²⁵ × 10⁷⁵

  খ

  10²⁵

  গ

  2⁷⁵

  ঘ

  2⁷⁵ × 10²⁵
• The exponential form of$$\sqrt {\sqrt 2 \times \sqrt 3 } {\text{ is = ?}}$$
  ক

  $${{\text{6}}^{ - \frac{1}{2}}}$$

  খ

  $${{\text{6}}^{\frac{1}{2}}}$$

  গ

  $${{\text{6}}^{\frac{1}{4}}}$$

  ঘ

  6
• (3x - 2y) : (2x + 3y) = 5 : 6, then one of the value of $${\left( {\frac{{\root 3 \of x + \root 3 \of y }}{{\root 3 \of x - \root 3 \of y }}} \right)^2}{\text{ is = ?}}$$
  ক

  $$\frac{1}{{25}}$$

  খ

  5

  গ

  $$\frac{1}{5}$$

  ঘ

  25
• What are the values of x and y that satisfy the equation, $${{\text{2}}^{0.7x}}{\text{.}}{{\text{3}}^{ - 1.25y}}{\text{ = }}\frac{{8\sqrt 6 }}{{27}}{\text{ ?}}$$
  ক

  x = 2.5, y = 6

  খ

  x = 3, y = 5

  গ

  x = 3, y = 4

  ঘ

  x = 5, y = 2
• Given 2^x = 8^y+1 and 9^y = 3^x-9 , then value of x + y is = ?
  ক

  18

  খ

  21

  গ

  24

  ঘ

  27
• $$\frac{{{6^2} + {7^2} + {8^2} + {9^2} + {{10}^2}}}{{\sqrt {7 + 4\sqrt 3 } - \sqrt {4 + 2\sqrt 3 } }}$$     is equal to = ?
  ক

  330

  খ

  355

  গ

  305

  ঘ

  366
• $$\frac{{\sqrt {10 + \sqrt {25 + \sqrt {108 + \sqrt {154 + \sqrt {225} } } } } }}{{\root 3 \of 8 }} $$       = ?
  ক

  8

  খ

  4

  গ

  $$\frac{1}{2}$$

  ঘ

  2
• If 3^2x-y = 3^x+y = $$\sqrt {27} {\text{,}}$$  the value of y is = ?
  ক

  $$\frac{1}{2}$$

  খ

  $$\frac{1}{4}$$

  গ

  $$\frac{3}{2}$$

  ঘ

  $$\frac{3}{4}$$
• If 3^(x-y) = 27 and 3^(x+y) = 243, then x is equal to = ?
  ক

  0

  খ

  2

  গ

  4

  ঘ

  6
• If abc = 1, then $${\frac{1}{{1 + a + {b^{ - 1}}}} + }$$   $${\frac{1}{{1 + b + {c^{ - 1}}}} + }$$   $${\frac{1}{{1 + c + {a^{ - 1}}}}}$$   = ?
  ক

  0

  খ

  1

  গ

  $$\frac{1}{{{\text{ab}}}}$$

  ঘ

  ab
• The value of $$\frac{1}{{\sqrt 7 - \sqrt 6 }} - $$  $$\frac{1}{{\sqrt 6 - \sqrt 5 }} + $$  $$\frac{1}{{\sqrt 5 - 2 }} - $$  $$\frac{1}{{\sqrt 8 - \sqrt 7 }} + $$  $$\frac{1}{{3 - \sqrt 8 }} = ?$$
  ক

  0

  খ

  1

  গ

  5

  ঘ

  7
• Suppose 4^a = 5, 5^b = 6, 6^c = 7, 7^d = 8, then the value of abcd is = ?
  ক

  1

  খ

  $$\frac{3}{2}$$

  গ

  2

  ঘ

  $$\frac{5}{2}$$
• 1 + (3 + 1)(3² + 1)(3⁴ + 1)(3⁸ + 1)(3¹⁶ + 1)(3³² + 1) is equal to =?
  ক

  $$\frac{{{3^{64}} - 1}}{2}$$

  খ

  $$\frac{{{3^{64}} + 1}}{2}$$

  গ

  3⁶⁴ - 1

  ঘ

  3⁶⁴ + 1
• If m and n are whole numbers such that mⁿ = 121, then the value of (m - 1)ⁿ⁺¹ is = ?
  ক

  1

  খ

  10

  গ

  121

  ঘ

  1000
• Given that 10^0.48 = x, 10^0.70 = y and x^z = y² then the value of z is close to = ?
  ক

  1.45

  খ

  1.88

  গ

  2.9

  ঘ

  3.7
• If $$\frac{{4 + 3\sqrt 3 }}{{\sqrt {7 + 4\sqrt 3 } }} = A + \sqrt B {\text{,}}$$      then B - A is = ?
  ক

  -13

  খ

  $${\text{2}}\sqrt {13} $$

  গ

  13

  ঘ

  $${\text{3}}\sqrt 3 - \sqrt 7 $$
• Evaluate : $$\sqrt {20} + \sqrt {12} + \root 3 \of {729} \,\, - $$     $$\frac{4}{{\sqrt 5 - \sqrt 3 }} \,- $$   $$\sqrt {81} = ?$$
  ক

  $$\sqrt 2 $$

  খ

  $$\sqrt 3 $$

  গ

  0

  ঘ

  $$2\sqrt 2 $$
• If $$\frac{{\left( {x - \sqrt {24} } \right)\left( {\sqrt {75} + \sqrt {50} } \right)}}{{\sqrt {75} - \sqrt {50} }}$$      = 1 then the value of x is = ?
  ক

  $$\sqrt 5 $$

  খ

  5

  গ

  $${\text{2}}\sqrt 5 $$

  ঘ

  $${\text{3}}\sqrt 5 $$
• If N = $$\frac{{\sqrt {\sqrt 5 + 2} + \sqrt {\sqrt 5 - 2} }}{{\sqrt {\sqrt 5 + 1} }} - $$     $$\sqrt {3 - 2\sqrt 2 } {\text{,}}$$   then the value of N is = ?
  ক

  $${\text{2}}\sqrt 2 - 1$$

  খ

  3

  গ

  1

  ঘ

  2
• $$\sqrt {6 - 4\sqrt 3 + \sqrt {16 - 8\sqrt 3 } } $$       is equal to = ?
  ক

  $${\text{1}} - \sqrt 3 $$

  খ

  $$\sqrt 3 - 1$$

  গ

  $${\text{2}}\left( {2 - \sqrt 3 } \right)$$

  ঘ

  $${\text{2}}\left( {2 + \sqrt 3 } \right)$$
• $$\sqrt {8 - 2\sqrt {15} } $$   is equal to = ?
  ক

  $${\text{3}} - \sqrt 5 $$

  খ

  $$\sqrt 5 - \sqrt 3 $$

  গ

  $${\text{5}} - \sqrt 3 $$

  ঘ

  $$\sqrt 5 + \sqrt 3 $$
• The value of $$\sqrt {40 + \sqrt {9\sqrt {81} } }$$    is = ?
  ক

  $$\sqrt {111} $$

  খ

  9

  গ

  7

  ঘ

  11
• $$\left( {\frac{{1 + \sqrt 2 }}{{\sqrt 5 + \sqrt 3 }} + \frac{{1 - \sqrt 2 }}{{\sqrt 5 - \sqrt 3 }}} \right)$$     simplifies to = ?
  ক

  $$\sqrt 5 + \sqrt 6 $$

  খ

  $${\text{2}}\sqrt 5 + \sqrt 6 $$

  গ

  $$\sqrt 5 - \sqrt 6 $$

  ঘ

  $${\text{2}}\sqrt 5 - 3\sqrt 6 $$