91. The value of $$\frac{1}{{\sqrt 7 - \sqrt 6 }} - \frac{1}{{\sqrt 6 - \sqrt 5 }} + \frac{1}{{\sqrt 5 - 2}} - \frac{1}{{\sqrt 8 - \sqrt 7 }} + \frac{1}{{3 - \sqrt 8 }}{\text{is:}}$$
92. If (√2 + √5 - √3) × k = -12, then what will be the value of k?
93. Which of the following statement(s) is/are TRUE?
$$\eqalign{
& {\text{I}}.\sqrt {12} > \root 3 \of {16} > \root 4 \of {24} \cr
& {\text{II}}.\root 3 \of {25} > \root 4 \of {32} > \root 6 \of {48} \cr
& {\text{III}}.\root 4 \of 9 > \root 3 \of {15} > \root 6 \of {24} \cr} $$
$$\eqalign{ & {\text{I}}.\sqrt {12} > \root 3 \of {16} > \root 4 \of {24} \cr & {\text{II}}.\root 3 \of {25} > \root 4 \of {32} > \root 6 \of {48} \cr & {\text{III}}.\root 4 \of 9 > \root 3 \of {15} > \root 6 \of {24} \cr} $$
94. Which of the following relation is/are true?
$$\eqalign{
& {\text{I}}.{\left( {27} \right)^{\frac{1}{3}}} > {\left( {13} \right)^{\frac{1}{2}}} < {\left( {47} \right)^{\frac{1}{6}}} \cr
& {\text{II}}.{\left( {23} \right)^{\frac{1}{3}}} < {\left( {49} \right)^{\frac{1}{2}}} < {\left( {52} \right)^{\frac{1}{6}}} \cr
& {\text{III}}.{\left( {53} \right)^{\frac{1}{6}}} < {\left( {41} \right)^{\frac{1}{3}}} < {\left( {37} \right)^{\frac{1}{2}}} \cr} $$
$$\eqalign{ & {\text{I}}.{\left( {27} \right)^{\frac{1}{3}}} > {\left( {13} \right)^{\frac{1}{2}}} < {\left( {47} \right)^{\frac{1}{6}}} \cr & {\text{II}}.{\left( {23} \right)^{\frac{1}{3}}} < {\left( {49} \right)^{\frac{1}{2}}} < {\left( {52} \right)^{\frac{1}{6}}} \cr & {\text{III}}.{\left( {53} \right)^{\frac{1}{6}}} < {\left( {41} \right)^{\frac{1}{3}}} < {\left( {37} \right)^{\frac{1}{2}}} \cr} $$
95. The value of $$\sqrt {2\root 3 \of {4\sqrt {2\root 3 \of 4 } } } ......$$ is?
96. If $$\left( X \right) = \frac{1}{x} - \frac{1}{{x + 1}},$$ then what is the value of f(1) + f(2) + f(3) + . . . . . + f(10)?
97. A tap is dripping at a constant rate into a container. The level (L cm) of the water in the container is given by the equation L = 2 - 2t, where t is time taken in hours. Then the level of water in the container at the start is.
98. Find the simplest value of $$2\sqrt {50} + \sqrt {18} - \sqrt {72} $$ (given √2 = 1.414).
99. Let $$\root 3 \of a = \root 3 \of {26} + \root 3 \of 7 + \root 3 \of {63} $$ then
100. If $${{\text{x}}^{\frac{1}{6}}} = {{\text{y}}^{\frac{2}{3}}},$$ then relation between x and y is.
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