61. If x = $$\sqrt {a\root 3 \of {ab\sqrt {a\root 3 \of {ab} } } } ..... \propto ,$$ then the value of x is:
62. The value of $$\frac{{3 \times {9^{n + 1}} + 9 \times {3^{2n - 1}}}}{{9 \times {3^{2n}} - 6 \times {9^{n - 1}}}}$$ is equal to-
63. If M = 0.1 + (0.1)2 + (0.01)2 and N = 0.3 + (0.03)2 + (0.003)2, then what is the value of M + N?
64. If a = bp, b = cq, c = ar then pqr is
65. If $$x = \sqrt {1 + \frac{{\sqrt 3 }}{2}} - \sqrt {1 - \frac{{\sqrt 3 }}{2}} ,$$ then the value of $$\frac{{\sqrt 2 - x}}{{\sqrt 2 + x}}$$ will be closest to:
66. Which of the following statements(s) is/are true?
$$\eqalign{
& {\text{I}}.\frac{3}{{71}} < \frac{5}{{91}} < \frac{7}{{99}} \cr
& {\text{II}}.\frac{{11}}{{135}} > \frac{{12}}{{157}} > \frac{{13}}{{181}} \cr} $$
$$\eqalign{ & {\text{I}}.\frac{3}{{71}} < \frac{5}{{91}} < \frac{7}{{99}} \cr & {\text{II}}.\frac{{11}}{{135}} > \frac{{12}}{{157}} > \frac{{13}}{{181}} \cr} $$
67. If $$N = \frac{{\sqrt 7 - \sqrt 3 }}{{\sqrt 7 + \sqrt 3 }},$$ then what is the value of $$N + \frac{1}{N}?$$
68. The value of (1 - √2) + (√2 - √3) + (√3 - √4) + . . . . . . + ($$\sqrt {15} $$ - $$\sqrt {16} $$ ) is-
69. Evaluate $$\sqrt {20} + \sqrt {12} + \root 3 \of {729} - \frac{4}{{\sqrt 5 - \sqrt 3 }} - \sqrt {81} $$
70. Which of the following relation(s) is/are true?
I. 333 > 333
II. 333 > 333
III. 333 > 333
I. 333 > 333
II. 333 > 333
III. 333 > 333
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