Correct Answer: A. 1/3

Correct Answer: C. 1

Explanation

\(\frac{25 \frac{2}{3} \div 25 \frac{1}{6}}{( \frac{1}{5})^{-\frac{7}{6}} \times ( \frac{1}{5})^{\frac{1}{6}}}\) = \(\frac{25^{4 - \frac{1}{6}}}{(\frac{1}{5})^{-7 + \frac{1}{6}}}\)

= \(\frac{25^{\frac{1}{2}}}{(\frac{1}{5})^{-1}}\)

= \(\frac{(5^2)^{\frac{1}{2}}}{(5^{-1})^{-1}}\)

= \(\frac{5}{5}\)

= 1

Correct Answer: C. 0.0081

Correct Answer: A. 3/4

Correct Answer: B. \(3 + \sqrt{7}\)

Explanation

Rationalizing \(\frac{2}{3 - \sqrt{7}}\) by multiplying through with \(3 + \sqrt{7}\),

\(\frac{2}{3 - \sqrt{7}} \frac{(3 + \sqrt{7})}{(3 + \sqrt{7})} = \frac{6 + 2\sqrt{7}}{9 - 7}\)

= \(\frac{6 + 2\sqrt{7}}{2} = 3 + \sqrt{7}\)

Correct Answer: C. 3

Explanation

Mean = {0 + (x+2) + (3x+6) + (4x+8)}/4 = 4

=> 0 + (x+2) + (3x+6) + (4x+8) = 16

8x + 16 = 16

x = 0

Now prepare a table showing the deviation of each of 0, (x+2), (3x+6) and (4x+8), adding the deviations will give 12.

Thus M.D = 12/4 = 3

Correct Answer: B. 3.35 years

Explanation

Mean(age) = \(\frac{(1 \times 2) + (2 \times 3) + (3 \times 5) + (4 \times 6) + (5 \times 4)}{2 + 3 + 5 + 6 + 4}\)

= \(\frac{2 + 6 + 15 + 24 + 20}{20}\)

= \(\frac{67}{20}\)

= 3.35yrs

Correct Answer: D. 400.4

Explanation

\((1 + ax)^{n} = ^{n}C_{n} (1)^{n} + ^{n}C_{n - 1} (1)^{n - 1} (ax) + ^{n}C_{n - 2} (1)^{n - 2} (ax)^{2} + ...\)

= \(1 + nax + (\frac{n(n - 1)}{2})(ax)^{2} + ... \)

Given

\(an = 2 .... (1)\)

\(\frac{n^{2} - n}{2}) a^{2} = \frac{3}{2} ... (2)\)

\(\frac{a^{2}n^{2} - a^{2} n}{2} = \frac{3}{2}\)

\(\frac{(an)^{2} - a(an)}{2} = \frac{3}{2} ... (3)\)

From (1), \(an = 2\). (3) becomes

\(\frac{2^{2} - a(2)}{2} = \frac{3}{2}\)

\(\frac{4 - 2a}{2} = \frac{3}{2}\)

\(2 - 2a = \frac{3}{2} \implies 2a = \frac{1}{2}\)

\(\therefore a = \frac{1}{4}\)

Recall \(an = 2\)

\(\frac{n}{4} = 2 \implies n = 8\)

Correct Answer: B. q