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U = {1, 2, 3, 4, 5......14} P = {2, 4, 6, 8, 10, 12, 14} P' = {1, 3, 5, 7, 9, 11,13}

\(\frac{0.026 \times 0.36}{0.69}\) = \(\frac{26 \times 10^-3 \times 36 \times 10^-2}{69 \times 10^-2}\) = 0.01356 = 1.36 x 10-2

Let x represent total number of pencils shared B : S : T 2 : 3 : 5 2+3+5 = 10 \(\frac{2}{10}\) x x = 5 \(\frac{2x}{10}\) = 5 2x = 50 x = 25

Perimeter = 2r + \(\frac{\theta}{360}\) x 2\(\pi\)r 2(9) + \(\frac{36}{360}\) x 2 x \(\pi\) x 9 = 18 + \(\frac{9\pi}{5}\)

\(\frac{27^\frac{1}{3} - 8^\frac{2}{3}}{16^\frac{2}{4} \times 2}\) \(\frac{27^\frac{1}{3} - 8^\frac{2}{3}}{16^\frac{2}{4} \times 2}\) = \(\frac{3\sqrt{27} - 3\sqrt{8}^2}{\sqrt{16} \times 2}\) \(\frac{3 - 4}{4 \times 2}\) = \(\frac{-1}{8}\)

Listing the scores according to the number of times they occur in ascending order 2, 2, 2, 2, 2, 2,3, 3, 5, 5, 5, 5, 6, 6, 6, Median = 3

y = \(\frac{2}{3}\)x\(^3\) - \(\frac{4}{x}\) \(\frac{dy}{dx}\) = 2x\(^2\) - (-4)x\(^{-2}\) = 2x\(^2\) + \(\frac{4}{x^2}\)

\(\frac{0.8 \times 0.43 \times 0.031}{0.05 \times 0.72 \times 0.021}\) x \(\frac{10}{10}\) = 14.11

Length or arc = \(\frac{\theta}{360}\) x 2\(\pi\)r = \(\frac{30}{360}\) x 2 x \(\frac{22}{7}\) x 12 = \(\frac{1}{12}\) x 2 x \(\pi\) x 12 = 2\(\pi\)cm

\(\int\limits_0^\frac{\pi}{2}\) sin xdx = -cosx|\(\frac{\pi}{2}\) = -(cos\(\frac{\pi}{2}\) - cos0) = -(0-1) = 1

L = \(\frac{\theta}{360}\) x 2\(\pi\)r 16\(\pi\) = \(\frac{80}{360}\) x 2\(\pi\)r \(\frac{16\pi \times 360}{80 \times 2\pi}\) = r r = 36cm

Mean = \(\frac{2 - t + 4 + t + 3 - 2t + 2 + t + t - 1}{5}\) = \(\frac{10}{5}\) = 2

\(\frac{12.02 \times 20.06}{26.04 \times 60.06}\) = \(\frac{241.1212}{15698.96}\) = 0.154

y = 2x3 + 6x2 + 6x + 1 \(\frac{dy}{dx}\) = 6x2 + 12x + 6

3,9,27,81,..... r = \(\frac{9}{8}\) = 3 Tn = arn-1 Tn = 3(3)n-1 = \(\frac{3(3^2)}{3}\)