Correct Answer: C. 101.33cm

Correct Answer: B. 2

Correct Answer: D. undefined

Explanation

(2, -3)(2, 5)

gradient = \(\frac{y_2 - y_1}{x_2 - x_1} = \frac{5 - (-3)}{2 - 2}\)

= \(\frac{5 + 3}{0}\)

= \(\frac{8}{0}\)

= undefined

Correct Answer: C. \(\frac{2}{3}\)\(\sqrt{5}\) + \(\frac{5}{6}\sqrt{2}\) + \(\frac{1}{2}\sqrt{10}\) + 2

Explanation

\(\frac{(\sqrt{5} + 3)(4 + \sqrt{10})}{(4 - \sqrt{10})(4 + \sqrt{10})}\)

= \(\frac{4\sqrt{5} + \sqrt{50} + 12 + 3\sqrt{10}}{4^2 - (\sqrt{10})^2}\)

= \(\frac{4\sqrt{5} + 5\sqrt{2} + 12 + 3\sqrt{10}}{16 - 10}\)

= \(\frac{4 \sqrt{5}}{6} + \frac{5 \sqrt{2}}{6} + \frac{12}{6} + \frac{3\sqrt{10}}{6}\)

= \(\frac{2}{3}\)\(\sqrt{5}\) + \(\frac{5}{6}\sqrt{2}\) + \(\frac{1}{2}\sqrt{10}\) + 2

Explanation

(a) \(17x = 375^{2} - 356^{2}\)

\(17x = (375 + 356)(375 - 356)\)

\(17x = (731)(19)\)

\(x = \frac{731 \times 19}{17} = 817\)

(b) \(4^{x} = 2^{\frac{1}{2}} \times 8\)

\(2^{2x} = 2^{\frac{1}{2}} \times 2^{3}\)

\(2^{2x} = 2^{3\frac{1}{2}}\)

\(\implies 2x = 3\frac{1}{2} \implies x = \frac{7}{4}\)

(c) \(S_{n} = \frac{n}{2} (2a + (n - 1)d)\) (sum of terms of an A.P)

\(S_{9} = \frac{9}{2} [2a + (9 - 1) d] = \frac{9}{2} [2a + 8d]\)

\(72 = 9(a + 4d) \implies 8 = a + 4d ... (1)\)

\(S_{9 + 4} = S_{13} = \frac{13}{2} [2a + (13 - 1)d] = \frac{13}{2} [2a + 12d]\)

\(72 + 71 = 143 = 13(a + 6d) \implies 11 = a + 6d ... (2)\)

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

\(a + 4(1\frac{1}{2}) = 8 \implies a + 6 = 8\)

\(\implies a = 8 - 6 = 2\)

\(\therefore \text{The A.P is } 2, 3\frac{1}{2}, 5, 6\frac{1}{2}, 8,...\)

Correct Answer: C. \(130^0\)

Explanation

∠EHI = ∠DEH = 40° (alternate angles are equal)

∠BEH = 90° (given)

∠BED = 90° - 40° = 50°

∠BEF = 180° - 50° = 130° (sum of angles on a straight line is 180o)

∠BEF = ∠ABE = 130° (alternate angles are equal)

∴ m = 130°

Correct Answer: A. 1/6

Correct Answer: C. 5cm

Explanation

Volume of a cube with side a cm = a\(^3\)

a\(^3\) = 64 \(\implies\) a = 4cm

Base area of a cube = a\(^2\)

= 4\(^2\)

= 16 cm\(^2\)

\(\implies\) Base area of the cuboid = 16 cm\(^2\)

Volume of cuboid = Base area x height

80 = 16 x h

h = \(\frac{80}{16}\)

= 5 cm

Correct Answer: C. 41 \(ms ^{-2}\)

Explanation

\(S = 5t^3 - \frac{19}{2} t^2 + 6t - 4\)

\(v(t)=\frac{dS}{dt}=15t^2-19t+6\)

\(a(t)=\frac{dv}{dt}=30t-19\)

∴a(2)=30(2)-19=60-19=41 \(ms ^{-2}\)

Correct Answer: D. 528cm²

Explanation

TSA of a cylinder = \(2\pi r^2 + 2\pi rh\)

= \(2\pi r (r + h)\)

= \(2 \times \frac{22}{7} \times 7 (7 + 5)\)

= \(44 \times 12\)

= \(528 cm^2\)