Correct Answer: D. \(\frac{1}{4}\) sin 4x + k

Correct Answer: B. 2

Explanation

Log₁₀4 + Log₁₀25 = Log₁₀(4 x 25)

= Log₁₀100 = Log₁₀10²

= 2Log₁₀10 = 2 x 1 = 2

Correct Answer: B. \(\frac{3}{8}\)

Explanation

Let \(p(head) = p = \frac{1}{2}\) and \(p(tail) = q = \frac{1}{2}\)

\((p + q)^{4} = p^{4} + 4p^{3}q + 6p^{2}q^{2} + 4pq^{3} + q^{4}\)

The probability of equal heads and tails = \(6p^{2}q^{2} = 6(\frac{1}{2}^{2})(\frac{1}{2}^{2})\)

= \(\frac{6}{16} = \frac{3}{8}\).

Correct Answer: (d) 1/x

Correct Answer: (b) 95

Correct Answer: B. 0

Explanation

\(\log_{10} (\frac{1}{3} + \frac{1}{4}) + 2\log_{10} 2 + \log_{10} (\frac{3}{7})\)

\(\frac{1}{3} + \frac{1}{4} = \frac{7}{12}\)

= \(\log_{10} (\frac{7}{12} \times 2^{2} \times \frac{3}{7})\)

= \(\log_{10} 1 = 0\)

Correct Answer: C. 18

Explanation

\(\int^0_0 \sqrt{x} dx\)

\(\frac{x^{\frac{1}{2}} + 1}{\frac{1}{2} + 1}\) |\(^9_0\)

\(\frac{2x^{\frac{3}{2}}}{3}\)|\(^9_0\)

= \(\frac{2(9)^{\frac{3}{2}}}{3}\)

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

= \(\frac{2 \times 27}{3}\)

= 2 x 9

= 18

Correct Answer: A. 8cm

Explanation

Using pythagoras formula:

Hyp\(^2\) = adj\(^2\) + opp\(^2\)

5\(^2\) = opp\(^2\) + 3\(^2\)

5\(^2\) - 3\(^2\) = adj\(^2\)

4 = adj

length of the chord = 2 * 4 = 8cm

Correct Answer: A. 2.17%

Explanation

% error = \(\frac{Error}{Actual Value}\) x 100%

Student's Value = 18mL

Actual Value = 18.4mL

Error = 18.4 - 18 = 0.4

∴ % error = \(\frac{0.4}{18.4}\) x 100% = 2.17%

Correct Answer: C. 51