Explanation

(a) \(\log_{10} p = a ; \log_{10} q = b ; \log_{10} s = c\)

\(\log_{10} (\frac{p^{\frac{1}{3}}q^{4}}{s^{2}} = \log_{10} p^{\frac{1}{3}} + \log_{10} q^{4} - \log_{10} s^{2}\)

= \(\frac{1}{3}\log_{10} p + 4\log_{10} q - 2\log_{10} s\)

= \(\frac{1}{3}a + 4b - 2c\)

(b) Area of circle = \(\pi r^{2}\)

Given r = 6cm.

\(\frac{\mathrm d A}{\mathrm d r} = 2\pi r\)

\(\frac{\mathrm d A}{\mathrm d t} = \frac{\mathrm d A}{\mathrm d r} \times \frac{\mathrm d r}{\mathrm d t}\)

\(20 = 2\pi (6) \times \frac{\mathrm d r}{\mathrm d t}\)

\(\frac{\mathrm d r}{\mathrm d t} = \frac{20}{12\pi}\)

= \(\frac{5}{3\pi}\)

Correct Answer: c. 10%

Correct Answer: A. 16x²y(2 - 3xy²)

Correct Answer: B. 5/3

Correct Answer: B. 14cm

Explanation

1/3 πr\(^2\) x 9 = 1848

3 x πr2 = 1848 r2 = 1848/3 x 7/22 r = 14

\(\text{Volume of a cone} = \frac{1}{3} \pi r^2 h\)

\(\frac{1}{3} \times \frac{22}{7} \times r^2 \times 9 = 1848\)

\(r^2 = \frac{1848 \times 7}{22 \times 3}\)

\(r^2 = 196 \therefore r = 14cm\)

Explanation

(a) \(r = (10N, 090°) = \begin{pmatrix} 10 \cos 90° \\ 10 \sin 90° \end{pmatrix}\)

= \(\begin{pmatrix} 0 \\ 10 \end{pmatrix}\)

\(q = (8N, 135°) = \begin{pmatrix} 8 \cos 135° \\ 8 \sin 135° \end{pmatrix}\)

= \(\begin{pmatrix} -8 \cos 45° \\ 8 \sin 45° \end{pmatrix}\)

= \(\begin{pmatrix} -4\sqrt{2} \\ 4\sqrt{2} \end{pmatrix}\)

(b) \((r + q) = \begin{pmatrix} 0 \\ 10 \end{pmatrix} + \begin{pmatrix} -4\sqrt{2} \\ 4\sqrt{2} \end{pmatrix}\)

= \(\begin{pmatrix} -4\sqrt{2} \\ 10 + 4\sqrt{2} \end{pmatrix}\)

= \(\begin{pmatrix} -5.66 \\ 15.66 \end{pmatrix}\).

Correct Answer: B. 130°

Explanation

< TSR = 180 - (80 + 50)

= 180 - (130)

= 50\(^o\)

< QPR = < TSR corresponding < s

< NPR + QPR = < NPR

180\(^o\) - < QPR = < NPR

180\(^o\) - 50 = < NPR

< NPR = 130\(^o\)

Correct Answer: D. 17°

Explanation

\(\bigtriangleup\) ABC, A + 153 = 180 (angles on straight line)

< A = 180 - 153 = 27

< B = 2m(vertically opposite angles)

< C = 7m (corresponding ngles)

< A +< B +< C = 180 (sum of int. angles of \(\bigtriangleup\))

i.e. 27 + 2m + 7m = 180^o

9m = 180 - 27

9m = 153

m = \(\frac{153}{9}\)

= 17

Correct Answer: D. 16

Explanation

2(\(x^2 - y^2\))

= 2(x + y)(x - y)

= 2(3 + (-1))(3 - (-1))

= 2(2)(4) = 16

Correct Answer: D. 13, 21, 34