Correct Answer: D. 13³/₅cm

Explanation

Perimeter of sector = \(\frac{\theta}{360°} \times 2\pi r + 2r\)

= \(\frac{108}{360} \times 2 \times \frac{22}{7} \times \frac{7}{2} + 2(\frac{7}{2})\)

= \(6 \frac{3}{5} + 7\)

= \(13 \frac{3}{5} cm\)

Correct Answer: D. 72°

Explanation

The formula for the exterior angle of a regular polygon = \(\frac{360}{n}\).

Among the options, only 72° is divisible by 360° to give an integer.

Correct Answer: A. 20°

Explanation

< DBC = 35° (base angles of an isosceles triangle)

< CDB = 180° - (35° + 35°)

= 110°

< ADB = 70°; < ADB = 90°

\(\therefore\) < BAO = 180° - (70° + 90°)

= 20°

Correct Answer: B. 93°

Explanation

a = 52^o [vertical opp. ?s are equal]

a = b = 52^o [Alternate ?s]

b = c = 52^o [vertical opp ?s]

c + x + 35^o = 180^o [sum of angles in a triangle]

52^o + x + 35^o = 180^o

x + 87^o = 180^o

x = 180^o - 87^o = 93^o

Correct Answer: D. Un= 18-7n

Explanation

A.P 11, 4, -3

1st term = 11

A.P = a, a + d, a + 2d ...... a + (n - 1)d

If a = 11

a + d = 4

d = 4 - 11 = -7

nth term = a + (n-1)d

= 11 + (n-1)(-7)

= 11 - 7n + 7

= 18 - 7n

Correct Answer: D. 30°

Explanation

4x + 3x + 2x + 90 =360° [angle at a point]

9x + 90 = 360°

9x = 360° - 90°

9x = 270

x = 270/9

x = 30°

Correct Answer: C. N4.00

Explanation

Ratio = 6 + 7 + 8 = 21

21 = N10.50

1 = 1050K/21 = 50K

6 = 6 x 50K = N3.00

7 = 7 x 50K = N3.50

8 = 8 x 50K = N4.00

the Largest share = N4.00

Correct Answer: A. 0.117

Explanation

log\(_{10}\) x = \(\bar{2}.3675\) => x = 0.023

log\(_{10}\) y = \(\bar{2}.9738\) => y = 0.094

x + y = 0.117

Explanation

Number of blue balls = 5

Number of black balls = 3

Number of red balls = 2

= 10 balls.

(a) P(two red balls) = \(\frac{2}{10} \times \frac{2}{10} = \frac{1}{25}\)

(b) P(2 blue or 2 black balls) = P(2 blue) or P(2 black)

= \((\frac{5}{10} \times \frac{5}{10}) + (\frac{3}{10} \times \frac{3}{10})\)

= \(\frac{25}{100} + \frac{9}{100}\)

= \(\frac{34}{100} = \frac{17}{50}\)

(c) P( one red and one black in any order) = P(one red, one black) or P(one black, one red)

= \((\frac{2}{10} \times \frac{3}{10}) + (\frac{3}{10} \times \frac{2}{10})\)

= \(\frac{12}{100} = \frac{3}{25}\)

Correct Answer: B. 66cm²

Explanation

T.S.A of a cone = \(\pi r^2 + \pi rl\)

= \(\frac{22}{7} \times 3^2 + \frac{22}{7} \times 3 \times 4\)

= \(\frac{198}{7} + \frac{264}{7}\)

= \(\frac{462}{7}\)

= 66 cm\(^2\)