Twenty girls and y boys sat on an examination. The mean marks obtained by the girls and boys were 52 and 57 respectively. if the total score for both girls and boys was 2750, find y.

Let the total score for the girls and the boys be A and B respectively. \(\frac{A}{20} = 52 \implies A = 52 \times 20\) A = 1040 \(\frac{B}{y} = 57 \implies B = 57y\) 1040 + 57y = 2750 57y = 2750 - 1040 57y = 1710 y = \(\frac{1710}{57}\) y = 30

A sector of angle 120° is cut out from a circle of radius 13.5cm. what area of the circle is remaining ? (π = \(\frac{22}{7}\))

A. 14.1cm^{2}

B. 95.5cm^{2}

C. 190.9cm^{2}

D. 381.9cm^{2}

E. 763.7cm^{2}

D

3.

Two ladders of length 5m and 7m lean against a pole and make angles 45° and 60° with the ground respectively. What is their distance apart on the pole correct to two decimal places?

A. 9.60m

B. 6.06m

C. 2.54m

D. 2.53m

E. 2.00m

D

4.

The chances of Usman and Dele passing a Mathematics test are 12 and 13 respectively. What is the probability that neither of them passes the test?

A. \(\frac{3}{5}\)

B. \(\frac{2}{5}\)

C. \(\frac{4}{15}\)

D. \(\frac{1}{5}\)

E. \(\frac{2}{15}\)

C

5.

x varies directly as y and inversely as z. when x = 5, y = 2 and z = 1. What is the value of x when y = 5 and z = 2?

A. 2.5

B. 5

C. 6.25

D. 6.52

E. 7.5

C

6.

Find the mean deviation of 20, 25, 21, 27, 28, 29, to the nearest whole number

A. 2

B. 3

C. 4

D. 5

E. 6

B

7.

Calculate the area of a parallelogram whose diagonals are of length 8cm and 12cm and intersect at an angle of 135°

A. 271.5cm^{2}

B. 135.8cm^{2}

C. 96.0cm^{2}

D. 48.0cm^{2}

E. 33.9cm^{2}

E

8.

The ratio of the base area of a hollow cone to that of its curved surface is 1:4. If its base radius is 7cm, calculate the slant height of the cone