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JAMB Mathematics Past Questions & Answers - Page 156

776.

One of the following statements is wrong. Which is it?

If a triangle is equiangular then it is also equilateral

If a triangle is equilateral then it is also then it is also equiangular

If two triangles are similar then they are also congurent

The sum of the interior angles of any triangle is 180 degrees

View answer & explanation

Correct answer is C

Two similar triangles are not also congruent

777.

Simplify 2 $\frac{5}{12}$ - 1 $\frac{7}{8}$ x $\frac{6}{5}$

$\frac{1}{6}$

$\frac{13}{20}$

$\frac{11}{30}$

$\frac{9}{4}$

$\frac{5}{3}$

View answer & explanation

Correct answer is A

2 $\frac{5}{12}$ - 1 $\frac{7}{8}$ x $\frac{6}{5}$ = $\frac{29}{12}$ - $\frac{15}{8}$ x $\frac{6}{5}$

= $\frac{29}{12}$ - $\frac{9}{4}$

= $\frac{29 - 27}{12}$

= $\frac{2}{12}$

= $\frac{1}{6}$

778.

A ladder resting on a vertical wall makes an angles whose tangent is 2.4 with the ground. If the distance between the foot of the ladder and the wall is 50cm, What is the length of the ladder?

1.1m

1.2m

0.9m

1.3m

View answer & explanation

Correct answer is E

If tan $\theta$ = 2, 4

$\theta$ = tan^-1(2.4)

= 67^o 25

By sin formula $\frac{x}{sin 90^o}$ = $\frac{50}{sin 22^o 37}$

= $\frac{50}{sin(9o - \theta)}$

sin90^o = 1

x = 50 cosec 22^o 37

= 50 x 2.604x

= 130cm

but 100cm = 1m

130cm = 1.3m

779.

Simplify $\frac{x^2 + y^2 + xy}{x + y}$ - $\frac{x^2 + y^2}{x - y}$

$\frac{x^2 + y^2} {(x - y)^2}$

$\frac{2y^3} {y^2 - x^2}$

$\frac{3x^2 + y^2} {(2x - y)^2}$

$\frac{x^2 + y^2} {(x^2 - y)}$

View answer & explanation

Correct answer is B

$\frac{x^2 + y^2 + xy}{x + y}$ - $\frac{x^2 + y^2}{x -y}$

= $\frac{-y^3 - y^3}{x^2 - y^2}$

= $\frac{2y^3}{x^2 - y^2}$

= $\frac{2y^3}{y^2 - x^2}$

780.

A steel ball of radius 1 cm is dropped into a cylinder of radius 2cm and height 4cm. If the cylinder is now filled with water, what is the volume of the water in the cylinder?

$\frac{44}{3}$ $\pi$ cm³

12 $\pi$ cm³

$\frac{38}{3}$ $\pi$ cm³

$\frac{40}{3}$ $\pi$ cm³

$\frac{32}{33}$ $\pi$ cm³

View answer & explanation

Correct answer is A

Volume of steel ball = $\frac{4\pi r^2}{3}$

= $\frac{4}{3}$ $\pi$ x 1

= $\frac{4 \pi}{3}$ cm³

Vol. of cylinder = $\pi$ r²h

= $\pi$ x 2² x 3

Vol. of water = 16 $\pi$ - $\frac{4 \pi}{3}$

= $\frac{48 - 4 \pi}{3}$

= $\frac{44 \pi}{3}$ cm³