GEOMETRY AND TRIGONOMETRY - Jamb Mathematics Past Questions and Answers

Question 116:

• JAMB 1978

If sec² \(\theta\) + tan² \(\theta\) = 3, then the angle \(\theta\) is equal to

A. 30^o
B. 45^o
C. 60^o
D. 90^o
E. 105^o

Question 117:

• JAMB 1978

A hollow right prism of equilateral triangular base of side 4cm is filled with water up to a certain height. If a sphere of radius \(\frac{1}{2}\)cm is immersed in the water, then the rise of water is

A. 1cm
B. \(\sqrt{\frac{3\pi}{24}}\)
C. \(\frac{\pi}{24\sqrt{3}}\)
D. 24\(\sqrt{3}\)

Question 118:

• JAMB 1978

A solid sphere of radius 3cm, a solid right cone of radius 3cm and height 12cm and a solid right circular cycular of radius 3cm and height 4cm.Which of the following statements is true?

A. The volume of the sphere is greater than the volume of the cone
B. The volume of the cone is less than the volume of the cylinder
C. The total surface area of the cone is greater than that of the sphere
D. The total surface area of the cylinder is less than that of the sphere
E. The total sufeac area of the cone is equal to that of the cylinder

Question 119:

• JAMB 1978

Two triangles have the same areas if

A. Two sides in one triangle are equal to two sides in the other
B. Three sides in one triangle are equal to three sides in the other
C. Two angles in the triangle are equal to two angles in the other
D. Three angles in one triangle are equal to three angles in the other
E. One side and the opposite angle in one triangle are equal to one side and the opposite angle in the other

Question 120:

• JAMB 1978

The locus of all points having a distance of 1 unit from each of the two fixed points a and b is

A. A line parallel to the line ab
B. A line perpendicular to the line ab through the mid-point of ab
C. A circle through a and b with centre at the mid-point of ab
D. A circle with centre at a and passes through b
E. A circle in a plane perpendicular to ab and centre at the mid-point of the line ab