CE Board Examination Mathematics & Surveying May 2003

The length of common tangent of a compound horizontal curve is 520 m. D₁ = 3°, l₁ = 50°, l₂ = 35°. Compute the radius of the second curve. 

Area of a given cross section is 31.7 m². The road width is 10 m with side sloping to 2 horizontal to 1 vertical.

\({9.8\over2.4},{0\over x},{7.4\over1.2}\)

Compute the value of x.

A car travelling at 65 mph sees an obstruction ahead. If the reaction distance covered is 72.2m. Compute the reaction time (PIEV).

The distance form the middle of the curve to the point of intersection of tangents of a circular curve is 14.2 m. The radius of the curve is 200 m. Find the central angle.

Lot ABCDEFA is a closed traverse in the form of regular hexagon. If the bearing of line A is N25°E, what is the bearing of line CD?

Find the sum of coefficients of the expansion (a+b)⁶

The cost of the machine is P 140 000 and has a useful life of 8 years. If the salvage value is P 10 000, find the depreciation during fourth year using Double Declining Balance Method. 

What is the present worth of an annuity P2000 for 8 years if the first annual payment us at the end of 10 years? The rate of interest is 5% compounded annually. 

An item can be sold P60 000 in 60 days and P57 000 if sold in 15 days. What is the simple interest rate?

Find the radius of the circle defined by the equation x² + y² + 4x - 10y - 92 = 0

Given an equation of an ellipse 9x² + 16y² -144 = 0. Compute the ratio of minor axis and major axis.

The area of the 1st and 2nd quadrant bounded by the curve 4x² + 25y² = 100 is to be revolved about x-axis. Compute the volume generated.

Evaluate the integral sin⁶2xdx, x= 0 to \(x = {\pi\over4} \)

The side of a regular tetrahedron is 50 cm. Find the height.

The base of a truncated prism is a triangle with sides 8 cm, 12 cm and 10 cm. If the heights are 20 cm, 18 cm and 12 cm. Compute the volume.

The volume of a spherical wedge is 12 cu. cm, and subtended angle is 1.8 radian. Find the radius of the sphere.

The distance between po4ints (4, 7, z) and (5, 1, 6) is 7.28. Find z.

If a and b are positive numbers, a, -4, b form a geometric progression and 14, a, b forms arithmetic progression. Find a. 

The area of a circle inscribe in an octagon is 224 cm². Find the area of the octagon.

A car weighing 1000kg traveling at 60 kph around an unbanked circular curve of radius 100 m. What is the required friction resistant to sliding?

Find the value of x in the equation (x + yi)(1 - 2i) = 7 - 4i

If log_x 12 = 2.262, find log_x 3

Find the first derivative of 2cos(2 + x³)

Find the curvature of the curve y² = 16x at (4,8).

Find the total length of the curve r = 4\(\sin \theta \) 

The transit is inclined 0°4'00" with respect to the horizontal axis. If the first sight is at vertical angle of 50° and the second is -30°, what is the error in horizontal angle?

In a triangle ABC: AB = 14 cm, BC = 18 cm and CA = 24 cm. Find the length of median to the longest side.

These are employed the direct flow of current in rivers with a view to the establishment of the more favorable and fixed channel and also to prevent scow and erosion and the carrying away of river banks.

The angles in a triangle were as follows: (See most pattached picture)

Compute the most probable value of angle A.