Civil Engineering Board Exam May 2002 - Mathematics & Surveying

Compute the minimum distance from the curve y² = 8x to point (4.2).

An object moves along a path whose parametric equations are \(y = 2t^2\) and \(x = t^3\) where x and y are distances traveled in meter and t in second. Compute the acceleration after 3 seconds.

Find the sum of numerical coefficient of the expansion \((A+B)^5\)

Find n from the linear permutation \(nP_5 = 6nP_3\)

The coordinate of the geometric figure (4,0), (4,4), (10,8),  (12,4) and (12,0). Locate the distane of the centroid from the y-axis.

A circle having a diameter of 8 cm is inscribed in a sector of a circle whose angle is 80°. Find the area of the sector. 

In a triangle ABC, the side AB = 30 cm, BC = 36 cm and CA = 48 cm. Compute the distance from the intersection of angular bisectors to side AB.

The elevation of point A is 2402 m and measures 18586.21 m from point C. If the average radius of curvature is 25821 m., compute the sea level distance.

A conical vessel 10 ft. across the top and 12 ft high is full of liquid whose unit weight is 62.4 pcf. Compute the work done by pumping out the liquid.

A closed conical vessel has diameter of 2.4 m across the top and a height of 4.8 m. It contains water at a depth of 2.4 m. If the vessel is inverted, how deep is the water inside?

A lot is in the form of an equilateral triangle each of whose sides is 2 km. Compute the length of the line parallel to one side that will divide the area into two parts.

The line of sight was inclined at 4°30' with the horizontal. It intercepts the stadia rod with the length of 1.8 m. The stadia interval factor is 100 and stadia constant is 0.3. Compute the vertical distance of the point sighted above the instrument.

Compute the distance between two vertices of an ellipse having an equation of \(64x^2 + 25y^2 + 768x - 200y +1104 =0\)

A car travelling around a circular curve of radius of 500 m and has an impact factor of 0.15. Compute the maximum velocity a car can travel?

A string 72 cm long is divided unequally into two parts. Each part is then bent to form a square. If the sum of the areas of square is 194 cm², find the diffrence between the sides of square.

The rate of flow at a certain point in the highway is 676.2 vehicles per hour. If the density is 14 vehicles per kilometer, find the space mean speed in miles per hour.

Compute the y - intercept of a line passing through point (5,3) and a slope of 3/4.

Find theh base diameter of a cylindrical tank open at the top if its height is 1.5 times the base diameter. The total surface area of the tank is 53.4 cm^2.

The lenght of spiral easement curve is 100 m with a central curve of radius 300 m. Compute the offset distance from tangent to the second quarter point of spiral.

Evaluate the \(\lim_{x \to 0} ({{tan 2x - 2 sinx}\over x^3})\)