ece board 1998.docx

ECE Board April 1998QuestText Choice1 Choice2 Choice3 Choice4 Subj Sources

A balloon is rising vertically over a point A on the ground at the rate of 15 ft/s. A point B on the ground level with an observer 30 ft from A. When the balloon is 40 ft from A, at what rate is its distance from B changing?

12 fps 13 fps 14 fps 15 fps Physics ECE Board April 1998

A baseball is thrown from a horizontal plane following a parabolic path with an initial velocity of 100 m/s at an angle of 30 degrees above the horizontal. How far from the throwing point will the ball attain its original level?

883 m 889 m 785 m 379 m Physics ECE Board April 1998

A man find the angle of elevation of the top of a tower to be 30 degrees. He walks 85 meters nearer the tower and finds its angle of elevation to be 60 degrees. What is the height of the tower?

73.61 m 73.16 m 73.31 m 76.31 m Trigonometry ECE Board April 1998

A semiconductor company will hire 7 men and 4 women. In how many ways can the company choose from 9 men and 6 women who qualified for the position?

540 680 51 36 Probability&Statistics ECE Board April 1998

A statue 3 m. high is standing on a base of 4 m. high. If an observer’s eye is 1.5 m. above the ground, how far should he stand from the base in order that the angel subtended by the statue is maximum?

3.71 3.71 4.41 3.51 Differential Calculus ECE Board April 1998

A trapezoid has an area of 36 sq. m. and altitude of 2 m. Its two bases have ratio of 4:5. What are the lengths of the bases.

16 and 20 12 and 15 8 and 10 20 and 25 Solid Geometry ECE Board April 1998

By the condition of a will, the sum of P2,000 is left to a girl to be held trust fund by her guardian until it amounts to P50,000.00. When will the girl received the money if the fund is invested at 8% compounded quarterly?

11.57 years 10.24 years 7.98 years 10.45 years Engineering Economics

ECE Board April 1998

Determine B such that 3x + 2y -7 = 0 is perpendicular to 2x - By + 2 = 0.

3 4 5 2 Analytic Geometry ECE Board April 1998

Evaluate the integral of (cos 3A)^8 dA fro 0 to pi/6. 35pi/768 28pi/768 42pi/768 zero Integral Calculus ECE Board April 1998


Evaluate the limit of (x - 4) / (x^2 - x - 12) as x approaches 4. 1/7 0 undefined infinity Differential Calculus ECE Board April 1998

Find the 1987th digit in the decimal equivalent to 1785/9999 starting from decimal point.

8 1 7 5 Algebra ECE Board April 1998

Find the area (in sq. units) bounded by the parabola x^2 – 2y = 0 and x^2 = – 2y + 8

10.7 4.7 9.7 11.7 Integral Calculus ECE Board April 1998

Find the equation of the axis of symmetry of the function y = 2x^2 - 7x + 5.

4x - 7 = 0 7x - 4 = 0 x - 4 = 0 x - 7 = 0 Differential Calculus ECE Board April 1998

Find the point in the parabola y^2 = 4x at which the rate of change of the ordinate and abscissa are equal.

(1,2) (2,1) (4,4) (-1,4) Differential Calculus ECE Board April 1998

Find the sum of the infinite geometric progression 6, -2, 2/3,... 9/2 5/2 7/2 11/2 Algebra ECE Board April 1998

Find the value of k for which the equation x^2 + y^2 + 4x - 2y - k = 0 represents a point circle.

-5 5 -6 6 Analytic Geometry eCE Board April 1998

How much must you invest today in order to withdraw P2,000 annually for 10 years if the interest rate is 9%?

P12,835.32 P12,385.32 P12,881.35 P12,853.35 Engineering Economics


If the equation is unchanged by the substitution of y for x, its curve is symmetric with respect to the

origin x - axis y - axis line 45 degrees with the x - axis

Trigonometry ECE Board April 1998

If the sides of a parallelogram and an included angle are 6, 10, and 100 degrees respectively, find the length of the shorter diagonal.

10.73 10.63 10.23 10.53 Analytic Geometry ECE Board April 1998

In the expansion (x + 4y)^12, the numerical coefficient of the 5th term is

126,720 63,360 506,680 253,440 Algebra ece Board April 1998

It can be defined as the set of all points in the plane whose distances from fixed points is a constant.

ellipse circle hyperbola parabola Mathematics Terms ECE Board April 1998

It describes the luminous flux incidence per unit area and is expressed in lumens per square meter.

illiminance luminance luminous intensity

radiance Physics ECE Board April 1998

Money borrowed today is to be paid in six equal payments at the end of six quarters. If the interest is 12% compounded




quarterly. How much was initially borrowed if quarterly payment is P2,000.00?Point P(x,y) moves with a distance from point (0,1) one-half of its distance from line y = 4. The equation of its locus is

4x^2 + 3y^2 = 12 2x^2 - 4y^2 = 5 2x^2 + 5y^3 = 3 x^2 + 2y^2 = 4 Analytic Geometry ECE Board April 1998

Points of derivatives which do not exists (and so equals zero) are called

Minimum and maximum points

Minimum points Maximum points

Stationary points

Differential Calculus ECE Board April 1998

The amount of P12,800 in 4 years at 5% compounded quarterly is



The angle of a sector is 30 degrees and the radius is 15 cm. What is the area of the sector in sq. cm.?

58.9 59.8 89.5 85.9 Trigonometry ECE Board April 1998

The angle or inclination of ascend of a road having a 8.25% grade is

4.71 degrees 4.17 degrees 5.12 degrees 1.86 degrees Mechanics ECE Board April 1998

The area of the region bounded by two concentric circles is called

annulus ring washer circular disk Mathematics Terms ECE Board April 1998

The arithmetic mean of 6 numbers is 17. If two numbers are added to the progression, the new set of numbers will have an arithmetic mean of 19. What are the two numbers if their difference is 4?

23 and 27 21 and 25 8 and 12 16 and 20 Probability&Statistics ECE Board April 1998

The arithmetic mean of 80 numbers is 55. If two numbers namely 250 and 850 are removed, what is the arithmetic mean of the remaining numbers?

42.307 38.625 50 57.12 Probability&Statistics ece Board April 1998

The diameter of a circle described by 9x^2 + 9y^2 = 16 is 8/3 4/3 16/9 4 Analytic Geometry ece Board April 1998

The distance that the top surface is displaced to the direction of the force divided by the thickness of the body is known as

longitudinal strain Linear strain Shear strain Volume strain Strength of Materials ECE Board April 1998

The equation y^2 = cx is the general equation of y' = y / 2x y' = 2x / y y' = 2y / x y' = x / 2y Differential Equation ECE Board April 1998

The segment from (-1, 4) to (2, -2) is extended three times its own length. The terminal point is

(11, -20) (-11, 20) (11, 20) (-11, -20) Analytic Geometry ECE Board April 1998


The sides of a triangle are 8, 15 and 17 units. If each side is doubled , how many square units will the area of the new triangle be?

240 420 320 200 Differential Calculus ECE Board April 1998

The sum of the first 10 terms of a geometric progression 2, 4, 8, 16,... Is

2046 1023 225 1596 Algebra ECE Board April 1998

To maximize the horizontal range of the projectile, which of the following applies?

The tangent function of the angle of trajectory must be equal to one

Maximize the angle of elevation and velocity

Maximize the angle of elevation

Maximize velocity

Physics ECE Board April 1998

Two electrons have speeds of 0.7c and x respectively. If their relative velocity is 0.65c. Find x.

0.09c 0.12c 0.15c 0.05c Physics ECE Board April 1998

What is the inertia of a bowling ball (mass is 0.5 kg and radius of 15 cm.) rotating at an angular speed of 10 rpm for 6 seconds?

0.0045 kg - m^2 0.001 kg - m^2 0.002 kg - m^2 0.045 kg - m^2 Physics ECE Board April 1998

What is the kinetic energy of a 4,000-lb automobile, which is moving at 44 fps?

1.21 x 10^5 ft=lb 1.12 x 10^5 ft=lb 2.01 x 10^5 ft=lb

1.01 x 10^5 ft=lb

Physics ECE Board April 1998

What is the lowest common factor of 10 and 32? 2 320 180 90 Algebra ECE Board April 1998

What is the speed of a synchronous earth's satellite situated 4.5 x 10^7 meters from the earth?

11,777 kph 12,000 kph 12,077 kph 11,070 kph Physics ECE Board April 1998

ece board 1998.docx

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