All Evaluation Exam

Question 1

The three-dimensional coordinate system is divided into eight parts which are known as
A. octants
B. quadrants
C. coordinates
D. axis

Answer 1

octants

Question 2

A line segment is a side of a square and also the hypotenuse of an isosceles right triangle. What is the ratio of the area of the square to the area of the triangle?
A. 2:1
B. 4:1
C. 1:1
D. 3:2

Answer 2

4:1

Question 3

The axis of the hyperbola through its foci is known as:
A. conjugate axis
B. transverse axis
C. major axis
D. minor axis

Answer 3

transverse axis

Question 4

What is the conic section x^2 + 6x - y + 12 = 0?
A. circle
B. parabola
C. ellipse
D. hyperbola

Answer 4

parabola

Question 5

The curve being described by the equation 5x^2 + 5y^2 - 10x - 20y + 25 = 0 is a
A. hyperbola
B. circle
C. ellipse
D. parabola

Answer 5

circle

Question 6

Describe the locus represented by |z + 2i| + |z - 2i| = 6
A. ellipse
B. circle
C. hyperbola
D. parabola

Answer 6

ellipse

Question 7

The product of the slopes of any two straight lines is negative 1, one of the lines are said to be _______.
A. perpendicular
B. parallel
C. non intersecting
D. skew

Answer 7

perpendicular

Question 8

The locus of the point that moves such that the difference of its distance between two fixed points is constant.
A. hyperbola
B. ellipse
C. parabola
D. circle

Answer 8

hyperbola

Question 9

The curve which has an eccentricity equals to zero.
A. circle
B. parabola
C. hyperbola
D. ellipse

Answer 9

circle

Question 10

A tangent to a conic is a line _______.
A. Which is parallel to the normal
B. Which passes inside the conic
C. Which touches the conic only at one point
D. All of the above

Answer 10

Which touches the conic only at one point

Question 11

B^2 - 4AC < 0 describes a/an ________.
A. circle
B. ellipse
C. parabola
D. hyperbola

Answer 11

ellipse

Question 12

What curve is described by the equation y2 + 4y + x - 1 = 0?
A. hyperbola
B. parabola
C. circle
D. ellipse

Answer 12

parabola

Question 13

A conic whose eccentricity is less than one (1) is known as
A. parabola
B. an ellipse
C. a circle
D. a hyperbola

Answer 13

ellipse

Question 14

The _______ of a parabola is the line which passes through the focus and is parallel to the directrix.
A. latus rectum
B. axis
C. eccentricity
D. tangent line

Answer 14

Latus rectum

Question 15

The locus of a point which moves so that the sum of its distances between two fixed points is constant is called
A. hyperbola
B. circle
C. parabola
D. ellipse

Answer 15

ellipse

Question 16

A triangular corner lot has perpendicular sides of length 90 m and 60 m. Find the dimensions of the largest rectangular building that can be constructed on the lot with sides parallel to the streets.
A. 30 m x 30 m
B. 25 m x 40 m
C. 45 m x 30 m
D. 24 m x 24 m

Answer 16

45 m x 30 m

Question 17

If the average value of a periodic function over one period is zero, and it consists of only odd harmonics; then it must be possessing _______ symmetry.
A. half wave
B. even quarter-wave
C. odd quarter-wave
D. odd

Answer 17

half wave

Question 18

In the polar coordinate system, the distance from a point to the pole is
A. polar angle
B. radius vector
C. y-coordinate
D. x-coordinate

Answer 18

radius vector

Question 19

The inverse Laplace transform of s / s^2 + w^2 is
A. cos wt
B. tan wt
C. sin wt
D. sec wt

Answer 19

cos wt

Question 20

longer axis of ellipse

Answer 20

prolate

Question 21

shorter axis of ellipse

Answer 21

oblate

Question 22

sine angles at maximum ratio of sides

Answer 22

1:1:1

Question 23

area under arch of hypocycloid

Answer 23

3 pi a^2

Question 24

centroid of semicircle

Answer 24

4r/3pi where r is radius

Question 25

cylinder with elliptical cross section

Answer 25

cylindroid

Question 26

line segment joining two point

Answer 26

chord

Question 27

closed cylindrical container

Answer 27

2radius = height

Question 28

Find the equation of orthogonal trajectories of the system of parabolas y^2 = 2x + C

Answer 28

y = Ce^-x

Question 29

Solve xy' (2y -1) = y(1-x) A. ln xy = x - 2y + C B. ln xy = x + 2y + C C. ln xy = 2y - x + C D. ln xy = 2(x-y) + C

Answer 29

ln xy = x + 2y + C

Question 30

Find the maximum value of 3^sin(3x) A. 1/3 B. infinity C. 1 D. 3

Answer 30

3

Question 31

If in the fourier series of a periodic function, the coefficient of a0 = 0 and an = 0, then it must be having ________ symmetry. A. odd B. odd quarter wave C. even D. either a or b

Answer 31

either a or b