Surveyor • 2019 • Technical Paper-II
In DABC right angled at B, AB = 24 cm, BC = 7 m. Determine SinA :
A)
3/25
B)
6/25
C)
7/25
D)
5/30
Right triangle AC=25, sinA=opposite/hyp=BC/AC=7/25.
Surveyor • 2019 • Technical Paper-II
The co-ordinates of the centroid of a triangle whose vertices are P(x1,y1), Q(x2,y2) and R(x3,y3) are
A)
((x1-x2+x3)/3, (y1-y2+y3)/3)
B)
((x1+x2+x3)/3, (y1+y2+y3)/3)
C)
((x1+x2-x3)/3, (y1+y2-y3)/3)
D)
((x1+x2+x3)/3, (y1+y2+y3)/3)
Centroid is average of vertices ((x1+x2+x3)/3,(y1+y2+y3)/3). Option D identical.
Surveyor • 2019 • Technical Paper-II
The lines y = 5x - 3 and y = 2x + 9 intersect at P. What are the coordinates of P?
A)
(2,7)
B)
(2,13)
C)
(4,17)
D)
(5,3)
Solving 5x-3=2x+9 gives x=4, y=17, so (4,17).
Surveyor • 2019 • Technical Paper-II
From a point 20m away from the foot of a tower, the angle of elevation of top of the tower is 30°, find the height of the tower :
A)
35m
B)
12√3m
C)
20√3/3 m
D)
12m
Height=20·tan30=20/√3=20√3/3 m.
Surveyor • 2019 • Technical Paper-II
The formula for finding the area of a triangle is :
A)
l x b x h
B)
4a2
C)
1/2 x b x h
D)
2(l + b + h)
Triangle area=½·base·height.
Surveyor • 2019 • Technical Paper-II
There is/are ______tangent(s) at a point on a circle.
A)
One
B)
Two
C)
Three
D)
None of these
Correct option: A. One. The selected option best matches the fact, rule, calculation, or passage-based inference required. Topic: Quantitative Aptitude.
Surveyor • 2019 • Technical Paper-II
An observer 1.5m tall is 20.5 metres away from a tower 22m high. Determine the angle of elevation of the top of the tower from the eye of the observer.
A)
0°
B)
30°
C)
45°
D)
60°
Height above eye =22-1.5=20.5, distance 20.5 => tan=1 =>45°.
Surveyor • 2019 • Technical Paper-II
The most used theorem for finding the length of the side of a right angled triangle is :
A)
Bernouli’s theorem
B)
Pythagoras theorem
C)
Euler’s formula
D)
All of the above
Correct option: B. Pythagoras theorem. The selected option best matches the fact, rule, calculation, or passage-based inference required. Topic: Quantitative Aptitude.
Surveyor • 2019 • Technical Paper-II
The lengths of the diagonals of a rhombus are 16cm and 12cm. Then, find the length of the side of the rhombus :
A)
16cm
B)
20cm
C)
12cm
D)
10cm
Side=√((16/2)²+(12/2)²)=√(64+36)=10cm.
Surveyor • 2019 • Technical Paper-II
The distance of a point from the x-axis is called its :
A)
Origin
B)
Abscissa
C)
Ordinate
D)
None of these
Distance from x-axis is y-coordinate, called ordinate.
Surveyor • 2019 • Technical Paper-II
A toy is in the form of a cone mounted on a hemisphere of common base radius of 7cm. The total height of the toy is 31cm. Find the total surface area of the toy.
A)
465
B)
912
C)
769
D)
858
Cone height 24, l=25, total CSA=πr l+2πr²=550+308=858.
Surveyor • 2019 • Technical Paper-II
The abscissa and ordinate of a point together are called :
A)
Quadrant
B)
Coordinates
C)
Origin
D)
None of these
Abscissa and ordinate together are called coordinates.
Surveyor • 2019 • Technical Paper-II
A ladder 15m long just reaches the top of vertical wall. If the ladder makes an angle with the wall, find the height of the wall :
A)
7.5m
B)
12m
C)
5.6m
D)
2.5m
Assuming 60° with wall (common version), height=l·cos60=15·0.5=7.5m; if 60° with ground height=12m.
Surveyor • 2019 • Technical Paper-II
Length of an altitude of an equilateral triangle whose side is 2a is :
A)
3
B)
3a
C)
√3 a
D)
3a
Altitude of equilateral side 2a is (√3/2)·2a=√3 a.
Surveyor • 2019 • Technical Paper-II
P is the point (4,-2). Q is the point (-3,-5). What is the length of PQ?
A)
45
B)
60
C)
58
D)
50
PQ = sqrt((4+3)^2 + (-2+5)^2) = sqrt(49+9)=sqrt58 ≈7.62; squared distance is 58, so option C matches the numerical part.
Surveyor • 2019 • Technical Paper-II
The slant height of a frustum of a cone is 4cm and the perimeter of its circular ends are 18cm and 6cm. Find the curved surface area of the frustum. Use π = 22/7
A)
65 cm2
B)
52 cm2
C)
36 cm2
D)
48 cm2
CSA frustum=(P1+P2)/2·l=(18+6)/2·4=48 cm².
Surveyor • 2019 • Technical Paper-II
sin = ?
A)
Hypotenuse / Perpendicular
B)
Perpendicular / Base
C)
Perpendicular / Hypotenuse
D)
Hypotenuse / Base
sinθ = Perpendicular/Hypotenuse.
Surveyor • 2019 • Technical Paper-II
1 + tan2 = ?
A)
cot2
B)
Sec2
C)
Cos2
D)
Cosec2
Identity 1+tan²θ=sec²θ.
Surveyor • 2019 • Technical Paper-II
The formula for finding the area of a semi-circle is :
A)
πr2
B)
1/2 πr2
C)
2πr
D)
2πrh
Area semi-circle=½πr².
Surveyor • 2019 • Technical Paper-II
The distance of a point from the y-axis is called its :
A)
Origin
B)
None of these
C)
Ordinate
D)
Abscissa
Distance from y-axis is x-coordinate, called abscissa.
Surveyor • 2019 • Technical Paper-II
Find the value of p for which the points (–5, 1), (1, p) and (4, –2) are collinear.
A)
–3
B)
–2
C)
0
D)
–1
Collinearity slope (-5,1)-(4,-2)=-1/3, using line for x=1 gives y=-1, so p=-1.
Surveyor • 2019 • Technical Paper-II
A triangle in which all the three sides have different length is called :
A)
Equilateral
B)
Isosceles
C)
Right angled triangle
D)
Scalene triangle
Correct option: D. Scalene triangle. The selected option best matches the fact, rule, calculation, or passage-based inference required. Topic: Quantitative Aptitude.
Surveyor • 2019 • Technical Paper-II
The curved surface area of right circular cylinder is :
A)
2πr(h+r)
B)
2πr
C)
2πr2h
D)
2πrh
Curved surface area cylinder=2πrh.
Surveyor • 2019 • Technical Paper-II
A pole 6cm high casts a shadow of 2√3 m long on the ground, then find the sun’s elevation?
A)
30°
B)
60°
C)
90°
D)
45°
tan elevation =6/(2√3)=√3 => 60°.
Surveyor • 2019 • Technical Paper-II
Find the value of cosec²30° - sin²45° - sec²60°
A)
4
B)
-3
C)
6
D)
-2
cosec²30=4, sin²45=0.5, sec²60=4, result -0.5; closest listed negative option D -2, correct mathematically -0.5 with given options erroneous.
