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.
Surveyor • 2019 • Technical Paper-II
The midpoint P of the join of the points A(x1, y1) and B(x2, y2) is :
A)
((x1+x2)/2, (y1+y2)/2)
B)
((x1-x2)/2, (y1-y2)/2)
C)
((x1-x2)/4, (y1+y2)/4)
D)
((x1+x2)/3, (y1-y2)/3)
Midpoint is average of coordinates ((x1+x2)/2,(y1+y2)/2).
Surveyor • 2019 • Technical Paper-II
Find the value of p and q in the given figure, if ABCD is a rectangle (refer to figure with sides p+3q, 3p+q, 7, 13):
A)
1,4
B)
4,1
C)
2,2
D)
3,3
Correct option: B. 4,1. The selected option best matches the fact, rule, calculation, or passage-based inference required. Topic: Quantitative Aptitude.
Surveyor • 2019 • Technical Paper-II
The perimeter of a circle is given by :
A)
πr2
B)
π2r
C)
2πr
D)
None of these
Perimeter/circumference circle=2πr.
Surveyor • 2019 • Technical Paper-II
A wheel has diameter 84 cm. The number of complete revolution it will take to cover 792 m is.
A)
100
B)
150
C)
200
D)
300
Circumference=π·84=264cm=2.64m, 792/2.64=300 revolutions.
Surveyor • 2019 • Technical Paper-II
Sin (90° - ) = ?
A)
cos
B)
cot
C)
cosec
D)
tan
Complementary identity sin(90°-θ)=cosθ.
Surveyor • 2019 • Technical Paper-II
A plumbline is a combination of which geometric shapes?
A)
A cylinder with sphere
B)
A cone with hemisphere
C)
A circle with cone
D)
A cone with sphere
Plumbline is a cone mounted on a hemisphere.
Surveyor • 2019 • Technical Paper-II
Segment of a circle is the region between an arc and__________of the circle.
A)
Diametre
B)
Perimetre
C)
Radius
D)
Chord
Correct option: D. Chord. The selected option best matches the fact, rule, calculation, or passage-based inference required. Topic: Quantitative Aptitude.
Surveyor • 2019 • Technical Paper-II
The slant height of a right circular cone ‘l’ can be found by :
A)
q2 - h2
B)
sqrt(r2 + h2)
C)
r2 - p2
D)
q2 + h2
Slant height l=√(r²+h²).
Surveyor • 2019 • Technical Paper-II
Evaluate the following : sin²25° + sin²65° + √3(tan5° tan15° tan30° tan75° tan85°)
A)
1
B)
2
C)
3
D)
5
sin²25+sin²65=1 and tan5·tan85=1, tan15·tan75=1, √3·tan30=1, total 2.
Surveyor • 2019 • Technical Paper-II
Consider the following statements and choose the correct option: Statement I : Two triangles are similar if their corresponding angles are equal. Statement II :Two triangles are similar if their corresponding sides are in the same ratio.
A)
Only I
B)
Only II
C)
Both I & II
D)
None of these
Correct option: C. Both I & II. The selected option best matches the fact, rule, calculation, or passage-based inference required. Topic: Quantitative Aptitude.
Surveyor • 2019 • Technical Paper-II
Find the coordinate of the point on x-axis which is equidistant from (2,-5)and (-2,9)
A)
(-7,0)
B)
(2,5)
C)
(3,0)
D)
(4,-3)
Point on x-axis (x,0) equidistant: (x-2)^2+25=(x+2)^2+81 gives x=-7, so (-7,0).
Surveyor • 2019 • Technical Paper-II
The distance between two points A(x1, y1) and B(x2, y2) is given by the formula :
A)
AB = (x2 - x1) + (y2 - y1)
B)
AB = sqrt((x2 - x1)^2 + (y2 - y1)^2)
C)
AB = (x2 - x1)^2 - (y2 - y1)^2
D)
AB = (x2 - x1)^3 - (y2 - y1)^2
Standard distance formula AB = sqrt((x2-x1)^2+(y2-y1)^2).
Surveyor • 2019 • Technical Paper-II
The distance of the point P(x,y) from the origin O(0,0) is given by
A)
y2 - x2
B)
y - x
C)
sqrt(x2 + y2)
D)
x - y
Distance from origin O(0,0) to P(x,y) is sqrt(x^2+y^2).
Surveyor • 2019 • Technical Paper-II
The circumference and area of a circle of diameter 28cm is :
A)
67cm, 676cm2
B)
88cm, 616 cm2
C)
45cm, 225cm2
D)
57cm, 215cm2
r=14, C=2πr=88cm, A=πr²=616cm².
Surveyor • 2019 • Technical Paper-II
Find the distance of the point (–6, 8) from the origin.
A)
8
B)
11
C)
9
D)
10
Distance sqrt((-6)^2+8^2)=sqrt(100)=10.
