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
If the distance between the points (4,p) and (1,0) is 5. Then the value of p is :
A)
3
B)
-4
C)
4
D)
±4
Distance sqrt((4-1)^2+p^2)=5 => 9+p^2=25 => p=±4.
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.
Surveyor • 2019 • Technical Paper-II
The side of a square whose diagonal is 16cm is :
A)
16√5cm
B)
8√2cm
C)
5cm
D)
7.5cm
Side=diagonal/√2=16/√2=8√2cm.
Surveyor • 2019 • Technical Paper-II
The volume of sphere can be measured by using :
A)
πr3
B)
4/3 πr3
C)
4/3 πr2
D)
4/3 πr2
Volume sphere=4/3πr³.
Surveyor • 2019 • Technical Paper-II
The coordinates of a point in the third quadrant are in the form :
A)
+, +
B)
+, -
C)
-, -
D)
-, +
Third quadrant both coordinates negative (-,-).
Surveyor • 2019 • Technical Paper-II
From the following figure (triangle PQR with sides 12cm, 13cm, 5cm), find tan P :
A)
25/12
B)
7/12
C)
4/25
D)
5/12
In 5-12-13 right triangle tan P = opposite/adjacent =5/12 assuming figure labels.
Surveyor • 2019 • Technical Paper-II
The angle of depression of the top and bottom of a tower as seen from the top of a 100m high cliff are 30° and 60° respectively. Find the height of the tower.
A)
60m
B)
55.67m
C)
67.45m
D)
66.67m
Let d=100/tan60, 100-h=d·tan30=100/3 => h=66.67m.
Surveyor • 2019 • Technical Paper-II
Section formula in coordinates geometry is :
A)
((mx2 + m1x1, my2 + m1y1) / (m1 + m2))
B)
((mx2 - m1x1, my2 - m1y1) / (m1 + m2))
C)
((mx2 + m1x1, my2 + m1y1) / (m2 - m1))
D)
None of these
Internal section formula ((m*x2+m1*x1)/(m1+m2),(m*y2+m1*y1)/(m1+m2)).
Surveyor • 2019 • Technical Paper-II
Sin2 + Cos2 = ?
A)
2
B)
3
C)
1
D)
4
Identity sin²θ+cos²θ=1.
Surveyor • 2019 • Technical Paper-II
A line which intersects a circle in two distinct points is called a_______of the circle.
A)
Secant
B)
Cosecant
C)
Tangent
D)
Cotangent
Correct option: A. Secant. The selected option best matches the fact, rule, calculation, or passage-based inference required. Topic: Quantitative Aptitude.
Surveyor • 2019 • Technical Paper-II
In an isosceles triangle ABC, AB=AC=25cm and BC =14cm. The altitude from A on BC is:
A)
24cm
B)
22cm
C)
27cm
D)
25.5cm
Altitude=√(25²-7²)=√576=24cm.
