Mensuration Model Questions Set 2 Section-Wise Topic Notes With Detailed Explanation And Example Questions
MOST IMPORTANT quantitative aptitude - 2 EXERCISES
The following question based on Mensuration topic of quantitative aptitude
(a) 154 metres
(b) 160 metres
(c) 172 metres
(d) None of these
The correct answers to the above question in:
Answer: (b)
Let the height of canal = h.
Then, area of canal = $1/2$ × h(9 + 7)
or = 1280 = $1/2$ h(16)
∴ h = ${1280 × 2}/{16}$ = 160m
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Read more model questions set 2 Based Quantitative Aptitude Questions and Answers
Question : 1
In the figure given above, what is ∠CBA?
a) 50°
b) 30°
c) 45°
d) 60°
Answer »Answer: (d)
The sum of opposite angles in cyclic quadrilateral is always 180°.
∴ ∠ACQ + ∠APQ = 180°
75° + ∠APQ = 180°
∴ ∠APQ = 180° – 75° = 105°
∠ACQ + ∠QCR = 180° (∵ Straight line)
75° + ∠QCR = 180°
∠QCR = 180° – 75° = 105°
∠CQR = 180° – 105° – 30° = 45°
Since, ∠APQ + ∠BPQ = 180° (Straight line)
∴ 105° + ∠BPQ = 180°
∠BPQ = 75°
In ΔBPQ ∠B + ∠P + ∠Q = 180°
∠B + 75° + 45° = 180°
⇒ ∠B = 60° ∴ ∠CBA = 60°
Question : 2
What is the area of the largest circular disc cut from a square of side $2/√π$ units?
a) $π^2$ square units
b) π square units
c) 1 square unit
d) 2 square units
Answer »Answer: (c)
Side of square = $2/√π$
radius of circular disc = $2/√π × 1/2 = 1/√π$
area of disc = $π r^2 = π (1/√π)^2$ = 1 unit 2
Question : 3
If a square of side x and an equilateral triangle of side y are inscribed in a circle, then what is the ratio of x to y ?
a) $3/√2$
b) $√{2/3}$
c) $√{3/2}$
d) $√2/3$
Answer »Answer: (b)
Let Radius of circle be r
Case I (Square)
side = x
$x^2 + x^2 = (2r)^2$
$2x^2 = 4r^2$
x = $√2$r
Case II (equilateral triangle)
y cos30° = h
y × $√3/2$ = h
r = $2/3 × √3/2$ y
r = $y/√3$
[if h= 3 r = 2]
$y/{2r} = √3/2$
y = ${2 √3r}/2 = √3r$
$x/y = {√2 r}/{√3 r} = √{2/3}$
Question : 4
Assertion (A)
Triangles on the same base and between the same parallel lines are equal in area.
Reason (R)
The distance between two parallel lines is same everywhere.
a) A is true but R is false
b) Both A and R individually true and R is the correct explanation of A
c) Both A and R are individually true but R is not the correct explanation of A
d) A is false but R is true
Answer »Answer: (b)
A. By the properties of triangle, it is true.
R. It is also true that the distance between two parallel lines is same everywhere.
Hence, A and R are true and R is the correct explanation of A.
Question : 5
If the sum of the circumferences of two circles with radii $R_1$ and $R_2$ is equal to the circumference of a circle of radius R, then
a) $R_1 + R_2$ < R
b) $R_1 + R_2$ = R
c) $R_1 + R_2 > R_3$
d) Nothing definite can be said about the relation among $R_1.R_2$ and R
Answer »Answer: (b)
Question : 6
In the figure given above, AB is a diameter of the circle with centre O and EC = ED. What is ∠EFO?
a) 25°
b) 15°
c) 20°
d) 30°
Answer »Answer: (c)
The Given,
⇒ ∠EDC = ∠ECD = 35°
Since, ∠OCD = 55°
Then, ∠OCE = 20°
By using then theorem that triangle on the same segment of a circle makes as equal angles.
Here, OE is a segment, which makes a ΔOFE and ΔOCE.
Therefore, ∠OCE = ∠EFO = 20°
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