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) 6.0 cm
(b) 5.6 cm
(c) 5.8 cm
(d) 6.2 cm
The correct answers to the above question in:
Answer: (b)
We know that when two triangles are similar then ratio of their areas is equal to square of corresponding sides.
${\text"area of ΔABC"}/{\text"area of ΔXYZ"} = {AB^2}/{XY^2} ⇒ {32}/{60.5} = {AB^2}/{(7.7)^2}$
⇒ ${32 × 59.29}/{60.5} = AB^2 ⇒ 31.36 = AB^2$
∴ AB = $√{31.36}$ = 5.6 cm
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Read more model questions set 2 Based Quantitative Aptitude Questions and Answers
Question : 1
In the figure given above, C and D are points on the semi-circle described on AB as diameter. If ∠ABD = 75° and ∠DAC = 35°, then what is the ∠BDC?
a) 90°
b) 130°
c) 110°
d) 100°
Answer »Answer: (b)
Since, DADB is a right angled triangle at D.
∴ ∠DAB = 180° – (90° + 75°)
⇒ ∠DAB = 15°
Also, ABCD is cyclic quadrilateral.
∴ ∠CAB + ∠BDC = 180°
⇒ ∠BDC = 180° – (35° + 15°) = 130°
Question : 2
The probability that at least one of the events A and B occurs is 0.7 and they occur simultaneously with probability 0.2. Then P($\ov{A}$) + P($\ov{B}$) =
a) 0.6
b) 1.1
c) 1.8
d) 0.4
Answer »Answer: (b)
We have P (A ∪ B) = 0.7 and P (A ∩ B) = 0.2
Now, P(A ∪ B) = P(A) + P(B) - P (A ∩ B)
⇒P(A) + P(B) = 0.9⇒1-P($\ov{A}$) + 1 - P($\ov{B}$) = 0.9
⇒P($\ov{A}$) + P($\ov{B}$) = 1.1
Question : 3
The number of ways of choosing a committee of 2 women and 3 men from 5 women and 6 men, if Mr. A refuses to serve on the committee if Mr. B is a member and Mr. B can only serve, if Miss C is the member of the committee, is
a) 84
b) 124
c) 60
d) None of these
Answer »Answer: (b)
(i) Miss C is taken
(1) B included ⇒A excluded ⇒$^4C_1 . ^4C_2$ = 24
(2) B excluded ⇒$^4C_1 . ^5C_3$ = 40
(ii) Miss C is not taken
⇒B does not comes ; $^4C_2 . ^5C_3$ = 60⇒Total = 124
Question : 4
a, b, c, b are non-zero integers such that (ab) divides (cd). If a and c are coprime, then which one of the following is correct?
a) a is a factor of d
b) a is a factor of c
c) a is a factor of b
d) d is a factor of a
Answer »Answer: (a)
Since we are given that a and c are co-prime i.e. HCF of a and c is 1, therefore we can say that a definitely divides d exactly.
So, a is a factor of d.
Question : 5
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 : 6
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
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