Mensuration Model Questions Set 1 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) 75°
(b) 45°
(c) 60°
(d) 90°
The correct answers to the above question in:
Answer: (c)
Let the radius of the bigger circle be a and radius of the smaller circle be b.
Then the angle made by direct common tangents when two circles of radius a and b touch externally is given by θ = $2sin^{- 1}({a - b}/{a + b})$
We are given that area of the bigger circle = 9 area of the smaller circle
⇒ $πa^2 = 9πb^2 ⇒ a^2 = 9b^2 ⇒ a = 3b$
Let us consider ∠BAC = θ
Thus,
θ = $2 sin^{-1} ({a - b}/{a + b}) = 2 sin^{-1} ({3b - b}/{3b + b}) = 2sin^{-1} ({2b}/{4b})$
= $2 sin^{-1} (1/2) = 2 sin^{-1}$ (sin 30°) = 2 × 30° = 60°
Discuss Form
Read more model questions set 1 Based Quantitative Aptitude Questions and Answers
Question : 1
In the figure given above, LM is parallel to QR. If LM divides the ΔPQR such that area of trapezium LMRQ is two times the area of ΔPLM, then what is ${PL}/{PO}$ equal to?
a) $1/2$
b) $1/√2$
c) $1/√3$
d) $1/3$
Answer »Answer: (c)
In the given figure.
ar MRQL = 2 ar ΔPLM
Let area of ΔPLM be x, then
∴ the area of trapezium = 2x
∴ ar ΔPQR = 2x + x = 3x
Here it is clear from the given figure that ΔPQR ∼ ΔPLM
∴ ${\text"ar ΔPQR"}/{\text"ar ΔPLM"} = {3x}/x$
${PL^2}/{PQ^2} = 1/3 ∴ = {PL}/{PQ} = 1/√3$
Question : 2
The dimensions of a field are 15 m by 12 m. A pit 8 m long, 2.5 m wide and 2 m deep is dug in one corner of the field and the earth removed is evenly spread over the remaining area of the field. The level of the field is raised by
a) 25 cm
b) 15 cm
c) 20 cm
d) ${200}/9$ cm
Answer »Answer: (a)
Volume of pit = l b h = 8 × 2.5 × 2 = 40 $m^3$.
Let the label of the earth spread over remaining area = h.
Volume of the earth spread = Volume of a pit
⇒ [(12 × 15) – (8 × 2.5)] × h = 40
∴ h = ${40}/{180 - 20} = {40}/{160} = 1/4$m = 25 cm
Question : 3
ABCD is a quadrilateral with AB = 9 cm, BC = 40 cm, CD = 28 cm, DA = 15 cm and angle ABC is a right-angle.
What is the area of quadrilateral ABCD ?
a) 312 $cm^2$
b) 300 $cm^2$
c) 306 $cm^2$
d) 316 $cm^2$
Answer »Answer: (c)
In right triangle ABC,
AC = $√{(AB)^2 + (BC)^2} = √{(40)^2 + (9)^2}$ = 41 cm
Area of ΔABC = $1/2 × 9 × 40 = 180 cm^2$
∵ Area of quadrilateral ABCD
= 126 + 180 = 306 $cm^2$
Question : 4
Consider an equilateral triangle of a side of unit length. A new equilateral triangle is formed by joining the midpoints of one, then a third equilateral triangle is formed by joining the mid-points of second. The process is continued. The perimeter of all triangles, thus formed is
a) 6 units
b) 2 units
c) 3 units
d) Infinity
Answer »Answer: (a)
Sides of equilateral triangle are follows:
3, $3/2, 3/4, 3/8$ ... so on
These sequence formed a GP serves.
So sum of GP for Infinite terms.
S = $a/{1 - r}$
Here a = 3, r = $1/2$
S = $3/{1 - 1/2}$ =6 units
Question : 5
In the figure given below, PQ is parallel to RS and PR is parallel to QS. If ∠LPR = 35° and ∠ UST = 70°, then what is ∠MPQ equal to ?
![mensuration area and volume aptitude mcq 21 50](https://careericons.com/adminicon/bunch/images/mensuration-area-and-volume-aptitude-mcq-21-50.png)
a) 75°
b) 55°
c) 70°
d) 80°
Answer »Answer: (a)
PQ || RS
PR|| QS
∴ PQRS is a || gm
∠LPR = 35° and ∠UST = 70°
∠UST = ∠RSQ (Vertically opposite)
∠RSQ = ∠RPQ (opposite angle of 11 gm)
∠LPR + ∠RPQ + ∠MPQ = 180°
35° + 70° + ∠MPQ = 180°
∠MPQ = 180 – 105
∠MPQ = 75°
Question : 6
The medians of ΔABC intersect at G. Which one of the following is correct?
a) Three times the area of ΔAGB is equal to the area of ΔABC
b) Five times the area of ΔAGB is equal to four times the area of ΔABC
c) Four times the area of ΔAGB is equal to three times the area of ΔABC
d) None of the above
Answer »Answer: (a)
Suppose ΔABC is an equilateral triangle.
A median divides an equilateral triangle into the three equal area of triangles.
ΔAGB = ar ${(ΔABC)}/3$ = ar BGC = ar ΔAGC
∴ ar ΔAGB = $1/3$ ΔABC.
GET Mensuration PRACTICE TEST EXERCISES
Mensuration Model Questions Set 1
Mensuration Model Questions Set 2
Mensuration Shortcuts and Techniques with Examples
Verbal Reasoning
Question & Answer Quiz
Non Verbal Reasoning
Question & Answer Quiz
Quantitative Aptitude
Question & Answer Quiz
Computer MCQ
Question & Answer Quiz
General English
Question & Answer Quiz
History GK
Question & Answer Quiz
Polity GK
Question & Answer Quiz
Geography GK
Question & Answer Quiz
Economy GK
Question & Answer Quiz
General Awareness GK
Question & Answer Quiz
Recently Added Subject & Categories For All Competitive Exams
100+ Quadratic Equation Questions Answers PDF for Bank
Quadratic Equation multiple choice questions with detailed answers for IBPS RRB SO. more than 250 Attitude practice test exercises for all competitive exams
Continue Reading »
IBPS Aptitude Linear Equations MCQ Questions Answers PDF
Linear equations multiple choice questions with detailed answers for IBPS RRB SO. more than 250 Attitude practice test exercises for all competitive exams
Continue Reading »
New 100+ Compound Interest MCQ with Answers PDF for IBPS
Compound Interest verbal ability questions and answers solutions with PDF for IBPS RRB PO. Aptitude Objective MCQ Practice Exercises all competitive exams
Continue Reading »
100+ Mixture and Alligation MCQ Questions PDF for IBPS
Most importantly Mixture and Alligation multiple choice questions and answers with PDF for IBPS RRB PO. Aptitude MCQ Practice Exercises all Bank Exams
Continue Reading »