mensuration area volumes Model Questions & Answers, Practice Test for ibps so prelims 2023
ibps so prelims 2023 SYLLABUS WISE SUBJECTS MCQs
Number System
Simplification
Ratio & Proportion
Profit & Loss
Time & Work
Simple Interest & Compound Interest
Mensuration: Area & Volumes
Quadratic Equations
In the figure shown above, the radius OA is equal to the chord AB. Then, what is ∠APB?
Answer: (b)
OA = OB = AB
(given)
So, ΔAOB is an equilateral triangle.
⇒ ∠AOB = 60°
We know that, the angle subtended at the centre of circle is twice the angle subtended at circumference of the circle.
∴ ∠AOB = 2 ∠APB
⇒ ∠APB = ${60°}/2$ = 30°
AB is a line segment of length 2a, with M as mid–point. Semicircles are drawn on one side with AM, MB and AB as diameter as shown in the above figure. A circle with centre O and radius r is drawn such that this circle touches all the three semicircles. The value of r is
Answer: (a)
AB = 2a i.e., AL = LM = MN = NB = $a/2$
Let OC = r
In ΔOML, OM= a – r and OL = OP + PL = r + $a/2$
∴ $(a/2)^2 + (a - r)^2 = (r + a/2)^2$
⇒ $a^2/4 + a^2 - 2ar + r^2 = r^2 + a^2/4 + ar$
⇒ $a^2 = 3ar ⇒ r = a/3$
So, option is correct.
A river 2.5 m deep and 45 m wide is flowing at the speed of 3.6 km/hour. The amount of water that runs into the sea per minute is
Answer: (c)
Water running per hour in the river
= 2.5 × 45 × 3600 $m^3$.
Water running per minutes in the river
= ${2.5 × 45 × 3600}/{60} m^3$
= 2.5 × 45 × 60
= 6750 $m^3$
So, option (c) is correct
The perimeter of a right-angled triangle is k times the shortest side. If the ratio of the other side to hypotenuse is 4 : 5, then what is the value of k ?
Answer: (a)
Let BC is shortest side in right angle triangle ΔABC,
such that AB : AC = 4 : 5.
∴ BC = $√{(AC)^2 - (AB)^2}$
= $√{(5x)^2 - (4x)^2}$ = 3x
ABC
Perimeter = AB + BC + AC = 4x + 3x + 5x = 12x
According to the question
12x = k(3x)
∴ k = ${12x}/{3x}$ = 4
The side BC of a ΔABC is produced to D, bisectors of the ∠ABC and ∠ACD meet at P. If ∠BPC = x° and ∠BAC = y°, then which one of the following option is correct?
Answer: (d)
Given ∠BAC = y°
and ∠BPC = x°
According to triangle property, the angle subtended by the bisector of an internal angle and an external angle is half of the third angle.
∴ y° = 2x° or x = $y/2$
Alternate Method:—
In ΔABC, y° + ∠ABC + ∠ACB = 180° ... (i)
In ΔBPC, ∠BPC + ∠PBC + ∠PCB = 180°
x° + ${∠ABC}/2 + ({∠ACD}/2 + ∠ACB)$ = 180° ... (ii)
Comparing equation (i) and (ii)
x° = ${y°}/2$
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