mensuration Model Questions & Answers, Practice Test for ibps clerk prelims 2024
ibps clerk prelims 2024 SYLLABUS WISE SUBJECTS MCQs
Ratio & Proportion
Percentage
Time & Work
Time & Distance
Mensuration
Trigonometric Ratios & Identities
The angles of a triangle are in the ratio 1 : 1 : 4. If the perimeter of the triangle is k times its largest side, then what is the value of k ?
Answer: (b)
We know that, sum of angles of any triangle = 180°
x + x + 4x = 180°
x = ${180°}/6$ = 30°
So, angle of triangles are 30°, 30°, 120°.
Let side of the triangles ABC are x, x and y
From cosine formula,
cos(120°) = ${AB^2 + AC^2 - BC^2}/{2.AB.AC} = {x^2 + x^2 - y^2}/{2.x.x}$
${-1}/2 = {2x^2 - y^2}/{2x^2} ⇒ y^2 = 3x^2$
y ∼ = $√3x$
Perimeter of the triangle = (x + x + y) = k(y) (given)
$(2/√3 y + y) = K.y = ∴ K = 1 + 2/√3$
A regular hexagon is inscribed in a circle of radius 5 cm. If x is the area inside the circle but outside the regular hexagon, then which one of the following is correct?
Answer: (b)
OB = OA = radius
Also, ∠AOB = 60° $({360°}/6 = 60°)$
and ∠OAB = ∠OBA = 60°
So, ΔAOB is an equilateral triangle.
Then, AB = 5 cm
So, Area, x = Area of circle – Area of hexagon
= $πr^2 - {3√3 (a)^2}/2$
= ${22}/7 × (5)^2 - {3√3}/2 × (5)^2$
(∵ r = a = 5)
= 78.57 – 64.95 = 13.62 $cm^2$
ABCD is a plate in the shape of a parallelogram. EF is the line parallel to DA and passing through the point of intersection O of the diagonals AC and BD. Further, E lies on DC and F lies on AB. The triangular portion DOE is cut out from the plate ABCD. What is the ratio of area of remaining portion of the plate to the whole?
Answer: (d)
Area (DOE) =${\text"Area(ABCD)"}/8$
Reqd. Ratio = $7/8$
From a solid wooden right circular cylinder, a right circular cone whose radius and height are same as the radius and height of the cylinder, respectively is carved out. What is the ratio of the volume of the utilised wood to that of the wasted wood?
Answer: (b)
Let height and radius of cylinder is h and r respectively.
Volume of cylinder = $πr^2h$
Volume of circular cone = $1/3 πr^2h$
∴ Required ratio = ${\text"Volume of utilised wood"}/{\text"Volume of wasted wood"}$
Volume of right circular cone
= ${\text"(Volume of right circular cylinder"}/{\text"–Volume of right circular cone)"}$
= ${1/3 π r^2 h}/{π r^2 h - 1/3 π r^2 h} ⇒ {1/3 π r^2 h}/{2/3 π r^2 h} ∼ = 1/2 = 1 : 2$
The length, breadth and height of a room are X, Y and Z feet respectively. The cost of whitewashing the four walls of this room is Rs.2500. Find the cost of preparing another room whose length, breadth and height are double that of the previous room.
Answer: (a)
Surface area of the walls of the first room
= 2(XZ + YZ)
Surface area of the walls of the second room
= 2(4XZ + 4YZ) = 8(XZ + YZ) = 4 times the first area
⇒Cost required = 4 × 2500 = Rs.10,000.
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