Mensuration Aptitude Mcq Model Questions & Answers, Practice Test for ibps po mains 2024 2025

Answer: (c)

In parallelogram ABCD.

AC = 2 mn, BD = $m^2 – n^2$ and AB = ${m^2 + n^2}/2$

We know that,

$(AC^2 + BD^2)= 2(AB^2 + BC^2)$

⇒ $(m^2 + n^2 + m^4 + n^4 – 2m^2 n^2)$

= $2[1/4 (m^2 + n^2)^2 + BC^2]$

⇒ $(m^2 + n^2)^2 = 1/2 (m^2 + n^2)^2 + 2BC^2$

⇒ $2BC^2 = 1/2 (m^2 + n^2)^2$

⇒ $BC^2 = {(m^2 + n^2)^2}/4$

⇒ BC = ${m^2 + n^2}/2$

Therefore, ABCD is a rhombus.

Let AC > BD ⇒ 2mn > $m^2 – n^2$

⇒ $(m + n)^2 > 2m^2$

which is always true for every positive integers m and n, where n < m < 2n.

Answer: (b)

The altitude and medians of an equilateral triangle are congruent but centroid divide the altitude in 2 : 1. So, Statements 1 and 2 are correct.

Answer: (b)

Given that,

$α/β = 1/5$

α = k and β = 5k (say)

or complementary angles,

α = 90° – β ⇒ k = 90° – 5k

⇒ k = 15°

∴ α = 15° and β = 75°

∴ Difference between angles = 75° – 15° = 60°

Answer: (d)

Since the sphere is dropped in the cylindrical vessel partially filled with water and is completely immersed, therefore the volumes of 3d-shapes will be equal. Let r be the radius of cylinder and R be the radius of the sphere.

Thus, volume of cylinder = volume of sphere

$π r^2 h = 4/3 π R^2 ⇒ 30 × 30 × h = 4/3 × 15 × 15 × 15$

⇒ h = ${4 × 15 × 15 × 15}/{3 × 30 × 30}$ ⇒ h = 5 cm

Answer: (a)

Total surface area of cube = 6 × $(Side)^2$

∴ 150 = 6 × $(Side)^2$

⇒ $Side^2 = {150}/6$ = 25

∴ Side = $√{25}$ = 5cm

∴ Volume of cube = $(Side)^3$

= 5 × 5 × 5 = 125 $cm^3$