mensuration area volumes Model Questions & Answers, Practice Test for ibps so prelims 2023

Answer: (a)

Answer: (c)

Here, Area of Rectangle lies between 40$cm^2$ and 45$cm^2$

Given that one sides = 5cm.

Area of Rectangle = 5 × second sides

Now, If Area = 40$cm^2$

then, 40 = 5 × second sides

∵ second sides = 8cm.

Again, If Area = 45$cm^2$

45 = 5 × second sides.

∵ Second sides = 9cm.

it means that second sides varies. between 8 cm to 9 cm.

Let diagonal = d

⇒ $√{8^2 + 5^2} < d < √{5^2 + 9^2}$

⇒ $√{64 + 25} < d < √{25 + 81}$

⇒ $√{87} < d < √{106}$

⇒ $√{81} < √{89} < d < √{106} < √{121}$

⇒ $√{81} < d < √{121}$

⇒ 9cm < d < 11cm.

Answer: (c)

Required ratio = ${\text"Area of circle"}/{\text"Area of ΔACD"}$

= ${πr^2}/{1/2 × 2r × r}$ = π

Answer: (c)

Given, In ΔABC

∠C = 2∠A

∠B = 90°

∠A + 90° + 2∠A = 180°

∠3A = 180° – 90° = 90°

∠A = ${90°}/3$ = 30°

∴ ∠C = 2 × 30° = 60°

sin 30° = ${BC}/{AC}$

$1/2 = {BC}/{AC} ⇒ BC = 1/2$ AC

Now, sin 60° = ${AB}/{AC} ⇒ √3/2 = {AB}/{AC}$

AB = $√3/2$ AC ... (ii)

Squaring on both sides.

$AB^2 = 3/4 AC^2$, Now putting the value of AC.

$AB^2 = 3/4 × 4 BC^2 ⇒ AB^2 = 3BC^2$

Answer: (d)

PC = PB (radii of circle)

∠PBC = ∠PCB

(angles opposite to equal sides)

⇒ ∠PCB = 35°

and ∠ACB = 90°

(angle in semi-circle)

⇒ ∠PCA + ∠PCB = 90°

⇒ ∠PCA = 90° – 35° = 55°