mensuration area volumes Model Questions & Answers, Practice Test for ssc cgl tier 1 2023

Answer: (b)

Area of triangle $(A_1) = - (7 - 4√3)$

= $(2^2 + (√3)^2 - 2.2.√3)$

= $(2 - √3)^2$

Area of triangle $(A_2) = + (7 + 4√3)$

= $(2^2 + (√3)^2 + 2.2.√3) = (2 + √3)^2$

Ratio of corresponding sides = $√{({A_1}/{A_2})}$

= $√{{(2 - √3)^2}/{(2 + √3)^2}} = {2 - √3}/{2 + √3} = 7 - 4 √3$

Answer: (d)

Area = ∼ ${340}/{360} × π × (30)^2$ = 850 π

Answer: (b)

On single face of cube no. of right angled

Triangles formed = 4 (i.e., ΔABD, ΔABC, ΔABD, ΔACD)

Total faces of a cube = 6

So, no. of right angle triangles = 4 × 6 = 24

So, option (b) is correct.

Answer: (b)

In ΔCAD and ΔCEB,

∠C =∠C (common)

∠CEB = ∠ADC (each 90°)

∠CAD = ∠CBE (rest angle)

∴ ΔCAD ∼ CEB

Since, the sides will be in same proportion,

${CA}/{CB} = {CD}/{CE}$

and ${AD}/{BE} = {CD}/{CE}$

Hence, all three statements are correct.

Answer: (d)

In ΔPYX and ΔPR

${PX}/{PQ} = {PY}/{PR}$

⇒ ${1.5}/{7.5} = 2/{10}$

⇒ $1/5 = 1/5$

Now corresponding ratios of two triangles are equal.

Also ∠P = ∠P (Common)

⇒ ΔPXY ∼ ΔPQR by SAS similarity

⇒ ${PX}/{PQ} = {PY}/{PR} = {XY}/{QR}$

⇒ $1/5 = 1/5 = {XY}/{QR}$

⇒ QR = 5XY

Also QR || XY (By B.P.T)

∴ Option (d) is correct.