mensuration Model Questions & Answers, Practice Test for ssc chsl tier 1 2024

Answer: (a)

Given, ∠ABC = 105°

∠DAB = 120°

∠DCX = 120°

⇒ ∠DCB = 180° – 120° = 60°

Angles of a quadrilateral is equal to 360°

∴ ∠ADC = 360° – (120° + 105° + 60°)

= 360° – 285° = 75°

Answer: (c)

Given that r = ${70}/2$ cm = 0.35 cm. h = 4 m

∴ Surface area of cylinder

= 10 (2πrh) = $10(2 × {22}/7 × 0.35 × 4)$ = 88 m

∴ Total cost of painting at the rate of Rs.5 per sq m.

= 88 × 5 = Rs.440

Answer: (a)

Statement-1

If the diagonal of a parallelogram ABCD are perpendicular then ABCD may Rectangle or Rhombus.

So it is true.

Statement-II

If the diagonal of quadrilateral ABCD are equal and perpendicular then it is square.

So it is also true.

Answer: (d)

From figure.

By proportionality law,

${AB}/{CD} = {EF}/{GH} ⇒ 4/3 = 12/x$

∴ x = 3 × 3 = 9

Answer: (c)

Let ∠CAD = ∠ACD = x

Since AD = CD = BC

∵ AD = CD ∼

⇒ ∠A = ∠C

Also CD = BC

⇒ ∠D = ∠B

In Δ ACD

∠A + ∠C + ∠D = 180°

⇒ ∠D = 180° – 2x

∠CDB = 180° – ∠CDA

= 180° – (180° – 2x)

= 2x

⇒ ∠CDB = ∠CBD = 2x ⇒ ∠DCB = 180° – (2x + 2x)

= 180° – 4x

At point c, we have

x + (180° – 4x) + 96° = 180°

⇒ 180° – 3x + 96° = 180°

⇒ – 3x = – 96°

⇒ x = 32°

Hence ∠DBC = 2x = 2 × $3^2$ = 64°

∴ Option b is correct.