simplification Model Questions & Answers, Practice Test for ibps rrb po officer scale 1 prelims 2024

Answer: (b)

We know that,

$a^3 + b^3 + c^3$ – 3abc

= (a + b + c)$(a^2 + b^2 + c^2 – ab – bc – ca)$

⇒(a + b + c) =$ ({a^3 + b^3 + c^3 - 3abc}/{a^2 + b^2 + c^2 - ab - bc - ca})$ ... (i)

Given that,

= $[(2.247)^3 + (1.730)^3 + (1.023)^3 - 3 × 2.247 × 1.730 × 1.023]/[(2.247)^2 + (1.730)^2 + (1.023)^2 - (2.247 × 1.730) - (1.730 × 1.023) - (2.247 × 1.023)]$

= (2.247 + 1.730 + 1.023)

[from Eq. (i)]

= 5.000 = 5

Answer: (b)

a/ (b + c) = b/ (c + a) = c/ (a + b)

Taking reciprocal and adding 1 to each ratio we get;

(b + c)/a + 1 = b/ (c + a) + 1= c/ (a + b) + 1

or (a + b + c)/a = (a + b + c)/b = (a + b + c)/c

So this can only be equal when a = b = c or a + b + c = 0

When a = b = c we get a/ (b + c) = ½

When a + b + c = 0 we get b + c = – a

So a/ (b + c) = – 1 So the ratios are ½ or – 1

Answer: (e)

206.72

Answer: (c)

If (x–5) is a factor of $x^3 –3x^2$ + hx –10

then x – 5 = 0⇒x = 5

So, ⇒$(5)^3 – 3 × (5)^2$ + k × 5 – 10 = 0

⇒125 – 75 + 5k – 10 = 0

⇒5 k = – 40

∴ = k –8

Answer: (b)

Putting x = -4 in equations we find option c satisfy the equation $x^2$ – 7x - 44 = 0

$(-4)^2$ – 7 (–4) – 44 = 0

44 – 44 = 0