simplification Model Questions & Answers, Practice Test for ibps rrb po officer scale 1 prelims 2024
ibps rrb po officer scale 1 prelims 2024 SYLLABUS WISE SUBJECTS MCQs
Number System
Lcm & Hcf
Simplification
Percentage
Time & Work
Time & Distance
What is the value of ${[(2.247)^3 + (1.730)^3 + (1.023)^3 - 3 × 2.247 × 1.730 × 1.023]}/{[(2.247)^2 + (1.730)^2 + (1.023)^2 - 2.247 × 1.730 - 1.730 × 1.023 - 2.247 × 1.023]}$ ?
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
If $a/{b + d} = b/{c + a} = c/{a + b}$, then which one of the following statements is correct ?
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
For what value of k is (x – 5) a factor of $x^3 –3x^2$ + kx – 10?
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
(x + 4) is a factor of which one of the following expressions ?
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
ibps rrb po officer scale 1 prelims 2024 IMPORTANT QUESTION AND ANSWERS
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