RRB NTPC CBT 2 Level 6 May-2-2022 Shift 1 Exam Previous Question Paper with Solutions

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46) K is the product of the greatest and the smallest of the numbers
$\frac14,\frac23,\frac45,\frac58,\frac34$ Find the value of $(\frac1k+4)(\frac1k-2)$

A) $\frac{189}{25}$
B) 27
C) $\frac{171}{25}$
D) 7

View Answer

B) 27

Explanation:Let’s solve the problem step by step.
Step 1: Identify the greatest and smallest numbers
We are given the numbers:
$\frac{1}{4}, \frac{2}{3}, \frac{4}{5}, \frac{5}{8}, \frac{3}{4}$
To determine the greatest and smallest numbers, let’s convert them to decimal form:
– ( $\frac{1}{4} = 0.25$ )
– ( $\frac{2}{3} \approx 0.6667$ )
– ( $\frac{4}{5}$ = 0.8 )
– ( $\frac{5}{8}$ = 0.625 )
– ( $\frac{3}{4}$ = 0.75 )
Now, it’s clear that the smallest number is ( $\frac{1}{4}$ ), and the greatest number is ( $\frac{4}{5}$ ).
Step 2: Calculate the product ( k )
We are asked to find the product of the greatest and smallest numbers, i.e.,
$k = \frac{1}{4} × \frac{4}{5}$
Now, multiply these fractions:
$k = \frac{1 × 4}{4 × 5} = \frac{4}{20} = \frac{1}{5}$
Step 3: Evaluate the expression $( \left( \frac{1}{k} + 4 \right) \left( \frac{1}{k} - 2 \right) )$
We are asked to find the value of the expression:
$\left( \frac{1}{k} + 4 \right) \left( \frac{1}{k} - 2 \right)$
Since ( k = \frac{1}{5} ), we have:
$\frac{1}{k} = 5$
Now substitute ( \frac{1}{k} = 5 ) into the expression:
$\left( 5 + 4 \right) \left( 5 - 2 \right)$
Simplifying:
(9)(3) = 27
Final Answer:
The value of $( \left( \frac{1}{k} + 4 \right) \left( \frac{1}{k} - 2 \right) )$ is 27.

47) A person covers a certain distance at a certain speed. If he increases his speed by 30%, then he takes 15 minutes less to cover the same distance. Find the time taken by him to cover the distance when travelling at his original speed.

A) 1hour 12 minutes
B) 1 hour
C) 1 hour 05 minutes
D) 1 hour 10 minutes

View Answer

C) 1 hour 05 minutes

Explanation:Let’s solve this step-by-step using the concept of time, speed, and distance.
Given:
– The person increases his speed by 30%.
– The time saved is 15 minutes (or 15/60 = 0.25 hours).
– We need to find the time taken by the person to cover the distance at his original speed.
Step 1: Let the original speed be S and the original time taken be T.
We know:
– Distance = Speed × Time
– Let the distance be D. So, the equation becomes:
D = S × T
Step 2: Increase in speed:
– The new speed is 30% more than the original speed.
– Therefore, the new speed is ( S_{\text{new}} = S × 1.30 ).
Step 3: Time taken at the new speed:
– The new time taken at the increased speed is given by:
$T_{\text{new}} = \frac{D}{S_{\text{new}}} = \frac{D}{S × 1.30}$
– Substituting for ( D = S × T ), we get:
$T_{\text{new}} = \frac{S × T}{S × 1.30} = \frac{T}{1.30}$
Step 4: Time difference:
– The time saved is ( 0.25 ) hours (15 minutes).
– Therefore, the difference between the original time and the new time is:
$T - T_{\text{new}} = 0.25$
– Substituting ( T_{\text{new}} = \frac{T}{1.30} ) into this equation:
$T - \frac{T}{1.30} = 0.25$
– Solving for ( T ):
$T \left( 1 - \frac{1}{1.30} \right) = 0.25$
$T \left( \frac{1.30 - 1}{1.30} \right) = 0.25$
$T × \frac{0.30}{1.30} = 0.25$
$T = \frac{0.25 × 1.30}{0.30}$
$T = \frac{0.325}{0.30} = 1.0833 \text{ hours}$
T = 1 hour 5 minutes
Final Answer:
The time taken by the person to cover the distance at his original speed is 1 hour 5 minutes.

48) If 1st January 2017 was a Thursday, then what day of the week was it on 31st March of that year?

A) Friday
B) Tuesday
C) Thursday
D) Wednesday

View Answer

B) Tuesday

49) The circumference of a circle is given as 308 m. What is the area of the circle?
[Use π = $\frac{22}7$ ]

A) 7646 m²
B) 7546 m²
C) 7556 m²
D) 7446 m²

View Answer

B) 7546 m²

Explanation:We are given that the circumference of a circle is 308 meters, and we need to find the area of the circle. The formulae we need are:
»1. Circumference of a circle:
$C = 2\pi r$
»2. Area of a circle:
A = π r²
Step 1: Find the radius of the circle
From the given information, the circumference is 308 meters:
C = 308 m
Substitute the value of π = $(\frac{22}{7})$ into the formula for the circumference:
$308 = 2 × \frac{22}{7} × r$
Now, solve for r (radius):
$308 = \frac{44}{7} × r$
$r = \frac{308 × 7}{44} = \frac{2156}{44} = 49 \, \text{m}$
So, the radius of the circle is 49 meters.
Step 2: Find the area of the circle
Now, we can use the formula for the area of a circle:
$A = \pi r^2$
Substitute r = 49 meters and π = $(\frac{22}{7})$ :
$A = \frac{22}{7} × (49)^2$
$A = \frac{22}{7} × 2401 = \frac{22 × 2401}{7} = \frac{52822}{7} = 7546 \, \text{m}^2$
Thus, the area of the circle is 7546 m².