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

RRB NTPC Home

101) Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.
Statements:
All camels are donkeys.
Some cats are camels.
All dolphins are cats.
Conclusions:
I. All dolphins are donkeys.
II. Some dolphins are donkeys.
III. Some donkeys are cats.
IV. All cats are donkeys.

A) Only conclusion IV follows
B) Only conclusion III follows
C) Both conclusions I and III follow
D) Both conclusions II and III follow

View Answer

B) Only conclusion III follows

102) Padma Shri Minati Mishra was an Indian classical dancer and actress, known for her expertise in which of the following Indian classical dance forms?

A) Kathak
B) Kathakali
C) Bharatanatyam
D) Odissi

View Answer

D) Odissi

103) The radius of the base of a conical tent is 9 m and its height is 12 m, find the cost of the material needed to make it if it costs ₹100 per πm².

A) ₹14,500
B) ₹13,000
C) ₹15,000
D) ₹13,500

View Answer

D) ₹13,500

Explanation:Understanding the Problem
We are given:
– Radius (r) of the base of a conical tent: 9 meters
– Height (h) of the conical tent: 12 meters
– Cost of material: ₹100 per πm²
We need to find the total cost of the material required to make the tent.
Step 1: Recall the Formula for the Surface Area of a Cone
The surface area of a cone consists of two parts:
1. Base Area: The area of the circular base.
2. Lateral (Side) Surface Area: The area of the cone’s side.
However, for a tent, we typically consider only the lateral surface area since the base is usually open.
The formula for the lateral surface area (LSA) of a cone is:
LSA = π r l
where:
– ( r ) is the radius of the base
– ( l ) is the slant height of the cone
Step 2: Find the Slant Height (( l ))
To find the slant height, we can use the Pythagorean theorem in the right triangle formed by the radius, height, and slant height.
$l = \sqrt{r^2 + h^2}$
Given:
– ( r = 9 ) m
– ( h = 12 ) m
Plugging in the values:
$l = \sqrt{9^2 + 12^2} = \sqrt{81 + 144} = \sqrt{225} = 15 \text{ m}$
So, the slant height ( l ) is 15 meters.
Step 3: Calculate the Lateral Surface Area (LSA)
Using the formula for LSA:
$LSA = π r l = π × 9 × 15 = 135π \text{ m}^2$
Step 4: Determine the Total Cost
The cost of the material is ₹100 per πm². Therefore, the total cost ( C ) is:
$C = \text{LSA} × \text{Cost per } π \text{m}^2 = 135π × 100 = 13,500π \text{ ₹}$
However, since the cost is given per πm², the π in the area and the π in the cost cancel out:
C = 135 × 100 = 13,500 ₹
Step 5: Conclusion
The total cost of the material needed to make the conical tent is ₹13,500.

104) P, Q, R can do a piece of work in 40 days, 90 days and 36 days, respectively. P started the work. Q joined him after 7 days. If R joined them after 8 days from the beginning, then for how many days did R work?

A) $11\frac8{23}$
B) $12\frac8{23}$
C) $15\frac8{23}$
D) $13\frac8{23}$

View Answer

B) $12\frac8{23}$

Explanation:We are given that:
– P can complete the work in 40 days.
– Q can complete the work in 90 days.
– R can complete the work in 36 days.
Step 1: Calculate the daily work rate of each person.
– P’s rate of work = $(\frac{1}{40})$ (since P can complete the work in 40 days)
– Q’s rate of work = $(\frac{1}{90})$ (since Q can complete the work in 90 days)
– R’s rate of work = $(\frac{1}{36})$ (since R can complete the work in 36 days)
Step 2: Work done during the first 7 days when only P is working.
In the first 7 days, P works alone, so the amount of work done by P is:
$\text{Work done by P in 7 days} = 7 × \frac{1}{40} = \frac{7}{40}$
Step 3: Work done in the next 1 day when P and Q are working together.
After 7 days, Q joins P, so for the next 1 day, P and Q work together. The total work done by P and Q in 1 day is:
$\text{Work done by P and Q in 1 day} = \left( \frac{1}{40} + \frac{1}{90} \right)$
To simplify, find a common denominator:
$\frac{1}{40} + \frac{1}{90} = \frac{9}{360} + \frac{4}{360} = \frac{13}{360}$
Thus, the work done by P and Q in 1 day is:
$\frac{13}{360}$
Step 4: Work done in the next 8 days when P, Q, and R are working together.
After 8 days, R joins P and Q. So for the next 8 days, P, Q, and R work together. The total work done by P, Q, and R in 1 day is:
$\text{Work done by P, Q, and R in 1 day} = \left( \frac{1}{40} + \frac{1}{90} + \frac{1}{36} \right)$
Find a common denominator:
$\frac{1}{40} + \frac{1}{90} + \frac{1}{36} = \frac{9}{360} + \frac{4}{360} + \frac{10}{360} = \frac{23}{360}$
Thus, the work done by P, Q, and R in 8 days is:
$8 × \frac{23}{360} = \frac{184}{360} = \frac{23}{45}$
Step 5: Calculate the total work done after 16 days.
Now, add up the work done in all stages:
– Work done by P in the first 7 days: $(\frac{7}{40})$
– Work done by P and Q in the next 1 day: $(\frac{13}{360})$
– Work done by P, Q, and R in the next 8 days: $(\frac{23}{45})$
Total work done after 16 days:
$\frac{7}{40} + \frac{13}{360} + \frac{23}{45}$
To simplify, find a common denominator. The LCM of 40, 360, and 45 is 360. So convert all fractions to have the denominator 360:
$\frac{7}{40} = \frac{63}{360}, \quad \frac{13}{360} = \frac{13}{360}, \quad \frac{23}{45} = \frac{184}{360}$
Now, add these fractions:
$\frac{63}{360} + \frac{13}{360} + \frac{184}{360} = \frac{260}{360} = \frac{13}{18}$
So, after 16 days, the total work done is $(\frac{13}{18})$ .
Step 6: Work remaining.
The total work is 1 unit, so the remaining work is:
$1 - \frac{13}{18} = \frac{5}{18}$
Step 7: Work done by P, Q, and R on the 17th day.
On the 17th day, all three (P, Q, and R) are working together. The work done in 1 day by P, Q, and R is $(\frac{23}{360})$ .
Now, find the number of days required to complete the remaining $(\frac{5}{18})$ of the work. Let the number of days be (d). The total work done in (d) days is:
$d × \frac{23}{360} = \frac{5}{18}$
Solve for (d):
$d = \frac{5}{18} × \frac{360}{23} = \frac{5 × 20}{23} = \frac{100}{23}$
This simplifies to approximately:
$d = 4 \frac{8}{23}$
Step 8: Total number of days R worked.
R worked for 8 days when P, Q, and R worked together, plus $(4 \frac{8}{23})$ days on the 17th day. Thus, the total number of days R worked is:
$8 + 4 \frac{8}{23} = 12 \frac{8}{23}$

105) A man can do a work in 20 days and a woman can do the same work in 30 days. In how many days will 2 men and 3 women do the work?

A) 5½
B) 5
C) 6
D) 4

View Answer

B) 5

Explanation:To solve this problem, we need to calculate how long it will take for 2 men and 3 women to complete the work together.
Step 1: Find the rate of work for each person
– A man can complete the work in 20 days, so his rate of work is:
$\text{Rate of work for 1 man} = \frac{1}{20} \text{ of the work per day}.$
– A woman can complete the work in 30 days, so her rate of work is:
$\text{Rate of work for 1 woman} = \frac{1}{30} \text{ of the work per day}.$
Step 2: Find the combined rate of work for 2 men and 3 women
– The total rate of work for 2 men is:
$2 × \frac{1}{20} = \frac{2}{20} = \frac{1}{10} \text{ of the work per day}.$
– The total rate of work for 3 women is:
$3 × \frac{1}{30} = \frac{3}{30} = \frac{1}{10} \text{ of the work per day}.$
– So, the combined rate of work for 2 men and 3 women is:
$\frac{1}{10} + \frac{1}{10} = \frac{2}{10} = \frac{1}{5} \text{ of the work per day}.$
Step 3: Find the number of days required to complete the work
Since the combined rate of work is $( \frac{1}{5} )$ of the work per day, the time required to complete the entire work is:
$\text{Time} = \frac{1}{\frac{1}{5}} = 5 \text{ days}.$
Final Answer:
The number of days required to complete the work is 5 days.