RRB NTPC CBT 2 Level 5 June-12-2022 Shift 1 Exam Previous Question Paper with Solutions

26) What is the smallest cubic number, which is divisible by 72, 108 and 300?

A) 3375
B) 27000
C) 5400
D) 21600

View Answer

B) 27000

Explanation:To find the smallest cubic number divisible by 72, 108, and 300, follow this shortcut method:
—
Step 1: Find the LCM of 72, 108, and 300
Prime factorizations:
72 = $2^3 \cdot 3^2$
108 = $2^2 \cdot 3^3$
300 = $2^2 \cdot 3 \cdot 5^2$
Take the highest powers of all primes:
$\text{LCM} = 2^3 \cdot 3^3 \cdot 5^2 = 8 \cdot 27 \cdot 25 = 5400$
✅ So the LCM = 5400
—
Step 2: Make it a perfect cube
Now, check whether 5400 is a perfect cube:
$5400 = 2^3 \cdot 3^3 \cdot 5^2$
We need exponents in multiples of 3 for it to be a cube.
Current exponents:
2³ ✅
3³ ✅
5² ❌ → Need one more 5 to make it $5^3$
Multiply 5400 by 5 →
$5400 \cdot 5 = 27000 = 2^3 \cdot 3^3 \cdot 5^3$
Now it’s a perfect cube!
—
✅ Final Answer: Option 2. 27000 ✅
Would you like a quick trick for recognizing perfect cubes too?

27) Into how many books is the Akbar Nama divided?

A) 3 books
B) 4 books
C) 2 books
D) 5 books

View Answer

A) 3 books

28) Which of the following lakes is a brackish water lake?

A) Pulicat Lake
B) Dal Lake
C) Loktak Lake
D) Wular Lake

View Answer

A) Pulicat Lake

29) The length of each edge of a cube is 2.6 cm. What is the total surface area (in cm²) of the cube?

A) 39.96
B) 40.56
C) 40.76
D) 40.36

View Answer

B) 40.56

Explanation:To find the total surface area of a cube, use the formula:
$\text{TSA} = 6a^2$
Where $a$ is the length of one edge.
—
Given:
$a = 2.6\ \text{cm} \Rightarrow a^2 = 2.6 × 2.6 = 6.76$
Now:
$\text{TSA} = 6 × 6.76 = 40.56\ \text{cm}^2$
—
✅ Final Answer: Option 2. 40.56 cm² ✅
Want a shortcut for squaring decimals like 2.6 quickly?

30) Ravi has to go from Hyderabad to Delhi. The distance between Hyderabad and Delhi is 1,200 kms. He decides to travel 25% of the distance on foot, 30% of the distance by bus, 15% of the distance by train and the remaining distance by an airplane. What is the distance travelled by Ravi by an Airplane?

A) 300 km
B) 360 km
C) 580 km
D) 425 km

View Answer

B) 360 km

Explanation:We’re given:
Total distance = 1200 km
Ravi travels:
25% on foot
30% by bus
15% by train
Remaining by airplane
—
Step-by-step shortcut:
Total percentage traveled before airplane:
$25\% + 30\% + 15\% = 70\% \Rightarrow \text{Remaining} = 100\% - 70\% = 30\%$
$\text{Distance by airplane} = 30\% \text{ of } 1200 = \frac{30}{100} × 1200 = 360\ \text{km}$
—
✅ Final Answer: Option 2. 360 km ✅
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