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

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51) Which of the following characters is used to create absolute address in MS-Excel?

A) Dollar (S)
B) Ampersand (&)
C) Percent (%)
D) Hash (#)

View Answer

A) Dollar (S)

52) When did the Maharashtra government launch the ‘Jail Tourism’ initiative?

A) November 2021
B) May 2021
C) August 2021
D) January 2021

View Answer

D) January 2021

53) If y= $\sqrt[3]6$ -4 then what is the value of y³ + 12y² + 48y + 100?

A) 42
B) 0
C) 106
D) 6

View Answer

A) 42

Explanation:We are given that $( y = \sqrt[3]{6} - 4 )$ , and we need to find the value of the expression:
$y^3 + 12y^2 + 48y + 100$
Step 1: Simplify the expression using the given value of ( y )
We know:
$y = \sqrt[3]{6} - 4$
This means that ( y + 4 = $\sqrt[3]{6}$ ).
Step 2: Cube both sides
Let’s cube both sides of ( y + 4 = \sqrt[3]{6} ):
$(y + 4)^3 = (\sqrt[3]{6})^3$
This simplifies to:
$(y + 4)^3 = 6$
Step 3: Expand the cube
Now, expand ( (y + 4)^3 ) using the binomial expansion:
$(y + 4)^3 = y^3 + 3 \cdot y^2 \cdot 4 + 3 \cdot y \cdot 4^2 + 4^3$
$= y^3 + 12y^2 + 48y + 64$
So, the equation becomes:
$y^3 + 12y^2 + 48y + 64 = 6$
Step 4: Solve for ( y^3 + 12y^2 + 48y )
We now subtract 64 from both sides:
$y^3 + 12y^2 + 48y = 6 - 64$
$y^3 + 12y^2 + 48y = -58$
Step 5: Add 100 to both sides
Now, add 100 to both sides:
$y^3 + 12y^2 + 48y + 100 = -58 + 100$
$y^3 + 12y^2 + 48y + 100 = 42$

54) In a certain code language, MUSIC is written as ‘LTTJD’, and ‘CONCEPT’ is written as ‘BNMDFQU’. How will ‘SINGING’ be written in that language?

A) RHMHJOH
B) RHOHJOF
C) TJOHHOF
D) RHMFHOJ

View Answer

A) RHMHJOH

Explanation:Given:
– MUSIC → LTTJD
– CONCEPT → BNMDFQU
– We need to find how SINGING will be written in that language.
Step 1: Identify the pattern from “MUSIC” → “LTTJD”
Let’s compare the corresponding letters in MUSIC and LTTJD:
– M → L: Move 1 step back (M – 1 = L)
– U → T: Move 1 step back (U – 1 = T)
– S → T: Move 1 step forward (S + 1 = T)
– I → J: Move 1 step forward (I + 1 = J)
– C → D: Move 1 step forward (C + 1 = D)
So, the pattern is:
– The first two letters decrease by 1.
– The last three letters increase by 1.
Step 2: Identify the pattern from “CONCEPT” → “BNMDFQU”
Let’s compare the corresponding letters in CONCEPT and BNMDFQU:
– C → B: Move 1 step back (C – 1 = B)
– O → N: Move 1 step back (O – 1 = N)
– N → M: Move 1 step back (N – 1 = M)
– C → D: Move 1 step forward (C + 1 = D)
– E → F: Move 1 step forward (E + 1 = F)
– P → Q: Move 1 step forward (P + 1 = Q)
– T → U: Move 1 step forward (T + 1 = U)
So, the pattern is:
– The first three letters decrease by 1.
– The last four letters increase by 1.
Step 3: Apply the pattern to “SINGING”
Let’s apply the same pattern to SINGING:
– S → R: Move 1 step back (S – 1 = R)
– I → H: Move 1 step back (I – 1 = H)
– N → M: Move 1 step back (N – 1 = M)
– G → H: Move 1 step forward (G + 1 = H)
– I → J: Move 1 step forward (I + 1 = J)
– N → O: Move 1 step forward (N + 1 = O)
– G → H: Move 1 step forward (G + 1 = H)
Step 4: Final answer
So, the code for SINGING is “RHMHJOH”.

55) A sum increases by 75% in 10 years at certain rate of simple interest per annum. By what percentage will the same sum increase in 6 years at the same rate of simple interest per annum?

A) 42%
B) 45%
C) 38%
D) 48%

View Answer

B) 45%

Explanation:We are given that a sum increases by 75% in 10 years at a certain rate of simple interest per annum, and we are asked to find by what percentage the same sum will increase in 6 years at the same rate of interest.
Step 1: Understanding the problem
Let the principal sum be ( P ) and the rate of interest be ( r \% ) per annum.
For simple interest, the formula for the total amount ( A ) after ( t ) years is:
$A = P + \text{SI} = P + \frac{P \cdot r \cdot t}{100}$
We know the sum increases by 75% in 10 years, so after 10 years, the total amount is ( P + 0.75P = 1.75P ).
Thus, after 10 years:
$1.75P = P + \frac{P \cdot r \cdot 10}{100}$
Simplifying:
$1.75P = P + \frac{10P \cdot r}{100}$
$1.75P - P = \frac{10P \cdot r}{100}$
$0.75P = \frac{10P \cdot r}{100}$
Now, cancel ( P ) from both sides (since ( P \neq 0 )):
$0.75 = \frac{10r}{100}$
$0.75 = \frac{r}{10}$
Multiplying both sides by 10:
r = 7.5\%
So, the rate of interest is ( 7.5\% ) per annum.
Step 2: Calculate the increase in 6 years
Now that we know the rate of interest ( r = 7.5\% ), we can calculate the percentage increase in the sum after 6 years.
Using the simple interest formula:
$\text{SI} = \frac{P \cdot r \cdot t}{100}$
For ( t = 6 ) years:
$\text{SI} = \frac{P \cdot 7.5 \cdot 6}{100} = \frac{45P}{100} = 0.45P$
Thus, the sum increases by 0.45P after 6 years. The percentage increase in the sum is:
$\frac{0.45P}{P} × 100 = 45\%$
Conclusion:
The sum will increase by 45% in 6 years at the same rate of interest.