RRB NTPC Graduate Level (24th March 2026 Shift 3) — RRB NTPC 2025

• Key Fact: The Regulating Act of 1773 was the first major step taken by the British Parliament to control and regulate the affairs of the East India Company in India.

• Supporting Detail: It designated the Governor of Bengal as the 'Governor-General of Bengal' (Warren Hastings was the first) and created an Executive Council of four members to assist him, centralising the administration.

• Why others wrong: Pitt's India Act (1784) established the Board of Control to manage political affairs. The Charter Act of 1813 ended the company's trade monopoly. The Government of India Act 1858 transferred power directly to the British Crown after the 1857 revolt.

• Exam Trick: 'First step to regulate' = Regulating Act of 1773.

• Given: Equations: (1) $X + 2Y + 4Z = 12$, (2) $2X + 2Y + 3Z = 10$, (3) $3X + 2Y + Z = 8$.

• Basic Method (Solution):
Step 1: Subtract Eq (1) from Eq (2) to eliminate Y.
$(2X + 2Y + 3Z) - (X + 2Y + 4Z) = 10 - 12 \implies X - Z = -2$ --- (Eq 4)
Step 2: Subtract Eq (2) from Eq (3) to eliminate Y.
$(3X + 2Y + Z) - (2X + 2Y + 3Z) = 8 - 10 \implies X - 2Z = -2$ --- (Eq 5)
Step 3: Subtract Eq (5) from Eq (4) to solve for Z.
$(X - Z) - (X - 2Z) = -2 - (-2) \implies Z = 0$.
Step 4: Substitute $Z = 0$ into Eq 4.
$X - 0 = -2 \implies X = -2$.
Step 5: Substitute $X = -2$ and $Z = 0$ into Eq 1.
$-2 + 2Y + 4(0) = 12 \implies 2Y = 14 \implies Y = 7$.
Solution is X = -2, Y = 7, Z = 0.

• Shortcut Method: Directly plug the options into the simplest equation, $X + 2Y + 4Z = 12$.
Test Option A (-2, 7, 0): $-2 + 2(7) + 0 = -2 + 14 = 12$. (Matches)
Test Option B (0, 2, 2): $0 + 4 + 8 = 12$. (Matches)
Now test A and B in the second equation: $2X + 2Y + 3Z = 10$.
Test A: $2(-2) + 2(7) + 3(0) = -4 + 14 = 10$. (Matches perfectly).
Test B: $2(0) + 2(2) + 3(2) = 4 + 6 = 10$. (Matches)
Now test A and B in the third equation: $3X + 2Y + Z = 8$.
Test A: $3(-2) + 2(7) + 0 = -6 + 14 = 8$. (Correct!).
Test B: $3(0) + 2(2) + 2 = 4 + 2 = 6 \neq 8$. (Incorrect).

• Final Answer: X = -2, Y = 7, Z = 0

• Given conditions: Find the pattern: [Letter] $\rightarrow$ [Letter] $\rightarrow$ [Symbol].

• Deduction process:
Let's scan the series from left to right to find pairs of consecutive letters first:
Series: B R © # # # W & S @ Z @ @ A & L @ @ I © O ©
1) The first consecutive letters are 'B R'. The letter 'R' is preceded by letter 'B'. Now check what follows 'R': it is the symbol '©'.
So, [Letter 'B'] $\rightarrow$ [Letter 'R'] $\rightarrow$ [Symbol '©'] perfectly matches the condition. (1 Match).
2) Keep scanning for any other instances of two consecutive letters.
Next letters: W, S, Z, A, L, I, O. None of these letters are immediately preceded by another letter. They are all preceded by symbols.
Therefore, 'R' is the only letter in the entire series that satisfies the given condition.

• Exam Trick: Do not check every single letter. The condition requires a letter preceded by another letter (i.e., two letters back-to-back). Just scan the series rapidly for any two letters together. Only 'BR' exists. Check the symbol after 'R' and you are done in 2 seconds.

• Final Answer: 1

• Given: Expression: $(-9) - (-60) \div (-6) + (-2) \times 9$

• Basic Method (Solution):
Step 1: Strictly follow the BODMAS rule (Bracket, Order, Division, Multiplication, Addition, Subtraction).
Step 2: Perform Division first.
$(-60) \div (-6) = +10$.
Step 3: The expression becomes: $(-9) - (+10) + (-2) \times 9$.
Step 4: Perform Multiplication next.
$(-2) \times 9 = -18$.
Step 5: The expression becomes: $(-9) - 10 + (-18)$.
Step 6: Perform Addition and Subtraction from left to right.
$-9 - 10 = -19$.
$-19 - 18 = -37$.

• Shortcut Method: Treat terms separated by '+' and '-' as independent blocks.
Block 1: $-9$
Block 2: $- (-60 / -6) = - (+10) = -10$
Block 3: $+ (-2 \times 9) = -18$
Sum: $-9 - 10 - 18 = -37$.

• Final Answer: -37

• Given: $3x + 2y = 10$ and $2xy = 3$. Find the positive value of $3x - 2y$.

• Basic Method (Solution):
Step 1: We use the algebraic identity connecting $(A-B)^2$ and $(A+B)^2$.
Formula: $(A - B)^2 = (A + B)^2 - 4AB$.
Step 2: Let $A = 3x$ and $B = 2y$.
Then $(3x - 2y)^2 = (3x + 2y)^2 - 4(3x)(2y)$.
Step 3: Simplify the formula.
$(3x - 2y)^2 = (3x + 2y)^2 - 24xy$.
Step 4: We are given $2xy = 3$, so multiply by 12 to find $24xy$.
$24xy = 12 \times (2xy) = 12 \times 3 = 36$.
Step 5: Substitute the known values into the identity.
$(3x - 2y)^2 = (10)^2 - 36$.
$(3x - 2y)^2 = 100 - 36 = 64$.
Step 6: Take the square root of both sides to find $3x - 2y$.
$3x - 2y = \pm \sqrt{64} = \pm 8$.
Since the question asks for the positive value, $3x - 2y = 8$.

• Shortcut Method: Mentally evaluate $(10)^2 - 4 \times (3 \times 2) \times (xy)$. Note that $xy = 1.5$. So $4 \times 6 \times 1.5 = 24 \times 1.5 = 36$. $100 - 36 = 64$. Square root is 8.

• Final Answer: 8

• Given: Initial Men ($M_1$) = 100. Initial Days ($D_1$) = 27. Men left = 46. Final Men ($M_2$) = $100 - 46 = 54$. Find Final Days ($D_2$).

• Basic Method (Solution):
Step 1: The total amount of provisions can be calculated as the product of the number of men and the number of days the provisions last (Man-Days).
Total Provisions $= M_1 \times D_1 = 100 \times 27 = 2700 \text{ man-days}$.
Step 2: 46 men leave, so the remaining number of men ($M_2$) is $100 - 46 = 54$ men.
Step 3: Let the provisions last for $D_2$ days for these 54 men. Since the total provisions remain the same, we equate the man-days.
$M_1 \times D_1 = M_2 \times D_2$
$2700 = 54 \times D_2$
Step 4: Solve for $D_2$.
$D_2 = \frac{2700}{54}$.
Step 5: We know $54 imes 5 = 270$. Therefore, $54 imes 50 = 2700$.
$D_2 = 50 \text{ days}$.

• Shortcut Method: Remaining men are 54. Total food = 2700. $2700 / 54 = 50$. Alternatively, Men are almost halved (from 100 to 54), so days will almost double (from 27 to roughly 54). Exact inverse proportion: $100/54 imes 27 = 100/2 = 50$.

• Final Answer: 50

• Key Fact: Renowned Indian badminton champion Saina Nehwal graced the inauguration ceremony as the chief guest for the 58th Inter-IIT Sports Meet hosted by IIT Hyderabad.

• Supporting Detail: The Inter-IIT Sports Meet is a prestigious annual tournament where students from all Indian Institutes of Technology compete across various sports. Inviting prominent local sporting icons (Saina Nehwal is based in Hyderabad) is a customary tradition to inspire the student athletes.

• Why others wrong: Pullela Gopichand (her former coach) is also a prominent figure but was not the chief guest. Prof B S Murty is the Director of IIT Hyderabad, and BVR Mohan Reddy is the Chairman of its Board of Governors; they were hosts, not the chief guest.

• Exam Trick: Inter-IIT Sports at Hyderabad = Hyderabad's own Badminton icon Saina Nehwal as Chief Guest.

• Key Fact: Particulate Matter 2.5 (PM2.5) consistently remains identified by the WHO as the most perilous air pollutant primarily responsible for severe respiratory and cardiovascular illnesses globally.

• Supporting Detail: Due to its microscopic size (2.5 micrometers or smaller in diameter), PM2.5 can bypass the body's natural defenses, penetrating deep into the lungs and even entering the bloodstream, causing asthma, bronchitis, and lung cancer.

• Why others wrong: While Carbon monoxide is toxic, Sulphur dioxide causes acid rain and airway constriction, and ground-level Ozone exacerbates asthma, PM2.5 drives the vast majority of global mortality and severe systemic illnesses linked to air pollution.

• Exam Trick: Primary cause of respiratory illness / Air Quality Index danger = PM2.5.

• Given: A's salary = B's salary + 13%. Find how much % B's salary is less than A's.

• Basic Method (Solution):
Step 1: Let B's salary be 100 units.
Step 2: Since A's salary is 13% more than B, A's salary $= 100 + 13 = 113$ units.
Step 3: The difference in their salaries is $113 - 100 = 13$ units.
Step 4: To find by what percent B's salary is less than A, we must use A's salary as the base (denominator).
Required % $= (\frac{\text{Difference}}{\text{A's Salary}}) \times 100$.
Step 5: Required % $= (\frac{13}{113}) \times 100 = \frac{1300}{113}$.
Step 6: Perform the division: $1300 \div 113$.
$113 \times 10 = 1130$. Remaining $= 170$.
$113 \times 1 = 113$. Remaining $= 57$.
Put decimal. 570. $113 \times 5 = 565$. Remaining = 5.
So, $11.5044...\%$
Rounding to two decimal places, it is 11.50%.

• Shortcut Method: Standard formula for "if A is $R\%$ more than B, then B is less than A by": $\frac{R}{100 + R} \times 100$. Here $R=13$, so $\frac{13}{113} \times 100 = \frac{1300}{113} \approx 11.50\%$.

• Final Answer: 11.50%

• Key Fact: The Trans-Siberian Railway is the longest continuous railway line in the world, stretching over 9,289 kilometers from Western Russia (St. Petersburg/Moscow) to Vladivostok on the Pacific coast in the Russian Far East.

• Supporting Detail: This monumental railway spans eight time zones and was critical in connecting isolated Siberian regions to the European mainland, facilitating massive trade and military movement.

• Why others wrong: Novosibirsk and Irkutsk are major cities located along the route, but they are deep inland in Siberia, not on the Pacific coast. Moscow is the main western terminus alongside St. Petersburg.

• Exam Trick: Pacific Coast terminus = Vladivostok (which literally translates to 'Ruler of the East').