RRB NTPC Graduate Level (22nd March 2026 Shift 3) — RRB NTPC 2025

• Given: Amount doubles ($2$ times) in $T_1 = 6$ years. Target: Amount becomes $16$ times in $T_2 = ?$ years.

• Basic Method (Solution):
Step 1: Formula for compound interest amount is $A = P(1 + \frac{R}{100})^t$.
Step 2: $2P = P(1 + \frac{R}{100})^6 \implies 2 = (1 + \frac{R}{100})^6$.
Step 3: We need the amount to be $16P$. So, $16 = (1 + \frac{R}{100})^{T_2}$.
Step 4: Express $16$ as a power of $2$: $16 = 2^4$.
Step 5: Substitute $2$ from Step 2: $16 = [(1 + \frac{R}{100})^6]^4 = (1 + \frac{R}{100})^{24}$.
Step 6: Comparing powers, $T_2 = 24$ years.

• Shortcut Method: In compound interest, if a sum becomes $x$ times in $t$ years, it becomes $x^n$ times in $n \times t$ years. Here, it becomes $2$ times in $6$ years. We need $16$ times, which is $2^4$. So, time required $= 4 \times 6 = 24$ years.

• Final Answer: 24

• Given: Mathematical expression $16 + 20 \div 4 - 3 \times 4$.

• Basic Method (Solution):
Step 1: Apply the BODMAS rule (Brackets, Orders, Division, Multiplication, Addition, Subtraction).
Step 2: Solve the Division part first.
$20 \div 4 = 5$.
Step 3: The expression becomes: $16 + 5 - 3 \times 4$.
Step 4: Solve the Multiplication part next.
$3 \times 4 = 12$.
Step 5: The expression becomes: $16 + 5 - 12$.
Step 6: Solve Addition and Subtraction from left to right.
$16 + 5 = 21$.
$21 - 12 = 9$.

• Shortcut Method: Mentally isolate the operations separated by addition/subtraction. Block 1 is $16$. Block 2 is $20 \div 4 = 5$. Block 3 is $3 \times 4 = 12$. The result is simply $16 + 5 - 12 = 9$.

• Final Answer: 9

• Key Fact: According to Article 84(b) of the Indian Constitution, the minimum age required to become a member of the House of the People (Lok Sabha) is twenty-five years.

• Supporting Detail: The same article states that the minimum age requirement for the Council of States (Rajya Sabha) is thirty years.

• Related Concept: To be elected as the President or Vice-President of India, or to be appointed as a Governor, the minimum age is 35 years.

• Why others wrong: 18 years is the universal voting age (reduced from 21 by the 61st Amendment). 21 years is the minimum age for contesting Panchayat/Municipality elections. 30 years is for the Rajya Sabha.

• Exam Trick: Lok Sabha (Lower House) = Lower age (25). Rajya Sabha (Upper House) = Upper age (30).

• Additional Info: A candidate must also be a citizen of India and make an oath or affirmation bearing true faith and allegiance to the Constitution.

• Key Fact: The 'Ananth Centre of Excellence for Navigation' is India's first private-sector navigation innovation hub, inaugurated in 2025 by the ISRO Chairman.

• Supporting Detail: Established by Ananth Technologies, the center is designed to develop advanced, indigenous navigation technologies supporting India's NavIC (Navigation with Indian Constellation) system and reducing reliance on foreign GPS.

• Related Concept: This aligns directly with the government's push to privatize parts of the space sector and foster deep-tech startups under the IN-SPACe framework.

• Why others wrong: The other options are generic, fabricated names that sound official but do not refer to this specific, groundbreaking private-sector initiative.

• Exam Trick: "Ananth" Technologies is a long-standing, major private partner of ISRO. If a new, major private space hub is opened, it is highly likely associated with them.

• Additional Info: The center focuses on both civilian applications (like smartphones and fleet tracking) and defense requirements.

• Key Fact: The Lucknow Pact of 1916 was a historic agreement reached between the Indian National Congress and the All-India Muslim League, pioneered primarily by Bal Gangadhar Tilak and Muhammad Ali Jinnah.

• Supporting Detail: The pact was highly significant as it marked the reconciliation of the Moderate and Extremist factions of the Congress, while simultaneously forging Hindu-Muslim political unity to demand self-government from the British.

• Related Concept: Through this pact, the Congress controversially agreed to the Muslim League's demand for separate electorates for Muslims in provincial legislatures.

• Why others wrong: Naoroji and Banerjee were early Moderates. Lala Lajpat Rai and Bipin Chandra Pal were part of the extremist Lal-Bal-Pal trio but were not the chief architects of this specific pact. Gokhale passed away in 1915, before the pact was signed.

• Exam Trick: Jinnah was famously hailed as the "Ambassador of Hindu-Muslim Unity" by Sarojini Naidu specifically for his role in architecting the Lucknow Pact alongside Tilak.

• Additional Info: The joint demands included increasing the number of elected members in legislatures and ensuring half of the Viceroy's Executive Council were Indians.

• Key Fact: MS Excel is an example of Application Software, which is designed to help the user perform specific tasks (in this case, creating spreadsheets, crunching numbers, and data analysis).

• Supporting Detail: Application software runs on top of the operating system and is utilized directly by end-users to fulfill particular requirements like word processing, web browsing, or gaming.

• Related Concept: System Software, on the other hand, operates and controls the computer hardware, providing a platform for application software to run.

• Why others wrong: Windows and Linux are Operating Systems (classic examples of System Software). BIOS (Basic Input/Output System) is firmware that initializes hardware during the booting process.

• Exam Trick: If a program is something you actively open to do work or play (Word, Excel, Chrome, Photoshop), it is an Application. If it runs in the background managing the computer itself, it's System Software.

• Additional Info: Software is broadly categorized into System Software, Application Software, and Utility Software (like antiviruses).

• Key Fact: Black soot forming on the bottom of a cooking vessel indicates that the combustion of the fuel is incomplete.

• Supporting Detail: Incomplete combustion occurs when there is a lack of sufficient oxygen to burn the fuel completely. Instead of fully converting to carbon dioxide and water, the fuel leaves behind unburned carbon particles (soot), which deposit on the vessel.

• Related Concept: Complete combustion typically produces a clean, blue flame (like a well-functioning LPG stove), while incomplete combustion produces a yellow/orange, sooty flame.

• Why others wrong: If the fuel were fully burned, there would be no soot (clean blue flame). Undercooked food or moisture in the fuel do not directly cause heavy black soot deposits; the lack of oxygen during burning does.

• Exam Trick: Black soot = Unburned Carbon = Incomplete Combustion.

• Additional Info: In gas stoves, this often happens if the air holes in the burner get blocked, reducing the oxygen supply.

• Given: Principal $P = ₹7200$. Simple Interest $SI = ₹1080$. Rate $R = 6\%$ p.a. Find Time $T$.

• Basic Method (Solution):
Step 1: Write down the standard formula for Simple Interest.
$SI = \frac{P \times R \times T}{100}$
Step 2: Rearrange the formula to solve for Time ($T$).
$T = \frac{SI \times 100}{P \times R}$
Step 3: Substitute the given values into the formula.
$T = \frac{1080 \times 100}{7200 \times 6}$
Step 4: Simplify the expression.
Cancel the two zeros: $T = \frac{1080}{72 \times 6}$
$72 \times 6 = 432$
$T = \frac{1080}{432}$
Step 5: Perform the division.
Divide by 108: $\frac{1080 \div 108}{432 \div 108} = \frac{10}{4} = 2.5$ years.

• Shortcut Method: Find the interest for 1 year first.
$1\%$ of $7200 = 72$. So $6\%$ for 1 year is $72 \times 6 = 432$.
Total interest needed is $1080$.
Time $= \frac{1080}{432} = 2.5$ years.

• Final Answer: 2.5

• Key Fact: When two identical waves (having the same frequency and amplitude) travel in opposite directions and interfere with each other, they produce a 'Standing Wave' (or stationary wave).

• Supporting Detail: In a standing wave, the wave profile does not appear to move forward through the medium. Instead, it oscillates vertically in place, creating points of zero amplitude (nodes) and points of maximum amplitude (antinodes).

• Related Concept: This phenomenon is commonly observed in musical instruments, such as a plucked guitar string (where the wave reflects back from the fixed ends) or air columns in flutes.

• Why others wrong: Incident waves are just waves striking a boundary. Longitudinal and Transverse refer to the direction of particle vibration relative to wave propagation, not the result of opposite interference.

• Exam Trick: "Moving in opposite directions" + "Interference" = Standing Wave (because they effectively cancel each other's forward momentum, standing still).

• Additional Info: The distance between two consecutive nodes or antinodes in a standing wave is exactly half the wavelength ($\lambda/2$).

• Given: Race = 1200m. Amit runs 1200m, Bhushan runs $1200-200 = 1000$m. Amit starts 20s later. Amit overtakes 4 mins (240s) after Amit starts. Amit finishes 10s before Bhushan. Find Amit's speed ($V_A$).

• Basic Method (Solution):
Step 1: Let Amit's speed be $V_A$ and Bhushan's speed be $V_B$.
Step 2: Analyze the overtake condition.
Amit runs for 4 minutes $= 240$ seconds. Distance Amit runs $= 240 V_A$.
Bhushan started 20 seconds earlier. So Bhushan has been running for $240 + 20 = 260$ seconds. Distance Bhushan runs $= 260 V_B$.
Since Amit overtakes Bhushan, their absolute position from the start line is identical. Bhushan had a 200m head start.
Equation 1: $240 V_A = 200 + 260 V_B$.
Step 3: Analyze the finish condition.
Amit's total time to run 1200m $= \frac{1200}{V_A}$.
Bhushan's total time to run 1000m $= \frac{1000}{V_B}$.
Amit started 20s late and finished 10s early. This means Amit's running time is exactly 30 seconds less than Bhushan's running time.
Equation 2: $\frac{1200}{V_A} = \frac{1000}{V_B} - 30 \implies \frac{1000}{V_B} = \frac{1200}{V_A} + 30$.
Step 4: Solve the equations.
From Eq 1: $24V_A = 20 + 26V_B \implies 12V_A = 10 + 13V_B \implies 13V_B = 12V_A - 10 \implies V_B = \frac{12V_A - 10}{13}$.
Substitute $V_B$ into Eq 2:
$\frac{1000}{\frac{12V_A - 10}{13}} = \frac{1200}{V_A} + 30$
$\frac{13000}{12V_A - 10} = \frac{1200 + 30V_A}{V_A}$
$\frac{1300}{12V_A - 10} = \frac{120 + 3V_A}{V_A}$
$1300V_A = (12V_A - 10)(120 + 3V_A)$
$1300V_A = 1440V_A + 36V_A^2 - 1200 - 30V_A$
$1300V_A = 36V_A^2 + 1410V_A - 1200$
$36V_A^2 + 110V_A - 1200 = 0$
Divide by 2:
$18V_A^2 + 55V_A - 600 = 0$
Using quadratic formula: $V_A = \frac{-55 \pm \sqrt{3025 - 4(18)(-600)}}{36} = \frac{-55 \pm \sqrt{3025 + 43200}}{36} = \frac{-55 \pm \sqrt{46225}}{36} = \frac{-55 \pm 215}{36}$.
Since speed is positive: $V_A = \frac{160}{36} = \frac{40}{9} = 4\frac{4}{9}$ m/s.

• Shortcut Method: Use the options to satisfy the equations.
Option C gives $V_A = 40/9$.
From $12V_A = 10 + 13V_B$, $12(40/9) = 160/3$.
$13V_B = 160/3 - 30/3 = 130/3 \implies V_B = 10/3$.
Check the time gap:
Amit's time $= 1200 / (40/9) = 30 \times 9 = 270$s.
Bhushan's time $= 1000 / (10/3) = 300$s.
The difference is 30s. Since Amit starts 20s late and finishes 10s early, his running duration should be exactly 30s less. It matches perfectly!

• Final Answer: $4 \frac{4}{9}$