16th March 2025 Shift 1 — RRB NTPC 2025

• Given: Sides of $\triangle$PQR in ratio 4:5:6, perimeter = 90 cm; Area(ABCD) = 2 $\times$ Area(PQR); $\sqrt{7}=2.6$.

• Basic Method (Solution):
Step 1: Let sides be $4x$, $5x$, $6x$. Then $4x+5x+6x=90 \Rightarrow 15x=90 \Rightarrow x=6$.
Step 2: Sides = 24, 30, 36 cm.
Step 3: Semi-perimeter $s = 45$ cm.
Step 4: Area by Heron's formula $= \sqrt{s(s-a)(s-b)(s-c)} = \sqrt{45(45-36)(45-30)(45-24)} = \sqrt{45 \times 9 \times 15 \times 21} = \sqrt{127575}$.
Step 5: $127575 = 25 \times 5103 = 25 \times 9 \times 567 = 25 \times 9 \times 81 \times 7$. Thus $\sqrt{127575} = 5 \times 3 \times 9 \times \sqrt{7} = 135 \times 2.6 = 351$ cm$^2$.
Step 6: Area(ABCD) $= 2 \times 351 = 702$ cm$^2$.

• Shortcut Method: After finding sides 24, 30, 36, note that they form a scaled 4-5-6 triangle. Area of 4-5-6 triangle $= \sqrt{7.5(7.5-6)(7.5-5)(7.5-4)}$. Scaling factor $x=6$, area scales by $x^2=36$, so area $= 36 \times \sqrt{(15/2)(3/2)(5/2)(7/2)} = 36 \times (\sqrt{1575}/4)$. But direct Heron with $s=45$ quickly yields $135\sqrt{7}=351$, then double to 702.

• Final Answer: 702 cm2

• Given conditions: Series 89, 87, 84, 79, 72, ?

• Deduction process: Differences: 89−87=2, 87−84=3, 84−79=5, 79−72=7. The differences are consecutive prime numbers 2, 3, 5, 7. Next prime is 11. So 72−11=61.

• Exam Trick: Look for prime-number difference pattern; primes increase by successive primes.

• Final Answer: 61

• Given: 20% of number = 20% of 620 + 210; find the number.

• Basic Method (Solution):
Step 1: $0.2x = 0.2 \times 620 + 210$
Step 2: $0.2x = 124 + 210 = 334$
Step 3: $x = 334 / 0.2 = 1670$

• Shortcut Method: 20% of number − 20% of 620 = 210 $\Rightarrow$ 20% of (number − 620) = 210 $\Rightarrow$ number − 620 = 210 $\times$ 5 = 1050 $\Rightarrow$ number = 1050 + 620 = 1670.

• Final Answer: 1670

• Key Fact: Hydraulic lift and hydraulic brakes work on Pascal's law, which states that pressure applied to an enclosed fluid is transmitted equally in all directions.

• Supporting Detail: Pascal's law is the principle behind hydraulic systems where a small force on a small piston creates a large force on a larger piston.

• Related Concept: Hydraulic machines multiply force using the relation $F_1/A_1 = F_2/A_2$.

• Why others wrong: Faraday's law relates to electromagnetic induction; Gay-Lussac's law relates pressure and temperature of gases; Coulomb's law is about electrostatic force.

• Exam Trick: Remember “Pascal → Pressure → Hydraulic”.

• Additional Info: Blaise Pascal formulated this law in the 17th century.

• Given conditions: 7 people circular, facing centre. 1 between U-P (right of U); 1 between P-R; 1 between U-Q; 2 between V-R; 1 between T-Q.

• Deduction process: From U, right side one person then P. From P one then R. From U one then Q (so Q is on the other side of U). Two between V and R. One between T and Q. Possible arrangement (clockwise): U, S, P, V, R, T, Q. Counting from left of T to V gives 1 person (R).

• Exam Trick: Fix U and place others relative to it using “from the right of” as clockwise or anticlockwise consistently; draw both possible directions and eliminate.

• Final Answer: 1

• Key Fact: Turkey unveiled the powerful non-nuclear bomb named Gazap at the 17th IDEF in July 2025.

• Supporting Detail: IDEF is Turkey’s major international defence exhibition held in Istanbul.

• Related Concept: Non-nuclear high-explosive bombs are developed for precision strike capabilities without nuclear fallout.

• Why others wrong: Nebula, Phantom-X and Titan are not the names associated with the Turkish bomb unveiled at IDEF 2025.

• Exam Trick: Link “Turkey + IDEF 2025 → Gazap”.

• Additional Info: Gazap means “wrath” in Turkish, reflecting its destructive power.

• Given: Total = 1407; rate 10% CI; Anil’s amount after 15 yr = Ashok’s amount after 16 yr; find Ashok’s share.

• Basic Method (Solution):
Step 1: Let Ashok get $x$, Anil get $1407-x$.
Step 2: $(1407-x)(1.1)^{15} = x(1.1)^{16}$
Step 3: $(1407-x)/x = 1.1 \Rightarrow 1407-x = 1.1x \Rightarrow 1407 = 2.1x \Rightarrow x = 1407/2.1 = 670$.

• Shortcut Method: Since amounts are equal after 15 and 16 years, Ashok’s principal is Anil’s principal multiplied by 1.1. Ratio Anil : Ashok = 1 : 1.1 = 10 : 11. Total parts 21; Ashok = $(11/21)\times1407 = 670$.

• Final Answer: 670

• Key Fact: Article 39(d) of the Directive Principles of State Policy directs the State to secure equal pay for equal work for both men and women.

• Supporting Detail: Article 39 is part of Part IV (DPSP) and contains principles of policy to be followed by the State.

• Related Concept: Equal Remuneration Act, 1976 gives statutory force to this principle.

• Why others wrong: Article 42 deals with just and humane conditions of work and maternity relief; Article 15 prohibits discrimination; Article 14 is equality before law.

• Exam Trick: Remember “39(d) = equal pay for equal work”.

• Additional Info: The principle was also recognised by the Supreme Court as a fundamental right under Article 14 in certain cases.

• Given conditions: Series VPG 7, ZTK 11, DXO 15, HBS 19, ?

• Deduction process: Letters: V→Z (+4), Z→D (+4, wrap), D→H (+4); P→T (+4), T→X (+4), X→B (+4); G→K (+4), K→O (+4), O→S (+4). Numbers increase by +4 each time: 7, 11, 15, 19 → next 23. Next letters: H+4=L, B+4=F, S+4=W → LFW 23.

• Exam Trick: Each letter advances +4 in alphabet; number +4; check wrap-around from Z to A.

• Final Answer: LFW 23

• Given conditions: EGDH → FIFI; JMHL → KOJM; find for NPRS.

• Deduction process: Pattern: each letter +1, +2, +3, +4 respectively. E+1=F, G+2=I, D+3=G→I? Wait: actually E→F (+1), G→I (+2), D→F (+2)? Recheck: EGDH to FIFI: E+1=F, G+2=I, D+5? Better: reverse pairs or alternate. Observed: first letter +1, second +2, third +5? Consistent pattern: positions advance by +1, +2, +5, +2? Actual observed: E→F (+1), G→I (+2), D→F (+2), H→I (+1) no. Looking at both examples: EGDH → F I F I; JMHL → K O J M. Pattern is +1, +2, +2, +1? E+1=F, G+2=I, D+2=F, H+1=I. Yes! J+1=K, M+2=O, H+2=J, L+1=M. Perfect. So N+1=O, P+2=R, R+2=T, S+1=T → ORTT.

• Exam Trick: Check successive +1,+2,+2,+1 pattern on consecutive letters.

• Final Answer: ORTT