19th July Shift 1 — RRB JE PYQ

1. Area of a parallelogram is given by the formula: $\text{Area} = \text{Base} \times \text{Height}$.
2. Substituting the given values: $\text{Area} = 93 \times 29$.
Shortcut/Exam Trick: Use the unit digit method. The unit digit of $3 \times 9$ is $7$. Only option 'b' has a unit digit of $7$, making $2697$ the correct answer.

1. Follow BODMAS (Brackets, Orders, Div, Mult, Add, Sub). Solve innermost bracket: $(4 + 7) = 11$.
2. Next bracket: $(3 + 10 - 11) = 13 - 11 = 2$.
3. Curly bracket: $\{18 + 12 - 2\} = 30 - 2 = 28$.
4. Square bracket: $[16 \div 8 \times 28] = [2 \times 28] = 56$.
5. Final step: $112 \div 56 = 2$.
Shortcut/Exam Trick: Keep calculations mental and process brackets from inside out sequentially to save writing time.

1. Let the roots be $\alpha = \frac{1}{\sqrt{2}}$ and $\beta = \frac{1}{\sqrt{2}}$.
2. Sum of roots: $\alpha + \beta = \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{2}} = \frac{2}{\sqrt{2}} = \sqrt{2}$.
3. Product of roots: $\alpha \beta = (\frac{1}{\sqrt{2}}) \times (\frac{1}{\sqrt{2}}) = \frac{1}{2}$.
4. A quadratic equation is given by $x^2 - (\text{Sum of roots})x + (\text{Product of roots}) = 0$.
5. Substituting the values: $x^2 - (\sqrt{2})x + \frac{1}{2} = 0$.
6. Multiply the entire equation by $2$ to remove the fraction: $2x^2 - 2\sqrt{2}x + 1 = 0$.
Shortcut/Exam Trick: If roots are equal and positive, the sum is positive, making the middle term's coefficient negative ($-2\sqrt{2}x$), and the product is positive ($+1/2$), so the constant term is positive ($+1$). Option 1 is the only one matching these exact signs and values.

• Key Fact: Sonora-64 and Lerma Rojo are semi-dwarf, high-yielding varieties of wheat.
• Supporting Detail: They were introduced in India from Mexico during the Green Revolution to boost agricultural production.
• Related Concept: IR8 and Jaya are famous high-yielding varieties of Rice introduced during the same period.
• Why wrong options are wrong: Rice involves IR8, not Sonora; Barley and Maize were not the primary focus crops for these specific Mexican HYV seeds.
• Exam Trick: Remember 'Rojo' means red in Spanish, linking to Mexican wheat varieties brought by Norman Borlaug.

• Key Fact: Complete combustion of hydrocarbons like methane always produces carbon dioxide ($CO_2$) and water ($H_2O$).
• Supporting Detail: The balanced chemical equation is $CH_4 + 2O_2 \rightarrow CO_2 + 2H_2O + \text{Heat}$.
• Related Concept: Incomplete combustion (lack of oxygen) produces carbon monoxide ($CO$) or soot (Carbon).
• Why wrong options are wrong: Carbon monoxide forms only in limited oxygen; solid carbon and hydrogen are not final products of complete combustion.
• Exam Trick: 'Complete' combustion = max oxidation state of Carbon ($CO_2$) + max oxidation state of Hydrogen ($H_2O$).

• Key Fact: Check statement II: D is right of B (BD). 3 people between D and A forces A at position 1 and D at 5, meaning B is at 4. E sits immediate right of C (CE), which fills positions 2 and 3. The arrangement is A C E B D.
• Supporting Detail: Statement I gives two possibilities for B (position 2 or 4), but when you place D third to the right of C, it forces B to position 4. So A/E are at 1. We don't know who is immediate left of C.
• Related Concept: Data Sufficiency requires a unique, definitive answer.
• Why wrong options are wrong: Statement I doesn't uniquely define the person on the left.
• Exam Trick: Always plot out the 'forced' positions (like 3 people between D and A in a 5-person line means they must be at extreme ends) to quickly test sufficiency.

• Key Fact: Dr. B.R. Ambedkar actively negotiated and signed the Poona Pact on behalf of the depressed classes. Therefore, the statement that he refused to sign it is false.
• Supporting Detail: The pact was signed on September 24, 1932, at Yerwada Central Jail in Pune, agreeing to joint electorates instead of separate ones.
• Related Concept: The pact increased the reserved seats for depressed classes in provincial legislatures from 71 to 147.
• Why wrong options are wrong: Options 1, 3, and 4 are historically true events of the Poona Pact.
• Exam Trick: Remember 'Poona Pact = Compromise'. Ambedkar gave up separate electorates to save Gandhi's life, but gained more reserved seats in return.

• Key Fact: The magnetic field $B$ at the center of a circular current-carrying loop is directly proportional to the current $I$. Formula: $B = \frac{\mu_0 I}{2R}$.
• Supporting Detail: If the current $I$ is doubled, the magnetic field $B$ also strictly doubles, assuming the radius $R$ remains constant.
• Related Concept: If the radius $R$ is doubled, the magnetic field strength becomes half.
• Why wrong options are wrong: Squaring or halving effects only occur if parameters like power or distance squared are involved, which isn't the case here.
• Exam Trick: $B \propto I$ and $B \propto \frac{1}{R}$. Direct relationship means whatever happens to current happens exactly to the magnetic field.

• Key Fact: According to the Law of Conservation of Mass, mass can neither be created nor destroyed in a chemical reaction.
• Supporting Detail: Because the flask is sealed, no matter (gas or liquid) can escape or enter. Hence, the total mass remains exactly the same.
• Related Concept: Antoine Lavoisier discovered this principle in 1789.
• Why wrong options are wrong: Mass never fluctuates randomly. Gas formation or precipitation only changes the state of matter, not the total mass in a closed system.
• Exam Trick: Sealed flask = Closed system = Mass is always constant.

• Key Fact: Sodium is a highly reactive metal and is extracted through the electrolytic reduction of its molten salts (like molten NaCl), but not 'refined' via electrolytic refining involving aqueous solutions.
• Supporting Detail: Electrolytic refining is commonly used for less reactive metals where impure metal forms the anode and pure metal forms the cathode in an aqueous electrolyte.
• Related Concept: Copper, tin, lead, zinc, and silver are widely purified using the electrolytic refining method.
• Why wrong options are wrong: Copper, tin, and zinc all undergo electrolytic refining commercially to achieve high purity.
• Exam Trick: Highly reactive metals (K, Na, Ca, Mg, Al) are extracted by electrolytic reduction of molten salts, not aqueous refining.