RRB Group D — free MCQ practice

The general identity $a^3+b^3+c^3 - 3abc = (a+b+c)(a^2+b^2+c^2-ab-bc-ca)$ collapses when $a+b+c = 0$: the RHS is zero, so $a^3+b^3+c^3 = 3abc$. A frequent slip is to pick option A — that would require *all three* numbers to be zero, not just their sum.

The difference-of-cubes identity is $a^3 - b^3 = (a-b)(a^2 + ab + b^2)$ (note the **plus** sign on $ab$). Option B has the wrong sign — that's the *sum*-of-cubes companion identity $a^3 + b^3 = (a+b)(a^2 - ab + b^2)$.

Answer: D. SEPARATION OF POWERS is the best safeguard of liberty in a liberal democracy. The DOCTRINE OF SEPARATION OF POWERS — articulated by MONTESQUIEU in 'The Spirit of the Laws' (1748) drawing on Locke — holds that LIBERTY IS BEST PROTECTED when the THREE FUNCTIONS OF GOVERNMENT (legislative, executive, judicial) are vested in DISTINCT INSTITUTIONS / PERSONS, each with the means to check the others. **Montesquieu warned:** 'When the legislative and executive powers are united in the same person, or in the same body of magistrates, there can be no liberty... Again, there is no liberty if the judiciary power be not separated from the legislative and executive.' WHY SEPARATION OF POWERS IS THE BEST SAFEGUARD: - It PREVENTS CONCENTRATION of state power in any single authority. - It creates a SYSTEM OF CHECKS AND BALANCES so each branch can resist encroachments by the others. - It allows JUDICIAL REVIEW of legislative/executive actions for compliance with constitution and fundamental rights. - It guarantees that NO BRANCH BECOMES TYRANNICAL because it cannot make, execute, and judge laws all by itself. - It is structurally protective, not dependent on the goodwill of rulers. The Indian Constitution embraces a soft separation (functional rather than rigid) and the Supreme Court has held it part of the BASIC STRUCTURE (Kesavananda Bharati 1973, Indira Gandhi vs Raj Narain 1975). Why other options are WRONG: (A) 'A committed judiciary' — a judiciary 'committed' to a particular political philosophy or ruling regime is DANGEROUS for liberty, because it abandons impartiality. Liberty needs an INDEPENDENT and IMPARTIAL judiciary, not a committed one. Indira Gandhi's 1970s formulation of 'committed judiciary' is widely regarded as anti-liberal. (B) Centralisation of powers — the OPPOSITE of liberty-protection it concentrates power and risks tyranny. (C) Elected government — democratic, but elected governments can themselves abuse power (tyranny of the majority). Election alone does not safeguard liberty without institutional separation. Source: syllabus Political Theory / Montesquieu 'The Spirit of the Laws' / Kesavananda Bharati (1973).