SSC CGL 2024 Tier-I · 18 September 2024, Shift 2 · Quantitative Aptitude · Question 16 of 99

Text as printed on a candidate's response sheet for this shift; answer per SSC's tentative key as marked on that sheet. Solution last reviewed 10 September 2026.

Where this paper and its answers come from

SSC does not publish CGL question papers or a public answer key. The questions and options here are reproduced as printed on a candidate's own response sheet for this shift — the Commission's text, unchanged. Each answer is SSC's tentative key as marked on that sheet; SSC allowed challenges to it and never publishes a final key. The solutions are written by UnlockIAS.

The mean proportional of 4a² and x is 1⁄5a, where a is a positive number, then the value of x is ______.

Answer

Why

Correct — D. The stem and all four options are printed as images. The stem reads: The mean proportional of 4a² and x is 1⁄5a, where a is a positive number, then the value of x is ___.

Rule: m² = pq — the mean proportional m of p and q squares to their product.

Square the given mean: m² = (1⁄5a)² = 1⁄25a²
Set it against the product: 4a² × x = 1⁄25a²
Divide by 4a²: x = 1⁄(25a² × 4a²)
Collect: 25 × 4 = 100 and a² × a² = a⁴, so x = 1⁄100a⁴ → option (d).

Check it backwards: 4a² × 1⁄100a⁴ = 1⁄25a², whose square root is 1⁄5a.

Why the others are wrong

(a)
Option (a) is 1⁄100a². The 25 has been multiplied by 4 correctly, but a² × a² is a⁴, not a² — the power of a is lost in the same division that produced the 100.
(b)
Option (b) is 1⁄25a⁴. The 4 in 4a² has gone missing: dividing by a² alone takes 1⁄25a² to 1⁄25a⁴, while the full divisor 4a² also turns the 25 into 100.
(c)
Option (c) is 1⁄25a², which is m² itself. Squaring the given mean is only the first step; you still have to divide that square by the known term 4a².

Concept

The mean proportional of p and q — its other name is the geometric mean — is the m for which p : m = m : q.

Cross-multiplying that proportion gives m² = pq, and every question in this family is that one equation read in whichever direction the stem leaves blank.

Given both terms, square-root their product. Given the mean and one term, as here, square the mean and divide by the term. The arithmetic is trivial; the exponent bookkeeping is where the marks go.

In the printed image the whole of 5a sits under the bar, so the mean is 1 over 5a, not one-fifth of a. Squaring it gives 1⁄25a², which is why every option carries a 25 or a 100.

The condition that a is positive fixes the mean proportional as the positive square root, so there is no negative branch to argue about.

Key facts

The mean proportional m of p and q satisfies m² = pq, so m = √(pq).
Squaring 1⁄5a gives 1⁄25a², because the 5 and the a are both squared.
Dividing 1⁄25a² by 4a² gives 1⁄100a⁴, since 25 × 4 = 100 and a² × a² = a⁴.

Study next

Mean proportional as the geometric mean, m² = pqRecovering the missing term when the mean proportional and one term are givenLaws of exponents applied to a variable sitting in a denominator

Common traps

Stopping at 1⁄25a², the square of the given mean, instead of dividing it by 4a².
Multiplying 25 by 4 but leaving the power of a at 2.
Reading 1⁄5a as one-fifth of a, which changes every constant in the working.

SSC asks the same equation from both ends. Both terms given, find the mean: 12 Sep 2024, 16:00, Quant Q.18 asks for the mean proportional of 2 and 32, and 18 Sep 2024, 09:00, Quant Q.24 asks it for 36 and 100.

The mean given, find a term — this row's direction — runs at 23 Sep 2024, 09:00, Quant Q.15, where 30 is the mean proportional of 18 and A.

Related PYQs

No directly related past PYQ was found.