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Part CCSIR NET June 2024at-an-eigenvalue-solvability-is-a-condition

At an eigenvalue solvability is a condition

For c∈Rc \in \mathbb{R}, consider the following Fredholm integral equation y(x) = 1 + x + cx2+2∫01(1−3^{2} + 2\int_{0}^{1} (1 - 3xt)y(t)dt. Then the values of c for which the integral equation admits a solution are

  1. A.−8✓ Correct
  2. B.−6
  3. C.2
  4. D.6

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward, and why this one tests existence vs uniqueness.

See pricing

50 are analysed free — try those first.

The trap it tests

Existence vs uniqueness

A theorem giving one was read as giving both.

Drill statements like this

Related counterexample: Every integral equation of the second kind has a unique solution

More on this topic

The chapter behind this: Integral equations: Fredholm vs Volterra — free to read

From Linear Integral Equations › Fredholm and Volterra equations

Last revised . Found a mistake? Tell us — corrections are the fastest thing we act on.

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