Part CCSIR NET June 2024the-bound-on-lambda-kills-the-second-mode

The bound on lambda kills the second mode

For $λ \in R$ such that | $λ$ | < 5/32, let $R (x, t, λ)$ and u denote the resolvent kernel and the solution, respectively, of the Fredholm integral equation $u (x) = x + (λ /2) \int$ ₋ $_{2}^{2} ($ xt $+ x^{2} t^{2}) u (t)$ dt. Then which of the following statements are true?

A. $R (x, t, λ) = 3$ xt $/ (3 - 8 λ) - 5 x^{2} t^{2} / (5 - 32 λ)$
B. $R (x, t, λ) = 3$ xt $/ (3 - 8 λ) + 5 x^{2} t^{2} / (5 - 32 λ)$ ✓
C. $u (1) = - 5/ (5 - 32 λ)$
D. $u (1) = 3/ (3 - 8 λ)$ ✓

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.

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50 are analysed free — try those first.

The bound on lambda kills the second mode

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