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19. Explain the knowledge dimensions in Revised Bloom Taxonomy with suitable examples from
Mathematics. (3 Marks)
20. Elucidate the need of diagnostic testing and remedial teaching in Mathematics. (3 Marks)
21. Differentiate between Holistic rubric and Analytic rubric. (3 Marks)
22. Let V be the space of all real-valued continuous functions defined on ಔ and T : V ‏ناج‎ be defined by
॥॥॥॥ = ಗ f(t)dt; fe 0,೬ ‏غ1 ع‎ . Show that 7 has no eigenvalues. (5 Marks)
23. Let | be the Lebesgue measure, f > 0 and 1५ ദ്ധ = 0. Show that f= 0 almost everywhere on E. (5 Marks)
24. Show that if X 15 a compact metric space, then ೫ is separable. (5 Marks)
25. Prove or disprove, The symmetric group 5 has exactly 3 normal subgroups for ஈ > 5. (5 Marks)
26. Let f(z) be a non constant analytic function defined in a domain 0 = (2: |2| < 1} and continuous on

2.

28.

:ور

30.

2D such that |f(z)| > m on 2D. If |f(0)| > m, show that there exists atleast one zero in |2| > (5 Marks)

Suppose X and Y are F-spaces, ‏لا : م‎ > Y is linear and G = {(x, A(x)) : x € X}is closed in X x ¥. Then

show that ^\ is continuous. (5 Marks)
2. 219 32
+2°)|——xy——+x2=0
Solve the PDE (y? +2] न ⋅ (5 Marks)
If a prime p does not divide a then prove that ௪7-12 1 (mod p). (5 Marks)

Explain briefly the cognitive development model. (5 Marks)