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1. Explain the importance of science and technology in Rural Development. (4)
2. As a teacher, explain how you will integrate ICT in the classrooms. (any 4 methods) (4)
3. Mental health and well-being activities for teachers should be ongoing and holistic. Substantiate. (4)
4. How technology integration in education helped to enhance quality performance of students ? (4)
5. What do you mean by research ethics? What are the ethical issues in educational research ? (4)
6. Briefly examine the forms of community engagement. (6)
7. Mention any four reasons to state that ICT plays an important role in the assessment of learner. Briefly explain any four softwares that can be used to develop quizzes in ICT based classroom. (6)
8. Explain the relationship between education and social change and the functions of education in social change. (6)
9. Justify the role of research and innovations in improving classroom teaching of teachers. (6)
10. What do you mean by 'Criticism of Data' in historical research ? Differentiate 'External Criticism' from 'Internal Criticism' ? (6)
11. For a quantum system of two identical particles, each of which can be in one of 'n' quantum states, find no. of symmetric states of the system. (3)
12. Among the following interactions, which ones are allowed? Which ones are forbidden? Explain why?
a) π⁻ + p → K⁻ + Σ⁺
b) π⁺ + p → K⁰ + Σ⁺
c) π⁻ + p → Ξ⁻ + K⁺ + K⁰
d) Λ → Σ⁻ + π⁺
e) K⁻ + p → K⁰ + n
f) π⁺ + p → Λ + K⁺ + π⁺ (3)
13. φ₁ and φ₂ are normalised eigenfunctions corresponding to the same eigenvalue. If ∫φ₁*φ₂ dτ = d, where d is real, find normalised linear combinations of φ₁ and φ₂ orthogonal to (a) φ₁ and (b) φ₁ + φ₂. (4)
14. A deuteron gas is heated at temperature T. For which temperature nuclear process occur? Which is the interaction involved? (4)
15. A rigid wheel has principal moments of inertia I₁ = I₂ ≠ I₃ about its body fixed principal axes x̂, ŷ and ẑ. The wheel is attached at its centre of mass to a bearing which allows frictionless rotation about one space-fixed axis. The wheel can rotate at constant ω⃗ ≠ 0 and exert no torque on its bearing. What conditions must the components of ω⃗ satisfy? Find ω₁, ω₂, ω₃ and hence |ω⃗|. (6)
16. State Residue theorem. Hence evaluate the integral ∮C dz/sinh 2z, where ‘C’ is the circle |z| = 2, the contour being taken in the positive sense. (6)
17. The saturation magnetic induction of Nickel is 0.65 wb/m². If the density of nickel is 8906 kg/m³ and its atomic weight is 58.7, calculate the magnetic moment of nickel atom in Bohr magneton. (6)
18. Find the electric field at a distance ‘z’ above the centre of a plane circular disc of radius R, which carries a uniform surface charge σ. What happens to the formula in the limit R → ∞? Also express the case z >> R. (6)
19. For the ideal Op Amp shown, what should be the value of resistor R₁ to get a gain of 5?
[Circuit diagram: Vᵢ through 1 kΩ to the non-inverting input with 2 kΩ to ground; the inverting input has 3 kΩ to ground and feedback resistor R₁ from Vₒ.] (6)
20. The spacing between the lines in the microwave spectrum of H³⁵Cl is 6.350 × 10¹¹ Hz. Find the bond length of H³⁵Cl. (6)
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