20. Show that \( \sqrt{3} \) is an irrational number. 21. Show that \( ((p \Rightarrow q) \wedge(q \Rightarrow r)) \Rightarrow(p \Rightarrow r) \) is tautology or not. (2 pts) 22. Show that \( p \Rightarrow(q \vee r) \) and \( (p \Rightarrow q) \vee(p \Rightarrow r) \) are equivalent. ( 2 pts)

1ple 3: Prove that \( (A \cup B)^{\prime}=A^{\prime} \cap B^{\prime} \) (i) Using Venn diagrams (ii) rigorously

11. If 'North-East' becomes 'West' and 'South-East' becomes South and so on. What will 'West'become? यदि उतर-पूर्व, पश्चिम हो जाता है और दक्षिण-पूर्व, दक्षिण हा जाता है, तो पश्चिम क्या होगा? (a) South-East/दक्षिण पूर्व (b) North-West/उत्तर-पश्चिम (c) South-West/दक्षिण पश्चिम (d) North-East/उत्तर पूर्व

Compute \( \operatorname{det} A^{4} \), where \( A=\left(\begin{array}{lll}0 & 1 & 2 \\ 1 & 2 & 2 \\ 2 & 1 & 2\end{array}\right) \)

11. Write any three objectives of teaching Mathematics at Primary level, 12. What is the Socio-Cultural background of mathematical knowledge? 13. Give three merits of Play-Way method. 14. Draw the Indian place value chart and represent the number 58308 . 15. Add \( 2.342,3.04 \) and 8.2 . 16. Divide 0.245 by 6 . 17. Define Scalene triangle, Isosceles triangle and Equilateral triangle. 18. What do you mean by comprehensiveness of evaluation? 19. Mention any three purposes of evaluation. 20. Give a list of three tools and three techniques of evaluation in Mathematics.

10. Найти собственные значения и собственные и присоединенные векторы матрицы лнейного оператора и найти вид этой матрицы в базисе пз собственных и присоединенных векторов \[ \left[\begin{array}{rrr}5 & 4 & -4 \\ -1 & 3 & 1 \\ 0 & 2 & 2\end{array}\right] \]