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  1. Group ‘B’ ( 4x4=16)
  2. 6. a. state and prove D-Morgan’s law of set theory.
  3.     b. Sketch the curve y = -x2+4x-3.
  4. 7. a. Prove by the method of induction that 1.3 +2.4 +3.5 +………+ n(n+2) = (n(n+1)(2n+7))/6
  5.     b. Prove that 4(cot-13+cosec-1√5) = π
  6.  
  7.                   Or
  8.        Solve: Sec x. Tan x = √2
  9. 8. a. If 1/(a+c)+a/(b+c)=3/(a+b+c)  prove that C=60°
  10.                  Or
  11.     Given, a√6,b=2,c=√3-1 .solve triangle
  12. 9. a. State De – Moivre’s Theorem. Use it to find the cube root of unity.
  13.     b. If the pair of line x2 -2pxy –y2 =6 and x2-2qxy – y2 be such that each pair bisects the angle between other pair. Prove that pq= -1.
  14. 10. a. A function f(x) is defined as
  15.         F(x) =      f(x)={(2x^2-18)/█(x-3@K                    for x =3) for x ≠ 3┤
  16. Find value of K if f(x) is continuous at x = 3.
  17.                      Or
  18.  Evaluate:    (xsinθ-θsinx)/(x-θ)
  19. b. Integrate ∫_ ^ ▒dx/(x^2 √(x^2-a))
  20.         Or
  21. Find the area of circle x2+y2=25.
  22.    
  23.                                        Group C (6x5=30)
  24. 11. Find the sum to n terms: 1 +2/2+3/2^2 +4/2^3 + …… …… …..
  25. 12. Prove that circles x2 +y2 +2ax +c2 =0 and x2+y2+2by+c2 =0 touch if 1/a^2 +1/b^2 =1/c^2  .
  26. 13. Find the derivative of √sin2x by first principle.
  27. 14. If roots of equation a (b-c)x2 +b(c-a)x + c(a-b) = 0 are equal, prove that
  28.                    1/a+1/c=2/b .
  29. 15. State and prove cosine law. Also prove that a/sinA=b/sinB=c/sinC = 2R, where R is radius of circum circle
  30. Nashjo90@gmail.com
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