loveu3000ts

Group ‘B’ ( 4x4=16)
6. a. state and prove D-Morgan’s law of set theory.
    b. Sketch the curve y = -x2+4x-3.
7. a. Prove by the method of induction that 1.3 +2.4 +3.5 +………+ n(n+2) = (n(n+1)(2n+7))/6
    b. Prove that 4(cot-13+cosec-1√5) = π

                  Or
       Solve: Sec x. Tan x = √2
8. a. If 1/(a+c)+a/(b+c)=3/(a+b+c)  prove that C=60°
                 Or
    Given, a√6,b=2,c=√3-1 .solve triangle
9. a. State De – Moivre’s Theorem. Use it to find the cube root of unity.
    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.
10. a. A function f(x) is defined as
        F(x) =      f(x)={(2x^2-18)/█(x-3@K                    for x =3) for x ≠ 3┤
Find value of K if f(x) is continuous at x = 3.
                     Or
 Evaluate:    (xsinθ-θsinx)/(x-θ)
b. Integrate ∫_ ^ ▒dx/(x^2 √(x^2-a))
        Or
Find the area of circle x2+y2=25.

                                       Group C (6x5=30)
11. Find the sum to n terms: 1 +2/2+3/2^2 +4/2^3 + …… …… …..
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  .
13. Find the derivative of √sin2x by first principle.
14. If roots of equation a (b-c)x2 +b(c-a)x + c(a-b) = 0 are equal, prove that
                   1/a+1/c=2/b .
15. State and prove cosine law. Also prove that a/sinA=b/sinB=c/sinC = 2R, where R is radius of circum circle
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