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If x+iy=(a+ib)/(a-ib), prove that x^(2)+...

If `x+iy=(a+ib)/(a-ib)`, prove that `x^(2)+y^(2)=1`

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OSWAAL PUBLICATION-SOLVED PAPER 2019-1-EXERCISE
  1. Prove that tan 3x= (3tan x-tan^3 x)/(1-3tan^2 x)

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  2. Represent the complex number Z = 1 = isqrt(3) in the polar form .

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  3. If x+iy=(a+ib)/(a-ib), prove that x^(2)+y^(2)=1

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  4. In how many of distinct permutations of the letters in the word MISSIS...

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  5. Find the term independent of x in the expansion of((3x^2)/2-1/(3x))^6.

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  6. In an AP if m^th term is n and the n^th term is m,where m ne n,find th...

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  7. Find the sum of the sequence 8, 88, 888, 8888, . . . To n terms.

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  8. Find the centre and the radius of the circle x^2+y^2+8x+10y-8=0

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  9. Find the derivative of cos x from first principle.

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  10. Verify by the method of contradiction that sqrt7 is irrational number

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  11. If E and F are two events such that P(E)=1/4, P(E)=1/2 and P(E and F)=...

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  12. One card is drawn from a well shuffled deck of 52 cards.If each outcom...

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  13. One card is drawn from a well shuffled deck of 52 cards.If each outcom...

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  14. One card is drawn from a well shuffled deck of 52 cards.If each outcom...

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  15. Define modulus function, draw the graph of it, write its domain and ra...

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  16. Prove that cos^(2)+x+cos^(2) (x+pi/3)+cos^(2)(x-pi/3)=3/2 and hence fi...

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  17. 1^(2)+2^(2)+3^(2)+............+n^(2)=(n(n+1)(2n+1))/6 forall n in N.

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  18. Solve the following system of inequalities graphically : 5x + 4y ...

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  19. A group consists of 5 girls and 7 boys.In how many ways can a team of ...

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  20. State and prove Bionomial theorem for any positive integer n.

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