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If w be a imaginary cube root of uniyt a...

If w be a imaginary cube root of uniyt and a+b+c=0 then show that `(a+bw+cw^2)^3+(a+bw^2+cw)^3=27abc`

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UNITED BOOK HOUSE-BETHUNE COLLEGIATE SCHOOL.-EXERCISE
  1. Prove that (1+sec2A)(1+sec2^2A)(1+sec2^3A).....(1+sec2^nA)=(tan2^nA)/(...

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  2. Prove that ,tan(alpha+beta)tan(alpha-beta)=(sin^2alpha-sin^2beta)/(cos...

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  3. How many 5 digit numbers can be formed using the digits 0,2,5,6,7 with...

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  4. Show that ,((1+i)/(1-i))^2+((1-i)/(1+i))^2is a real number.

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  5. Find the distance between the lines 3x+4y=9 and 6x+8y+15=0.

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  6. Find the value of :lim(xrarr0)(sin2x+sin6x)/(sin5x-sin3x)

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  7. In an examination 60% passed in mathematics,68% passes in statistics a...

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  8. If alpha!=betaand atanalpha+b tanbeta=(a+b)tan((alpha+beta)/2),then sh...

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  9. For any three sets A,Band C show that :Acap(BcupC)=(AcapB)cup(AcapC)

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  10. Prove using principle of mathematical induction that sum of the cube t...

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  11. If w be a imaginary cube root of uniyt and a+b+c=0 then show that (a+b...

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  12. Find the sum upto n terms of the following series 4+44+444+….n.

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  13. Show that the straight lines 5x-y=6,x+5y-22=0,5x-y-32=0 and x+5y+4=0 f...

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  14. Find the value of :lim(xrarra)(xsina-asinx)/(x-a)

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  15. Prove that :cot(A-B)cot(B-c)+cot(B-c)cot(C-A)+cot(A-B)cot(B-C)=1

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  16. Provethat: (cos3theta)/(sin2thetasin4theta)+(cos5theta)/(sin4thetasin6...

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  17. Two parallel straight lines contains 5 points and 10 points respective...

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  18. Find the sum of the following series (1)+(2+3)+(4+5+6)+(7+8+9+10)+…to ...

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  19. If ab+bc+ca=0 then prove that the straight lines x/a+y/b=1/c,x/b+y/c=1...

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  20. Evaluate lim(xrarrpi//4)(4sqrt2-(cosx+sinx)^5)/(1-sin2x)

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