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Prove that by mathematical induction,4^n...

Prove that by mathematical induction,`4^n+15n-1`is divisible ny 9 when `n in N`.

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UNITED BOOK HOUSE-MODEL QUESTION PAPERS-SET 10-EXERCISE
  1. Show that tan6^@tan42^@tan66^@tan78^@=1

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  2. Solve :2+2cos2x.cos5x=sin^2 2x

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  3. Prove that by mathematical induction,4^n+15n-1is divisible ny 9 when n...

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  4. Prove that ((i-sqrt3)/(i+sqrt3))^200+((i+sqrt3)/(-i+sqrt3))^200= -1

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  5. If the sum of 1st n tenn of a GP is Sn=1 and S(2n)=4,show that S(3n):S...

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  6. In the expansion of (x+P)^n,the 6th ,7th,8th and 9th terms are a,b,c a...

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  7. Show that the straight lines x/a+y/b=1/c, x/b+y/c=1/a and x/c+y/a=1/b ...

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  8. The co-ordinates of the end points of a diagonal of a rectangle are (...

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  9. Find the equation of a circle which is passes through the point (4,3) ...

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  10. Show that the points (0. 7, 10), (-1, 6, 6) and (-4, 9, 6) form a righ...

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  11. Differentiate (from 1st principle) sinx/xwith respect to x

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  12. Prove that the statement , “If all the angles of a triangle are equal,...

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  13. Prove that sqrt2 irrational, (use the method of contradiction).

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  14. Two unbiased dice are thrown. Find the probability that the upper fac...

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  15. If x costheta=y cos (theta+(2pi)/3)=z cos(theta+(4pi)/3)show that xy +...

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  16. if tan (theta/2)=sqrt((1-e)/(1+e))tan (varphi/2),then prove that cos v...

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  17. If x=-1+i sqrt2 and the value of x^(4)+4x^(3)+6x^(2)+4x+9.

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  18. If p, q. r in G.P and1/(p-a),1/(r-p),1/(q-r) are in AP.show that p+4q+...

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  19. Solve graphically and find the common solution region of the system of...

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  20. If the vertices of an equilateral traingle be represented by the compl...

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