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By mathematical induction show that 3^n>...

By mathematical induction show that `3^n>n^3`when `nge4`. N is an integer.

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UNITED BOOK HOUSE-MODEL QUESTION PAPERS-SET 7-EXERCISE
  1. Prove that cosalpha/(sin3alpha)+(cos3alpha)/(sin9alpha)+(cos9alpha)/(s...

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  2. Solve : sectheta-1=(sqrt2-1)tantheta

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  3. By mathematical induction show that 3^n>n^3when nge4. N is an integer.

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  4. Find the co-efficient of 1/xof the expansion of (1+x)^n(1+1/x)^nwhere ...

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  5. Find the sum up to n terms :n.1+(n-1).2+(n-2)3+(n-3).4+....

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  6. If n(p(r-1))/a=n(pr)/b=n(p(r+1))/c,then show that b^2=a(b+c)

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  7. Show that the four lines 2x+y+1=0,2x+y+7=0,x+2y-1=0 and x+2y+5=0 form ...

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  8. Find the equation-of the bisector of the obtused angle between the st...

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  9. The co-ordinate of centre and the diameter of a circle are (3, 7) and ...

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  10. Find the ratio in which the YZ. plane divides the line segment joining...

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  11. Evaluate :lim(xrarr0)(sqrtcosx-root(3)(cosx))/(sin^2x)

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  12. Find, form 1st principles, the derivatives of tansqrtxwith respect to ...

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  13. Using contrapositive method show that the following statement is true....

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  14. Find the validity of the following biconditional Statement. A triangle...

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  15. For any three events A. B.' C show thatP(AcupBcupC)=P(A)+P(B)+P(C)-P(A...

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  16. The mean and SD of the scoreing marks of 100 students are 40 and 5.1 r...

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  17. if tan (beta/2)=4 tan (alpha/2),show that tan( (beta-alpha)/2)=(3sinal...

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  18. If xcos(theta+120^@)=y cos (theta+240^@),show that x-y=-(x+y)sqrt3tant...

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  19. If one root is the square of another of an equationax^2+2ibx+ic=0,then...

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  20. If the sum of 1st M terms of an AP is m. and the sum of 1st N terms is...

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