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Using the principle of mathematical induction prove that `3^(2n+1)+2^(n+2)`is divisible by 7`[n in N]`

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UNITED BOOK HOUSE-NAVA NALANDA-EXERCISE
  1. A+B+C=pi,prove that sin^2(A/2)+sin^2(B/2)+sin^2(C/2)=1-2sin(A/2)sin(B/...

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  2. Solve :tanx+tan(x+pi/3)+tan(x+(2pi)/3)=3

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  3. Using the principle of mathematical induction prove that 3^(2n+1)+2^(n...

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  4. If alpha and beta are different complex numbers with |beta|=1, then fi...

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  5. A question paper contains 12 questions divided into three parts.Parts...

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  6. Prove that the inequations (2x+1)/(7x-1)>5and (x+7)/(x-8)>2have no sol...

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  7. Exhibit graphically the solution region of the following system of 'in...

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  8. Prove that the product of the lengths of the perpendiculars drawn from...

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  9. Find the equation of a circle which touches both the axes and the line...

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  10. The focus of a parabola is (1,5)and its directrix is x+y+2=0.Find the...

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  11. 3(1-x) lt 2(x+4)

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  12. Prove that every function can be expressed as the sum of an -even and ...

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  13. A,B,C are three finite sets such that n(A)=17,n(B)=13,n(C)=15,n(AcapB)...

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  14. Draw the graph of f(x)=|x-1|+|x-2|.

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  15. Whats is the probability of arrangement of the letters of the word SOC...

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  16. The mean and standard deviation of 100 observations were calculated as...

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  17. Prove that tan6^@tan42^@tan66^@tan78^@=1

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  18. Solve :cos3x+cos2x=sin((3x)/2)+sin(x/2), (0lexlepi)

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  19. if (1-ix)/(1+ix)=a-ib,then prove that a^2+b^2=1(a,b x are real).

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  20. Solve graphically :|x-y|ge3.

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