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For every natural number n, show that 7^...

For every natural number n, show that `7^(2n)+2^(3n-3)*3^(n-1)` is always divisible by 25.

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CHHAYA PUBLICATION-MISCELLANEOUS EXAMPLES-ALGEBRA
  1. If x in RR then find the solution set of the inquation |3x-7| gt 4.

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  2. Solve the following quadratic equation: \ x^2-(5-i)x+(18+i)=0

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  3. For every natural number n, show that 7^(2n)+2^(3n-3)*3^(n-1) is alway...

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  4. If the coefficients of the (r-1) th and (2r+3) th terms in the equatio...

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  5. If n is a positive integer then using the indentiy (1+x)^(n)=(1+x)^(3)...

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  6. If S(1), S(2), S(3),...S(n) are the sums of infinite geometric series,...

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  7. If u(r)=(1)/(r!) then show that u(0)u(n)+8u(1)+u(n-1)+8^(2)u(2)u(n-2...

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  8. a series is given by the following form : 1+(x+x^(2))+(x^(3)+x^(4)+x...

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  9. If x= cos theta+i sin theta and 1+ sqrt(1-a^(2))=na, show that, (a)/(...

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  10. Show that (a+ omega +omega ^(2))(a+omega ^(2)+omega ^(4))(a+omega ^(4)...

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  11. Let z and omega tow complex number. If |z|= |omega| and areg (z) +arg...

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  12. If z(1)+z(2) are two complex number and |(barz(1)-2bar z(2))/(2-z(1)ba...

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  13. If x+iy moves on the line 3x+4y+5=0, prove that the minimum value of ...

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  14. If |z^(2)|=9|z|, find the maximum and minimum values of |z|.

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  15. Find the greatest value of |z| when |z-(6)/(z)|=2,z being a complex nu...

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  16. Find the least value of |z+(1)/(z)| if |z| ge 3 (z being a complex ...

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  17. If the roots of the equation ix^(2)-(b^(2)+c^(2))x+(c^(2)+d^(2))^(2)=0...

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  18. If one root of the equation ax^(2)-2ibx-ic=0 be square of the other, t...

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  19. Solve (7y^(2)+1)/(y^(2)-1)-4 ((y^(2)-1)/(7y^(2)+1))=-3

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  20. Solve (x-(x)/(x+1))^(2)+2x((x)/(x+1))=3

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