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By using mathematical induction prove th...

By using mathematical induction prove that `3^(2n)-8n-1`is divisible by 64 when n is an integer.

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UNITED BOOK HOUSE-MODEL QUESTION PAPERS-SET 1-EXERCISE
  1. If x=a+b,y=aw+bw^2,z=aw^2+bw,show that xyz=a^3+b^3

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  2. If ,p,q,a,b are 6th,7th,8th and 9th term of the expansion of (x+r)^n,t...

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  3. By using mathematical induction prove that 3^(2n)-8n-1is divisible by ...

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  4. If a,b,c are in G.P and x,y are the arithmetic mean of a and b aand b,...

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  5. Prove that the straight lines ax+by+c=0,bx+cy+a=0and cx+ay+b=0 are con...

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  6. Find the equation of the straight line which divides perepndicularly t...

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  7. If the image of the co-ordinate of a point (x1,y1)is (x2,y2)with respe...

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  8. 3x+y=5 and x+y-1=0 are the equations of two diamters to the circle,whi...

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  9. Evaluate :lim(xrarr1)(x+x^2+x^3+...+x^n-n)/(x-1)

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  10. If sqrt(1-x^4)+sqrt(1-y^4)=k(x^2-y^2),show that y1=(xsqrt(1-y^4))/(ysq...

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  11. Prove that the cpmpound statement “If x and y are odd integers, then x...

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  12. Prove by method of contradiction that sqrt5is an irrational number

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  13. 6 boys and 6 girls occuppy seats ina row at random.What is the probabi...

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  14. Two samples of sizes 60 and 90 have 52 and 48 as the respective A.Ms. ...

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

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  16. Solve :sin^3thetacostheta-cos^3thetasintheta=1/4

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  17. Draw the graph and find the solution (common) region of the following ...

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  18. Solve 12ix^2-x+6i=0

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  19. Find the sum upto nth term :1+4/5+7/5^2+10/5^3+.....

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  20. How many ways of selecting 4 letters from the words EXAMINATION.

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