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Using binomial theorem, prove that 6^n-5...

Using binomial theorem, prove that `6^n-5n`always leaves remainder 1 when divided by 25.

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FULL MARKS-MODEL TEST PAPER-PART-IV
  1. Find the range of the function (1)/(2cosx-1).

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  2. If the equations x^(2) - ax + b = 0 and x^(2) - ex + f = 0 have one ro...

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  3. Using binomial theorem, prove that 6^n-5nalways leaves remainder 1 wh...

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  4. If .^(n+2) C(8) : ^((n-2)) P(4) = 57: 16 , find the value of n.

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  5. Show that the points (1, 3), (2, 1) and (1/2, 4) are collinear, by usi...

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  6. The sum of the distance of a moving point from the points (4,0) and (-...

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  7. Verify the property A(B+C) = AB+AC, when the matrices A,B, and C are g...

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  8. Show that the vector veci -2 vec j +3 vec k , -2 vec i + 3 vecj -4 vec...

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  9. Evaluate int (cos2x)/((sin x + cos x)^(2))dx.

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  10. Evaluate int sin^(-1) xdx.

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  11. Evaluate Lim(x rarr pi/4) (4sqrt(2)-(cos x + sin x)^(5))/(1-sin 2 x)

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  12. Suppose the chances of hitting a target by a person X is 3 times in 4 ...

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  13. Find the range of the function (1)/(2cosx-1).

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  14. If the equations x^(2) - ax + b = 0 and x^(2) - ex + f = 0 have one ro...

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  15. Prove that cos theta + cos ((2pi)/(3)- theta)+ cos ((2pi)/(3)+ theta)=...

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  16. Using Binomial theorem, prove that 6^(n)-5n always leaves remainder 1 ...

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  17. If .^(n+2) C(8) : ^((n-2)) P(4) = 57: 16 , find the value of n.

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  18. Show that the points (1, 3), (2, 1) and (1/2, 4) are collinear, by usi...

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    |

  19. The sum of the distance of a moving point from the points (4,0) and (-...

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  20. Verify the property A(B+C) = AB+AC, when the matrices A,B, and C are g...

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    |