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Prove by mathematical induction. 1.1! + ...

Prove by mathematical induction. `1.1! + 2. 2! + 3. 3! + ... +n . n! = (n + 1)! - 1, where` n ∈ N`.

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UNITED BOOK HOUSE-MODEL QUESTION PAPERS-SET 11-EXERCISE
  1. For any two positive acute angles theta and phi if sin(theta+phi)=k s...

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  2. Solve :sqrt3sinx+cosx=2

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  3. Prove by mathematical induction. 1.1! + 2. 2! + 3. 3! + ... +n . n! = ...

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  4. If z = x + iy then l z - 8| + Iz + 8| = 20. represents a ellipse

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  5. If (1+x)^n=c0+c1x+c2x^2+....+cnx^n,then show that c0/1+c2/3+c4/5+...=2...

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  6. If the ath and bth term of an AP are 1/b and 1/a,then show that (ab)th...

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  7. In /\XYZthe co-ordinate of Y and Z are (-a, 0) and (a, 0), andangle XZ...

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  8. If the three straight lines ax + 2y + 1 = 0, 3y + bx + 1 = 0 and cx+ 4...

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  9. If the circles x^2+y^2+2ax+c^2=0and x^2+y^2+2by+c^2=0touch each other,...

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  10. Find the co-ordinate of a point equidistance from the points' (0, 0. 0...

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  11. Prove that lim(xrarr1)(x^2-sqrtx)/(sqrtx-1)=3

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  12. Prove that sqrt5 is irrational, (use the method of contradiction).

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  13. In xy plane, |x — y | = 1 represents an equation of a circle and one d...

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  14. Find the mean diaviation with respect to median of the frequency dist...

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  15. If (acosthetasecphi-x)/(asin(theta+phi))=(y-bsinthetasecphi)/(bcos(th...

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  16. If sinalpha+sinbeta=1/2,cosalpha+cosbeta=5/4find the value of tanalpha...

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  17. Solve :(x+1)(x+2)(x+3)(x+4)=120

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  18. In a polygon, the mesurement of least internal angle is 120^@. If thea...

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  19. Out of 15 boys, 7 are skaut. In how mariy different way can 12 boys be...

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  20. Draw the graph of the following system of inequation and show the comm...

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