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Evaluate:underset(x rarr 0)(lim)((e^(x)-...

Evaluate:`underset(x rarr 0)(lim)((e^(x)-1)log(1+x))/(sin^(2)x)`

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UNITED BOOK HOUSE-ANNUAL EXAMINATION QUESTION PAPERS 2017-EXERCISE
  1. Prove that the middle term in the expansion of (1+x)^(2n)is(1.3.5........

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  2. If the ratio the sum of 1st n terms of two arithemtic series is (4n-13...

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  3. Find the equations of the lines passing thorugh the point (4,5)making ...

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  4. If the equation of the side BC of an equilateral triangle ABC is x+y=2...

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  5. A circle in the first quadrant touches both the axes its centre lies o...

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  6. Evaluate:underset(x rarr 0)(lim)((e^(x)-1)log(1+x))/(sin^(2)x)

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  7. Find from the first principle,the derivative of f(x)=sec2xat x=pi/8.

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

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  9. Prove that truth table ~(pvq)=~p~q.

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  10. If 30 dates are named at random,find the probability that 5 of them wi...

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  11. calculate the mean deviation about median for the following data:

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  12. Solve: 4 sin x sin 2x sin 4x =sin3x.

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  13. if tan (theta/2)=sqrt((1-e)/(1+e))tan (varphi/2),then prove that cos v...

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  14. Solve the following inequation (|x+2|+2x)/(x+2)>2.

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  15. Solve applying formula: 3x^2-(2-i)x+10-4i=0

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  16. Out of 14 marbles 10 are red in colour and remaining 4 are of differen...

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  17. Find the sum to n terms :1/2+3/2^2+5/2^3+...+(2n-1)/2^n

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  18. Prove that the locus of the mid-points of chords of length 2d units of...

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  19. The co-ordinates of end points of a focal chord of an ellipse are (x1,...

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  20. The ellipse x^2/a^2+y^2/b^2=1passes through the point of intersection ...

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