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show that lim(nrarr0)(root(3)(n+1)-1)/n=...

show that `lim_(nrarr0)(root(3)(n+1)-1)/n=1/3`

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UNITED BOOK HOUSE-MODEL QUESTION PAPERS-SET 13-EXERCISE
  1. The co-ordinate of the vertices of a triangle are (2, -2), (4, 2) and ...

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  2. Find the co-ordinate of that point which divides the line segment join...

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  3. show that lim(nrarr0)(root(3)(n+1)-1)/n=1/3

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  4. If y = x/(x+a),show that x dy/dx = y (1- y)

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  5. A box contains 50 articles of which 4 are defective. One article is ta...

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  6. Find the mean deviation of 36, 72, 46,60, 42, 45, 53. 46, 51, 49.

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  7. For any three sets A, B, C, Prove that A cap(BcupC)=(AcapB)cup (A cap ...

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  8. If tan (theta/2)=tan^3 (phi/2)and tanphi=2tanalpha,then prove that the...

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  9. In a triangle ABC if a cos^2(C/2)+c cos^2(A/2)=((3b)/2)show that sides...

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  10. Prove that by mathematical induction : 3^(2n+ 2) - 8n - 9 is divisible...

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  11. If x=a+b,y=aw+bw^2,z=aw^2+bw,show that xyz=a^3+b^3

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  12. if the ratio of the sum of n terms of two A Ps is (3n + 5) : (5n - 9)...

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  13. The coefficient of three consecutive terms in the expansion of (1+x)^n...

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  14. Show that the straight line (a + 2b) x + (a -3b)y + b -a = 0 always p...

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  15. Find the equations of straight line which are perpendicular to the str...

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  16. y = 2x is a chord of the circle x^2 + y^2 -10 x = 0. Find the equation...

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  17. Find the ratio in which the plane 2x + 2y - 2z = 1 divides the line se...

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  18. Evaluate :lim(xrarroo)[(1^(1//x)+2^(1//x)+3^(1//x))/3]

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  19. Differentiate x^(-2/3) with respect to x, with behalf of definition.

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  20. Prove that sqrt3is irrational, (use the method of contradiction)

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