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lim(x -> pi/6) sin(x -pi/6)/(sqrt3 -cosx...

`lim_(x -> pi/6) sin(x -pi/6)/(sqrt3 -cosx)`

A

0

B

`1/(sqrt3-2)`

C

1

D

`oo`

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Let S denotes the sum of an infinite geometric progression whose first term is the value of the functions f(x)=(sin(x-pi//6))/(sqrt3-2cosx) at x=pi/6, if f(x) is continuous at x=pi/6 and whose common ratio is the limiting value of the function g(x)=(sin(x)^(1//3) ln(1+3x))/((arc tansqrtx)^2 (e^(5*x^(1//3))-1)) as x rarr 0. Find the value of 2S.

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IPUCET PREVIOUS YEAR PAPERS-GGSIPU MATHEMATICS 2014-MCQs
  1. If =a+b,y=aomega+bomega^2 and z=aomega^2+bomega, prove tht xyz=a^3+b^3

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  2. lim(ntooo)((2n^(3))/(2n^(2)+3)+(1-5n^(2))/(5n+1)) is equal to

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  3. lim(x -> pi/6) sin(x -pi/6)/(sqrt3 -cosx)

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  4. lim(xtooo)((2x^(2)+3)/(2x^(2)+5))^(8x^(2)+3) is equal to

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  5. Find the slope of the normal to the curve 4x^(3)+6x^(2)-5xy-8y^(2)+9x+...

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  6. The value of lim(x-> 0) (sin3x^2)/(lncos(2x^2-x)) is

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  7. int(-pi//2)^(pi//2)cosxln((1+x)/(1-x))dx is equal to

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  8. lim(ntooo)((root(3)(n!))/n) is equal to

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  9. int0^pi(sqrt(1+cos2x))/2dx

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  10. The quadrangle with the vertices A(3, 5, 6), B(1, -5, 7), C(8, -3, -1)...

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  11. In the triangle with vertices A(1, -1, 2), B(5, -6, 2) and C(1, 3, -1)...

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  12. If 1/(b-a) +1/(b-c)=1/a+1/c , then a,b and c are in

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  13. Compute the shortest distance between the circle x^(2)+y^(2)-10x-14y-1...

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  14. On the ellipse 9x^(2)+25y^(2)=225, find the point whose distance to th...

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  15. On the parabola y^(2)=64x, find the point nearest to the straight line...

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  16. The determinant [[x,y,x+y],[y,x+y,x],[x+y,x,y]] is divisible by

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  17. The curve 5x^2 + 12xy - 22x - 12y -19 = 0 is.

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  18. The derivative of y=x^(2^(x)) w.r.t. x is

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  19. lim(xto pi/2)(pi-2x)^(cosx) is equal to

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  20. Evaluate the following : int(0)^(1)x tan^(-1)xdx

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