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A moving st.line always passes through a fixed pt.`(alpha,beta)`.Prove that the locus of the middle point of the portion of the line intercepted between the axes is `alpha/x+beta/y=2`

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UNITED BOOK HOUSE-THE SCOTTISH CHURCH COLLEGIATE SCHOOL-EXERCISE
  1. Find the sum to n terms :1/2+3/2^2+5/2^3+...+(2n-1)/2^n

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  2. Find the term inedpendent of X in the expansion of (1+x)^3(1-1/x)^6

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  3. A moving st.line always passes through a fixed pt.(alpha,beta).Prove t...

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  4. Find the image of the pt.(-3,-1)with respect to the st.line 2x+3y+22=0

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  5. Find equations of all possible circles that touch the y axis at the po...

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  6. Find the equation of the circles which touche the y axes id and passes...

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  7. Show that lim(xrarr1)(1-x)tan((pix)/2)=2/pi

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  8. If 2f(x)+3f(-x)=x^2-x-1,then find f'(1).

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  9. Find from the first principle,the derivative of tan 2x at x=pi/8

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  10. If f(x) is differentiable at x=a then show that lim(xrarr0)(x^2f(a)-a^...

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  11. Prove the following by contradiciton ."The sum of a rational and an ir...

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  12. Let a statement p:/\ABCis right angle triangle,and another statement q...

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  13. Let a statement p:/\ABCis right angle triangle,and another statement q...

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  14. Let a statement p:/\ABCis right angle triangle,and another statement q...

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  15. Let a statement p:/\ABCis right angle triangle,and another statement q...

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  16. Find the range of the function f(x)=1/(3sinx+4cosx+6)

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  17. Prove thatcos^2alpha+cos^2(120^@-alpha)+cos^2(120^@+alpha)=3/2

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  18. Let f(x)=4^x/(4^x+2)prove.that f(x) + f(1- x)= 1. Hence prove that f(1...

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  19. Ifx+iy=3/(2+costheta+i sintheta)then show that x^2 + y^2 = 4x - 3.

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  20. If S be the sum. P be the product,and R the sum of the reciprocals of ...

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