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If t1and t2 are the roots of the equatio...

If `t_1`and `t_2` are the roots of the equation `t^2+lambdat+1=0`,where `lambda`is an orbitary constant,then prove that the line joining the point `(at_1^2,2at_1)`and `(at_2^2,2at_2)`always passes through a fixed point.Also find that point.

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UNITED BOOK HOUSE-JODHPUR PARK BOYS'S SCHOOL-EXERCISE
  1. Find the vaue of 9^(1/3)9^(1/9)9^(1/27)...oo

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  2. Prove that the area of a triangle is invariant under the translation o...

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  3. If t1and t2 are the roots of the equation t^2+lambdat+1=0,where lambda...

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  4. Prove that Axx(BcupC)=(AxxB)cup(AxxC)

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  5. Find the distance from the eye at which a coin must be placed so as ju...

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  6. If cos(alpha+beta)=4/5.sin(alpha-beta)=5/13and alpha,betalie between 0...

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  7. Prove that cos((2pi)/7)+cos((4pi)/7)+cos((6pi)/7)=-1/2

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  8. Solve :6x^2-(5+3i)x+11i-3=0in the complex plane C.

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  9. Find the sum of first n terms of the series:1/(1+1^2+1^4)+2/(1+2^2+2^4...

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  10. Find n, if the ratio of the fifth term from beginning to the fifth ter...

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  11. Find the natural number a for which sum(k=1)^nf(a+k)=16(2^n-1)where th...

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  12. The line joing two points A(2,0)and B(3,1)I rotated about A in anti cl...

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  13. In what direction should a line be drawn through the pont (1,2) so tha...

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  14. If (alpha^2,alpha)lies inside the triangle bounded by the lines x-5y+6...

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  15. Find the equations of the circles which passes through the origin and ...

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  16. Show that :tan(142(1^@/2))=2+sqrt2-sqrt3-sqrt6

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  17. If A+B+C=pi,prove that :cosA+cosB-cosC=-1+4cosA/2cosB/2sinC/2.

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  18. Solve :(|x+3|+x)/(x+2)>1,x inR,

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  19. Find principal amplitude of (1+itan((3pi)/5))

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  20. A square is draw by joing the mid points of the sides of a given squar...

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