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Consider two circles C(1):x^(2)+y^(2)=25...

Consider two circles `C_(1):x^(2)+y^(2)=25` and `C_(2):(x-alpha)^(2)+y^(2)=16`, where `alpha in(5,9)`. Let the angle between the two radii (one to each circle) drawn from one of the intersection points of `C_(1)` and `C_(2)` be `sin^(-1)((sqrt(63))/(8))` .If the length of common chord of `C_(1)` and `C_(2)` is `beta` ,then the value of `(alpha beta)^(2)` equals________.

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JEE MAINS PREVIOUS YEAR-JEE MAIN 2024 ACTUAL PAPER-Question
  1. The variance sigma^(2) of the data

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  2. Let a line passing through the point (-1,2,3) intersect the lines L(1)...

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  3. Consider two circles C(1):x^(2)+y^(2)=25 and C(2):(x-alpha)^(2)+y^(2)=...

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  4. Let S(n) be the sum to "n" -terms of an arithmetic progression 3,7,11,...

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  5. The number of real solutions of the equation x(x^(2)+3|x|+5|x-1|+6|x-2...

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  6. Let Y=Y(X) be a curve lying in the first quadrant such that the area e...

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  7. The area of the region enclosed by the parabola (y-2)^(2)=x-1 ,the lin...

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  8. The number of symmetric relations defined on the set {1,2,3,4} which a...

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  9. Let alpha=sum(k=0)^(n)(((""^(n)C(k))^(2))/(k+1)) and beta=sum(k=0)^(n-...

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  10. In an examination of Mathematics paper,there are "20" questions of equ...

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  11. If one of the diameters of the circle x^(2)+y^(2)-10x+4y+13=0 is a cho...

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  12. The distance of the point Q(0,2,-2) form the line passing through the ...

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  13. lim(x rarr0)(e^(2|sin x|)-2|sin x|-1)/(x^(2))

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  14. Let "a" be the sum of all coefficients in the expansion of (1-2x+2x^(2...

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  15. The solution curve of the differential equation y(dx)/(dy)=x(log(e)x-l...

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  16. Let vec a=3 hat i+hat j-2 hat k,vec b=4 hat i+hat j+7 hat k and vec c=...

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  17. Three rotten apples are accidently mixed with fifteen good apples. Ass...

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  18. The area of the region {(x,y):y^(2)le4x,x<4,(xy(x-1)(x-2))/((x-3)(x-4)...

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  19. Let y=y(x) be the solution of the differential equation (dy)/(dx)=((ta...

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  20. For 0 lt c lt b lt a ,let (a+b-2c)x^(2)+(b+c-2a)x+(c+a-2b)=0 and alpha...

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