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If the value of (1+(2)/(3)+(6)/(3^(2))+(...

If the value of `(1+(2)/(3)+(6)/(3^(2))+(10)/(3^(3))+...."upto "oo)^(log_((0.25))((1)/(3)+(1)/(3^(2))+(1)/(3^(3))+....."upto "oo)` is l , then `l^(2)` is equal to _______.

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JEE MAINS PREVIOUS YEAR-JEE MAINS 2021-MATHEMATICS (SECTION -B)
  1. Let vec(a), vec(b), vec(c ) be three mutually perpendicular vectors o...

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  2. Let A = ((1,-1,0),(0,1,-1),(0,0,1))andB=7A^(20)-20A^(7)+2I, where I is...

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  3. Let P be a plane passing through the points (1,0,1),(1,-2,1) and (0,1,...

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  4. The number of rational terms in the binomial expansion of (4^((1)/(4))...

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  5. If the shortest distance between the lines vec(r(1))=alphahat(i)+2hat...

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  6. Let T be the tangent to the ellipse E : x^(2) + 4y^(2) = 5 at the poin...

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  7. Let a,b,c,d be in arithmetic progression with common difference lambda...

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  8. There are 15 playears in a cricket team, out of which 6 are bowlers, 7...

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  9. Let y = mx + c, m gt 0 be the focal chord of y^(2) = - 64 x, which is...

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  10. If the value of lim(xto0) (2 - cosx sqrt(cos2x))^(((x+2)/(x^(2)))) is ...

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  11. Let y=y(x) be solution of the following differential equation e^(y)(d...

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  12. If the value of (1+(2)/(3)+(6)/(3^(2))+(10)/(3^(3))+...."upto "oo)^(lo...

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  13. Consider the following frequency distribution : If the sum of a...

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  14. Let vecp=2hati+3hatj+hatkandvecq=hati+2hatj+hatk be two vectors .If a ...

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  15. The ratio of the coefficient of the middle term in the expansion of (1...

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  16. Let M={A=({:(a,b),(c,d):}):a,b,c,d in { +-3,+-2,+-1,0}. Define f:Mt...

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  17. There are 5 students in class 10, 6 students in class 11 and 8 student...

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  18. If alpha,beta are roots of the equation x^(2)+5(sqrt(2))x+10=0,alphagt...

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  19. The term independent of 'x' in the expansion of ((x+1)/(x^(2//3)-x^(1/...

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  20. Let S={n inN|({:(0,i),(1,0):})^(n)({:(a,b),(c,d):})=({:(a,b),(c,d):})A...

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