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Given, sn=1+q+q^2++q^n ,Sn=1+(q+1)/2+((q...

Given, `s_n=1+q+q^2++q^n ,S_n=1+(q+1)/2+((q+1)/2)^2++((q+1)/2)^n ,q!=1` prove that `^n+1C_1+^(n+1)C_2s_1+^(n+1)C_3s_2++^(n+1)C_(n+1)s_n2^n S_ndot`

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Given, s_n=1+q+q^2+.....+q^n ,S_n=1+(q+1)/2+((q+1)/2)^2+...+((q+1)/2)^n ,q!=1 prove that "^(n+1)C_1+^(n+1)C_2s_1+^(n+1)C_3s_2+......+^(n+1)C_(n+1)s_n=2^n S_ndot

Prove that ^n C_0 .^n C_0-^(n+1)C_1 . ^n C_1+^(n+2)C_2 . ^n C_2-=(-1)^ndot

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The value of |1 1 1^n C_1^(n+2)C_1^(n+4)C_1^n C_2^(n+2)C_2^(n+4)C_2| is

Let S_n=1+q+q^2 +...+q^n and T_n =1+((q+1)/2)+((q+1)/2)^2+...((q+1)/2)^n If alpha T_100=^101C_1 +^101C_2 x S_1 ...+^101C_101 x S_100, then the value of alpha is equal to (A) 2^99 (B) 2^101 (C) 2^100 (D) -2^100

JEE MAINS PREVIOUS YEAR ENGLISH-JEE MAINS-All Questions
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  2. Set of value of x for which f(x)=sin|x|-|x|+2(x-pi)cos|x| is not diffe...

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  3. Given, sn=1+q+q^2++q^n ,Sn=1+(q+1)/2+((q+1)/2)^2++((q+1)/2)^n ,q!=1 p...

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  4. If f(x)=x/sqrt(a^2+x^2)-((d-x))/sqrt(b^2+(d-x)^2) then (A) f(...

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  5. Given (b+c)/(11) = (c+a)/(12) = (a+b)/(13) for a Delta ABC with usu...

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  6. If Det(A A^T B)=8 and Det(AB^-1)=8, then the value of Det(BB^T A^-1) ...

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  7. If |(a-b-c, 2a, 2a),(2b, b-a-c, 2b),(2c, 2c, c-a-b)|=(a+b+c)(x+a+b+c)^...

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  8. If (x+10)^50+(x−10)^50=a0+a1 x+a2x^2+........a50x^2+...........+a50x^5...

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  9. If |z|+z=3+i, then value of |z| is (A) 5//3 (B) 3//...

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  10. If set A={1, 2, 3, ...,20 }, then the find the number of onto function...

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  11. Two points A(7, 0, 6) and B(3, 4, 2) lie on a plane P1 and Plane P2:2x...

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  12. intcos(logx)dx is equal to (A) x/2(cos(logx)-sin(logx))+c ...

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  13. Let f(x)=f(a-x) and g(x)+g(a-x)=4 then int0^af(x)g(x)dx is equal to ...

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  14. Consider three boxes, each containing 10 balls labelled 1, 2, …,10. Su...

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  15. A dice is thrown repeatedly till two successive 4\'s are obtained then...

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  16. If the difference between the roots of the equation x^2+""a x""+""1"...

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  17. The equation of a tangent to the parabola y^2=""8x""i s""y""=""x""+...

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  18. ((p^^q)vv(pvv~q))^^(~p^^~q)) is equivalent to (A) ~p^^~q ...

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  19. A particle just clears a wall of height b at distance a and strikes...

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  20. The equation of a tangent to the parabola y^2=""8x""i s""y""=""x""+...

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