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If S {x in RR : sin^-1((x+1)/(sqrtx^2+2x...

If `S {x in RR : sin^-1((x+1)/(sqrtx^2+2x+2))-sin^-1(x/(sqrt((x)^2+1))) =pi/4}`, then `sum _(x in s)(sin((x^2+x+5)pi/2))- cos ((x^2+x+5)pi))` is equal to _____.

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JEE MAINS PREVIOUS YEAR-JEE MAIN 2023-Question
  1. Let m1 and m2 be the slopes of the tangents drawn from the point P(4,...

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  2. Let w=zbarz +k1z+k2iz+lambda(1+i),k1,k2 in RR. Let Re(w)=0 be the circ...

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  3. If S {x in RR : sin^-1((x+1)/(sqrtx^2+2x+2))-sin^-1(x/(sqrt((x)^2+1)))...

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  4. Let veca=3hati+hatj-hatk and vecc= 2hati-3hatj+3hatk . If vecb is a v...

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  5. Let the image of the point ((5)/(3),(5)/(3),(8)/(3)) in the plane x-2y...

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  6. Let the mean of the data be 5 . If m and sigma^2 are respectively ...

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  7. The number of seven digit positive integers formed using the digits 1,...

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  8. Let N be the foot of perpendicular from the point P(1,-2,3) on the lin...

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  9. Let S = {z in CC : barz =i (z^2 + Re(bar z))} Then sum sum(z in s)|z|^...

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  10. If lim(xrarr0) (e^(ax)-cos (bx)-((cxe)/2)^(-cx))/(1-cos(2x)=17 , then ...

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  11. The value of (e^(-pi/4)+int(0)^(pi/4) e^(-x) tan^(50)xdx)/(int(0)^(pi/...

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  12. All word , with or without meaning ,are made using all the letters of ...

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  13. The range of f(x) =4 sin ^(-1) (x^2/(x^2+1)) is

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  14. Let (alpha,beta ) be the centroid of the triangle formed by the lines ...

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  15. Let the centre of a circle C be (alpha, beta ) and its radius r<8. Let...

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  16. Let for a triangle ABC, vec(AB) = -2hati +hatj+3hat k vec(CB) = alp...

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  17. The coefficient of x^5 in the expansion of (2x^3-1/(3x)^2)^5 is

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  18. If the system of equation 2x + y- =5 2x-5y +lambda =mu x+ 2y -5z...

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  19. The line , that is coplanar to the line (x+3)/(-3)=(y-1)/1 =(z-5)/5 ,i...

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  20. Let for A =[[1,2,3],[alpha,3,1],[1,1,2]], absA=2 . If |2adj (2 adj (2A...

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