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Let y = y(x) be the solution of the diff...

Let y = y(x) be the solution of the differential equation `(dy)/(dx)+(sqrt2y)/(2cos^4x-cos2x)=xe^(tan^(-1)(sqrt2cot2x)),0ltxltpi//2` with `y(pi/4)=pi^2/(32)` If `y(pi/3)=pi^2/18e^(-tan^(-1)(alpha))` then the value of `3alpha^2` is equal to ______

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JEE MAINS PREVIOUS YEAR-JEE MAINS 2022-Mathematics-Section B
  1. If relation defined on set A= {1,2,3, . . .,50} , and relation R1 {(p,...

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  2. The number of real solutions of the equation e^(4x)+4e^(3x)-58e^(2x)+4...

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  3. The mean and standard deviation of 15 - observations are found to be 8...

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  4. veca=2hati+hatj+3hatk , vecb=3hati+3hatj+hatk & vecc=c1hati+c2hatk+c3h...

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  5. A ray of light passing tb.rough the point P (2, 3) reflects on the x-a...

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  6. Let l be a line which is normal to the curve y = 2x^2 + x + 2 at a poi...

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  7. Let A ={1, a1, a2 .. .... A(18).77} be a set of intgers with 1lta1lta2...

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  8. The number of positive integers k such that the constant term in the b...

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  9. The number of elements in the set {z=a+ibinCC:a,binZ and 1lt|z-3+2i|lt...

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  10. Let the lines y+2x=sqrt(11)+7sqrt7 and 2y+x=2sqrt(11)+6sqrt7 be norma...

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  11. Let S = {z in C: |z – 2| le 1, z(1 + i) + barz(1 - i) le2} . Let |z – ...

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  12. Let y = y(x) be the solution of the differential equation (dy)/(dx)+(s...

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  13. Let d be the distance between the foot of perpendiculars of the points...

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  14. The number of elements in the set S = { theta in [-4pi , 4pi] : 3 cos^...

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  15. The number of solutions of equation 2 theta -cos^2 theta + sqrt2=0 is

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  16. 50 tan(3tan^(-1)(1/2)+2cos^(-1)(1/sqrt5))+4sqrt2tan(1/2tan^(-1)(2sqrt2...

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  17. Let c, k in R. If f(x)=(c+1)x^(2) + (1-c^(2))x + 2k and f(x+y)=f(x) + ...

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  18. Let H: x^2/a^2 -y^2/b^2 = 1, a gt 0, bgt0, be a hyperbola such that th...

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  19. Let P1 : vecr (2hati + hatj - 3hatk) = 4 be a plane. Let P2 be anothe...

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  20. Let b1b2b3b4 be a 4-element permutation with bi in {1, 2, 3......., 1...

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