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Let P be the plane sqrt 3x+2y+3z=16and l...

Let P be the plane `sqrt 3x+2y+3z=16`and let `S ={alphahati+betahatj+gammahatk:alpha ^2 + beta^2 +gamma^2 =1` and the distance of `(alpha,beta,gamma)` from the plane P is `7/2}`. Let `vecu,vecv and vecw` be three distinct vectors in S such that `|vecu-vecv|= |vecv -vecw|=vecw-vecu|`. Let V be the volume of the parallelepiped determined by vectors `vecu,vecv` and `vecw`. Then the value of `(80)/(sqrt3)V` is

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JEE ADVANCED PREVIOUS YEAR-JEE ADVANCED 2023-Question
  1. Let P be the plane sqrt 3x+2y+3z=16and let S ={alphahati+betahatj+gamm...

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  2. Let S = (0,1)uu(1,2)uu(3,4) and T ={0,1,2,3} . Then which of the follo...

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  3. Let T1 and T2 be two distinct common tangents to the ellipse E: (x^2)...

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  4. Let Q be the cube with the set of vertices {(x1,x2,x3) in RR^3:x1x2,x^...

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  5. Let X ={(,y) in ZZ timesZZ : (x^2)/8 +(y^2)/(20) < 1 and y^2 < 5x}. Th...

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  6. Let P be a point on the parabola y^2 =4ax , where a>0 . The normal to ...

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  7. Let tan^-1(x)in(-pi/2,pi/2) , for x in RR. Then the number of real sol...

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  8. Let nge2 be a natural number and f:[0,1]rarrRR be the function defined...

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  9. Let obrace(75* * *57)^(" r") denote the (r+2) digit number where the f...

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  10. Let A={(1967+ 1686i sin theta)/(7-3icostheta): theta in RR} . If A con...

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  11. Let a and b be two nonzero real numbers. If the coefficient of 5 x in...

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  12. Let alpha,beta and gamma be real numbers. Consider the following syst...

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  13. Consider the given data with frequency distribution {(xi,3,8,11,10,5...

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  14. Let l1 and l2 be the lines vec r1= gamma (hati+ hatj +hat k ) and vecr...

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  15. Let z be a complex number satisfying |z|^3 +2z^2 +4barz -8 =0 , where ...

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  16. Let f:[1,oo) to RR be a differentiable function such that f(1)=1/3 and...

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  17. Consider an experiment of tossing a coin repeatedly until the outcomes...

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  18. For any y in RR , let cot^-1(y) in (0,pi) and tan^-1(y) in (-pi/2,pi/2...

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  19. Let the position vectors of the points P ,Q, R and S be veca=hati +2ha...

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  20. Let M = (a(ij)) , i , j in {1,2,3}, be the 3 xx 3 matrix such that a(i...

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  21. Let f:(0,1) to RR be the function defined as f(x)=[4x](x-1/4)^2(x-1/2)...

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