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Let `vec v=alphahat i+2hat j-3hat k,vec w=2 alphahat i+hat j-hat k` and `vec u` be a vector such `|vec u|=alpha>0`.If the minimum value of the scalar triple product `[(vecu ,vecv ,vecw)]` is `-alpha sqrt(3401)` and `abs(vec u hati)^2=m/n` where `m` and `n` are co-prime natural numbers then `m+n` is equal to

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JEE MAINS PREVIOUS YEAR-JEE MAINS 2023 JAN ACTUAL PAPER-Question
  1. The negation of the expression q vv((~q)^^p) is equivalent to

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  2. If int(0)^(1)(x^(21)+x^(14)+x^(7))(2x^(14)+3x^(7)+6)^(1/7)dx=(1)/(l)(1...

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  3. Let vec v=alphahat i+2hat j-3hat k,vec w=2 alphahat i+hat j-hat k and ...

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  4. The number of 3 -digit numbers,that are divisible by 2 or 3 but not di...

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  5. Let A be the area bounded by the curve y=x|x-3|,the x -axis and the or...

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  6. The number of words, with or without meaning, that can be formed using...

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  7. A(2,6,2),B(-4,0,lambda),C(2,3,-1) and D(4,5,0),|lamda|le5 are the vert...

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  8. If f(x)=x^(2)+g'(1)x+g''(2) and g(x)=f(1)x^(2)+xf'(x)+f''(x),then the ...

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  9. Let f:IR rarr IR be a differential function such that f'(x)+f(x)=int(0...

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  10. If a(1)=8,a(2),a(3)......a(n),be an A.P.If the sum of first four terms...

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  11. The remainder,when 19^(200)+23^(200) is divided by 49,is

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  12. Let P(S) denote the power set of S = {1,2,3,…..,10}. Define the relati...

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  13. The sum sum(n=1)^oo(2n^(2)+3n+4)/((2n)!) is equal to

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  14. If y(x) = x^x , x gt 0 then y"(2) – 2y'(2) is equal to

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  15. Let veca= 2hati -7hatj+5hat k, vecb=hati+hat k and vec c =hat i +2hat ...

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  16. Let S ={X in R, 0 lt x lt 1 and 2 tan^(-1)((1-x)/(1+x)) =cos^(-1)((1-x...

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  17. For the system of linear equations alpha x + y + z = 1, x + alpha y + ...

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  18. The number of integral values of k, for which one root of the equation...

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  19. If A (1/2)[(1,sqrt3),(-sqrt3,1)] , then

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  20. Let vec a=5hat i -hat j -3hat k and vec b =hat i +3hat j +5hat k be tw...

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