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Let vec a= hat i+hat j+hat k,vec b=-hat ...

Let `vec a= hat i+hat j+hat k,vec b=-hat i-8 hat j+2 hat k` and `vec c=4 hat i+c_(2) hat j+c_(3) hat k` be three vectors such that `vec b timesvec a=vec c timesvec a` .If the angle between the vector `vec c` and the vector `3 hat i+4 hat j+hat k` is `theta`, then the greatest integer less than or equal to `tan^(2)theta` is______________

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JEE MAINS PREVIOUS YEAR-JEE MAIN 2024 ACTUAL PAPER-Question
  1. If (dx)/(dy)=(1+x-y^(2))/(y),x(1)=1 ,then 5x(2) is equal to.

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  2. If three successive terms of a G.P.with common ratio r(r>1) are the le...

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  3. Let vec a= hat i+hat j+hat k,vec b=-hat i-8 hat j+2 hat k and vec c=4 ...

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  4. Let A=I(2)-2MM^(T),where "M" is a real matrix of order 2times1 such th...

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  5. The lines L(1),L(2),...,L(20) are distinct.For n=1,2,3,...,10 all the ...

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  6. 3 point O(0,0),P(aa^2),Q(-b,b^2)(agt0,bgt0) are on the parabola y=x^2....

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  7. If y=((sqrt(x)+1)(x^(2)-sqrt(x)))/(x sqrt(x)+x+sqrt(x))+(1)/(15)(3cos^...

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  8. Let "ABC" be an isosceles triangle in which "A" is at (-1,0),/A=(2 pi)...

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  9. f:(0,infty)rarrR and F(x)=int(0)^(x)t f(t)dt If F(x^(2))=x^(4)+x^(5)...

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  10. The sum of squares of all possible values of "k" ,for which area of th...

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  11. A bag contains 8 balls,whose colours are either white or black. 4 ball...

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  12. The value of the integral int0^(pi/4) frac{xdx}{sin^4 2x+cos^4 2x} equ...

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  13. If A=[(sqrt2,1),(-1,sqrt2)],B=[(1,0),(0,1)], C=ABA^T,X=A^TC^2A then de...

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  14. If tan A = frac{1}{sqrt (x(x^2 + x + 1)}, tan B = frac{sqrt x}{sqrt (x...

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  15. If n is the number of ways five different employees can sit into four ...

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  16. Let S={ Z in C : | z - 1|=1 and (sqrt 2 - 1) (z + overline z) - i(z - ...

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  17. Let the median and the mean deviation about the median of 7 observatio...

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  18. Let vec a = - 5 hat i + hat j - 3 hat k, vec b = hat i + 2 hat j - 4 h...

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  19. Let S equiv {x in R : (sqrt 3 + sqrt 2)^x + (sqrt 3 - sqrt 2)^x = 10}....

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  20. The area bounded by xy+4y=16 and x+y=6 is

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