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If sinθ1+sinθ 2 +sinθ 3=3, then co...

If `sinθ1+sinθ 2 +sinθ 3=3`, then `cosθ 1+cosθ 2+cosθ3` is equal to

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ALLEN-TEST PAPERS-part-2 Mathematics
  1. If f:R rarr R is continous function satisying f(0) =1 and f(2x) -f(x)...

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  2. Consider the parabola y^(2)=8x, if the normal at a point P on the par...

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  3. If sinθ1+sinθ 2 +sinθ 3=3, then cosθ 1+cosθ 2+cosθ3 is equal to

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  4. The equations of the transverse and conjugate axes of a hyperbola are...

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  5. Find the locus of the midpoints of chords of hyperbola 3x^(2)-2y^(2)+4...

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  6. Let f(x) = x^(2) - 5x + 6, g(x) = f(|x|), h(x) = |g(x)| The set of v...

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  7. If θ is an acute angle and tanθ+cotθ=2 , find the value of tan^7θ...

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  8. Find the least value of k such that the equation (ln x) + k = e^(x-k) ...

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  9. Volume of tetrahedron formed by the planes x+y=0, y+z=0, z+x=0,x+y+z-1...

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  10. If f' ((x)/(y)). f((y)/(x))=(x^(2)+y^(2))/(xy) AA x,y in R^(+) and f(1...

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  11. Range of the function f defined by (x) =[(1)/(sin{x})] (where [.] an...

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  12. The vlaue of sqrt3cot20^(@)-4cos20^(@), is

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  13. Which of the following function is surjective but not injective. (a) ...

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  14. f:RrarrR is a function satisfying f(x+5)gef(x)+5 and f(x+1)lef(x)+1. ...

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  15. If f(x)=((1-tanx)/(1+sinx))^(cosec x) is to be made continuous at x=0,...

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  16. If a(1) is the greatest value of f(x) , where f(x) =((1)/(2+[sinx])) (...

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  17. The value of f(0), so that the function f(x)=((27-2x)^2-3)/(9-3(243+5x...

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  18. Let f:N rarr N be a function that (i) x-f(x)=19[x/19]-90[f(x)/90], f...

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  19. The range of f(x)=sin^(-1)((x^2+1)/(x^2+2)) is (a)[0,pi/2] (b) (0,pi/...

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  20. Let f:[-pi/3,(2pi)/3] rarr [0,4] be a function defined as f(x)=sqrt(3)...

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