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Total number of solutions of the equation `x² -4-[x]=0` are (where (.) denotes the greatest integer function)

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A DAS GUPTA-Miscellaneous Exercises-Exercise
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  2. log(3/4)log8(x^2+7)+log(1/2)log(1/4)(x^2+7)^(-1)=-2.

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  3. Total number of solutions of the equation x² -4-[x]=0 are (where (.) d...

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  4. Let a, b be the roots of the equation x^2 - kx + k = 0, k in R. If a^2...

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  5. Two parabola have the focus (3, 2). Their directrices are the x-axis a...

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  6. Let alpha in R. prove that a function f: R-R is differentiable at...

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  7. Find the lim(x to 0) frac{sqrt(x+2) -sqrt2}{root(3)(1-x) - sqrt(1+x)}.

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  8. Two parabolas y(2) = 4a(x – 1l(1)) and x(2) = 4a(y – l(2)) always touc...

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  9. Let 2x^2 +y^2-3xy = 0 be the equation of a pair of tangents drawn from...

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  10. Let f(x),xgeq0, be a non-negative continuous function, and let f(x)...

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  12. Let P be a point on the ellipse x^2/a^2+y^2/b^2=1 , 0 < b < a and le...

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  13. A hemi-spherical tank of radius 2 m is initially full of water and ...

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  14. I(n) is the area of n sided refular polygon inscribed in a circle unit...

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  15. For the circle x^(2)+y^(2)=r^(2), find the value of r for which the ar...

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  16. A right circular cone with radius R and height H contains a liquid whi...

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  17. If vecu, vercv, vecw be three noncoplanar unit vectors and alpha,beta,...

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  18. If P(1)=0a n d(d P(x))/(dx),sinx+2xgeq(3x(x+1))/pi . Explain the ident...

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  19. Normals are drawn from a point P with slopes m1,m2 and m3 are drawn fr...

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  20. Find a point on the curve x^2 + 2y^2 = 6, whose distance from the li...

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