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USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
- evaluate lim(xto1)(x^2-3x+2)/(x-1) .
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- If x^2+y^2=t-1/t and x^4+y^4=t^2+1/t^2 then prove that x^3ydy/dx=1.
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- Find the maximum and minimum of f(x)=|x+3|,for all x belongs to R.
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- Find the interval on which the function f(x)=x^x decreases.
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- Find the solution of the following differential equations: (4x+6y+5)dx...
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- Integrate int((1-cosx)/(1+cosx))dx .
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- Solve (x+y)^(2)(dy)/(dx)= a^(2).
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- If f is periodic with period 3 and f(1) = 1 then what is the value of ...
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- Evaluate int(-2)^2abs([x])dx .
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- Prove that (vec a × vec b)^(2) = a^(2)b^(2)-(vec a . vec b)^(2).
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- Find the perpendicular distance of the point (-1,3,9) from the line (x...
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- Prove that (vecaxxhati)^2+(vecaxxhatj)^2+(vecaxxhatk)^2=2veca^2 .
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- Find the equation of planes passing throught the points (6,-1,1), (5,1...
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- Find the co-ordinates of the foot of the perpendicular drawn from the ...
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- If e^(y//x)=(x)/(a+bx) then show that x^(3)(d)/(dx)((dy)/(dx))=(x(dy)/...
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- If 2x=y^(1/m)+y^(-1/m) , then prove that (x^2-1)y(n+2)+(2n+1)xy(n+1)+(...
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- Show that the rectangle of maximum area that can be inscribed in a giv...
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- Prove the following by vector method. Altitudes of a triangle are conc...
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- Find the magnitude and equation of the line of shotest distance betwee...
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- Solve the following by matrix method x-y+z=4, 2x+y-3z=0, x+y+z=2
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