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USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
- Find the value of a and b if the function given below is continuous. ...
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- If y=(sinx)^(tanx), find frac[dy][dx]
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- If y=log[x+sqrt(x^(2)+1)], then prove that (x^(2)+1)(d^(2)y)/(dx^(2))+...
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- Prove that all normals to the curve x = a cos t + at sin t, y = a sin ...
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- If y=(tan^(-1)x)^2 then show that (x^2+1)^2 (d^2y)/(dx^2)+2x(x^2+1)((d...
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- Find intsec^3xdx
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- int0^(pi/2)sin2x log(tanx)dx
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- Solve (1+x^2)frac[dy][dx]+2xy-4x^2=0 subject to the initial condition ...
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- Evaluate: intfrac[x+3][sqrt(5-4x+x^2)]dx
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- If with reference to the eight handed system of mutually perpendicular...
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- Let veca and vecb be two unit vector and alpha be the angle between th...
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- Find the distance between the two planes 2x+3y+4z=4 and 4x+6y+8z=12.
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- Solve for x: cot^(-1)(x-1)+cot^(-1)(x-2)+cot^(-1)(x-3)=0
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- Show that sin^(-1)frac[12][13]+cos^(-1)frac[4][5]+tan^(-1)frac[63][16]...
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- Prove that the following. [[a,b,c],[a^2,b^2,c^2],[bc,ca,ab]]=(b-c)(c-a...
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- It is given that for the function f given by f(x)=x^(3)+bx^(2)+ax,x in...
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- If x = (1-cos^2 theta)/(cos theta), y = (1-cos^(2n)theta)/(cos^n theta...
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- Evaluate int0^(frac[pi][2])sin2xcdotlog(tanx)dx
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- Evaluate int(sqrt(tan x)+sqrt(cot x))dx
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- Prove by vector method that the medians of a triangle are concurrent.
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