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USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
- Prove that cos^(-1)(frac[b+acosx][a+bcosx])=2tan^(-1)(sqrt(frac[a-b][a...
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- Show that the line y=mx+c touches the curve x^2/a^2-y^2/b^2 = 1 if c^2...
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- Show that the shrtest distance of the point (0, 8a) from the curve ax^...
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- Show that the curves y = 2^(x) and y = 5^(x) intersect at an angle tan...
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- Prove the following: [[(b+c)^2,a^2,bc],[(c+a)^2,b^2,ca],[(a+b)^2,c^2...
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- Find the inverse of the following matrix using elementary transformati...
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- If A is a singular matrix, then what is A(adjA)?
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- Give example of a function which is increasing in (-oo,2) and (3,oo) a...
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- If the direction angles of a line are alpha=30^@ and beta=60^@, find t...
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- Give an example of a relation which is not a function.
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- Write the integrating factor of the differential equation dy/dx(x+y+1)...
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- tan{(1/2)sin^(-1)((2x)/(1+x^(2)))+1/2cos^(-1)((1-y^(2))/(1+y^(2)))}.
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- What is the angle between vecaand vecb if abs(veca+vecb)=abs(veca-vecb...
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- If M=[(1,1,1),(1,1,1),(1,1,1)],then what is M^50 ?
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- Write the value x for which d/dxsin(sin^-1x)=1
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- What is the value of int(-1)^(1)ln(frac[4-x][4+x])dx?
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- Prove the following statements "cot"^(-1)9+"cosec"^(-1)sqrt(41)/(4)=...
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- Show that if R is an equivalence relation on X then dom R=rngR =X.
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- Solve graphically: Maximize Z=5x+6y subject to 2x+3yle6,x, yge0
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- Solve sin^(-1)(1-x)-2sin^(-1)x=frac[pi][2]
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