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FULL MARKS-SAMPLE PAPER 12-PART
- For any two vectors veca and vecb prove that |vecaxxvecb|^(2)+(veca*ve...
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- Find the derivative of x^(cosx) with respect to x.
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- Evaluate int(1)/(4-x^(2))dx.
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- The length of the perpendicular drawn from the origin to a line is 6 a...
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- Prove that sin 105^(@) + cos 105^(@) = cos 45^(@)
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- How many triangles can be formed by joining 15 points on the plane, in...
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- Find the equation of the locus of a point such that the sum of the squ...
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- If A^(T)=[(4,5),(-1,0),(2,3)]and B=[(2,-1,1),(7,5,-2)], verify the ...
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- Show that the points whose position vectors are 2veci+3vecj-5veck,3vec...
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- Test the existance of the limit lim(xto1)(4|x-1|+x-1)/(|x-1|),xne1
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- If y=tan^(-1)((1+x)/(1-x)) find y'.
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- Evalute int(5x^(2)-4+(7)/(x)+(2)/(sqrt(x)))dx
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- If x^(2) + x + 1 is a factor of the polynomial 3x^(3) + 8x^(2) + 8x ...
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- (a) If f(x)=(x-1)/(x+1) then show that. (i) f((1)/(x))=-f(x) (ii) ...
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- Determine the region in the plane determined by the inequalities. x l...
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- If the letters of the word GARDEN are permuted in all possible ways an...
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- If y=x+x^(2)/2+x^(3)/3+x^(4)/4+... then show that x=y-y^(2)/(2!)+y^(3)...
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- If A(i),B(i),C(i) are the cofactors of a(i),b(i),c(i) respectively,i=1...
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- lim(alphato0)(sin(alpha^(n)))/((sinalpha)^(m))
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- (a) Find (dy)/(dx) where y=(x^(2)+1)root(3)(x^(2)+2) (b) Evaluate ...
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