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USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
- If y=sinx+cosx then what is [dy/dx]^2.
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- Prove that f:X rarr Y is surjective iff for all B sube Y, f(f^(-1)(B))...
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- Find the maximum value of Z = 2x + 3y subject to conditions x+ yle1 an...
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- Prove that sin^(-1)(frac[sqrt(1+x)+sqrt(1-x)][2])=frac[pi][4]+frac[1][...
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- Show that the relation ~ on ZZ-{0}timesZZ-{0} defined by (m,n)~(p,q)Le...
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- Solve by matrix method. 2x + y = 5 , x-y =1
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- If A=[[(1,1)],[(1,1)]] and n inN, then A^n=2^(n-1)A .
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- If [[(x,y)],[(x,x/2+x)]]+[[(y,x+t)],[(x/2,x/2)]]=[[(1,4)],[(2,2)]] the...
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- Evaluate the determinant abs((4,6,-2),(1,-4,3),(7,-2,1)
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- If abs((a,b,a-b),(b,c,b-c),(2,1,0))=0 , then prove that a,b,c are in G...
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- 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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