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- If Dk=1nn2k n^2+n+1n^2+n2k-1n^2n^2+n+1a n dsum(k=1)^n Dk=56. then n eq...
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- If a!=p ,b!=q ,c!=r and |[p, b, c ],[a, q, c ],[a ,b, r]|=0, then find...
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- If x1,x2,x3 as well as y1, y2, y3 are in G.P. with same common rati...
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- If the lines a1x+b1y+1=0,a2x+b2y+1=0 and a3x+b3y+1=0 are concurrent,...
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- For a fixed positive integer n , if =|n !(n+1)!(n+2)!(n+1)!(n+2)!(n+3)...
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- Find the value of a for which the lines 2x+y-1=0, a x+3y-3=0, 3x+2...
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- if f(alpha,beta)=|[cos alpha,-sin alpha,1],[sin alpha,cos alpha,1],[co...
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- If the lines a x+y+1=0,x+b y+1=0 and x+y+c=0(a ,b ,c being distinct...
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- If (1+x+x^(2))^(25)=a(0)+a(1)x+a(2)x^(2)+...+a(50).x^(50), then a(0)+a...
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- Find the value of lambda for which the homogeneous system of equations...
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- If f,g,a n d \ h are differentiable functions of x and d(x)=|[f,g,h]...
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- Let a ,b ,c be positive and not all equal. Show that the value of the ...
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- if =|{:(x^(n),,n!,,2),(cos x,,cos.(npi)/(2),,4),(sin x,,sin .(npi)/(2)...
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- Without expanding a determinant at any stage, show that abs((x^2+x ,x+...
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- Prove that : |b c-c^2c a-^2a b-c^2c a-b^2a b-c^2b c-a^2a b-c^2b c-a^2c...
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- Show that the system of equations 3x-y + 4z = 3, x + 2y-3z =-2 and 6x ...
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- Let Delta = |{:(-bc,,b^(2)+bc,,c^(2)+bc),(a^(2)+ac,,-ac,,c^(2)+ac),(a^...
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- If y=|sinxcosxsinxcosx-sinxcosxx1 1|=fin d(dy)/(dx)dot
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- Consider the system of equation x+y+z=6,x+2y+3z=10 ,a n dx+2y+lambdaz=...
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- Consider the system linear equations in x ,y ,a n dz given by (sin3th...
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