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- By using properties of determinants , show that : {:[( a^(2) + 1, a...
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- Let vec ar=xr hat i+yr hat j+zr hat k ,r=1,2,3 be three mutually per...
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- The number of distinct real roots of |[sinx,cosx,cosx],[cosx,sinx,cosx...
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- Let a ,b ,c be real numbers with a^2+b^2+c^2=1. Show that the eq...
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- If lines p x+q y+r=0,q x+r y+p=0a n dr x+p y+q=0 are concurrent, th...
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- If plambda^4+qlambda^3+rlambda^2+slambda+t=|[lambda^2+3lambda, lambda-...
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- Find the value of lambda if 2x^2+7x y+3y^2+8x+14 t+lambda=0 represents...
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- If x ,y ,z are different from zero and "Delta"=|[a, b-y ,c-z],[ a-x, ...
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- If A , B ,C are angles of a triangles, then the value of |[e^(2i A),...
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- For the equation |[1,x,x^2],[x^2, 1,x],[x,x^2, 1]|=0, There are exa...
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- Let "Delta"r=|r-1n6(r-1)^2 2n^2 4n-2(r-1)^2 3n^3 3n^2-3n|dot Show that...
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- Let m be a positive integer and Deltar=|[2r-1,.^mCr,1],[m^2-1,2^m,m+1]...
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- Prove that |1+a 1 1 1 1 1+b 1 1 1 1 1+c ...
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- Find the area of a triangle having vertices A(3,2),B(11 ,8), and C(8,1...
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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!=ra n d|p b c a q c a b r|=0, then find the value of ...
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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 linesa1x+b1y+1=0,\ a2x+b2y+1=0\ a n d\ a3x+b3y+1=0 are concurre...
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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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- The number of values of a for which the lines 2x+y-1=0 , a x+3y-3=0, a...
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