If |(x^k,x^(k+2),x^(k+3)), (y^k,y^(k+2),...

If `|(x^k,x^(k+2),x^(k+3)), (y^k,y^(k+2),y^(k+3)), (z^k,z^(k+2),z^(k+3))|=(x-y)(y-z)(z-x){1/x+1/y+1/z}` then `k=`

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det [[x ^ (k), x ^ (k + 2), x ^ (k + 3) y ^ (k), y ^ (k + 2), y ^ (k + 3) z ^ (k) , z ^ (k + 2), z ^ (k + 3)]] = (xy) (yz) (zx) {(1) / (x) + (1) / (y) + (1) / ( from)}

Let x gt 0 , y gt 0 , z gt 0 are respectively the 2^(nd) , 3^(rd) , 4^(th) terms of a G.P. and Delta=|{:(x^(k),x^(k+1),x^(k+2)),(y^(k),y^(k+1),y^(k+2)),(z^(k),z^(k+1),z^(k+2)):}|=(r-1)^(2)(1-(1)/(r^(2))) (where r is the common ratio), then

If quad f(x)=((x-a)(x-b))/(x) and ((f(z))/((z-x)(z-y))+((f(y))/((y-z)(y-x))+((f(z))/((z-x)(z-y))=(k)/(xyz)) then k=

If |(x+y,y+z,z+x),(y+z, z+x,x+y),(z+x,x+y,y+z)| =k |(x,z,y),(y,x,z),(z,y,x)| , then k is equal to

z=x+iy,z^(1/3)=a-ib,(x)/(a)-(y)/(b)=k(a^(2)-b^(2)) then k is :

(x-k)/1=(y-2)/2=(z-3)/1, (x+1)/1=(y+2)/2=(z+3)/1 coplanar then find k

If the lines (x)/(1)=(y)/(2)=(z)/(3), (x-k)/(3)=(y-3)/(-1)=(z-4)/(h) and (2x+1)/(3)=(y-1)/(1)=(z-2)/(1) are concurrent, then the value of 2h-3k is equal to

if the lines (x - 1)/(-3) = ( y - 2)/(2k) = ( z -3)/(2) and (x -1) /(3k) = ( y - 5)/(1) = (z - 6 ) /(-5) are at night angle , then find the value of k .

If a^(x) = b , b^(y) = c, c^(z) = a, x = log_(b) a^(k_(1)) , y = log_(c)b^(k_(2)), z = log _(a) c^(k_(3)), , then find K_(1) K_(2) K_(3) .

AAKASH INSTITUTE-DETERMINANTS -SECTION - B

Find the value of k so that A^2=8A+kI where A=[(1,0),(-1,7)].
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If A=[{:(sinalpha,-cosalpha,0),(cosalpha,sinalpha,0),(0,0,1):}] then A...
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If A is a matrix of order 3 and |A|=2, then A |adj A| is
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The value of the determinant |{:(""^5C0,""^5C3,14),(""^5C1,""^5C4,1),(...
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If Delta1=|{:(10,4,3),(17,7,4),(4,-5,7):}|,Delta2=|{:(4,x+5,3),(7,x+12...
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The value of |{:(x,x^2-yz,1),(y,y^2-zy,1),(z,z^2-xy,1):}| is
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The value of |(i^m,i^(m+1),i^(m+2)),(i^(m+5),i^(m+4),i^(m+3)),(i^(m+6...
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The value of the determinant |(-(2^5 + 1)^2,2^10 -1,1/(2^5-1)),(2^10...
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If the determinant |(cos2x,sin^2 x,cos 4x),(sin^2 x,cos 2x,cos^2 x),(...
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if alpha,beta,gamma are non-real numbers satisfying x^3-1=0, then the ...
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The value of sum(n=1)^(N) Un=|{:(n,1,5),(n^2,2N+1,2N+1),(n^3,3N^2,3N):...
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If a gt0, bgt0,cgt0 are respectively the p^("th"),q^("th"),r^("th") te...
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Let a, b, c be positive and not all equal. Then possible value of the ...
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The greatest value of x satisfying the equation |(2^11-x,-2^12,2^11),...
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The system of equations ax + 4y + z = 0,bx + 3y + z = 0, cx + 2y + z =...
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Let {:A=[(0,0,-1),(0,-1,0),(-1,0,0)]:}. The only correct statement abo...
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The largest value of a third order determinant whose elements are equa...
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If |(x^k,x^(k+2),x^(k+3)), (y^k,y^(k+2),y^(k+3)), (z^k,z^(k+2),z^(k+3)...
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If all elements of a third order determinant are equal to 1 or -1. the...
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If A is a 3x3 matrix and det (3A) = k {det(A)} , k is equal to
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