If a(i), i=1,2,…..,9 are perfect odd squ...

If `a_(i)`, `i=1,2,…..,9` are perfect odd squares, then `|{:(a_(1),a_(2),a_(3)),(a_(4),a_(5),a_(6)),(a_(7),a_(8),a_(9)):}|` is always a multiple of

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If a_(1),a_(2),a_(3),….,a_(r) are in GP, then prove that the determinant |(a_(r+1),a_(r+5),a_(r+9)),(a_(r+7),a_(r+11),a_(4+15)),(a_(r+11),a_(r+17),a_(r+21))| is independent of r .

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Let A=[a_("ij")]_(3xx3) be a matrix such that A A^(T)=4I and a_("ij")+2c_("ij")=0 , where C_("ij") is the cofactor of a_("ij") and I is the unit matrix of order 3. |(a_(11)+4,a_(12),a_(13)),(a_(21),a_(22)+4,a_(23)),(a_(31),a_(32),a_(33)+4)|+5 lambda|(a_(11)+1,a_(12),a_(13)),(a_(21),a_(22)+1,a_(23)),(a_(31),a_(32),a_(33)+1)|=0 then the value of lambda is

If a_(1)gt0 for all i=1,2,…..,n . Then, the least value of (a_(1)+a_(2)+……+a_(n))((1)/(a_(1))+(1)/(a_(2))+…+(1)/(a_(n))) , is

If Delta=|(a_(11), a_(12), a_(13) ),(a_(21), a_(22), a_(23)),(a_(31), a_(32), a_(33))| and A_(i j) is cofactors of a_(i j) , then value of Delta is given by (A) a_(11)A_(31)+a_(12)A_(32)+a_(13)A_(33) (B) a_(11)A_(11)+a_(12)A_(21)+a_(13)A_(31) (C) a_(21)A_(11)+a_(22)A_(12)+a_(23)A_(13) (D) a_(11)A_(11)+a_(21)A_(21)+a_(31)A_(31)

OBJECTIVE RD SHARMA ENGLISH-DETERMINANTS-Exercise

The value of |(a,a^(2) - bc,1),(b,b^(2) - ca,1),(c,c^(2) - ab,1)|, is
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Find the number of real root of the equation |0x-a x-b x+a0x-c x+b x+c...
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The repeated factor of the determinant |(y +z,x,y),(z +x,z,x),(x +y,...
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The value of the determinant Delta = |((1 - a(1)^(3) b(1)^(3))/(1 - ...
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The determinant Delta = |(b,c,b alpha +c),(c,d,c alpha + d),(b alpha...
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Delta = |(1//a,1,bc),(1//b,1,ca),(1//c,1,ab)|=
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If |(1 +ax,1 +bx,1 + bx),(1 +a(1) x,1 +b(1) x,1 + c(1) x),(1 + a(2) x,...
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If abc!=0 then |{:(1+a,1,1),(1,1+b,1),(1,1,1+c):}| is
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If 1 + (1)/(a) + (1)/(b) + (1)/(c) = 0, then Delta = |(1 +a,1,1),(1,...
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If a, b and c are all different from zero and Delta = |(1 +a,1,1),(1...
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In a Delta ABC, a, b, c are sides and A, B, C are angles opposite to t...
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If |(-12,0,lamda),(0,2,-1),(2,1,15)| = -360, then the value of lamda i...
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If a(i), i=1,2,…..,9 are perfect odd squares, then |{:(a(1),a(2),a(3))...
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If maximum and minimum values of the determinant |{:(1+sin^(2)x,cos...
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If [x] denote the greatest integer less than or equal to x then in ord...
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If a, b gt 0 and Delta (x)= |(x,a,a),(b,x,a),(b,b,x)|, then
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If f(x)=ax^2+bx+c,a,b,cepsilonR and the equation f(x)-x=0 has imaginar...
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Let g(x)|f(x+c)f(x+2c)f(x+3c)f(c)f(2c)f(3c)f^(prime)(c)f^(prime)(2c)f^...
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If a^2+b^2+c^2=-2a n df(x)= |1+a^2x(1+b^2)x(1+c^2)x(1+a^2)x1+b^2x(1+c...
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The coefficicent of x in f(x) =|{:(x,1+sinx,cosx),(1, log(1+x),2),(x^2...
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