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1/((a+b)(b+c)(c+a)) |[-2a, a+b, a+c] , [...

`1/((a+b)(b+c)(c+a)) |[-2a, a+b, a+c] , [b+a, -2b, b+c] , [c+a, c+b, -2c]|=`

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Prove that: |[-2a, a+b,a+c],[ b+a,-2b,b+c],[c+a, c+b,-2c]|=4(a+b)(b+c)(c+a)

-2a,a+b,a+c(a+b)(b+c)(c+a),b+a,-2b,b+cc+a,c+b,-2c]|=

Using the factor theorem it is found that a+b , b+c and c+a are three factors of the determinant |[-2a ,a+b, a+c],[ b+a,-2b,b+c],[c+a ,c+b,-2c]|. The other factor in the value of the determinant is

prove that [ [a-b-c , 2a , 2a ] , [2b , b-c-a , 2b ] ,[2c ,2c,c-a-b]]= (a+b+c)^3

Find the value of the determinant |{:(a^2,a b, a c),( a b,b^2,b c), (a c, b c,c^2):}|

Show without expanding that |[1,a, a^2],[ 1,b,b^2],[ 1,c,c^2]|=|[1,b c, b+c],[1,c a, c+a],[1,a b, a+b]|

RESONANCE DPP-JEE MAINS-All Questions
  1. If a, b, c are distinct odd integers and omega is non real cube root o...

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  2. If A is square matrix such that A^2=A , then (I+A)^3-7A is equal to ...

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  3. 1/((a+b)(b+c)(c+a)) |[-2a, a+b, a+c] , [b+a, -2b, b+c] , [c+a, c+b, -2...

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  4. The number of ways of seven digit number with distinct digits of the f...

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  5. a, b, c in R, a!= 0 and the quadratic equationax^2+bx+c=0 has no real ...

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  6. If the vectors vec (a) = 2 hat (i) - hat (j) + hat (k) , vec ( b) = h...

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  7. The projection of point P( vec p) on the plane vec rdot vec n=qi s( v...

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  8. In a bag there are 4 Red, 3 Black, 2 Green Balls are drawn one by o...

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  9. If u and v are the roots of the equation x^2+2x-2=0 , then the value o...

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  10. If A O, then I+ A A2 (where I is the unit matrix of order same as that...

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  11. If f:R rarr [pi/6,pi/2], f(x)=sin^(-1)((x^(2)-a)/(x^(2)+1)) is an onto...

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  12. inte^(x)((1+sinx)/(1+cosx))dx=

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  13. (C0+C1)(C1+C2)(C2+C3)(C3+C4)...........(C(n-1)+Cn)=(C0C1C2.....C(n-1)(...

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  14. It is given that the Rolles theorem holds for the function f(x)=x^3...

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  15. If f^(prime)(1)=-2sqrt(2)a n dg^(prime)(sqrt(2))=4 , then the derivati...

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  16. The number of solution of the equation (x+2)^(log(x+2)(6+x-x^(2)))=(x-...

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  17. The mean and variance of a binomial distribution (p+q)^n are 20 and 16...

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  18. If N=(1-cos4beta)/(sec^2 2beta-1)+(1+cos4beta)/(cosec^2 2beta-1) then ...

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  19. The radius of the circle touching the line x+y=4" at "(1, 3) and inter...

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  20. Bag I contains 3 red and 4 black balls while another Bag II contain...

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