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Without expanding, show that the valu...

Without expanding, show that the value of each of the following determinants is zero: `|1^2 2^2 3^2 4^2\ \ \ 2^2 3^2 4^2 5^2\ \ \ 3^2 4^2 5^2 6^2\ \ \ 4^2 5^2 6^2 7^2|` (ii) `|a b c a+2x b+2y c+2z x y z|` (iii) `|(2^x+2^(-x))^2(2^x-2^(-x))^2 1(3^x+3^(-x))^2(3^x-3^(-x))^2 1(4^x+4^(-x))^2(4^x-4^(-x))^2 1|`

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RD SHARMA ENGLISH-DETERMINANTS-All Questions
  1. Without expanding, show that the value of each of the following dete...

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  2. Without expanding, show that the value of the following determinant ...

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  3. Without expanding, show that the value of each of the following det...

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  4. Without expanding, show that the value of the following determinant...

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  5. Without expanding, show that the value of each of the following dete...

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  6. Evaluate the following: |[1,a, b c],[1,b, c a],[1,c, a b]|

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  7. Evaluate the following: |[0,x y^2,x z^2],[x^2y,0,y z^2],[x^2z, z y^2,...

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  8. If "Delta"=|(1,x,x^2),( 1,y, y^2),( 1,z, z^2)| , "Delta"1=|(1, 1, 1),(...

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  9. Prove:\ |(a, b, c),( a-b,b-c,c-a),( b+c,c+a, a+b)|=a^3+b^3+c^3-3a b c

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  10. Prove: |[b+c ,a-b ,a], [c+a, b-c ,b], [a+b, c-a, c]|=3a b c-a^3-b^3-c^...

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  11. Prove: |(a+b,b+c,c+a),( b+c,c+a, a+b),( c+a, a+b,b+c)|=2|(a, b, c),( b...

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  12. Prove: |[a+b+2c, a, b], [c, b+c+2a, b], [c ,a ,c+a+2b]|=2(a+b+c)^3

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  13. Prove: |[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]|=(a+b+c)^3

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  14. Prove: |(1,b+c ,b^2+c^2),( 1,c+a ,c^2+a^2),( 1,a+b ,a^2+b^2)|=(a-b)(b-...

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  15. Prove: |(a, a+b, a+2b),( a+2b, a ,a+b ),(a+b, a+2b, a)|=9(a+b)b^2

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  16. Find dy/dx if x-y+x^5=sinx

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  17. Prove: |(z, x, y),( z^2,x^2,y^2),(z^4,x^4,y^4)|=|(x, y, z),( x^2,y^2,z...

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  18. Prove: |((b+c)^2, a^2, b c) ,((c+a)^2, b^2 ,c a),( (a+b)^2, c^2, a b)|...

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  19. Prove: |((a+1)(a+2),(a+2),1 ),((a+2)(a+3),(a+3),1), ((a+3)(a+4) ,(a+4)...

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  20. Prove: |(a^2,a^2-(b-c)^2,b c), (b^2,b^2-(c-a)^2,c a),( c^2,c^2-(a-b)^2...

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