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If x , y , z are in A.P. , then the valu...

If `x , y , z` are in A.P. , then the value of the determinant are in A.P. , then the value of the determinant `|a+2a+3a+2x a+3a+4a+2y a+4a+5a+2z|` is a. 1 b. `0` c. `2a` d. `a`

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ALLEN -DETERMINANTS-All Questions
  1. If the determinant |[a+p, l+x, u+f], [b+q, x+y, v+g], [c+r, n+z, w+h]|...

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  2. The values of lambda for which the system of equations x+y+z=6,x+2y+3z...

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  3. If x , y , z are in A.P. , then the value of the determinant are in A....

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  4. Let p be the sum of all possible determinabnts of order 2 having 0,...

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  5. Statement 1 is True: Statement 2 is True; Statement 2 is a correct e...

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  6. Statement 1 is True: Statement 2 is True; Statement 2 is a correct e...

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  7. Statement 1 is True: Statement 2 is True; Statement 2 is a correct e...

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  8. Without expanding the determinant prove that: {:|(0,p-q,p-r),( q-p,0, ...

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  9. Without expanding the determinant prove that: {:|(0,a,-b),(-a,0,-c),(...

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  10. Prove that: |[ax,by,cz], [x^2,y^2,z^2], [1,1,1]|=|[a,b,c],[x,y,z],[yz,...

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  11. Prove that: {:|(1,a, a^2-bc), (1,b,b^2-ca),(1,c,c^2-ab)|:}=0

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  12. Prove that: {:|(a^2+2a,2a+1,1), (2a+1,a+2,1),(3,3,1)|:}=(a-1)^3 .

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  13. Using properties of determinants or otherwise evaluate {:|(18, 40, 8...

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  14. Using the property of determinants andd without expanding in following...

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  15. Using the properties of determinants, prove the following |{:(a,b-c,...

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  16. Absolute value of sum of roots of the equation {:|(x+2,2x+3,3x+4), (2x...

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  17. If a+b+c=0 and |{:(a-x,c,b),(c,b-x,a),(b,a,c-x):}|=0 then find the val...

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  18. Suppose three digit numbers A28 , 3B9 and 52C , where A,B and C are in...

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  19. For a fixed positive integer n , if =|n !(n+1)!(n+2)!(n+1)!(n+2)!(n+3)...

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  20. If Dr=|2^(r-1)2(3^(r-1))4(5^(r-1))x y z2^n-1 3^n-1 5^n-1| then p...

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