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Prove that |{:(1+a,1,1),(1,1+b,1),(1,1,...

Prove that `|{:(1+a,1,1),(1,1+b,1),(1,1,1+c):}|` =abc `(1+(1)/(a)+(1)/(b)+(1)/(c))`

A

any integer

B

zero

C

an even integer

D

any odd integer

Text Solution

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The correct Answer is:
D
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ARIHANT MATHS-DETERMINANTS -Exercise (Questions Asked In Previous 13 Years Exam)
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  2. The value of |alpha| for which the system of equation alphax+y+z=alpha...

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  3. if a(1),a(2),…….a(n),……. form a G.P. and a(1) gt 0 , for all I ge 1 ...

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  4. If D =|{:(1,1,1),(1,1+x,1),(1,1,1+y):}|"for" " "xne0,yne0 then D is

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  5. Consider the system of equations x-2y+3z=-1 -x+y-2z=k x-3y+4z=1 ...

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  6. Let a,b,c, be any real number. Suppose that there are real numbers x,y...

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  7. Prove that |{:(1+a,1,1),(1,1+b,1),(1,1,1+c):}| =abc (1+(1)/(a)+(1)/(...

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  8. If f(theta)=|{:(1,tantheta,1),(-tantheta,1,tantheta),(-1,-tantheta,1):...

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  9. The number of values of k for which the linear equations 4x+ky+2...

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  10. If the trivial solution is the only solution of the system of equation...

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  11. The number of values of k, for which the system of equations (k""+""...

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  12. If f(n)=alpha^(n)+beta^(n) and |{:(3,1+f(1),1+f(2)),(1+f(1),1+f(2),1+f...

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  13. The set of all values of lambda for which the system of linear equ...

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  14. Which of the following values of alpha satisfying the equation |{:((1+...

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  15. The system of linear equations x+y+z=2,2x+y-z=3, 3x+2y+kz=4 has a uniq...

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  16. The total number of distinct x in R for which |{:(x,,x^(2),,...

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  17. Let a, lambda , mu in R.Consider the system of linear equations ax...

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  18. If S is the set of distinct values of 'b' for which the following ...

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