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Let a ,b , c be the real numbers. The fo...

Let `a ,b , c` be the real numbers. The following system of equations in `x ,y ,a n dz` `(x^2)/(a^2)+(y^2)/(b^2)-(z^2)/(a^2)=1,(x^2)/(a^2)-(y^2)/(b^2)+(z^2)/(a^2)=1,-(x^2)/(a^2)+(y^2)/(b^2)+(z^2)/(a^2)=1` has a. no solution b. unique solution c. infinitely many solutions d. finitely many solutions

A

no solution

B

unique solution

C

infinitely many solution

D

finitely many solutions

Text Solution

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The correct Answer is:
B
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OBJECTIVE RD SHARMA ENGLISH-DETERMINANTS-Exercise
  1. |{:(x,4, y+z),(y,4,z+x),(z,4,x+y):}| is equal to:

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  2. If f(x)=|{:(0,x-a,x-b),(x+a,0,x-c),(x+b,x+c,0):}|, then

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  3. Let a ,b , c be the real numbers. The following system of equations in...

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  4. A ,\ B are two matrices such that A B and A+B are both defined; sho...

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  5. If omega is an imaginary cube root of unity, then the value of |(a,b o...

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  6. If alpha, beta are non - real numbers satifying x^3-1=0 then the value...

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  7. The value of the determinant |(-1,1,1),(1,-1,1),(1,1,-1)| is equal to

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  8. In a third order determinant, each element of the first column consist...

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  9. A root of the equation |[3-x,-6,3],[-6,3-x,3],[3,3,-6-x]|=0

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  10. For positive numbers x, y and z, the numerical value of the determinan...

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  11. Calculate the value of the determinant |{:(1,1,1,1),(1,2,3,4),(1,3,6,1...

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  12. if Delta= |{:(3,,4,,5,,x),(4,,5,,6,,y),(5,,6,,7,,z),(x,,y,,z,,0):}|=0 ...

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  13. If A, B and C are the angles of a triangle and |(1,1,1),(1 + sin A,1...

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  14. If a,b,and c are the side of a triangle and A,B and C are the angles o...

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  15. If [ ] denotes the greatest integer less than or equal to the real num...

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  16. The coefficicent of x in f(x) =|{:(x,1+sinx,cosx),(1, log(1+x),2),(x^2...

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  17. The determinant |(cos C,tan A,0),(sin B,0,-tan A),(0,sin B,cos C)| h...

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  18. Using the factor theorem it is found that a+b , b+ca n dc+a are three ...

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  19. The value of |(a,a^(2) - bc,1),(b,b^(2) - ca,1),(c,c^(2) - ab,1)|, is

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  20. Find the number of real root of the equation |0x-a x-b x+a0x-c x+b x+c...

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