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The determinant Delta =|(a^2(1+x),ab,ac)...

The determinant `Delta =|(a^2(1+x),ab,ac),(ab,b^2(1+x),bc), (ac,bc,c^2(1+x))|` is divisible by 1)1+x 2)`(1+x)^2` 3)`x^2` 4) `x^2+1`

A

`1+x`

B

`(1+x)^2`

C

`x^2`

D

none of these

Text Solution

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The correct Answer is:
C
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FIITJEE-DETERMINANT-ASSIGNMENT PROBLEMS (OBJECTIVE) LEVEL-I
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  2. The number of values of k for which the system of the equations (k+1)x...

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  3. The determinant Delta =|(a^2(1+x),ab,ac),(ab,b^2(1+x),bc), (ac,bc,c^2(...

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  4. If alpha , beta and gamma the roots of the equation x^2(px + q) = r(x...

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  5. If the system of equations x+a y=0,a z+y=0 and a x+z=0 has infinite so...

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  6. If A+B+C =pi , then the value of determinant |{:(sin^2A,cotA,1),(sin^2...

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  7. For A=a^2+b^2+c^2,B=ab+bc+ca,(a^3,b^3c^3-3abc)^2 is equal to

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  8. If A, B, C are angle of a triangle ABC, then the value of the determi...

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  9. If the expression |{:(x^2+x+3,1,4),(2x^4+x^3+2x+1,2,3),(x^2+x,1,1):}| ...

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  10. The sum of two non integral roots of |{:(x,2,5),(3,x,3),(5,4,x):}|=0 i...

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  11. |[1,1,1] , [(2^x+2^(-x))^2, (3^x+3^(-x))^2, (5^x+5^(-x))^2] , [(2^x-2^...

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  12. There are three points (a,x) ,(b,y) and (c,z) such that the straight l...

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  13. If |{:(overset(n-2)underset(k=0)sum1,n(n-1),n^2),(overset(n)underset(k...

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  14. Delta=|{:(1+a^2+a^4,1+ab+a^2b^2,1+ac+a^2c^2),(1+ab+a^2b^2,1+b^2+b^4,1+...

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  15. If A(x1, y1), B (x2, y2) and C (x3, y3) are the vertices of a DeltaABC...

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  16. The number of distinct real roots of |s in x cos x cos x cos x s in x ...

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  17. If f(x) =("In"x)/x "then" |{:("In"x,x,0),(1//x,1,x),(-1//x^2,0,2):}| i...

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  18. Statement 1: If the system of equation lambdax+(b-a)y+(c-a)z=0,(a-b)x+...

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  19. If Ir^2+mr^2+nr^2=1 where r=1,2,3 and I1I2+m1m2+n1n2=0 …..etc. then ...

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  20. If alpha is a root of x^4 = 1 with negative principal argument then th...

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