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If Delta (x)=|{:(x,1+x^(2),x^(3)),(log(1...

If `Delta (x)=|{:(x,1+x^(2),x^(3)),(log(1+x^(2)),e^(x),sinx),(cosx,tanx,sin^(2)x):}|` then

A

`Delta`(x) is divisible by x

B

`Delta` (x)=0

C

`Delta`'(x)=0

D

None of these

Text Solution

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The correct Answer is:
A
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ARIHANT MATHS-DETERMINANTS -Exercise (Single Option Correct Type Questions)
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  2. Let Delta(x)=|(x+a,x+b,x+a-c),(x+b,x+c,x-1),(x+c,x+d,x-b+d)| and int0^...

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  3. If Delta (x)=|{:(x,1+x^(2),x^(3)),(log(1+x^(2)),e^(x),sinx),(cosx,tanx...

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  4. If a, b, c are sides of a triangle and |(a^2,b^2,c^2),((a+1)^2,(b+1...

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  5. If |{:(alpha,x,x,x),(x,beta,x,x),(x,x,gamma,x),(x,x,x,delta):}| =f(x)-...

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  6. If |{:(a,b-c,c+b),(a+c,b,c-a),(a-b,a+b,c):}|=0 the line ax +by +c=0 p...

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  7. If f(x) =a+bx+cx^(2) and alpha,beta "and" gamma are the roots of the...

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  8. When the determinant |{:(cos2x,sin^(2)x,cos4x),(sin^(2)x,cos2x,cos^(2)...

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  9. If [] denotes the greatest integer less than or equal to the real numb...

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  10. The determinant |{:(y^(2),-xy,x^(2)),(a,b,c),(a',b',c'):}| is equal to

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  11. If A,B and C are angle of a triangle of a triangle ,the value of |{:(...

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  12. If |{:(x^(n),x^(n+2),x^(2n)),(1,x^(a),a),(x^(n+5),x^(a+6),x^(2n+5)):}|...

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  13. If x,y and z are the integers in AP lying between 1 and 9 and x 51, ...

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  14. If a(1),b(1),c(1),a(2),b(2),c(2) "and" a(3),b(3),c(3) are three digit ...

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  15. If a,b,and c are sides of Delta ABC such that |{:(c,bcosB+alphabeta,ac...

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  16. If x(1),x(2) "and" y(1),y(2) are the roots of the equations 3x^(2) ...

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  17. The value of |(.^(10)C(4).^(10)C(5).^(11)C(m)),(.^(11)C(6).^(11)C(7).^...

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  18. The value of the determinant |{:(1,sin(alpha-beta)theta,cos (alpha-be...

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  19. If f(x), h(x) are polynomials of degree 4 and |(f(x), g(x),h(x)),(a, b...

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  20. If f(x) =|{:(cos (x+alpha),cos(x+beta),cos(x+gamma)),(sin (x+alpha),si...

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