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if alpha, beta , ne 0 " and " f(n) =alp...

if `alpha, beta , ne 0 " and " f(n) =alpha^(n)+beta^(n)`
`" and " |{:(3,,1+f(1),,1+f(2)),(1+f(1),,1+f(2),,1+f(3)),(1+f(2),,1+f(3),,1+f(4)):}|`
`=k(1-alpha)^(2)(1-beta)^(2)(alpha-beta)^(2)` then k is equal to

A

1

B

-1

C

`alphabeta`

D

`alphabetagamma`

Text Solution

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The correct Answer is:
A
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ARIHANT MATHS-DETERMINANTS -Exercise (Single Option Correct Type Questions)
  1. if alpha, beta , ne 0 " and " f(n) =alpha^(n)+beta^(n) " and " |{:(...

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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),e^(x),sinx),(cosx,tanx,sin...

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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. Find dy/dx if x^2+xy+y^2=100

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  6. Prove that |[b+c,a,a],[b,c+a,b],[c,c,a+b]| = 4abc

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  7. If f(x)=a+b x+c x^2 and alpha,beta,gamma are the roots of the equation...

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

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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-x y x^2a b c a ' b ' c '| is equal to

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  11. If A , B ,C are angles of a triangles, then the value of e^(2i A)e^(-i...

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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 ev...

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  15. Expand | (4,8),(6,7)|

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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. If |{:(.^(9)C(4),.^(9)C(5),.^(10)C(r)),(.^(10)C(6 ),.^(10)C(7),.^(11)C...

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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),g(x)andh(x) are three polynomials of degree 2 , then prove tha...

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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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