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If f(x)=|(1, x, x+1), (2x, x(x-1), (x+1)...

If `f(x)=|(1, x, x+1), (2x, x(x-1), (x+1)x), (3x(x-1), x(x-1)(x-2), (x+1)x(x-1))|` then `f(5000)` is equal to `0` b. `1` c. `500` d. `-500`

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ALLEN-DETERMINANTS-All Questions
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  2. Without expanding show that |b^2c^2 bc b+cc^2a^2 ca c+a a^2b^2a b a+...

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  3. If f(x)=|(1, x, x+1), (2x, x(x-1), (x+1)x), (3x(x-1), x(x-1)(x-2), (x+...

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  4. The value of the determinant |{:(a, b,0), (0,a, b),(b,0,a):}| is equal...

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  5. An equilateral triangle has each of its sides of length 6 cm. If (x1, ...

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  6. If the system of equations x + 2y + 3z = 4, x+ py+ 2z = 3, x+ 4y +u z ...

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  7. The maximum value of Δ= ∣ ∣ ∣ ​ 1 1 1+cosθ ​ 1 1+sinθ 1 ​ 1...

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  8. If f^(prime)(x)=|[mx, mx-p, m x+p], [n, n+p, n-p], [mx+2n, m x+2n+p, m...

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  9. The determinant |a b aalpha+bb c balpha+c aalpha+bbalpha+c0|=0, if a ...

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  10. Let f(x)=|1+sin^2x cos^2x4s in2xsin^2\ \ x1+cos^2x4s in2xsin^2xcos^...

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  11. The parameter on which the value of the determinant |[1,a...

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  12. If a^2+b^2+c^2=-2a n df(x)= |1+a^2x(1+b^2)x(1+c^2)x(1+a^2)x1+b^2x(1+c...

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  13. Given that q^2-p r ,0,\ p >0, then the value of |p q p x+q y q r...

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  14. The values of θ lying between 0 and π/2 and satisfying the equation ...

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  15. If |(a, a, x,),(m, m, m),(b, x, b)|=0 then x may be equal to- a.a b. ...

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  16. If ∣ -a a^2 ab ac ab -b^2 bc ac bc -c^2 | = ka^2b^2c^2...

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  17. The value of the determinant |(alpha,beta,l),(alpha,x, n),(alpha,beta,...

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  18. If the system of linear equations x+a y+a z=0,\ x+b y+b z=0,\ x+c y+...

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  19. If the system of equations x+y-3=0,\ (1+K)x+(2+K)y-8=0\ &\ x-(1+K)y+(2...

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  20. If the determinant |a+p l+x u+fb+q x+y v+gc+r n+z w+h| splits into exa...

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