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If maximum and minimum values of the det...

If maximum and minimum values of the determinant
`|{:(1+sin^(2)x,cos^(2)x,sin2x),(sin^(2)x,1+cos^(2)x,sin2x),(sin^(2)x,cos^(2)x,1+sin2x):}|`
are `alphaandbeta,` then

A

`alpha + beta^(99) = 4`

B

`alpha^(3) - beta^(17) = 26`

C

`alpha^(2n) - beta^(2n)` is always even integer for `n in N`

D

a triangle can be constructed having its sides as `alpha, beta and alpha - beta`

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The correct Answer is:
A, B, C
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OBJECTIVE RD SHARMA ENGLISH-DETERMINANTS-Exercise
  1. The value of |(a,a^(2) - bc,1),(b,b^(2) - ca,1),(c,c^(2) - ab,1)|, is

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

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  3. The repeated factor of the determinant |(y +z,x,y),(z +x,z,x),(x +y,...

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  4. The value of the determinant Delta = |((1 - a(1)^(3) b(1)^(3))/(1 - ...

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  5. The determinant Delta = |(b,c,b alpha +c),(c,d,c alpha + d),(b alpha...

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  6. Delta = |(1//a,1,bc),(1//b,1,ca),(1//c,1,ab)|=

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  7. If |(1 +ax,1 +bx,1 + bx),(1 +a(1) x,1 +b(1) x,1 + c(1) x),(1 + a(2) x,...

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  8. If abc!=0 then |{:(1+a,1,1),(1,1+b,1),(1,1,1+c):}| is

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  9. If 1 + (1)/(a) + (1)/(b) + (1)/(c) = 0, then Delta = |(1 +a,1,1),(1,...

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  10. If a, b and c are all different from zero and Delta = |(1 +a,1,1),(1...

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  11. In a Delta ABC, a, b, c are sides and A, B, C are angles opposite to t...

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  12. If |(-12,0,lamda),(0,2,-1),(2,1,15)| = -360, then the value of lamda i...

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  13. If a(i), i=1,2,…..,9 are perfect odd squares, then |{:(a(1),a(2),a(3))...

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  14. If maximum and minimum values of the determinant |{:(1+sin^(2)x,cos...

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  15. If [x] denote the greatest integer less than or equal to x then in ord...

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  16. If a, b gt 0 and Delta (x)= |(x,a,a),(b,x,a),(b,b,x)|, then

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  17. If f(x)=ax^2+bx+c,a,b,cepsilonR and the equation f(x)-x=0 has imaginar...

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  18. Let g(x)|f(x+c)f(x+2c)f(x+3c)f(c)f(2c)f(3c)f^(prime)(c)f^(prime)(2c)f^...

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

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