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If x in R and n in I then the determinan...

If `x in R` and `n in I` then the determinant `Delta= |[sin(npi), sinx-cosx, logtanx] , [cosx-sinx, cos{(2n+1)pi/2}, log cotx] , [logcotx, logtanx, tan(npi)]|=`

A

0

B

`log tan x-lot cot x`

C

`tan(pi//4-x)`

D

None of these

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The correct Answer is:
A
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MCGROW HILL PUBLICATION-DETERMINANTS-SOLVED EXAMPLES (LEVEL 1 SINGLE CORRECT ANSWER TYPE QUESTIONS)
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  2. Delta(1)=|{:(x,b,b),(a,x,b),(a,a,x):}| and Delta(2)=|{:(x,b),(a,x):}| ...

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  5. 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-...

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  6. If Delta(x)=|(1,1,1),((e^(x)+e^(-x))^(2),(pi^(x)+pi^(-x))^(2),2),((e^(...

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  7. If Delta (x)=|{:(1,cos x,1-cos x),(1+sin x,cos x,1+sinx-cosx),(sinx,si...

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  8. The determinant Delta=|{:(a,b,aalpha+c),(b,c,balpha+c),(aalpha+b,balph...

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  9. Prove that all values of theta: |(sintheta, costheta, sin2theta),(sin(...

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  10. If alpha, beta. gamma are the roots of x^3 + px^2 + q = 0, where q=0, ...

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  11. If A,B and C are angles of a triangle then the determinant |(-1,cosC...

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  12. If a^(2) + b^(2) + c^(2) = 0 and |(b^(2) + c^(2) ,ab,ac),(ab,c^(2) + a...

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  13. If theta, phi epsilon R, then the determinant Delta=|(cos theta, - s...

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  14. If Delta(1)=|(b+c,a-b,a),(c+a,b-c,b),(a+b,c-a,c)| and Delta(2)=|(a,b,c...

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  15. If x ,y ,z are different from zero and "Delta"=a b-y c-z a-x b c-z a-x...

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  16. If p + q + r = a + b + c = 0, then the determinant |{:(pa,qb,rc),(qc,r...

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  17. The number of real values of lambda for which the system of equations ...

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  18. The values of k for which the system of equations x+ky-3z=0……..1 3...

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  19. If the system of equations x+a y=0,a z+y=0,a n da x+z=0 has infinite s...

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  20. Given , 2x-y+2z=2, x-2y+z=-4, x+y+lambdaz=4, then the value of lam...

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