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Solve the following : [[x+1,omega,omega^...

Solve the following : `[[x+1,omega,omega^2],[omega,x+omega^2,1],[omega^2,1,x+omega]]`=0

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Evaluate the following determinants. [[1,omega,omega^2],[omega,omega^2,1],[omega^2,1,omega]]

if omega be the cube root of unit then what is the value of |[1,omega ,omega^2],[omega, omega^2,1],[omega^2,1,omega ]| ?

Fill in the blanks with appropriate answer from the bracket. [[1,omega,omega^2],[omega,omega^2,1],[omega^2,1,omega]] =_________

If omega is a complex cube root of 1,then for what value of. lamda the determinant |[1,omega,omega^(2)],[omega,lamda,1],[omega^(2),1,omega]|=0 ?

(1-omega +omega^2)(1+omega-omega^2)=4

Evaluate the following determinants. [[1,omega],[-omega,omega]]

IF omega is cube root of unity, then |{:(1,omega,omega^2),(omega,omega^2,1),(omega^2,1,omega):}| = ………. (1,0,omega, omega^2)

Evaluate |(1, omega, omega^(2)),(omega, omega^(2),1),(omega^(2),1,omega)| , where omega is a cube root of unity.

ARIHANT PRAKASHAN-EXAMINATION PAPER 2019-Group-B
  1. Let R be the relation on the set R of real numbers such that aRb iff a...

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  2. Solve for x, 2 tan ^(-1)(cos x) =tan^(-1) (2"cosec"x).

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  3. Find the probability distribution of number of heads in three tosses...

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  4. If A=[{:(1,2,0),(0,1,3),(-2,5,3):}] then verify that A+A is symmetric ...

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  5. If A=[{:(1,2,3),(3,-2,1),(4,2,1):}] then show that A^(3)-23A-40I=O

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  6. Solve the following : [[x+1,omega,omega^2],[omega,x+omega^2,1],[omega^...

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  7. A person takes 4 tests in succession. The probability of his passing t...

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  8. Find the point on the curve x^(2) + y^(2)- 4xy + 2= 0, where the norma...

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  9. Find the intervals in which the function y=(lnx)/(x) is increasing and...

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  10. If y=e^(x^(e^(x^(e^x)))), then find dy/dx.

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  11. Find (d^2y)/(dx^2) if x=a costheta,y=bsintheta.

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  12. Verify Lagrange.s mean value theorem for f(x)= x^(3)- 2x^(2)-x + 3 on ...

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  13. Find differential equation of the curve y=ae^(3x)+be^(5x).

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  14. Obtain the general solution of the following differential equations. (...

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  15. Find the area of the region bounded by the curve y=6x-x^2 and the x-ax...

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  16. If l(1), m(1), n(1) and l(2), m(2), n(2)  are the direction cosines of...

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  17. Find the point where the line (x-2)/1=y/(-1)=(z-1)/2 meets the plane 2...

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  18. Find a unit vector perpendicular to each of the vectors vec(a) + vec(b...

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  19. Prove that (vec a × vec b)^(2) = a^(2)b^(2)-(vec a . vec b)^(2).

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  20. Find the vector equation of a plane which is at a distance of 3 units ...

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