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If Delta = |(cos (alpha(1) - beta(1)),co...

If `Delta = |(cos (alpha_(1) - beta_(1)),cos (alpha_(1) - beta_(2)),cos (alpha_(1) - beta_(3))),(cos (alpha_(2) - beta_(1)),cos (alpha_(2) - beta_(2)),cos (alpha_(2) - beta_(3))),(cos (alpha_(3) - beta_(1)),cos (alpha_(3) - beta_(2)),cos (alpha_(3) - beta_(3)))|" then " Delta` equals

A

`cos alpha_(1) cos alpha_(2) cos alpha_(3) cos beta_(1) cos beta_(2) cos beta_(3)`

B

`cos alpha_(1) + cos alpha_(2) + cos alpha_(3) + cos beta_(1) + cos beta_(2) + cos beta_(3)`

C

`cos (alpha_(1) - beta_(1)) cos (alpha_(2) - beta_(2)) cos (alpha_(3) - beta_(3))`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
D
We have, `Delta = |("cos" alpha_(1),"sin" alpha_(1),0),("cos" alpha_(2),"sin" alpha_(2),0),("cos" alpha_(3),"sin" alpha_(3),0)||("cos" beta_(1),"sin "beta_(1),0),("cos" beta_(2),"sin" beta_(2),0),("cos"beta_(3),"sin "beta_(3),0)|`
`rArr Delta = 0 xx 0 = 0`
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OBJECTIVE RD SHARMA-DETERMINANTS-Section I - Solved Mcqs
  1. If Delta = |(cos alpha,- sin alpha,1),(sin alpha,cos alpha,1),(cos (al...

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  2. Let D(r) = |(a,2^(r),2^(16) -1),(b,3(4^(r)),2(14^(16) -1)),(c,7(8^(r))...

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  3. If Delta = |(cos (alpha(1) - beta(1)),cos (alpha(1) - beta(2)),cos (al...

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  4. The determinant |(y^(2),-xy,x^(2)),(a,b,c),(a',b',c')| is equal to

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  5. If |[p,q-y,r-z],[p-x,q,r-z],[p-x,q-y,r]|=0 find the value of p/x+q/y+r...

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  6. The number of distinct real roots of |(sinx, cosx, cosx),(cos x,sin x,...

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  7. The value of a for which system of equation , a^3x+(a+1)^3y+(a+2)^3z=0...

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  8. Let A = [(1,sin theta,1),(- sin theta,1,sin theta),(-1,-sin theta,1)],...

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  9. Let |(x,2,x),(x^(2),x,6),(x,x,6)| = ax^(4) + bx^(3) + cx^(2) + dx + e ...

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  10. If Delta(1) = |(1,1,1),(a,b,c),(a^(2),b^(2),c^(2))|, Delta(2) = |(1,bc...

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  11. If Dk=|1nn2k n^2+n+2n^2+n2k-1n^2n^2+n+2|a n d sum(k=1)^n Dk=48 ,t h e...

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  12. Let |(1 +x,x,x^(2)),(x,1 +x,x^(2)),(x^(2),x,1 +x)| = ax^(5) + bx^(4) +...

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  13. If A = int(1)^(sintheta) (t)/(1 + r^(2)) dt and B = int(1)^("cosec"the...

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  14. If I(n) = |(1,k,k),(2n,k^(2) + k + 1,k^(2) + k),(2n -1,k^(2) ,k^(2) + ...

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  15. If x is a positive integer, then |(x!,(x +1)!,(x +2)!),((x +1)!,(x +2)...

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  16. If f(x) = |(x + lamda,x,x),(x,x + lamda,x),(x,x,x + lamda)|, " then " ...

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  17. The value of the determinant |(bc,ca,ab),(p,q,r),(1,1,1)|, where a, b ...

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

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  19. If a , b , c are distinct, then the value of x satisfying |0x^2-a x^3-...

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  20. If the determinant |a b2aalpha+3bb c2balpha+3c2aalpha+3b2balpha+3c0|=0...

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