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The system of linear equations x + lam...

The system of linear equations
`x + lambda y-z =0, lambdax-y -z =0, x + y -lambda z =0`
has a non-trivial solution for

A

exactly two values of `lambda`.

B

exactly three values of `lambda`

C

infinitely many values of `lambda`

D

exactly one values of `lambda`

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The correct Answer is:
B
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DISHA PUBLICATION-DETERMINANTS-EXERCISE -2 CONCEPT APPLICATOR
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  3. If a(n)=(1)/(n+1)+1 then find the vaue of a(1)+a(3)+a(5)

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  4. If [] denotes the greatest integer less than or equal to the real numb...

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  5. Prove that |{:(x^(2),,x^(2)-(y-z)^(2),,yz),(y^(2),,y^(2)-(z-x)^(2),,zx...

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  6. If a , b , c are non-zero, then the system of equations (alpha+a)x+alp...

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  7. If m is a positive integer and Dr=|2r-1\ ^m Cr1m^2-1 2^m m+1s in^2(...

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  8. If x,y and z are the integers in AP lying between 1 and 9 and x 51, ...

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  9. If omega is a non-real cube root of unity, then Delta = |(a(1) + b(1) ...

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  10. prove that |{:((a-x)^(2),,(a-y)^(2),,(a-z)^(2)),((b-x)^(2),,(b-y)^(2),...

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  11. Evaluate |{:(.^(x)C(1),,.^(x)C(2),,.^(x)C(3)),(.^(y)C(1),,.^(y)C(2),,....

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  12. If |{:(x^(n),x^(x+2),x^(2n)),(1,x^(a),a),(x^(n+5),x^(a+6),x^(2n+5)):}|...

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  13. The value of the determinant |{:(1^(2),2^(2),3^(2),4^(2)),(2^(2),3^(2)...

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  14. The value of the determinant |{:(1 ,(5^(2x)-5^(-2x))^(2),(5^(2x)-5^(-2...

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  15. If a^(2)+b^(2)+c^(2)=-2 and |{:(1+a^(2)x,(1+b^(2))x,(1+c^(2))x),((...

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  16. If A1B1C1 , A2B2C2 and A3B3C3 are three digit numbers, each of which ...

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  17. If Sr = alpha^r + beta^r + gamma^r then show that |[S0,S1,S2],[S1,S2,S...

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  18. If f(x) = |{:(cos^(2)x, cosx.sinx, -sin x),(cos x sinx ,sin^(2)x ,cos ...

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  19. the value of the determinant |{:((a(1)-b(1))^(2),,(a(1)-b(2))^(2),,...

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  20. f'(x) = |{:(cos x , x , 1),(2sin x,x^(2),2x),(tan x, x,1):}| . The val...

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  21. If the matrix A = [{:(y+a,b,c),(a,y+b,c),(a,b,y+c):}] has rank 3, then

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