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If the system of linear equations x1+2x2...

If the system of linear equations `x_1+2x_2+3x_3=6,\ x_1+3x_2+5x_3=9,\ 2x_2+5x_2+a x_3=b` is consistent and has infinite number of solutions, then- `a in R-{8}a n d\ b in R-{15}` `a=8,\ b` can be any real number `a=8,\ b=15` `b=15 ,\ a` can be any real number

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ALLEN -DETERMINANTS-All Questions
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  2. Let a,b,c be such that b(a+c) ne 0. If |{:(a,a+1,a-1),(-b,b+1,b-1)...

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  3. Consider the system of linear equations; x1 +2x2+x3=3 2x1+3x2+x3=3 3x1...

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  4. The number of value of k for which the linear equations 4x+k y+2z=0,k ...

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  5. If the trivial solution is the only solution of the system of equation...

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  6. The number of values of k, for which the system of equations (k""+""...

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  7. If a ,b ,c are sides of a scalene triangle, then value of {:|(a, b, c)...

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  8. If the system of linear equations x1+2x2+3x3=6,\ x1+3x2+5x3=9,\ 2x2+5x...

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  9. Statement 1: The system of linear equations x+(sinalpha)y+(cosalpha)z=...

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  10. Consider the system of equations x+a y=0,\ y+a z=0\,z+a x=0.\ Then th...

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  11. If f(n)=alpha^n+beta^n then show that |{:(3,1+f(1),1+f(2)),(1+f(1),...

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  12. The set of all values of lamda for which the system of linear equation...

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  13. The system of linear equations x+lambday-z=0 lambdax-y-z=0 x+y-lambd...

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  14. The number of distinct real roots of the equation |cosx s in x s in x ...

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  15. Test the consistency and solve them when consistent the following s...

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  16. If a,b,c are real numbers such that 3(a^(2)+b^(2)+c^(2)+1)=2(a+b+c+ab...

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  17. The number of values of k for which the system of the equations (k+1)x...

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  18. The value of lambda for which the system of equations 2x-y-2z=2,x-2y +...

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  19. Statement I: cos e s^(-1)(cos e c9/5)=pi-9/5dot Statement II: cos e ...

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  20. The number of all possible values of theta\ w h e r e\ 0<theta<pi,\ f...

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