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What is the value of the following deter...

What is the value of the following determinant? `Delta=|[4,a, b+c],[4,b, c+a],[4,c, a+b]|`

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If a+b+c=4 and ab+bc+ca=0 , then what is the value of the following determinant? |(a, b, c),(b, c, a),(c, a, b)|

If a,b,c are unequal then what is the condition that the value of the following determinant is zero Delta =|(a,a^2,a^3+1),(b,b^2,b^3+1),(c,c^2,c^3+1)|

What is the value of the determinant |(a-b,b+c,a),(b-c,c+a,b),(c-a,a+b,c)| ?

What is the value of the determinant |{:(a-b,b+c,a),(b-c,c+a,b),(c-a,a+b,c):}| ?

If a,b,c are positive and unequal,show that value of the determinant Delta=det[[b,b,cb,c,ac,a,b]]

If a, b, c are positive and unequal, show that value of the determinant Delta=|(a,b,c),(b,c,a),(c,a,b)| is negative

|[b+c, a,a] , [b,c+a,b] , [c,c,a+b]|=4abc

Using properties of determinants, show that |(b+a,a,a),(b,c+a,b),(c,c,a+b)|=4abc

XII BOARDS PREVIOUS YEAR-BOARD PAPER SOLUTIONS-All Questions
  1. For what value of p , is ( hat i+ hat j+ hat k)p a unit vector?

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  2. Find | vec x| , if for a unit vector vec a ,\ ( vec x-\ vec a)dot( v...

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  3. What is the value of the following determinant? Delta=|[4,a, b+c],[4...

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  4. What is the domain of the function sin^(-1)x ?

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  5. If 'f' is an invertible function, defined as f(x)=(3x-4)/5, write f...

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  6. Write a square matrix of order 2, which is both symmetric and skew ...

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  7. Find the direction cosines of the line passing through the followin...

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  8. If A=[[1, 2],[ 4, 2]], then find the value of k if |2A|=k\ |A|

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  9. If | vec a|=sqrt(3)\ | vec b|=2\ \ and vec a.vec b=sqrt(3,)\ find t...

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  10. A pair of dice is thrown 4 times. If getting a doublet is considere...

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  11. Evaluate: int0^1 1/(1+x^2)\ dx

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  12. Write the principal value of cos^(-1)(1/2)-2sin^(-1)(-1/2)

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  13. Simplify : cos theta[[costheta,si ntheta],[-si ntheta,costheta]]+si nt...

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  14. Evaluate int1^4(x^2-\ x)\ dx as a limit of sums.

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  15. If Delta=|[5, 3 ,8],[ 2, 0 ,1],[ 1 ,2 ,3]| , write the minor of the el...

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  16. Evaluate : int(1-x)sqrt(x)\ dxdot

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  17. Evaluate: int0^(pi/4)(sinx+cosx)/(9+16sin2x)dx

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  18. Find lambda where projection of vec (a) = lambda hat (i) + hat (j) ...

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  19. If a line has direction ratios 2, –1, –2, then what are its directi...

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  20. Write the vector equation of the line given by (x-5)/3=(y+4)/7=(z-6...

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