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Without expanding the determinant prove the following. |[1,bc,a(b+c)],[1,ca,b(c+a)],[1,ab,c(a+b)]|=0

Evaluate Delta=|[1, a, bc],[ 1, b, c a],[ 1, c, a b]|

Prove that |[1 , a , a^3],[ 1, b, b^3],[ 1, c, c^3]|=(a-b)(b-c)(c-a)(a+b+c)

Find the value of the determinant |[1, a, b+c],[ 1, b, c+a],[ 1, c, a+b]|

If a, b and c are distinct reals and the determinant |{:(a ^(3) +1, a ^(2) , a ),( b ^(3) +1, b ^(2) , b ),( c ^(3) +1, c ^(2), c):}|= 0, then the product abc is

|(1,a,b+c),(1,b,c+a),(1,c,a+b)| =

Evaluate |[1,1,1],[a,b,c],[b+c,c+a,a+b]|

A=[[0 , 6 , 7 ],[ -6, 0 , 8 ],[ 7, -8, 0]] , B=[[0, 1 ,1],[ 1 , 0 ,2],[ 1 ,2 ,0]] , C=[[2 ],[ -2],[ 3]] Calculate AC , B C and (A+B) C . Also, verify that (A+B) C=A C+B C

If (b + c) (y + z) - ax = b - c, (c + a) (z + x) - by = c - a and (a + b) (x + y) - cz = a - b , where a + b + c ne 0, then x is equal to a) (c + b)/(a + b + c) b) (c - b)/(a + b + c) c) (a - b)/(a + b + c) d) (a + b)/(a + b + c)

A N EXCEL PUBLICATION-PROBABILITY-QUESTION BANK
  1. Find '|vecx|', if for a unit vector 'veca,(vecx-veca) .(vecx+veca)=12'

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  2. If |[x,2],[18,x]| = |[6,2],[18,6]|, then x =

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  3. prove |[1, b c, a(b+c)],[ 1, c a, b(c+a)],[ 1, a b, c(a+b)]|=0

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  4. Principal value of tan^-1sqrt3is ------------

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  5. Write the following functions in the simplest form : tan^(-1) sqrt((...

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  6. Find int(x^2)/(2x^3+1) dx=--------

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  7. Prove that the function f(x)=2x-5 is continuous at x=-2

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  8. If xsqrt(1+y)=sqrtx, prove that dy/dx=-1/(x^2)

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  9. The factor of 3 is

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  10. Solve: x-y+2z=7 3x+4y-5z=-5 2x-y+3z=12

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  11. On Z^+,a*b=2^sqrt(ab), value of 4*9 is--------

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  12. In each of the following cases, states whether the function is one-one...

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  13. If f(x)=2x+3, findf[f(x)].

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  14. The total revenue received from tha sale of x units of a product is R(...

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  15. Find the equation of the normal to the curve x^2=9y which passes throu...

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  16. Consider the lines l1:(x-1)/2=(y-1)/-1=z/1 l2:(x-2)/3=(y-1)/-5=(z+1)/...

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  17. Consider the lines l1:(x-1)/2=(y-1)/-1=z/1 l2:(x-2)/3=(y-1)/-5=(z+1)/...

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  18. The condition for the lines with direction ratio a1,b1,c1 and a2,b2,c2...

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  19. Find the angle between the lines (x+3)/3=(y-1)/5=(z+3)/4 and (x+1)...

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  20. Consider the differential equation dy/(dx)+y=cos(e^x) Write the orde...

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