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Show that |{:(1+a,1,1),(1,1+b,1),(1,1,1+...

Show that `|{:(1+a,1,1),(1,1+b,1),(1,1,1+c):}|=abc(1+(1)/(a)+(1)/(b)+(1)/(c)),(abcne0)`.

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Show that {:|( 1+a,1,1),( 1,1+b,1) ,( 1,1,1+c) |:}= abc ( 1+(1)/(a) +(1)/(b) +(1)/(c) ) = abc +bc +ca +ab

|{:(1,a,b+c),(1,b,c+a),(1,c,a+b):}|=0

|{:(b+c,a,1),(c+a,b,1),(a+b,c,1):}|=0

Answer the foll. Question : 2.show that |[1+a,1,1],[1,1+b,1],[1,1,1+c]| = abc(1+1/a+1/b+1/c) , (abc != 0)

|{:(-1,b,c),(a,-1,c),(a,b,-1):}|=(a+1)(b+1)(c+1)((a)/(a+1)+(b)/(b+1)+(c)/(c+1)-1)

The value of the determinant |(1+a,1,1),(1,1+b,1),(1,1,1+c)| is -

prove that : |{:(1,a,b),(-a,1,c),(-b,-c,1):}|=1+a^2+b^2+c^2

|{:(a-b,1,a),(b-c,1,b),(c-a,1,c):}|=|{:(a,1,b),(b,1,c),(c,1,a):}|

Show that |[-1,b,c],[a,-1,c],[a,b,-1]|=(a+1)(b+1)(c+1)(a/(a+1)+b/(b+1)+c/(c+1)-1)

|{:(1,a,bc),(1,b,ca),(1,c,ab):}|=|{:(1,a,a^2),(1,b,b^2),(1,c,c^2):}|

CHHAYA PUBLICATION-QUESTIONS PAPER -2019-WBJEE 2019
  1. Show that |{:(1+a,1,1),(1,1+b,1),(1,1,1+c):}|=abc(1+(1)/(a)+(1)/(b)+(1...

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  2. lim(xto0+)(x^n lnx),ngt0

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  3. If intcosxlog(tan""(x)/(2))=sinxlog(tan""(x)/(2))+f(x) then f(x) is eq...

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  4. y=intcos{2tan^(-1)sqrt((1-x)/(1+x))}dx is a equation of a family of

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  5. The value of integration int(-(pi)/(4))^((pi)/(4))(lambda|sinx|+(musin...

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  6. The value of lim(xto0)(1)/(x)[inty^ae^(sin^2t)dt-int(x+y)^ae^(sin^2t)d...

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  7. If int2^(2^x)*2^xdx=A*2^(2^x)+c, then A=

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  8. The value of the integral int(-1)^(1){(x^(2015))/(x^2+cosx)}dx is equa...

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  9. lim(ntooo)(3)/(n){1+sqrt((n)/(n+3))+sqrt((n)/(n+6))+sqrt((n)/(n+9))+.....

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  10. The general solution of the differential equation (1+e^((x)/(y)))dx+(1...

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  11. General solution of (x+y)^2(dy)/(dx)=a^2,ane0 is

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  12. Let P(4,3) be a point on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1. If t...

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  13. If the radius of a spherical balloon increases by 0.1%, then its volum...

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  14. Let A be a square matrix of order 3 whose all entries are 1 and let I3...

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  15. If M is any square matrix of order 3 over R and if M' be the transpose...

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  16. If A=({:(5,5x,x),(0,x,5x),(0,0,5):}) and |A^2|=25, then |x| is equal t...

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  17. Let A and B be two square matrices of order 3 and AB=O3, wher O3 denot...

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  18. Let: RtoR be defined by f(x)=x^2-(x^2)/(1+x^2) for all x inR. Then

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  19. Let the relation p be defined on R as apb iff 1+abgt0. Then

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  20. A problem in mathematics is given to 4 students whose chances of solvi...

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  21. If X is a random variable such that sigma(X)=2.6," then "sigma(1-4X) i...

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