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The determinant |(a^(2)+10,ab, ac),(ab...

The determinant
`|(a^(2)+10,ab, ac),(ab, b^(2)+10, bc),(ac, bc, c^(2)+10)|` is

A

divisible by 10 but not by 100

B

divisible by 100

C

not divisible by 100

D

not divisible by 10

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Without expanding the determinant, prove that {:|( a, a ^(2), bc ),( b ,b ^(2) , ca),( c, c ^(2) , ab ) |:} ={:|( 1, a^(2) , a^(3) ),( 1,b^(2) , b^(3) ),( 1, c^(2),c^(3)) |:}

Show that, |{:(a^2+10,ab,ac),(ab,b^2+10,bc),(ca,bc,c^2+10):}| is divisible by 100 .

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

Prove that {:|( a^(2) , bc, ac+c^(2)),( a^(2) +ab,b^(2) ,ac),( ab,b^(2) +bc,c^(2)) |:} =4a^(2) b^(2) c^(2)

"If "f(x)=|{:(x+a^(2),ab,ac),(ab, x+b^(2),bc),(ac,bc, x+c^(2)):}|," then prove that " f'(x)=3x^(2)+2x(a^(2)+b^(2)+c^(2)) .

If A=[{:(0,c,-b),(-c,0,a),(b,-a,0):}] and B=[{:(a^(2),ab,ac),(ab,b^(2),bc),(ac,bc,c^(2)):}] , then (A+B)^(2)= (a) A (b) B (c) I (d) A^(2)+B^(2)

WB JEE PREVIOUS YEAR PAPER-QUESTION PAPER 2021-MULTIPLE CHOICE QUESTION
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  2. If a(vecalpha xx vecbeta) + b(vecbeta xx vecgamma) +c(vecgamma xx veca...

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  3. If the tangent at the point P with co-ordinates (h, k) on the curve y^...

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  4. The co-efficient of a^(3)b^(4)c^(5) in the expansion of (bc+ca+ab)^(6)...

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  5. Three unequal positive numbers a, b, c are such that a, b, c are in G....

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  6. The determinant |(a^(2)+10,ab, ac),(ab, b^(2)+10, bc),(ac, bc, c^(2)...

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  7. Let R be the real line. Let the relations S and T on R be defined by ...

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  8. The plane lx + my = 0 is rotated about its line of intersection with t...

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  9. The points of intersection of two ellipses x^(2)+2y^(2) -6x-12y+20=0 a...

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  10. Let I= int(pi//4)^(pi//3) (sinx)/(x)dx. Then

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  11. If |z+i|-|z-1|=|z|-2=0 for a complex number z, then z =

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  12. |(x, 3x+2,2x-1),(2x-1,4x,3x+1),(7x-2,17x+6,12x-1)|=0 is true for

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  13. The remainder when 7^(7^(7^(...^(7))))(22 times 7) is divided by 48 is

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  14. int dx/((2+x)sqrt(1+x) =

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  15. A plane meets the co-ordinate axes at the points A, B, C respectively ...

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  16. Let P be a variable point on a circle C and Q be a fixed point outside...

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  17. underset(nrarrinfty)lim (sqrt1+sqrt2+.......+sqrt(n-1))/(nsqrtn) = ?

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  18. Let f(x)={(0", if"-1 le x lt 0),(1", if "x =0),(2", if "0 lt x le1):} ...

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  19. The greatest and least values of f(x)=tan^(-1)x -(1)/(2) ln x on [(1)...

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  20. Let f and g be periodic functions with the periods T(1) and T(2) respe...

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