Home
Class 12
MATHS
" If " Delta(1) =|{:(x,,b,,b),(a,,x,,b)...

`" If " Delta_(1) =|{:(x,,b,,b),(a,,x,,b),(a,,a,,x):}|" and " Delta_(2)= |{:(x,,b),(a,,x):}|` are the given determinants then

A

`Delta_(1)=3(Delta_(2))^(2)`

B

`(d)/(dx)(Delta_(1))=3Delta_(2)`

C

`(d)/(dx)(Delta_(1))=3(Delta_(2))^(2)`

D

`Delta_(1)=3Delta_(2)^(3//2)`

Text Solution

Verified by Experts

The correct Answer is:
B
`(b)` `Delta_(1)=x(x^(2)-ab)-b(ax-ab)+b(a^(2)-ax)`
`=x^(3)-3abx+ab^(2)+a^(2)b`
`:.(d)/(dx)(Delta_(1))=3x^(2)-3ab=3(x^(2)-ab)=3Delta_(2)`
Promotional Banner

Topper's Solved these Questions

  • DETERMINANT

    CENGAGE ENGLISH|Exercise Comprehension|2 Videos

  • DETERMINANT

    CENGAGE ENGLISH|Exercise Multiple Correct Answer|5 Videos

  • DEFINITE INTEGRATION

    CENGAGE ENGLISH|Exercise JEE ADVANCED|38 Videos

  • DETERMINANTS

    CENGAGE ENGLISH|Exercise All Questions|264 Videos

Similar Questions

Explore conceptually related problems

" if " Delta = |{:(-x,,a,,b),(b,,-x,,a),(a,,b,,-x):}|" then a factor of " Delta " is "

If Delta_(1)=|{:(Ax,x^(2),1),(By,y^(2),1),(Cz,z^(2),1):}|" and "Delta_(2)=|{:(A,B,C),(x,y,z),(yz,zx,xy):}| , then

If a, b gt 0 and Delta (x)= |(x,a,a),(b,x,a),(b,b,x)| , then

if a+b+c=0 then Delta=|{:(a-x,c,b),(c,b-x,a),(b,a,c-x):}|=0 is

If "Delta"_1=|x bb a x b a a x|a n d"Delta"_2=|x b a x| are the given determinants, then "Delta"_1=3("Delta"_2)^2 b. d/(dx)("Delta"_1)=3"Delta"_2 c. d/(dx)("Delta"_1)=3("Delta"_2)^2 d. "Delta"_1=3"Delta"2 3//2

If Delta(x)=|{:(a,b,c),(6,4,3),(x,x^(2),x^(3)):}| then find int_(0)^(1) Delta (x) dx.

If x^a y^b=e^m , x^c y^d=e^n ,Delta_1=|(m,b),(n,d)|,and Delta_2 =|(a,m),(c,n)| and Delta_3=|(a,b),(c,d)|, then the values of x and y are

Delta = |(a +x,b,c),(b,x +c,a),(c,a,x +b)| . Which of the following is a factor for the above determinant ?

Let Delta(x)=|(x+a,x+b,x+a-c),(x+b,x+c,x-1),(x+c,x+d,x-b+d)| and int_0^2 Delta(x)dx=-16, where a,b,c,d are in A.P. then the common difference (i) 1 (ii) 2 (iii) 3 (iv) 4

if Delta (x)= |{:(a_(1)+x,,b_(1)+x,,c_(1)+x),(a_(2)+x,,b_(2)+x,,c_(2)+x),(a_(3)+x,,b_(3)+x,,c_(3)+x):}| then show that Delta (x)=0 and that Delta (x)=Delta(0)+sx. where s denotes the sum of all the cofactors of all the elements in Delta (0)