If ai, bi in N for i 1,2,3, then coeffic...

If `a_i, b_i in N` for i 1,2,3, then coefficient of x in the determinant;`|((1+x)^(a_1b_1),(1+x)^(a_1b_2),(1+x)^(a_1b_3)),((1+x)^(a_2b_1),(1+x)^(a_2b_2),(1+x)^(a_2b_3)), ((1+x)^(a_3b_1),(1+x)^(a_3b_2),(1+x)^(a_3b_3))|`

`overset(3)underset(i=1)suma_1b_1`

none of these

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

DETERMINANT
FIITJEE|Exercise ASSIGNMENT PROBLEMS (OBJECTIVE) Level -II|19 Videos
DETERMINANT
FIITJEE|Exercise COMPREHENSIONS -I|3 Videos
DETERMINANT
FIITJEE|Exercise ASSIGNMENT PROBLEMS (SUBJECTIVE) Level -II|12 Videos
DEFINITE INTEGRAL
FIITJEE|Exercise NUMERICAL BASED|3 Videos
ELLIPSE
FIITJEE|Exercise NUMERICAL BASED|4 Videos

Similar Questions

Explore conceptually related problems

Find the coefficient of x in the determinant |((1+x)^(a_1 b_1),(1+x)^(a_1 b_2),(1+x)^(a_1 b_3)),((1+x)^(a_2 b_2),(1+x)^(a_2 b_2),(1+x)^(a_2 b_3)),((1+x)^(a_3 b_3),(1+x)^(a_3 b_2),(1+x)^(a_3 b_3))|=0.

If f(x)=det[[(1+x)^(a),(1+2x)^(b),11,(1+x)^(a),(1+2x)^(b)(1+2x)^(b),1,(1+x)^(a)(1+2x)^(b),1,(1+x)^(a) term and coefficient of x]]

If f(x)= |{:((1+x)^(a),(1+2x)^(b),1),(1,(1+x)^(a),(1+2x)^(b)),((1+2x)^(b),1,(1+x)^(a)):}|, a,b being positive integers then

Prove that if alpha, beta, gamma !=0 then |(alpha+a_1b_1, a_1b_2, a_1b_3), (a_2b_1, beta+a_2b_2, a_2b_3), (a_3b_1, a_3b_2, gamma+a_3b_3)|=alpha beta gamma [1+(a_1b_1)/alpha + (a_2b_2)/beta+(a_3b_3)/gamma]

Show that if x_(1),x_(2),x_(3) ne 0 |{:(x_(1) +a_(1)b_(1),,a_(1)b_(2),,a_(1)b_(3)),(a_(2)b_(1),,x_(2)+a_(2)b_(2),,a_(2)b_(3)),(a_(3)b_(1),,a_(3)b_(2),,x_(3)+a_(3)b_(3)):}| =x_(1)x_(2)x_(3) (1+(a_(1)b_(1))/(x_(1))+(a_(2)b_(2))/(x_(2))+(a_(3)b_(3))/(x_(3)))

(3x^(2)-8x+9)/((x+1)^(3))=(a)/(x+1)+(b)/((x+1)^(2))+(c)/((x+1)^(3)), then a+b+c=

Show that if x_1, x_2, x_3!=0 |x_1+a_1b1a_1b_2a_1b_3a_2b_1x_2+a_2b_2a_2b_3a_3b_1a_3b_2x_3+a_3b_3|=x_1x_2x_3(1+(a_1b_1)/(x_1)+(a_2b_2)/(x_2)+(a_3b_3)/(x_3)) .

(b) If (x^(2)+1)/(x)=3(1)/(3) and x>1 ; find x^(3)-(1)/(x^(3))

FIITJEE-DETERMINANT-ASSIGNMENT PROBLEMS (OBJECTIVE) LEVEL-I

If f(x)=|{:(cos(x+alpha),cos(x+beta),cos(x+gamma)),(sin(x+alpha),sin(x...
Text Solution
|
The value of f(pi/6) where f(theta)=|{:(cos^2theta,costhetasintheta,-s...
Text Solution
|
The system of equation 102x-95y+88z=81,3x+10y+17z=24, 57x+50y+43z=36 h...
Text Solution
|
IF ax^3+bx^2+cx+d=|(x^2,(x-1)^2, (x-2)^2),((x-1)^2 (x-2)^2, (x-3)^2), ...
Text Solution
|
In a Delta ABC |[1,1,1],[1+sinA,1+sinB,1+sinC][sinA+sin^2A,sinB+sin^2B...
Text Solution
|
If a,b,c are sides of a triangle and |(a^(2),b^(2),c^(2)),((a+1)^(2),(...
Text Solution
|
The value of |(.^(10)C(4).^(10)C(5).^(11)C(m)),(.^(11)C(6).^(11)C(7).^...
Text Solution
|
If D=|{:(2,1,[sin^2theta]),([sin^2theta],costheta,i),(i,1,sintheta):}|...
Text Solution
|
If alpha is a root of x^4 = 1 with negative principal argument then th...
Text Solution
|
If Delta(x)=|((e^x,sin2x,tanx^2)),((In(1+x),cosx,sinx)),((cosx^2,e^x-1...
Text Solution
|
Let x1y1z1,x2y2z2 and x3y3z3 be three 3-digit even numbers and Delta=|...
Text Solution
|
If alpha, beta, gamma are the roots of x^(3) + ax^(2) + b = 0, then th...
Text Solution
|
The product of all values of t , for which the system of equations (a-...
Text Solution
|
Let a,b,c , in R not all are equal and Delta(1)= |{:(a,,b,,c),(b,,c,...
Text Solution
|
The value of a for which system of equation , a^3x+(a+1)^3y+(a+2)^3z=0...
Text Solution
|
If Delta (x)=|{:(x,1+x^(2),x^(3)),(log(1+x^(2)),e^(x),sinx),(cosx,tanx...
Text Solution
|
If ai, bi in N for i 1,2,3, then coefficient of x in the determinant;|...
Text Solution
|
Statement 1: The product of two diagonal matrices of order 3 is also ...
Text Solution
|
Statement -1 : If Delta(x)=|{:(f1(x),f2(x),f3(x)),(a2,b2,c2),(a3,b3,c3...
Text Solution
|
Consider the system of equations x-2y+3z=-1 -x+y-2z=k x-3y+4z=1 ...
Text Solution
|