Value of `|1+x_1 1+x_1x1+x_1x^2 1+x_2 1+x_2x1+x_2x^2 1+x_3 1+x_3x1+x_3x^2|` depends upon `"xo n l y"` b. `"x"_1"o n l y"` c. `"x"_2on l y` d. none of these

Value of |{:(1+x_(1),1+x_(1)x,1+x_(1)x^(2)),(1+x_(2),1+x_(2)x,1+x_(2)x^(2)),(1+x_(3),1+x_(3)x,1+x_(3)x^(2)):}| depends upon

Value of |{:(1+x_(1),,1+x_(1)x,,1+x_(1)x^(2)),(1+x_(2),,1+x_(2)x,,1+x_(2)x^(2)),(1+x_(3),,1+x_(3)x,,1+x_(3)x^(2)):}| depends upon

|(2x_1y_1, x_1y_2+x_2y_1, x_1y_3+x_3y_1),(x_1y_2+x_2y_1, 2x_2y_2, x_2y_3+x_3y_2),(x_1y_3+x_3y_1, x_2y_3+x_3y_2, 2x_3y_3)|= (A) 0 (B) 1 (C) -1 (D) none of these

If |[ x y 1 1 ]|=2 and |[ x 3 y 2 ]|=1 then

y=|(x^2+x, x+1, x-2),(2x^2+3x+1, 3x, 3x-3),(x^2+3x+2, 2x-1, 2x-1)| represents (A) a straight line (B) a circle (C) a parabola (D) none of these

If (x_1-x_2)^2+(y_1-y_2)^2=a^2, (x_2-x_3)^2+(y_2-y_3)^2=b^2, (x_3-x_1)^2+(y_3-y_1)^2=c^2, and k|[x_1,y_1, 1],[x_2,y_2, 1],[x_3,y_3, 1]|=(a+b+c)(b+c-b)(c+a-b)xx(a+b-c) , then the value of k is 1 b. 2 c. 4 d. none of these

x^((x-1)- 1/2 (x-1)^2+1/3((x-1)^3).- 1/4((x-1)^4).+…….. is equal to (A) 2logx (B) logx (C) x^2 (D) none of these

If x_1 x_2 x_3 = 4(4 + x_1 + x_2 + x_3 ) , then what is the value of [1//(2 + x_1 )] + [1//(2 + x_2 )] + [1//(2 + x_3 )] ?

The value of (1-x^4)/(1+x)+(1+x^2)/xxx1/(x(1-x)) is (a) 1 (b) 1-x^2 (c) 1/x (d) 1+x (e) None of these

The value of |(a_(1) x_(1) + b_(1) y_(1),a_(1) x_(2) + b_(1) y_(2),a_(1) x_(3) + b_(1) y_(3)),(a_(2) x_(1) +b_(2) y_(1),a_(2) x_(2) + b_(2) y_(2),a_(2) x_(3) + b_(2) y_(3)),(a_(3) x_(1) + b_(3) y_(1),a_(3) x_(2) + b_(3) y_(2),a_(3) x_(3) + b_(3) y_(3))| , is