Determinants Te...

If the lines $$p_{1}x+q_{1}y=1,p_{2}x+q_{2}y=1 $$ and $$ p_{3}x+q_{3}y=1$$ be concurrent, then the points $$(p_{1},q_{1}),(p_{2},q_{2})$$ and $$(p_{3},q_{3})$$ ,

If the lines $${x}+{a}{y}+{a}=0,\ {b}{x}+{y}+{b}=0,\ {c}{x}+{c}{y}+1 =0 ({a}\neq{b}\neq {c}\neq1)\ $$ are concurrent, then the value of $$\displaystyle \frac{{a}}{{a}-1}+\frac{{b}}{{b}-1}+\frac{{c}}{{c}-1}$$, is

If $$x_1, x_2, x_3$$ as well as $$y_1, y_2, y_3$$ are in G.P. with same common ratio, then the points $$P(x_1, y_1), Q (x_2, y_2)$$ and $$R(x_3, y_3)$$

The values of $$|A^{50}|$$ equals

The value of $$|\cup|$$ equals

If A is a square matrix of order 3, then $$|(A - A^T)^{105}|$$ is equal to

Let $$ \begin{vmatrix}
 1+x         &                 x        &                x^{2}\\
   x           &               1+x   &                       x^{2} \\
  x^{2}        &                x       &                1+x
\end{vmatrix} =   ax^{5} + bx^{4} + cx^{3} + dx^{2} + \lambda x + \mu $$ be an identity in x, where a,b,c,d,$$ \lambda, \mu$$ are independent of x. Then the value of $$\lambda$$ is

The value of |B| is equal to

If the points $$\displaystyle(-2,0),(-1,\dfrac{1}{\sqrt{3}})$$ and $$\displaystyle(\cos\theta,\sin \theta)$$ are collinear, then the number of values of $$\displaystyle \theta \in [0,2\pi]$$ :

Let $$\begin{vmatrix} x& 2 & x\\ x^2 & x & 6\\ x & x & 6\end{vmatrix}  = \alpha x^4 + \beta x^3 + \gamma x^2 + \delta x + \lambda$$ then the value of $$5 \alpha + 4 \beta + 3\gamma + 2 \delta + \lambda = $$