| , * 20 c 1/a &1& bc 1/b &1& ca 1/c &1& ab , | = - Vidyadip

MCQ

$\left| {\,\begin{array}{*{20}{c}}{1/a}&1&{bc}\\{1/b}&1&{ca}\\{1/c}&1&{ab}\end{array}\,} \right| = $

✓
$0$
B
$abc$
C
$1/abc$
D
None of these

✓

Answer

Correct option: A.

$0$

a
(a) $\Delta = \frac{1}{a}[ab - ca] + 1\left[ {ca.\frac{1}{c} - \frac{1}{b}.ab} \right] + bc\left[ {\frac{1}{b} - \frac{1}{c}} \right]$

==>$\Delta = (b - c) + 1(a - a) + (c - b)$

==> $\Delta = 0$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Let $\mathrm{p}$ and $\mathrm{q}$ be real numbers such that $\mathrm{p} \neq 0, \mathrm{p}^3 \neq \mathrm{q}$ and $\mathrm{p}^3 \neq-\mathrm{q}$. If $\alpha$ and $\beta$ are nonzero complex numbers satisfying $\alpha+\beta=-\mathrm{p}$ and $\alpha^3+\beta^3=\mathrm{q}$, then a quadratic equation having $\frac{\alpha}{\beta}$ and $\frac{\beta}{\alpha}$ as its roots is

The projection of the line segment joining the points $(1,-1,3)$ and $(2,-4,11)$ on the line joining the points $(-1,2,3)$ and $(3,-2,10)$ is

Area of the triangle formed by the lines $x -y = 0, x + y = 0$ and any tangent to the hyperbola $x^2 -y^2 = a^2$ is :-

Three concentric circles of which the biggest is $x^2 + y^2 = 1$, have their radii in $A.P.$ If the line $y = x + 1$ cuts all the circles in real and distinct points. The interval in which the common difference of the $A.P.$ will lie is

An ellipse is described by using an endless string which is passed over two pins. If the axes are $6\ cm$ and $4\ cm$, the necessary length of the string and the distance between the pins respectively in $cm$, are

If the geometric mean between $a$ and $b$ is $\frac{{{a^{n + 1}} + {b^{n + 1}}}}{{{a^n} + {b^n}}}$, then the value of $n$ is

If $\frac{1}{{p + q}},\;\frac{1}{{r + p}},\;\frac{1}{{q + r}}$ are in $A.P.$, then

If $\int_0^{{t^2}} {xf(x)dx = } \frac{2}{5}{t^5},\,\,t > 0,$ then $f\left( {\frac{4}{{25}}} \right) = $

A closed conical vessel is filled with water fully and is placed with its vertex down. The water is let out at a constant speed. After $21\,min$, it was found that the height of the water column is half of the original height. How much more time in minutes does it require to empty the vessel?

$\mathop {\lim }\limits_{x \to \infty } \frac{{\sqrt {{x^2} + {a^2}} - \sqrt {{x^2} + {b^2}} }}{{\sqrt {{x^2} + {c^2}} - \sqrt {{x^2} + {d^2}} }} = $