Download App

DETERMINANTS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDETERMINANTS1 Mark
MCQ
Using the factor theorem it is found that a + b, b + c and c + a are three factors of the determinant $\begin{vmatrix}-2\text{a}&\text{a}+\text{b}&\text{a}+\text{c}\\\text{b}+\text{a}&-2\text{b}&\text{b}+\text{c}\\\text{c}+\text{a}&\text{c}+\text{b}&-2\text{c}\end{vmatrix}$ the other factor in the value of the determinant is:
  • ✓
    4
  • B
    2
  • C
    a + b + c
  • D
    None of these.
✓

Answer

Correct option: A.
4
$\triangle=\begin{vmatrix}-2\text{a}&\text{a}+\text{b}&\text{a}+\text{c}\\\text{b}+\text{a}&-2\text{b}&\text{b}+\text{c}\\\text{c}+\text{a}&\text{c}+\text{b}&-2\text{c}\end{vmatrix}$

Let a + b = 2C, b + c = 2A and c + a = 2B

⇒ a + b + b + c + c + a = 2A + 2B + 2C

⇒ 2(a + b + c) = (A + B + C)

Also, a = (a + b + c) - (b + c) = (A + B + C) - 2A = B + C - A

Similarly, b = C + A - B, c = A + B - C

Hence, 4 is the order factor of the determinant.

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

More "M.C.Q (1 Marks)" from DETERMINANTS→DETERMINANTS — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Let R be the relation in the set N given by R = {(a, b) : a = b – 2, b > 6}. Choose
the correct answer.
→
$\int_{}^{} {{x^5}.{e^{{x^2}}}dx = } $
→
If ${I_n} = \int_0^\infty {{e^{ - x}}{x^{n - 1}}dx,} $ then $\int_0^\infty {{e^{ - \lambda x}}{x^{n - 1}}dx = } $
→
If $P(A / B)=\frac{2}{5}, P(B)=\frac{1}{5}$, then the value of $P(A \cap B)$ is
→
Function $f\left( x \right) = \left( {x - 2} \right)\left| {x - 3} \right|$ is monotonically increasing in
 
→
The roots of the equation $\left| {\,\begin{array}{*{20}{c}}0&x&{16}\\x&5&7\\0&9&x\end{array}\,} \right| = 0$  are
→
Coffee is draining from a conical filter, height and diameter both $15 \,\,cms$ into a cylinderical coffee pot diameter $15 \,\,cm$. The rate at which coffee drains from the filter into the pot is $100 \,\,cu cm /min$.The rate in $cm s/min$ at which the level in the pot is rising at the instant when the coffee in the pot is $10 \,\,cm$, is
→
For $x \in R$ , $f\left( x \right) = \left| {\log 2 - \sin x} \right|$ and $g\left( x \right) = f\left( {f\left( x \right)} \right)$ then ..  .
→
If P and q are the order and degree of the differention $\text{y}\frac{\text{dy}}{\text{dx}}+\text{x}^{3}\frac{\text{d}^{2}\text{y}}{\text{dx}^{3}}+\text{xy}=\cos\text{x}$ then:
→
Two events A and B such that $P ( A )=\frac{1}{4}, P ( A \mid B )=\frac{1}{2}$, and $P(B \mid A)=\frac{2}{3}$, then value of $P(B)$ :
→