Download App

Determinants — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDeterminants1 Mark
MCQ
The value of $\left|\begin{array}{rrr}\cos (\alpha+\beta) & -\sin (\alpha+\beta) & \cos 2 \beta \\ \sin \alpha & \cos \alpha & \sin \beta \\ -\cos \alpha & \sin \alpha & \cos \beta\end{array}\right|$ is independent of
  • ✓
    $\alpha$
  • B
    $\beta$
  • C
    $\alpha, \beta$
  • D
    None of these
✓

Answer

Correct option: A.
$\alpha$
(a) : Expanding given determinant along $R_1$, we get $\cos ^2(\alpha+\beta)+\sin ^2(\alpha+\beta)+\cos 2 \beta=1+\cos 2 \beta$,
Which is independent of $\alpha$.

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

$f\left( x \right) = \int {\frac{{dx}}{{{{\sin }^6}\,x}}} $ is a polynomial of degree 
→
$a, b, c$ are three non-zero, non-coplanar vectors and $p, q, r$ are three other vectors such that $p = \frac{{b \times c}}{{a\,.\,b \times c}}$,$q = \frac{{c \times a}}{{a\,.\,b \times c}}$, $r = \frac{{a \times b}}{{a\,.\,b \times c}}$. Then $[p\,q\,r]$ equals
→
The domain of definition of the function $f (x) = {\log _{\left[ {x + \frac{1}{x}} \right]}}|{x^2} - x - 6|+ ^{16-x}C_{2x-1} + ^{20-3x}P_{2x-5}$  is

Where $[x]$ denotes greatest integer function.

→
solve $\frac{{1 - \left| x \right|}}{{2 - \left| x \right|}} \ge 0$
→
$\left| {\,\begin{array}{*{20}{c}}{b + c}&{a - b}&a\\{c + a}&{b - c}&b\\{a + b}&{c - a}&c\end{array}\,} \right| = $
→
If $\text{A}=\begin{bmatrix}1&0&0\\0&1&0\\\text{a}&\text{b}&-1\end{bmatrix},$ then A2 is equal to:
  1. A null matrix
  2. A unit matrix
  3. -A
  4. A
→
If $f(x) = \log \frac{{1 + x}}{{1 - x}}$, then $f(x)$ is
→
Let R be the relation over the set of all straight lines in a plane such that  $\text{l}_1\text{Rl}_2\Leftrightarrow\text{l}_1\bot\text{l}_2.$ Then, R is:
  1. Symmetric.
  2. Reflexive.
  3. Transitive.
  4. An equivalence relation.
→
The minimum value of $f(a) = (2{a^2} - 3) + 3(3 - a) + 4$ is
→
The order and degree of the differential equation $\frac{{{d^2}y}}{{d{x^2}}} + {\left( {\frac{{dy}}{{dx}}} \right)^{\frac{1}{3}}} + {x^{\frac{1}{4}}} = 0$ are respectively
→