Download App

Matrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsMatrices1 Mark
MCQ
If $\text{I}=\begin{bmatrix}1&0\\0&1\end{bmatrix},\text{J}=\begin{bmatrix}0&1\\-1&0\end{bmatrix}$ and $\text{B}=\begin{bmatrix}\cos\theta&\sin\theta\\-\sin\theta&\cos\theta\end{bmatrix},$ then $B$ equals:
  • ✓
    $\text{I}\cos\theta+\text{J}\sin\theta$
  • B
    $\text{I}\sin\theta+\text{J}\cos\theta$
  • C
    $\text{I}\cos\theta-\text{J}\sin\theta$
  • D
    $-\text{I}\cos\theta+\text{J}\sin\theta$
✓

Answer

Correct option: A.
$\text{I}\cos\theta+\text{J}\sin\theta$
Here,
$\text{I}\cos\theta+\text{J}\sin\theta$
$=\begin{bmatrix}1&0\\0&1\end{bmatrix}\cos\theta+\begin{bmatrix}0&1\\-1&0\end{bmatrix}\sin\theta$
$=\begin{bmatrix}\cos\theta&0\\0&\cos\theta\end{bmatrix}+\begin{bmatrix}0&\sin\theta\\-\sin\theta&0\end{bmatrix}$
$=\begin{bmatrix}\cos\theta&\sin\theta\\-\sin\theta&\cos\theta\end{bmatrix}$
$=\text{B}$

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 Matrices→Matrices — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Let $A=\left[a_{i j}\right]$ be a $3 \times 3$ matrix, where

$a_{i j}= 1 , \quad\quad\text { if } i=j$

$\quad\quad-x ,\quad \text { if }|i-j|=1$

$\quad\quad2 x+1, \text { otherwise }$

Let a function f: $\mathrm{R} \rightarrow \mathrm{R}$ be defined as $\mathrm{f}(\mathrm{x})=\operatorname{det}(\mathrm{A})$. Then the sum of maximum and minimum values of $f$ on $R$ is equal to:

→
Define a relation $R$ over a class of $n \times n$ real matrices $A$ and $B$ as $"ARB$ iff there exists a non-singular matrix $P$ such that $PAP ^{-1}= B "$ Then which of the following is true?
→
The number which exceeds its square by the greatest possible quantity is,
→
If $\text{A}=\begin{bmatrix}\alpha &\text{amp; 2} \\2 &\text{amp; }\alpha \end{bmatrix}$and $ |\text{A}^3|=125,$ then $\alpha$ is equal to:
→
Area of the region bounded by the curve $\text{y}=\sqrt{49-\text{x}^2}$ and the x - axis is:
→
Let $A + 2B =$ $\left[ {\begin{array}{*{20}{c}}1&2&0\\6&{ - 3}&3\\{ - 5}&3&1 \end{array}} \right]$ and $2A - B =$ $\left[ {\begin{array}{*{20}{c}}2&{ - 1}&5\\ 2&{ - 1}&6\\0&1&2\end{array}} \right]$ then $Tr (A) - Tr (B)$ has the value equal to
→
The figure shown below is the graph of the derivative of some function $y=f(x)$.Then,
→
Let $[.]$ , $ \{.\} $ and $sgn$$(.)$ denotes greatest integer function, fractional part function and signum function respectively, then value of determinant

$\left| {\begin{array}{*{20}{c}}
  {\left[ \pi  \right]}&{amp(1 + i\sqrt 3 )}&1 \\ 
  1&0&2 \\ 
  {\operatorname{sgn} ({{\cot }^{ - 1}}x)}&1&{\{ \pi \} } 
\end{array}} \right|$ is-

→
The function $\text{f(x)}=|\cos\text{x}|$ is :
→
Let $f(x) = \left[ {\begin{array}{*{20}{c}}
  {a{{\cot }^{ - 1}}\left( {\frac{{b + x}}{4}} \right),\,\,\frac{{ - 2}}{3}\, < \,x\, < \,0} \\ 
  {2\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,,\,x = 0} \\ 
  {\frac{{\ln (1 - cx)}}{x},\,0\, < \,x\, < \,\frac{2}{3}} 
\end{array}} \right.$ If the function $f(x)$ is differentiable at $x = 0,$ then find the value of $(b^2 -2a + c^6).$
→