MCQ 11 Mark
माना कि $A$ एक व्युत्क्रमणीय आव्यूह है जिसका कम $2 \times 2$ हैं, तो ladj $A l=\ldots \ldots$
- A
$2| A |$
- ✓
$| A |$
- C
$| A |^2$
- D
$| A |^3$
AnswerCorrect option: B. $| A |$
View full question & answer→MCQ 21 Mark
यदि $A$ एक वर्ग आव्यूह हो तो $A+A^{\prime}$ एक $\ldots . .$. होगा ।
View full question & answer→MCQ 31 Mark
अगर $A=\left[\begin{array}{ll}1 & 9 \\ 0 & 1\end{array}\right]$ तब $A^4$ बराबर है :
- A
$\left[\begin{array}{ll}1 & a^4 \\ 0 & 1\end{array}\right]$
- ✓
$\left[\begin{array}{ll}1 & 36 \\ 0 & 1\end{array}\right]$
- C
$\left[\begin{array}{ll}4 & a^4 \\ 0 & 4\end{array}\right]$
- D
$\left[\begin{array}{cc}1 & 4 a \\ 0 & 1\end{array}\right]$
AnswerCorrect option: B. $\left[\begin{array}{ll}1 & 36 \\ 0 & 1\end{array}\right]$
View full question & answer→MCQ 41 Mark
माना $A=\left[\begin{array}{ll}1 & 2 \\ 0 & 1\end{array}\right]$ तब $A^n=$ ?
- ✓
$\left[\begin{array}{cc}1 & 2 n \\ 0 & 1\end{array}\right]$
- B
$\left[\begin{array}{ll}2 & n \\ 0 & 1\end{array}\right]$
- C
$\left[\begin{array}{cc}1 & 2 n \\ 0 & 1\end{array}\right]$
- D
$\left[\begin{array}{ll}1 & n \\ 0 & 2\end{array}\right]$
AnswerCorrect option: A. $\left[\begin{array}{cc}1 & 2 n \\ 0 & 1\end{array}\right]$
View full question & answer→MCQ 51 Mark
अगर $\left[\begin{array}{cc}x+y & 3 \\ 4 & x-y\end{array}\right]=\left[\begin{array}{cc}1 & 3 \\ 4 & -3\end{array}\right]$ तब $(x, y)$ है :
- ✓
$(-1,2)$
- B
$(-1,-2)$
- C
$(-2,-1)$
- D
$(1,-2)$
AnswerCorrect option: A. $(-1,2)$
View full question & answer→MCQ 61 Mark
यदि $A=\left[\begin{array}{cc}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta\end{array}\right]$ तब $A d j A$ है :
- A
$\left[\begin{array}{cc}\cos \theta & -\sin \theta \\ \cos \theta & \cos \theta\end{array}\right]$
- B
$\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$
- ✓
$\left[\begin{array}{cc}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta\end{array}\right]$
- D
$\left[\begin{array}{cc}-1 & 0 \\ 0 & -1\end{array}\right] \quad$
AnswerCorrect option: C. $\left[\begin{array}{cc}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta\end{array}\right]$
View full question & answer→MCQ 71 Mark
यदि $A=\left[\begin{array}{cc}\cos \alpha & -\sin \alpha \\ \sin \alpha & \cos \alpha\end{array}\right]$ तो $A+A^1=I$ यदि $\alpha$ का मान है :
- A
$\frac{\pi}{6}$
- B
$\pi$
- ✓
$\frac{\pi}{3}$
- D
$\frac{3 \pi}{3}$
AnswerCorrect option: C. $\frac{\pi}{3}$
View full question & answer→MCQ 81 Mark
यदि $A$ एक उत्कमणीय आव्यूह है जिसका क्रम $n \times n$ है तो
- A
$n|A|$
- ✓
$|A|^{n-1}$
- C
$|A|$
- D
$|A|^n$
AnswerCorrect option: B. $|A|^{n-1}$
View full question & answer→MCQ 91 Mark
यदि $A=\left[\begin{array}{ll}3 & -2 \\ 4 & -2\end{array}\right]$ तब $K$ का मान यदि :
View full question & answer→MCQ 101 Mark
यदि $A=\left[\begin{array}{ll}3 & -2 \\ 4 & -2\end{array}\right]$ तब $K$ का मान यदि :
View full question & answer→MCQ 111 Mark
आव्यूह $\left[\begin{array}{ccc}1 & 0 & -5 \\ -4 & 5 & 7\end{array}\right]$ है :
- A
सममित आव्यूह (a symmetric matrix)
- B
असममित आव्यूह (a skew-symmetric matrix)
- C
विकर्ण आव्यूह (A diagonal matrix)
- ✓
View full question & answer→MCQ 121 Mark
आव्यूह $A$ समीकरण $\left[\begin{array}{cc}0 & 2 \\ -1 & 1\end{array}\right] A=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$ आता है तब आव्यूह $A$ है :
- A
$\left[\begin{array}{cc}2 & 0 \\ 1 & -1\end{array}\right]$
- B
$\left[\begin{array}{cc}1 & -2 \\ 1 & 0\end{array}\right]$
- ✓
$\left[\begin{array}{cc}1 / 2 & -1 \\ 1 / 2 & 0\end{array}\right]$
- D
$\left[\begin{array}{cc}1 & 2 \\ -1 & 0\end{array}\right]$
AnswerCorrect option: C. $\left[\begin{array}{cc}1 / 2 & -1 \\ 1 / 2 & 0\end{array}\right]$
View full question & answer→MCQ 131 Mark
एक आव्यूह 18 अवयव रखता है तब आव्यूह का धनात्मक कोटि है :
MCQ 141 Mark
यदि $A^2-A+I=0$ हो तंब $A$ का व्युत्क्रम है :
View full question & answer→MCQ 151 Mark
यदि $A=\left[\begin{array}{ll}\alpha & 2 \\ 2 & \alpha\end{array}\right]$ और $\left|A^3\right|=125$ तब $\alpha=$
- ✓
$\pm 3$
- B
$\pm 2$
- C
$\pm 5$
- D
$0$
AnswerCorrect option: A. $\pm 3$
View full question & answer→MCQ 161 Mark
यदि $A=\left[\begin{array}{ll}\alpha & 0 \\ 1 & 1\end{array}\right]$ और $B=\left[\begin{array}{ll}1 & 0 \\ 5 & 1\end{array}\right]$ तब $A^2=B$ सत्य है :
- A
$\alpha=1$ के लिए (for $\alpha=1$ )
- ✓
$\alpha$ की कोई कीमत नहीं (for no value of $\alpha$ )
- C
$\alpha=4$ के लिए (for $\alpha=4$ )
- D
$\alpha=-4$ के लिए (for $\alpha=-4$ )
AnswerCorrect option: B. $\alpha$ की कोई कीमत नहीं (for no value of $\alpha$ )
View full question & answer→MCQ 171 Mark
यदि $A=\left[\begin{array}{ll}a & b \\ b & a\end{array}\right]$ और $A^2=\left[\begin{array}{ll}\alpha & \beta \\ \beta & \alpha\end{array}\right]$ तब
- A
$\alpha=a^2+b^2, \beta=a b$
- ✓
$\alpha=a^2+b^2, \beta=2 a b$
- C
$\alpha=a^2+b^2, \beta=a^2-b^2$
- D
$\alpha=2 a b, \beta=a^2+b^2$
AnswerCorrect option: B. $\alpha=a^2+b^2, \beta=2 a b$
View full question & answer→MCQ 181 Mark
यदि $A=\left[\begin{array}{ll}1 & 2 \\ 4 & 2\end{array}\right]$ तो :
AnswerCorrect option: B. $4|A|$
View full question & answer→MCQ 191 Mark
$A=\left[\begin{array}{cc}1 & -1 \\ 2 & 3\end{array}\right]$ तब :
AnswerCorrect option: C. $|A|=5$
$|A|=5$
View full question & answer→MCQ 201 Mark
एक मैट्रिक्स $A=\left[a_{2 j}\right]_{n \times n}$ सममित है यदि :
- A
$a_{i j}=0$
- B
$a_{i j}=-a_{j i}$
- ✓
$a_{i j}=a_{j i}$
- D
${a_ij}=1$
AnswerCorrect option: C. $a_{i j}=a_{j i}$
View full question & answer→MCQ 211 Mark
यदि $A=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]$ तो $A^2$ बराबर होगा :
- A
$\left[\begin{array}{ll}a^2 & b^2 \\ c^2 & d^2\end{array}\right]$
- ✓
$\left[\begin{array}{ll}a^3 & b^3 \\ c^3 & d^3\end{array}\right]$
- C
$\left[\begin{array}{ll}b^2+b c & a b+b d \\ a c+d c & d c+d^2\end{array}\right]$
- D
AnswerCorrect option: B. $\left[\begin{array}{ll}a^3 & b^3 \\ c^3 & d^3\end{array}\right]$
View full question & answer→MCQ 221 Mark
यदि $ \begin{bmatrix} x+y & y \\ 2 x & x-y\end{bmatrix} \begin{bmatrix} 2 \\ -1\end{bmatrix} = \begin{bmatrix} 3 \\ 2\end{bmatrix} $ तो $x y$ बराबर होगा
View full question & answer→MCQ 231 Mark
यदि $A=\left[\begin{array}{lll}1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1\end{array}\right]$ तब $A^2=$ ?
View full question & answer→MCQ 241 Mark
$\left[\begin{array}{cc}\cos x & -\sin x \\ \sin x & \cos x\end{array}\right]$ का मान होगा :
- A
$\cos ^2 x-\sin ^2 x$
- B
$0$
- ✓
- D
View full question & answer→MCQ 251 Mark
यदि $A =\left[\begin{array}{lll}1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1\end{array}\right]$ तो $A ^2$ है :
View full question & answer→MCQ 261 Mark
किसी एकांक समूह I के लिए :
- ✓
$I ^2=1$
- B
$|I|=2$
- C
$|I|=0$
- D
$|I|=5$.
AnswerCorrect option: A. $I ^2=1$
View full question & answer→MCQ 271 Mark
यदि $A =\left[\begin{array}{ccc}1 & 0 & 0 \\ 0 & 1 & 0 \\ a & b & -1\end{array}\right]$ तो $A ^2=$
View full question & answer→MCQ 281 Mark
यदि $A =\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right], B =\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$ हो, तो $AB =$
- A
$\left[\begin{array}{ll}0 & 0 \\ 0 & 0\end{array}\right]$
- B
$\left[\begin{array}{ll}1 & 1 \\ 1 & 0\end{array}\right]$
- ✓
$\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$
- D
AnswerCorrect option: C. $\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$
View full question & answer→MCQ 291 Mark
यदि $A =\left[\begin{array}{ll}1 & 2 \\ 2 & 1\end{array}\right]$ तो सह-खंडन $A =$
- ✓
$\left[\begin{array}{cc}1 & -2 \\ -2 & 1\end{array}\right]$
- B
$\left[\begin{array}{ll}2 & 1 \\ 1 & 1\end{array}\right]$
- C
$\left[\begin{array}{cc}1 & -2 \\ -2 & -1\end{array}\right]$
- D
$\left[\begin{array}{cc}1 & -2 \\ 2 & 1\end{array}\right]$
AnswerCorrect option: A. $\left[\begin{array}{cc}1 & -2 \\ -2 & 1\end{array}\right]$
View full question & answer→MCQ 301 Mark
माना कि $A$ एक व्युत्क्मणीय आव्यूह है जिसका क्रम $2 \times 2$ है, तो $\left| A ^{-1}\right|=$
- A
$| A |$
- ✓
$\frac{1}{|A|}$
- C
$0$
- D
AnswerCorrect option: B. $\frac{1}{|A|}$
View full question & answer→MCQ 311 Mark
$A =\left[\begin{array}{ll}2 & 3 \\ 5 & k\end{array}\right]$ का व्युत्क्रम प्राप्त नहीं होगा यदि $k$ का मान है :
- A
- B
$\frac{3}{2}$
- C
$\frac{5}{2}$
- ✓
$\frac{15}{2}$
AnswerCorrect option: D. $\frac{15}{2}$
View full question & answer→MCQ 321 Mark
यदि $A =\left[\begin{array}{ll} i & 0 \\ 0 & i \end{array}\right]$ तो $A ^2=$
- A
$\left[\begin{array}{cc}1 & 0 \\ 0 & -1\end{array}\right]$
- ✓
$\left[\begin{array}{cc}-1 & 0 \\ 0 & -1\end{array}\right]$
- C
$\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$
- D
$\left[\begin{array}{cc}-1 & 0 \\ 0 & 1\end{array}\right]$
AnswerCorrect option: B. $\left[\begin{array}{cc}-1 & 0 \\ 0 & -1\end{array}\right]$
View full question & answer→MCQ 331 Mark
यदि $\left|\begin{array}{ll}x & 8 \\ 3 & 3\end{array}\right|=0, x$ का मान है :
View full question & answer→MCQ 341 Mark
एक मैट्रिक्स $A =\left[ a _{ o }\right]_{ m \times n }$ सममित है यदि :
- A
$a _{ ij }=0$
- B
$a_{i j}=-a_{j i}$
- ✓
$a_{i j}=a_{j i}$
- D
$a_{i j}=1$
AnswerCorrect option: C. $a_{i j}=a_{j i}$
View full question & answer→MCQ 351 Mark
यदि $\left|\begin{array}{cc}1-x & 2 \\ 18 & 6\end{array}\right|=\left|\begin{array}{cc}6 & 2 \\ 18 & 6\end{array}\right|$ तो $x=$
View full question & answer→MCQ 361 Mark
यदि $A =\left[\begin{array}{cc}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta\end{array}\right]$ तो सहखंडन $A$ है :
- A
$\left[\begin{array}{cc}\cos \theta & -\sin \theta \\ \cos \theta & \sin \theta\end{array}\right]$
- B
$\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$
- ✓
$\left[\begin{array}{cc}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta\end{array}\right]$
- D
$\left[\begin{array}{cc}-1 & 0 \\ 0 & -1\end{array}\right]$
AnswerCorrect option: C. $\left[\begin{array}{cc}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta\end{array}\right]$
View full question & answer→MCQ 371 Mark
यदि $A$ और $B$ वर्ग आव्यूह है, तो $( AB )^{\prime}=$
AnswerCorrect option: A. $B ^{\prime} A ^{\prime}$
View full question & answer→MCQ 381 Mark
$A=\left[a_{i j}\right]_{m \times n}$ एक वर्ग आव्यूह है यदि :
View full question & answer→MCQ 391 Mark
$\left[\begin{array}{cc}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta\end{array}\right]$ का व्युत्क्म है :
- A
$\left[\begin{array}{ll}-\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta\end{array}\right]$
- ✓
$\left[\begin{array}{cc}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta\end{array}\right]$
- C
$\left[\begin{array}{ll}\cos \theta & -\sin \theta \\ \sin \theta & -\cos \theta\end{array}\right]$
- D
AnswerCorrect option: B. $\left[\begin{array}{cc}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta\end{array}\right]$
View full question & answer→MCQ 401 Mark
यदि $A =\left[\begin{array}{ll}1 & 2 \\ 4 & 2\end{array}\right]$ तो $|2 A |=$
- A
$2| A |$
- ✓
$4 \mid Al$
- C
$8| A |$
- D
AnswerCorrect option: B. $4 \mid Al$
View full question & answer→MCQ 411 Mark
यदि $A =\left[\begin{array}{ll}\alpha & 0 \\ 1 & 1\end{array}\right] B =\left[\begin{array}{ll}1 & 0 \\ 5 & 1\end{array}\right]$, जह्ँ $A ^2= B$, तो $\alpha$ का मान है :
AnswerCorrect option: D. $\alpha$ का वास्तविक मान नहीं
View full question & answer→MCQ 421 Mark
$A=\left[\begin{array}{cc}3 & 6 \\ 5 & -4\end{array}\right], B=\left[\begin{array}{ll}7 & 8 \\ 5 & 6\end{array}\right] \Rightarrow 2 A+3 B=$ आव्यूह
- A
$\left[\begin{array}{ll}27 & 24 \\ 22 & 10\end{array}\right]$
- B
$\left[\begin{array}{ll}27 & 36 \\ 35 & 10\end{array}\right]$
- C
$\left[\begin{array}{ll}27 & 36 \\ 25 & 15\end{array}\right]$
- ✓
$\left[\begin{array}{ll}27 & 36 \\ 25 & 10\end{array}\right]$
AnswerCorrect option: D. $\left[\begin{array}{ll}27 & 36 \\ 25 & 10\end{array}\right]$
View full question & answer→MCQ 431 Mark
$A =\left[\begin{array}{cc}1 & -1 \\ -1 & 1\end{array}\right] \Rightarrow A^2=$
View full question & answer→MCQ 441 Mark
$A =\left[\begin{array}{ccc}9 & 10 & 11 \\ 12 & 13 & 14\end{array}\right], B =\left[\begin{array}{ccc}11 & 10 & 9 \\ 8 & 7 & 6\end{array}\right] \Rightarrow 2 A +2 B =$
- A
$\left[\begin{array}{lll}20 & 20 & 20 \\ 20 & 20 & 20\end{array}\right]$
- ✓
$\left[\begin{array}{lll}40 & 40 & 40 \\ 40 & 40 & 40\end{array}\right]$
- C
$\left[\begin{array}{rrr}20 & 20 & 20 \\ 40 & 40 & 40\end{array}\right]$
- D
$\left[\begin{array}{lll}40 & 40 & 40 \\ 20 & 20 & 20\end{array}\right] \quad$
AnswerCorrect option: B. $\left[\begin{array}{lll}40 & 40 & 40 \\ 40 & 40 & 40\end{array}\right]$
View full question & answer→MCQ 451 Mark
यदि $A =\left[\begin{array}{ccc}9 & 10 & 11 \\ 12 & 13 & 14\end{array}\right]$ और $B =\left[\begin{array}{ccc}11 & 10 & 9 \\ 8 & 7 & 6\end{array}\right]$ तो $A + B =\ldots .$.
- ✓
$\left[\begin{array}{lll}20 & 20 & 20 \\ 20 & 20 & 20\end{array}\right]$
- B
$\left[\begin{array}{lll}10 & 10 & 10 \\ 10 & 10 & 10\end{array}\right]$
- C
$\left[\begin{array}{rrr}10 & 5 & 10 \\ 5 & 10 & 10\end{array}\right]$
- D
$\left[\begin{array}{lll}25 & 10 & 15 \\ 15 & 10 & 25\end{array}\right]$
AnswerCorrect option: A. $\left[\begin{array}{lll}20 & 20 & 20 \\ 20 & 20 & 20\end{array}\right]$
View full question & answer→MCQ 461 Mark
यदि $A$ एक $3 \times 3$ आव्यूह हो ताकि $A^2=A$, तो $\left(A+I_3\right)^3-7 A$ किसके बराबर होगा ?
- ✓
$I _3$
- B
$A$
- C
$3 A$
- D
$I _3- A$
AnswerCorrect option: A. $I _3$
View full question & answer→MCQ 471 Mark
$A=\left[a_{i j}\right]_{m \times n}$ एक वर्ग आव्यूह है यदि :
View full question & answer→MCQ 481 Mark
यदि $A$ तथा $B$ समान कोटि के सममित आव्यूह हैं तो $A B-B A$ एक :
View full question & answer→MCQ 491 Mark
$3 \times 3$ कोटि के ऐसे आव्यूहों की कुल कितनी संख्या होगी जिनकी प्रत्येक प्रविष्टि 0 या 1 है :
View full question & answer→MCQ 501 Mark
यदि $\theta+\phi=90^{\circ}$, तो $\left|\begin{array}{cc}\cos \theta & \sin \theta \\ \sin \phi & \cos \phi\end{array}\right|=$
View full question & answer→