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Mathematics Quiz - Class 12 Mathematics Easy Level 34 Quiz

Question 1/50 Easy Mathematics Matrix Class 12 Level 34

मैट्रिक्स \(A=\begin{bmatrix}1&2&3\\4&5&6\end{bmatrix}\) का क्रम क्या है?

What is the order of the matrix \(A=\begin{bmatrix}1&2&3\\4&5&6\end{bmatrix}\)?

Explanation opens after your attempt

Correct Answer

A. \(2\times3\)

Step 1

Concept

This matrix has (2) rows and (3) columns. Order is always written as row \(\times\) column.

Step 2

Why this answer is correct

The correct answer is A. \(2\times3\). This matrix has (2) rows and (3) columns. Order is always written as row \(\times\) column.

Step 3

Exam Tip

इस मैट्रिक्स में (2) पंक्तियां और (3) स्तंभ हैं। क्रम हमेशा पंक्ति \(\times\) स्तंभ लिखा जाता है।

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Question 2/50 Easy Mathematics Matrix Class 12 Level 34

मैट्रिक्स \(B=\begin{bmatrix}7\\8\\9\end{bmatrix}\) किस प्रकार की मैट्रिक्स है?

What type of matrix is \(B=\begin{bmatrix}7\\8\\9\end{bmatrix}\)?

Explanation opens after your attempt

Correct Answer

B. स्तंभ मैट्रिक्सColumn matrix

Step 1

Concept

It has only (1) column and (3) rows. Such a matrix is called a column matrix.

Step 2

Why this answer is correct

The correct answer is B. स्तंभ मैट्रिक्स / Column matrix. It has only (1) column and (3) rows. Such a matrix is called a column matrix.

Step 3

Exam Tip

इसमें केवल (1) स्तंभ और (3) पंक्तियां हैं। ऐसे मैट्रिक्स को स्तंभ मैट्रिक्स कहते हैं।

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Question 3/50 Easy Mathematics Matrix Introduction to matrices Class 12 Level 34

मैट्रिक्स \(C=\begin{bmatrix}4&5&6\end{bmatrix}\) किस प्रकार की मैट्रिक्स है?

What type of matrix is \(C=\begin{bmatrix}4&5&6\end{bmatrix}\)?

Explanation opens after your attempt

Correct Answer

B. पंक्ति मैट्रिक्सRow matrix

Step 1

Concept

It has only (1) row. A matrix with only one row is called a row matrix.

Step 2

Why this answer is correct

The correct answer is B. पंक्ति मैट्रिक्स / Row matrix. It has only (1) row. A matrix with only one row is called a row matrix.

Step 3

Exam Tip

इसमें केवल (1) पंक्ति है। केवल एक पंक्ति वाली मैट्रिक्स को पंक्ति मैट्रिक्स कहते हैं।

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Question 4/50 Easy Mathematics Matrix Introduction to matrices Class 12 Level 34

यदि किसी मैट्रिक्स में (3) पंक्तियां और (4) स्तंभ हैं, तो उसमें कुल कितने अवयव होंगे?

If a matrix has (3) rows and (4) columns, how many elements does it have?

Explanation opens after your attempt

Correct Answer

B. (12)

Step 1

Concept

The total elements are \(3\times4=12\). The number of elements is found by multiplying rows and columns.

Step 2

Why this answer is correct

The correct answer is B. (12). The total elements are \(3\times4=12\). The number of elements is found by multiplying rows and columns.

Step 3

Exam Tip

कुल अवयव \(3\times4=12\) होते हैं। अवयवों की संख्या पंक्तियों और स्तंभों के गुणनफल से मिलती है।

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Question 5/50 Easy Mathematics Matrix Introduction to matrices Class 12 Level 34

मैट्रिक्स \(A=[a_{ij}]*{2\times3}\) में (i) क्या दर्शाता है?

In the matrix \(A=[a*{ij}]*{2\times3}\), what does (i) represent?

Explanation opens after your attempt

Correct Answer

B. पंक्ति संख्याRow number

Step 1

Concept

In \(a_{ij}\), (i) represents the row number. (j) represents the column number.

Step 2

Why this answer is correct

The correct answer is B. पंक्ति संख्या / Row number. In \(a_{ij}\), (i) represents the row number. (j) represents the column number.

Step 3

Exam Tip

(a*{ij}) में (i) पंक्ति संख्या को दर्शाता है। (j) स्तंभ संख्या को दर्शाता है।

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Question 6/50 Easy Mathematics Matrix Introduction to matrices Class 12 Level 34

मैट्रिक्स \(A=[a_{ij}]\) में \(a_{23}\) का अर्थ क्या है?

What does \(a_{23}\) mean in the matrix \(A=[a_{ij}]\)?

Explanation opens after your attempt

Correct Answer

A. दूसरी पंक्ति और तीसरे स्तंभ का अवयवElement in (2)nd row and (3)rd column

Step 1

Concept

In \(a_{23}\), (2) is the row number and (3) is the column number. So it is the element in the (2)nd row and (3)rd column.

Step 2

Why this answer is correct

The correct answer is A. दूसरी पंक्ति और तीसरे स्तंभ का अवयव / Element in (2)nd row and (3)rd column. In \(a_{23}\), (2) is the row number and (3) is the column number. So it is the element in the (2)nd row and (3)rd column.

Step 3

Exam Tip

\(a_{23}\) में (2) पंक्ति संख्या और (3) स्तंभ संख्या है। इसलिए यह दूसरी पंक्ति तीसरे स्तंभ का अवयव है।

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Question 7/50 Easy Mathematics Matrix Introduction to matrices Class 12 Level 34

मैट्रिक्स \(A=\begin{bmatrix}1&0\0&1\end{bmatrix}\) किस प्रकार की मैट्रिक्स है?

What type of matrix is \(A=\begin{bmatrix}1&0\0&1\end{bmatrix}\)?

Explanation opens after your attempt

Correct Answer

B. इकाई मैट्रिक्सIdentity matrix

Step 1

Concept

All main diagonal elements are (1) and the remaining elements are (0). Such a matrix is called an identity matrix.

Step 2

Why this answer is correct

The correct answer is B. इकाई मैट्रिक्स / Identity matrix. All main diagonal elements are (1) and the remaining elements are (0). Such a matrix is called an identity matrix.

Step 3

Exam Tip

मुख्य विकर्ण पर सभी अवयव (1) हैं और बाकी (0) हैं। ऐसी मैट्रिक्स को इकाई मैट्रिक्स कहते हैं।

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Question 8/50 Easy Mathematics Matrix Introduction to matrices Class 12 Level 34

मैट्रिक्स \(O=\begin{bmatrix}0&0\0&0\end{bmatrix}\) किस प्रकार की मैट्रिक्स है?

What type of matrix is \(O=\begin{bmatrix}0&0\0&0\end{bmatrix}\)?

Explanation opens after your attempt

Correct Answer

B. शून्य मैट्रिक्सZero matrix

Step 1

Concept

All elements of this matrix are (0). A matrix with all elements (0) is called a zero matrix.

Step 2

Why this answer is correct

The correct answer is B. शून्य मैट्रिक्स / Zero matrix. All elements of this matrix are (0). A matrix with all elements (0) is called a zero matrix.

Step 3

Exam Tip

इस मैट्रिक्स के सभी अवयव (0) हैं। सभी अवयव (0) हों तो उसे शून्य मैट्रिक्स कहते हैं।

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Question 9/50 Easy Mathematics Matrix Introduction to matrices Class 12 Level 34

कौन-सी मैट्रिक्स वर्ग मैट्रिक्स है?

Which matrix is a square matrix?

Explanation opens after your attempt

Correct Answer

C. क्रम \(4\times4\) वाली मैट्रिक्सMatrix of order \(4\times4\)

Step 1

Concept

In a square matrix, the number of rows and columns is equal. In \(4\times4\), both numbers are (4).

Step 2

Why this answer is correct

The correct answer is C. क्रम \(4\times4\) वाली मैट्रिक्स / Matrix of order \(4\times4\). In a square matrix, the number of rows and columns is equal. In \(4\times4\), both numbers are (4).

Step 3

Exam Tip

वर्ग मैट्रिक्स में पंक्तियों और स्तंभों की संख्या बराबर होती है। \(4\times4\) में दोनों संख्या (4) हैं।

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Question 10/50 Easy Mathematics Matrix Introduction to matrices Class 12 Level 34

कौन-सी मैट्रिक्स आयताकार मैट्रिक्स है?

Which matrix is a rectangular matrix?

Explanation opens after your attempt

Correct Answer

C. क्रम \(2\times5\) वाली मैट्रिक्सMatrix of order \(2\times5\)

Step 1

Concept

In a rectangular matrix, rows and columns are not equal. In \(2\times5\), \(2\ne5\).

Step 2

Why this answer is correct

The correct answer is C. क्रम \(2\times5\) वाली मैट्रिक्स / Matrix of order \(2\times5\). In a rectangular matrix, rows and columns are not equal. In \(2\times5\), \(2\ne5\).

Step 3

Exam Tip

आयताकार मैट्रिक्स में पंक्तियां और स्तंभ बराबर नहीं होते। \(2\times5\) में \(2\ne5\) है।

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Question 11/50 Easy Mathematics Matrix Introduction to matrices Class 12 Level 34

मैट्रिक्स \(A=\begin{bmatrix}2&0\0&3\end{bmatrix}\) किस प्रकार की मैट्रिक्स है?

What type of matrix is \(A=\begin{bmatrix}2&0\0&3\end{bmatrix}\)?

Explanation opens after your attempt

Correct Answer

A. विकर्ण मैट्रिक्सDiagonal matrix

Step 1

Concept

All elements outside the main diagonal are (0). Therefore it is a diagonal matrix.

Step 2

Why this answer is correct

The correct answer is A. विकर्ण मैट्रिक्स / Diagonal matrix. All elements outside the main diagonal are (0). Therefore it is a diagonal matrix.

Step 3

Exam Tip

मुख्य विकर्ण के बाहर सभी अवयव (0) हैं। इसलिए यह विकर्ण मैट्रिक्स है।

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Question 12/50 Easy Mathematics Matrix Introduction to matrices Class 12 Level 34

मैट्रिक्स \(A=\begin{bmatrix}5&0\0&5\end{bmatrix}\) किस प्रकार की मैट्रिक्स है?

What type of matrix is \(A=\begin{bmatrix}5&0\0&5\end{bmatrix}\)?

Explanation opens after your attempt

Correct Answer

B. अदिश मैट्रिक्सScalar matrix

Step 1

Concept

The main diagonal has equal elements (5), and the remaining elements are (0). Such a diagonal matrix is called a scalar matrix.

Step 2

Why this answer is correct

The correct answer is B. अदिश मैट्रिक्स / Scalar matrix. The main diagonal has equal elements (5), and the remaining elements are (0). Such a diagonal matrix is called a scalar matrix.

Step 3

Exam Tip

मुख्य विकर्ण पर बराबर अवयव (5) हैं और बाकी अवयव (0) हैं। ऐसी विकर्ण मैट्रिक्स अदिश मैट्रिक्स कहलाती है।

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Question 13/50 Easy Mathematics Matrix Introduction to matrices Class 12 Level 34

मैट्रिक्स \(A=\begin{bmatrix}1&2\3&4\end{bmatrix}\) में \(a_{12}\) का मान क्या है?

What is the value of \(a_{12}\) in \(A=\begin{bmatrix}1&2\3&4\end{bmatrix}\)?

Explanation opens after your attempt

Correct Answer

B. (2)

Step 1

Concept

\(a_{12}\) is the element of the first row and second column. The value there is (2).

Step 2

Why this answer is correct

The correct answer is B. (2). \(a_{12}\) is the element of the first row and second column. The value there is (2).

Step 3

Exam Tip

\(a_{12}\) पहली पंक्ति और दूसरे स्तंभ का अवयव है। वहां मान (2) है।

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Question 14/50 Easy Mathematics Matrix Introduction to matrices Class 12 Level 34

मैट्रिक्स \(A=\begin{bmatrix}6&7&8\9&10&11\end{bmatrix}\) में \(a_{21}\) का मान क्या है?

What is the value of \(a_{21}\) in \(A=\begin{bmatrix}6&7&8\9&10&11\end{bmatrix}\)?

Explanation opens after your attempt

Correct Answer

C. (9)

Step 1

Concept

\(a_{21}\) is the element in the second row and first column. At this position, the value is (9).

Step 2

Why this answer is correct

The correct answer is C. (9). \(a_{21}\) is the element in the second row and first column. At this position, the value is (9).

Step 3

Exam Tip

\(a_{21}\) दूसरी पंक्ति और पहले स्तंभ का अवयव है। इस स्थान पर (9) है।

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Question 15/50 Easy Mathematics Matrix Introduction to matrices Class 12 Level 34

दो मैट्रिक्स (A) और (B) बराबर कब कहलाती हैं?

When are two matrices (A) and (B) called equal?

Explanation opens after your attempt

Correct Answer

C. जब उनका क्रम समान हो और समान स्थानों के अवयव बराबर होंWhen their orders are same and corresponding elements are equal

Step 1

Concept

For two matrices to be equal, their order must be the same. Also, every corresponding element must be equal.

Step 2

Why this answer is correct

The correct answer is C. जब उनका क्रम समान हो और समान स्थानों के अवयव बराबर हों / When their orders are same and corresponding elements are equal. For two matrices to be equal, their order must be the same. Also, every corresponding element must be equal.

Step 3

Exam Tip

दो मैट्रिक्स बराबर होने के लिए उनका क्रम समान होना चाहिए। साथ ही हर corresponding अवयव बराबर होना चाहिए।

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Question 16/50 Easy Mathematics Matrix Introduction to matrices Class 12 Level 34

यदि \(A=\begin{bmatrix}x&2\3&4\end{bmatrix}\) और \(B=\begin{bmatrix}5&2\3&4\end{bmatrix}\) तथा (A=B), तो (x) का मान क्या है?

If \(A=\begin{bmatrix}x&2\3&4\end{bmatrix}\) and \(B=\begin{bmatrix}5&2\3&4\end{bmatrix}\) with (A=B), what is the value of (x)?

Explanation opens after your attempt

Correct Answer

D. (5)

Step 1

Concept

In equal matrices, corresponding elements are equal. Therefore (x=5).

Step 2

Why this answer is correct

The correct answer is D. (5). In equal matrices, corresponding elements are equal. Therefore (x=5).

Step 3

Exam Tip

बराबर मैट्रिक्स में समान स्थानों के अवयव बराबर होते हैं। इसलिए (x=5) होगा।

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Question 17/50 Easy Mathematics Matrix Introduction to matrices Class 12 Level 34

यदि \(A=[a_{ij}]{2\times2}\) और (a{ij}=i+j), तो \(a_{22}\) का मान क्या है?

If \(A=[a_{ij}]*{2\times2}\) and (a*{ij}=i+j), what is the value of \(a_{22}\)?

Explanation opens after your attempt

Correct Answer

C. (4)

Step 1

Concept

Here (i=2) and (j=2). So \(a_{22}=2+2=4\).

Step 2

Why this answer is correct

The correct answer is C. (4). Here (i=2) and (j=2). So \(a_{22}=2+2=4\).

Step 3

Exam Tip

यहां (i=2) और (j=2) है। इसलिए \(a_{22}=2+2=4\)।

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Question 18/50 Easy Mathematics Matrix Introduction to matrices Class 12 Level 34

यदि \(A=[a_{ij}]{3\times2}\) और (a{ij}=2i-j), तो \(a_{31}\) का मान क्या है?

If \(A=[a_{ij}]*{3\times2}\) and (a*{ij}=2i-j), what is the value of \(a_{31}\)?

Explanation opens after your attempt

Correct Answer

C. (5)

Step 1

Concept

For \(a_{31}\), (i=3) and (j=1). Thus (a_{31}=2(3)-1=5).

Step 2

Why this answer is correct

The correct answer is C. (5). For \(a_{31}\), (i=3) and (j=1). Thus (a_{31}=2(3)-1=5).

Step 3

Exam Tip

\(a_{31}\) के लिए (i=3) और (j=1) है। इसलिए (a_{31}=2(3)-1=5)।

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Question 19/50 Easy Mathematics Matrix Introduction to matrices Class 12 Level 34

यदि \(A=[a_{ij}]{2\times3}\) और (a{ij}=i), तो मैट्रिक्स (A) क्या होगी?

If \(A=[a_{ij}]*{2\times3}\) and (a*{ij}=i), what will the matrix (A) be?

Explanation opens after your attempt

Correct Answer

A. \(A=\begin{bmatrix}1&1&1\2&2&2\end{bmatrix}\)

Step 1

Concept

In \(a_{ij}=i\), all elements in a row equal the row number. The first row has (1) and the second row has (2).

Step 2

Why this answer is correct

The correct answer is A. \(A=\begin{bmatrix}1&1&1\2&2&2\end{bmatrix}\). In \(a_{ij}=i\), all elements in a row equal the row number. The first row has (1) and the second row has (2).

Step 3

Exam Tip

\(a_{ij}=i\) में प्रत्येक पंक्ति के सभी अवयव उसी पंक्ति संख्या के बराबर होंगे। पहली पंक्ति में (1) और दूसरी में (2) आएगा।

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Question 20/50 Easy Mathematics Matrix Introduction to matrices Class 12 Level 34

यदि \(A=[a_{ij}]{2\times2}\) और (a{ij}=j), तो (A) क्या है?

If \(A=[a_{ij}]*{2\times2}\) and (a*{ij}=j), what is (A)?

Explanation opens after your attempt

Correct Answer

A. \(A=\begin{bmatrix}1&2\1&2\end{bmatrix}\)

Step 1

Concept

In \(a_{ij}=j\), each element equals the column number. So each row becomes (1,2).

Step 2

Why this answer is correct

The correct answer is A. \(A=\begin{bmatrix}1&2\1&2\end{bmatrix}\). In \(a_{ij}=j\), each element equals the column number. So each row becomes (1,2).

Step 3

Exam Tip

\(a_{ij}=j\) में अवयव स्तंभ संख्या के बराबर होता है। इसलिए हर पंक्ति में (1,2) आएगा।

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Question 21/50 Easy Mathematics Matrix Introduction to matrices Class 12 Level 34

मैट्रिक्स \(A=\begin{bmatrix}1&2\3&4\5&6\end{bmatrix}\) में कितनी पंक्तियां हैं?

How many rows are there in \(A=\begin{bmatrix}1&2\3&4\5&6\end{bmatrix}\)?

Explanation opens after your attempt

Correct Answer

B. (3)

Step 1

Concept

The given matrix has (3) horizontal lists. Therefore the number of rows is (3).

Step 2

Why this answer is correct

The correct answer is B. (3). The given matrix has (3) horizontal lists. Therefore the number of rows is (3).

Step 3

Exam Tip

दिए गए मैट्रिक्स में क्षैतिज सूचियां (3) हैं। इसलिए पंक्तियों की संख्या (3) है।

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Question 22/50 Easy Mathematics Matrix Introduction to matrices Class 12 Level 34

मैट्रिक्स \(A=\begin{bmatrix}1&2&3&4\5&6&7&8\end{bmatrix}\) में कितने स्तंभ हैं?

How many columns are there in \(A=\begin{bmatrix}1&2&3&4\5&6&7&8\end{bmatrix}\)?

Explanation opens after your attempt

Correct Answer

C. (4)

Step 1

Concept

Each row has (4) elements, so there are (4) columns. Columns run from top to bottom.

Step 2

Why this answer is correct

The correct answer is C. (4). Each row has (4) elements, so there are (4) columns. Columns run from top to bottom.

Step 3

Exam Tip

हर पंक्ति में (4) अवयव हैं, इसलिए (4) स्तंभ हैं। स्तंभ ऊपर से नीचे बनते हैं।

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Question 23/50 Easy Mathematics Matrix Introduction to matrices Class 12 Level 34

यदि मैट्रिक्स का क्रम \(m\times n\) है, तो उसमें कुल अवयवों की संख्या क्या होगी?

If the order of a matrix is \(m\times n\), what is the total number of elements?

Explanation opens after your attempt

Correct Answer

C. (mn)

Step 1

Concept

The total elements are obtained by multiplying rows and columns. Therefore the number is (mn).

Step 2

Why this answer is correct

The correct answer is C. (mn). The total elements are obtained by multiplying rows and columns. Therefore the number is (mn).

Step 3

Exam Tip

कुल अवयव पंक्तियों और स्तंभों के गुणनफल से मिलते हैं। इसलिए संख्या (mn) है।

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Question 24/50 Easy Mathematics Matrix Introduction to matrices Class 12 Level 34

यदि किसी मैट्रिक्स में (15) अवयव हैं और (3) पंक्तियां हैं, तो स्तंभों की संख्या क्या है?

If a matrix has (15) elements and (3) rows, what is the number of columns?

Explanation opens after your attempt

Correct Answer

B. (5)

Step 1

Concept

Total elements (=) rows \(\times\) columns. Thus \(15=3\times n\) gives (n=5).

Step 2

Why this answer is correct

The correct answer is B. (5). Total elements (=) rows \(\times\) columns. Thus \(15=3\times n\) gives (n=5).

Step 3

Exam Tip

कुल अवयव (=) पंक्ति \(\times\) स्तंभ होता है। इसलिए \(15=3\times n\) से (n=5)।

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Question 25/50 Easy Mathematics Matrix Introduction to matrices Class 12 Level 34

यदि किसी मैट्रिक्स में (24) अवयव हैं और (6) स्तंभ हैं, तो पंक्तियों की संख्या क्या है?

If a matrix has (24) elements and (6) columns, what is the number of rows?

Explanation opens after your attempt

Correct Answer

A. (4)

Step 1

Concept

Total elements (=) rows \(\times\) columns. From \(24=m\times6\), we get (m=4).

Step 2

Why this answer is correct

The correct answer is A. (4). Total elements (=) rows \(\times\) columns. From \(24=m\times6\), we get (m=4).

Step 3

Exam Tip

कुल अवयव (=) पंक्ति \(\times\) स्तंभ है। \(24=m\times6\) से (m=4) मिलता है।

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Question 26/50 Easy Mathematics Matrix Introduction to matrices Class 12 Level 34

एक \(1\times1\) मैट्रिक्स में कितने अवयव होते हैं?

How many elements are there in a \(1\times1\) matrix?

Explanation opens after your attempt

Correct Answer

B. (1)

Step 1

Concept

Since \(1\times1=1\), it has only (1) element. The same rule applies even for small orders.

Step 2

Why this answer is correct

The correct answer is B. (1). Since \(1\times1=1\), it has only (1) element. The same rule applies even for small orders.

Step 3

Exam Tip

\(1\times1=1\), इसलिए इसमें केवल (1) अवयव होता है। छोटे क्रम में भी वही नियम लागू होता है।

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Question 27/50 Easy Mathematics Matrix Introduction to matrices Class 12 Level 34

मैट्रिक्स \(A=\begin{bmatrix}2&0&0\0&3&0\0&0&4\end{bmatrix}\) किस प्रकार की मैट्रिक्स है?

What type of matrix is \(A=\begin{bmatrix}2&0&0\0&3&0\0&0&4\end{bmatrix}\)?

Explanation opens after your attempt

Correct Answer

A. विकर्ण मैट्रिक्सDiagonal matrix

Step 1

Concept

All elements outside the main diagonal are (0). Therefore this is a diagonal matrix.

Step 2

Why this answer is correct

The correct answer is A. विकर्ण मैट्रिक्स / Diagonal matrix. All elements outside the main diagonal are (0). Therefore this is a diagonal matrix.

Step 3

Exam Tip

मुख्य विकर्ण के बाहर सभी अवयव (0) हैं। इसलिए यह विकर्ण मैट्रिक्स है।

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Question 28/50 Easy Mathematics Matrix Introduction to matrices Class 12 Level 34

मैट्रिक्स \(I=\begin{bmatrix}1&0&0\0&1&0\0&0&1\end{bmatrix}\) को क्या कहते हैं?

What is \(I=\begin{bmatrix}1&0&0\0&1&0\0&0&1\end{bmatrix}\) called?

Explanation opens after your attempt

Correct Answer

A. तीसरे क्रम की इकाई मैट्रिक्सIdentity matrix of order (3)

Step 1

Concept

The main diagonal has (1) and all other positions have (0). It is the \(3\times3\) identity matrix.

Step 2

Why this answer is correct

The correct answer is A. तीसरे क्रम की इकाई मैट्रिक्स / Identity matrix of order (3). The main diagonal has (1) and all other positions have (0). It is the \(3\times3\) identity matrix.

Step 3

Exam Tip

मुख्य विकर्ण पर (1) और बाकी स्थानों पर (0) हैं। यह \(3\times3\) इकाई मैट्रिक्स है।

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Question 29/50 Easy Mathematics Matrix Introduction to matrices Class 12 Level 34

किस प्रकार की मैट्रिक्स में केवल मुख्य विकर्ण के बाहर के अवयव (0) होना अनिवार्य है?

In which type of matrix must the elements outside the main diagonal be (0)?

Explanation opens after your attempt

Correct Answer

B. विकर्ण मैट्रिक्सDiagonal matrix

Step 1

Concept

In a diagonal matrix, all elements outside the main diagonal are (0). Main diagonal elements may be (0) or nonzero.

Step 2

Why this answer is correct

The correct answer is B. विकर्ण मैट्रिक्स / Diagonal matrix. In a diagonal matrix, all elements outside the main diagonal are (0). Main diagonal elements may be (0) or nonzero.

Step 3

Exam Tip

विकर्ण मैट्रिक्स में मुख्य विकर्ण के बाहर सभी अवयव (0) होते हैं। मुख्य विकर्ण के अवयव (0) या nonzero हो सकते हैं।

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Question 30/50 Easy Mathematics Matrix Introduction to matrices Class 12 Level 34

किस मैट्रिक्स में मुख्य विकर्ण के सभी अवयव समान होते हैं और बाकी अवयव (0) होते हैं?

In which matrix are all main diagonal elements equal and the remaining elements (0)?

Explanation opens after your attempt

Correct Answer

A. अदिश मैट्रिक्सScalar matrix

Step 1

Concept

In a scalar matrix, the main diagonal has the same number. All other elements are (0).

Step 2

Why this answer is correct

The correct answer is A. अदिश मैट्रिक्स / Scalar matrix. In a scalar matrix, the main diagonal has the same number. All other elements are (0).

Step 3

Exam Tip

अदिश मैट्रिक्स में मुख्य विकर्ण पर समान संख्या होती है। बाकी सभी अवयव (0) होते हैं।

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Question 31/50 Easy Mathematics Matrix Introduction to matrices Class 12 Level 34

किस मैट्रिक्स में मुख्य विकर्ण के सभी अवयव (1) और बाकी अवयव (0) होते हैं?

In which matrix are all main diagonal elements (1) and the remaining elements (0)?

Explanation opens after your attempt

Correct Answer

C. इकाई मैट्रिक्सIdentity matrix

Step 1

Concept

In an identity matrix, the main diagonal elements are (1). The remaining elements are (0).

Step 2

Why this answer is correct

The correct answer is C. इकाई मैट्रिक्स / Identity matrix. In an identity matrix, the main diagonal elements are (1). The remaining elements are (0).

Step 3

Exam Tip

इकाई मैट्रिक्स में मुख्य विकर्ण पर (1) होते हैं। बाकी अवयव (0) होते हैं।

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Question 32/50 Easy Mathematics Matrix Introduction to matrices Class 12 Level 34

मैट्रिक्स \(A=\begin{bmatrix}1&2\3&4\end{bmatrix}\) का परिवर्तित मैट्रिक्स \(A^T\) क्या है?

What is the transpose \(A^T\) of \(A=\begin{bmatrix}1&2\3&4\end{bmatrix}\)?

Explanation opens after your attempt

Correct Answer

A. \(A^T=\begin{bmatrix}1&3\2&4\end{bmatrix}\)

Step 1

Concept

In transpose, rows become columns. Hence \(A^T=\begin{bmatrix}1&3\2&4\end{bmatrix}\).

Step 2

Why this answer is correct

The correct answer is A. \(A^T=\begin{bmatrix}1&3\2&4\end{bmatrix}\). In transpose, rows become columns. Hence \(A^T=\begin{bmatrix}1&3\2&4\end{bmatrix}\).

Step 3

Exam Tip

परिवर्तित मैट्रिक्स में पंक्तियां स्तंभ बन जाती हैं। इसलिए \(A^T=\begin{bmatrix}1&3\2&4\end{bmatrix}\)।

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Question 33/50 Easy Mathematics Matrix Introduction to matrices Class 12 Level 34

यदि (A) का क्रम \(2\times3\) है, तो \(A^T\) का क्रम क्या होगा?

If the order of (A) is \(2\times3\), what will be the order of \(A^T\)?

Explanation opens after your attempt

Correct Answer

B. \(3\times2\)

Step 1

Concept

On taking transpose, rows and columns interchange. Therefore the transpose of \(2\times3\) has order \(3\times2\).

Step 2

Why this answer is correct

The correct answer is B. \(3\times2\). On taking transpose, rows and columns interchange. Therefore the transpose of \(2\times3\) has order \(3\times2\).

Step 3

Exam Tip

Transpose लेने पर पंक्तियां और स्तंभ आपस में बदल जाते हैं। इसलिए \(2\times3\) का transpose \(3\times2\) होगा।

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Question 34/50 Easy Mathematics Matrix Introduction to matrices Class 12 Level 34

मैट्रिक्स \(A=\begin{bmatrix}1&0\0&2\end{bmatrix}\) में मुख्य विकर्ण के अवयव कौन-से हैं?

What are the main diagonal elements in \(A=\begin{bmatrix}1&0\0&2\end{bmatrix}\)?

Explanation opens after your attempt

Correct Answer

A. (1) और (2)(1) and (2)

Step 1

Concept

The main diagonal goes from top-left to bottom-right. Therefore the elements are (1) and (2).

Step 2

Why this answer is correct

The correct answer is A. (1) और (2) / (1) and (2). The main diagonal goes from top-left to bottom-right. Therefore the elements are (1) and (2).

Step 3

Exam Tip

मुख्य विकर्ण ऊपर बाएं से नीचे दाएं जाता है। इसलिए अवयव (1) और (2) हैं।

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Question 35/50 Easy Mathematics Matrix Introduction to matrices Class 12 Level 34

मैट्रिक्स \(A=\begin{bmatrix}0&5\7&0\end{bmatrix}\) के off-diagonal अवयव कौन-से हैं?

What are the off-diagonal elements of \(A=\begin{bmatrix}0&5\7&0\end{bmatrix}\)?

Explanation opens after your attempt

Correct Answer

B. (5) और (7)(5) and (7)

Step 1

Concept

The elements outside the main diagonal are off-diagonal elements. Here they are (5) and (7).

Step 2

Why this answer is correct

The correct answer is B. (5) और (7) / (5) and (7). The elements outside the main diagonal are off-diagonal elements. Here they are (5) and (7).

Step 3

Exam Tip

मुख्य विकर्ण के बाहर वाले अवयव off-diagonal होते हैं। यहां वे (5) और (7) हैं।

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Question 36/50 Easy Mathematics Matrix Introduction to matrices Class 12 Level 34

कौन-सा कथन मैट्रिक्स की सही परिभाषा देता है?

Which statement gives the correct definition of a matrix?

Explanation opens after your attempt

Correct Answer

A. संख्याओं की आयताकार व्यवस्थाA rectangular arrangement of numbers

Step 1

Concept

A matrix is a rectangular arrangement of numbers or expressions. It is written in rows and columns.

Step 2

Why this answer is correct

The correct answer is A. संख्याओं की आयताकार व्यवस्था / A rectangular arrangement of numbers. A matrix is a rectangular arrangement of numbers or expressions. It is written in rows and columns.

Step 3

Exam Tip

मैट्रिक्स संख्याओं या व्यंजकों की आयताकार व्यवस्था है। इसे पंक्तियों और स्तंभों में लिखा जाता है।

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Question 37/50 Easy Mathematics Matrix Introduction to matrices Class 12 Level 34

मैट्रिक्स \(A=\begin{bmatrix}2&3&4\end{bmatrix}\) का क्रम क्या है?

What is the order of \(A=\begin{bmatrix}2&3&4\end{bmatrix}\)?

Explanation opens after your attempt

Correct Answer

A. \(1\times3\)

Step 1

Concept

It has (1) row and (3) columns. Therefore its order is \(1\times3\).

Step 2

Why this answer is correct

The correct answer is A. \(1\times3\). It has (1) row and (3) columns. Therefore its order is \(1\times3\).

Step 3

Exam Tip

इसमें (1) पंक्ति और (3) स्तंभ हैं। इसलिए इसका क्रम \(1\times3\) है।

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Question 38/50 Easy Mathematics Matrix Introduction to matrices Class 12 Level 34

मैट्रिक्स \(A=\begin{bmatrix}2\3\4\5\end{bmatrix}\) का क्रम क्या है?

What is the order of \(A=\begin{bmatrix}2\3\4\5\end{bmatrix}\)?

Explanation opens after your attempt

Correct Answer

B. \(4\times1\)

Step 1

Concept

It has (4) rows and (1) column. Therefore its order is \(4\times1\).

Step 2

Why this answer is correct

The correct answer is B. \(4\times1\). It has (4) rows and (1) column. Therefore its order is \(4\times1\).

Step 3

Exam Tip

इसमें (4) पंक्तियां और (1) स्तंभ है। इसलिए इसका क्रम \(4\times1\) है।

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Question 39/50 Easy Mathematics Matrix Introduction to matrices Class 12 Level 34

यदि \(A=[a_{ij}]{3\times3}\) है, तो (a{13}) किस स्थान का अवयव है?

If \(A=[a_{ij}]*{3\times3}\), then (a*{13}) is the element at which position?

Explanation opens after your attempt

Correct Answer

A. पहली पंक्ति और तीसरा स्तंभ(1)st row and (3)rd column

Step 1

Concept

In \(a_{13}\), (1) tells the row and (3) tells the column. The index order is always row then column.

Step 2

Why this answer is correct

The correct answer is A. पहली पंक्ति और तीसरा स्तंभ / (1)st row and (3)rd column. In \(a_{13}\), (1) tells the row and (3) tells the column. The index order is always row then column.

Step 3

Exam Tip

\(a_{13}\) में (1) पंक्ति को और (3) स्तंभ को बताता है। index का क्रम हमेशा पंक्ति फिर स्तंभ होता है।

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Question 40/50 Easy Mathematics Matrix Class 12 Level 34

यदि \(A=\begin{bmatrix}1&2&3\\4&5&6\end{bmatrix}\), तो दूसरी पंक्ति कौन-सी है?

If \(A=\begin{bmatrix}1&2&3\\4&5&6\end{bmatrix}\), which is the second row?

Explanation opens after your attempt

Correct Answer

B. (4,5,6)

Step 1

Concept

The second row is the lower horizontal list. Therefore the second row is (4,5,6).

Step 2

Why this answer is correct

The correct answer is B. (4,5,6). The second row is the lower horizontal list. Therefore the second row is (4,5,6).

Step 3

Exam Tip

दूसरी पंक्ति में नीचे वाली क्षैतिज सूची आती है। इसलिए दूसरी पंक्ति (4,5,6) है।

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Question 41/50 Easy Mathematics Matrix Class 12 Level 34

यदि \(A=\begin{bmatrix}1&2&3\\4&5&6\end{bmatrix}\), तो तीसरा स्तंभ कौन-सा है?

If \(A=\begin{bmatrix}1&2&3\\4&5&6\end{bmatrix}\), which is the third column?

Explanation opens after your attempt

Correct Answer

C. (3,6)

Step 1

Concept

The third column is the third vertical list. Therefore it contains (3) and (6).

Step 2

Why this answer is correct

The correct answer is C. (3,6). The third column is the third vertical list. Therefore it contains (3) and (6).

Step 3

Exam Tip

तीसरा स्तंभ तीसरी vertical सूची है। इसलिए उसमें (3) और (6) हैं।

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Question 42/50 Easy Mathematics Matrix Class 12 Level 34

यदि \(A=\begin{bmatrix}1&2\\3&4\end{bmatrix}\) और \(B=\begin{bmatrix}1&2\\3&5\end{bmatrix}\), तो कौन-सा कथन सही है?

If \(A=\begin{bmatrix}1&2\\3&4\end{bmatrix}\) and \(B=\begin{bmatrix}1&2\\3&5\end{bmatrix}\), which statement is correct?

Explanation opens after your attempt

Correct Answer

B. \(A\ne B\)

Step 1

Concept

Their order is the same, but the last elements (4) and (5) are not equal. Therefore \(A\ne B\).

Step 2

Why this answer is correct

The correct answer is B. \(A\ne B\). Their order is the same, but the last elements (4) and (5) are not equal. Therefore \(A\ne B\).

Step 3

Exam Tip

दोनों का क्रम समान है, पर अंतिम अवयव (4) और (5) बराबर नहीं हैं। इसलिए \(A\ne B\)।

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Question 43/50 Easy Mathematics Matrix Class 12 Level 34

यदि \(A=\begin{bmatrix}x&1\\2&y\end{bmatrix}\) और \(B=\begin{bmatrix}3&1\\2&4\end{bmatrix}\) तथा (A=B), तो ((x,y)) क्या है?

If \(A=\begin{bmatrix}x&1\\2&y\end{bmatrix}\) and \(B=\begin{bmatrix}3&1\\2&4\end{bmatrix}\) with (A=B), what is ((x,y))?

Explanation opens after your attempt

Correct Answer

A. ((3,4))

Step 1

Concept

In equal matrices, corresponding elements are equal. Therefore (x=3) and (y=4).

Step 2

Why this answer is correct

The correct answer is A. ((3,4)). In equal matrices, corresponding elements are equal. Therefore (x=3) and (y=4).

Step 3

Exam Tip

बराबर मैट्रिक्स में समान स्थानों पर बराबर अवयव होते हैं। इसलिए (x=3) और (y=4)।

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Question 44/50 Easy Mathematics Matrix Class 12 Level 34

मैट्रिक्स \(A=\begin{bmatrix}1&2&3\\4&5&6\end{bmatrix}\) का \(A^T\) किस क्रम का होगा?

What will be the order of \(A^T\) for \(A=\begin{bmatrix}1&2&3\\4&5&6\end{bmatrix}\)?

Explanation opens after your attempt

Correct Answer

B. \(3\times2\)

Step 1

Concept

The order of (A) is \(2\times3\). In transpose, the order changes to \(3\times2\).

Step 2

Why this answer is correct

The correct answer is B. \(3\times2\). The order of (A) is \(2\times3\). In transpose, the order changes to \(3\times2\).

Step 3

Exam Tip

(A) का क्रम \(2\times3\) है। transpose में क्रम बदलकर \(3\times2\) हो जाता है।

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Question 45/50 Easy Mathematics Matrix Introduction to matrices Class 12 Level 34

कौन-सा विकल्प \(2\times2\) शून्य मैट्रिक्स है?

Which option is the \(2\times2\) zero matrix?

Explanation opens after your attempt

Correct Answer

A. \(\begin{bmatrix}0&0\0&0\end{bmatrix}\)

Step 1

Concept

Every element in a zero matrix is (0). In the first option, all four elements are (0).

Step 2

Why this answer is correct

The correct answer is A. \(\begin{bmatrix}0&0\0&0\end{bmatrix}\). Every element in a zero matrix is (0). In the first option, all four elements are (0).

Step 3

Exam Tip

शून्य मैट्रिक्स में हर अवयव (0) होता है। पहले विकल्प में चारों अवयव (0) हैं।

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Question 46/50 Easy Mathematics Matrix Introduction to matrices Class 12 Level 34

कौन-सा विकल्प \(2\times2\) इकाई मैट्रिक्स है?

Which option is the \(2\times2\) identity matrix?

Explanation opens after your attempt

Correct Answer

B. \(\begin{bmatrix}1&0\0&1\end{bmatrix}\)

Step 1

Concept

An identity matrix has (1) on the main diagonal and (0) elsewhere. This form is in the second option.

Step 2

Why this answer is correct

The correct answer is B. \(\begin{bmatrix}1&0\0&1\end{bmatrix}\). An identity matrix has (1) on the main diagonal and (0) elsewhere. This form is in the second option.

Step 3

Exam Tip

इकाई मैट्रिक्स में मुख्य विकर्ण पर (1) और बाकी (0) होते हैं। यह रूप दूसरे विकल्प में है।

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Question 47/50 Easy Mathematics Matrix Introduction to matrices Class 12 Level 34

यदि \(A=[a_{ij}]{2\times2}\) और (a{ij}=0) सभी (i,j) के लिए है, तो (A) कैसी मैट्रिक्स है?

If \(A=[a_{ij}]*{2\times2}\) and (a*{ij}=0) for all (i,j), what type of matrix is (A)?

Explanation opens after your attempt

Correct Answer

B. शून्य मैट्रिक्सZero matrix

Step 1

Concept

When all elements are (0), the matrix is a zero matrix. This is a direct definition-based question.

Step 2

Why this answer is correct

The correct answer is B. शून्य मैट्रिक्स / Zero matrix. When all elements are (0), the matrix is a zero matrix. This is a direct definition-based question.

Step 3

Exam Tip

जब सभी अवयव (0) हों, तो मैट्रिक्स शून्य मैट्रिक्स होती है। यह definition पर आधारित सीधा प्रश्न है।

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Question 48/50 Easy Mathematics Matrix Introduction to matrices Class 12 Level 34

यदि \(A=[a_{ij}]{3\times3}\) और (a{ij}=1) जब (i=j), तथा \(a_{ij}=0\) जब \(i\ne j\), तो (A) कैसी मैट्रिक्स है?

If \(A=[a_{ij}]*{3\times3}\), (a*{ij}=1) when (i=j), and \(a_{ij}=0\) when \(i\ne j\), what type of matrix is (A)?

Explanation opens after your attempt

Correct Answer

B. इकाई मैट्रिक्सIdentity matrix

Step 1

Concept

(i=j) represents the main diagonal, where the elements are (1). For \(i\ne j\), the other elements are (0), so it is an identity matrix.

Step 2

Why this answer is correct

The correct answer is B. इकाई मैट्रिक्स / Identity matrix. (i=j) represents the main diagonal, where the elements are (1). For \(i\ne j\), the other elements are (0), so it is an identity matrix.

Step 3

Exam Tip

(i=j) मुख्य विकर्ण को दर्शाता है, जहां अवयव (1) हैं। \(i\ne j\) पर बाकी अवयव (0) हैं, इसलिए यह इकाई मैट्रिक्स है।

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Question 49/50 Easy Mathematics Matrix Class 12 Level 34

यदि \(A=\begin{bmatrix}3&0\\0&3\end{bmatrix}\), तो कौन-सा कथन सही है?

If \(A=\begin{bmatrix}3&0\\0&3\end{bmatrix}\), which statement is correct?

Explanation opens after your attempt

Correct Answer

A. (A) अदिश मैट्रिक्स है(A) is a scalar matrix

Step 1

Concept

The main diagonal has equal elements (3), and outside elements are (0). Therefore (A) is a scalar matrix.

Step 2

Why this answer is correct

The correct answer is A. (A) अदिश मैट्रिक्स है / (A) is a scalar matrix. The main diagonal has equal elements (3), and outside elements are (0). Therefore (A) is a scalar matrix.

Step 3

Exam Tip

मुख्य विकर्ण पर समान अवयव (3) हैं और बाहर के अवयव (0) हैं। इसलिए (A) अदिश मैट्रिक्स है।

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Question 50/50 Easy Mathematics Matrix Class 12 Level 34

मैट्रिक्स \(A=\begin{bmatrix}9&8\\7&6\end{bmatrix}\) में \(a_{22}\) का मान क्या है?

What is the value of \(a_{22}\) in \(A=\begin{bmatrix}9&8\\7&6\end{bmatrix}\)?

Explanation opens after your attempt

Correct Answer

D. (6)

Step 1

Concept

\(a_{22}\) is the element in the second row and second column. In the given matrix, it is (6).

Step 2

Why this answer is correct

The correct answer is D. (6). \(a_{22}\) is the element in the second row and second column. In the given matrix, it is (6).

Step 3

Exam Tip

\(a_{22}\) दूसरी पंक्ति और दूसरे स्तंभ का अवयव है। दिए गए मैट्रिक्स में यह (6) है।

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Class 12 Mathematics Easy Quiz

मैट्रिक्स \(A=\begin{bmatrix}1&2&3\\4&5&6\end{bmatrix}\) का क्रम क्या है?

Concept

Why this answer is correct

Exam Tip

मैट्रिक्स \(B=\begin{bmatrix}7\\8\\9\end{bmatrix}\) किस प्रकार की मैट्रिक्स है?

Concept

Why this answer is correct

Exam Tip

मैट्रिक्स \(C=\begin{bmatrix}4&5&6\end{bmatrix}\) किस प्रकार की मैट्रिक्स है?

Concept

Why this answer is correct

Exam Tip

यदि किसी मैट्रिक्स में (3) पंक्तियां और (4) स्तंभ हैं, तो उसमें कुल कितने अवयव होंगे?

Concept

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Exam Tip

मैट्रिक्स \(A=[a_{ij}]*{2\times3}\) में (i) क्या दर्शाता है?

Concept

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Exam Tip

मैट्रिक्स \(A=[a_{ij}]\) में \(a_{23}\) का अर्थ क्या है?

Concept

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Exam Tip

मैट्रिक्स \(A=\begin{bmatrix}1&0\0&1\end{bmatrix}\) किस प्रकार की मैट्रिक्स है?

Concept

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Exam Tip

मैट्रिक्स \(O=\begin{bmatrix}0&0\0&0\end{bmatrix}\) किस प्रकार की मैट्रिक्स है?

Concept

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Exam Tip

कौन-सी मैट्रिक्स वर्ग मैट्रिक्स है?

Concept

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Exam Tip

कौन-सी मैट्रिक्स आयताकार मैट्रिक्स है?

Concept

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Exam Tip

मैट्रिक्स \(A=\begin{bmatrix}2&0\0&3\end{bmatrix}\) किस प्रकार की मैट्रिक्स है?

Concept

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Exam Tip

मैट्रिक्स \(A=\begin{bmatrix}5&0\0&5\end{bmatrix}\) किस प्रकार की मैट्रिक्स है?

Concept

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Exam Tip

मैट्रिक्स \(A=\begin{bmatrix}1&2\3&4\end{bmatrix}\) में \(a_{12}\) का मान क्या है?

Concept

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Exam Tip

मैट्रिक्स \(A=\begin{bmatrix}6&7&8\9&10&11\end{bmatrix}\) में \(a_{21}\) का मान क्या है?

Concept

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Exam Tip

दो मैट्रिक्स (A) और (B) बराबर कब कहलाती हैं?

Concept

Why this answer is correct

Exam Tip

यदि \(A=\begin{bmatrix}x&2\3&4\end{bmatrix}\) और \(B=\begin{bmatrix}5&2\3&4\end{bmatrix}\) तथा (A=B), तो (x) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

यदि \(A=[a_{ij}]*{2\times2}\) और (a*{ij}=i+j), तो \(a_{22}\) का मान क्या है?

Concept

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Exam Tip

यदि \(A=[a_{ij}]*{3\times2}\) और (a*{ij}=2i-j), तो \(a_{31}\) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

यदि \(A=[a_{ij}]*{2\times3}\) और (a*{ij}=i), तो मैट्रिक्स (A) क्या होगी?

Concept

Why this answer is correct

Exam Tip

यदि \(A=[a_{ij}]*{2\times2}\) और (a*{ij}=j), तो (A) क्या है?

Concept

Why this answer is correct

यदि \(A=[a_{ij}]{2\times2}\) और (a{ij}=i+j), तो \(a_{22}\) का मान क्या है?

यदि \(A=[a_{ij}]{3\times2}\) और (a{ij}=2i-j), तो \(a_{31}\) का मान क्या है?

यदि \(A=[a_{ij}]{2\times3}\) और (a{ij}=i), तो मैट्रिक्स (A) क्या होगी?

यदि \(A=[a_{ij}]{2\times2}\) और (a{ij}=j), तो (A) क्या है?