Figure from the original question paper

(C) Only S1 and S3 are correct.

(D) Only S1 and S2 are correct.

(E) S1, S2, and S3 are all correct.

Figure from the original question paper

(C) Only S1 and S3 are correct.

(D) Only S1 and S2 are correct.

(E) S1, S2, and S3 are all correct.

Figure from the original question paper

(C) Only S1 and S3 are correct.

(D) Only S1 and S2 are correct.

(E) S1, S2, and S3 are all correct.

Maths 2 Quiz 1 PYQ Jan 2026: 15 Mar 2026 · IITM BS

Question 1

+4 marksOne correct option

A
Only S1 is correct.
B
Only S2 is correct.
C
Only S1 and S3 are correct.
D
Only S1 and S2 are correct.
E
S1, S2, and S3 are all correct.

Show answer

Correct answer

C
Only S1 and S3 are correct.

Question 1 on its own page

Question 2

+4 marksOne correct option

A
Only S1 is correct.
B
Only S2 is correct.
C
Only S1 and S3 are correct.
D
Only S1 and S2 are correct.
E
S1, S2, and S3 are all correct.

Show answer

Correct answer

C
Only S1 and S3 are correct.

Question 2 on its own page

Question 3

+4 marksOne correct option

A
Only S1 is correct.
B
Only S2 is correct.
C
Only S1 and S3 are correct.
D
Only S1 and S2 are correct.
E
S1, S2, and S3 are all correct.

Show answer

Correct answer

C
Only S1 and S3 are correct.

Question 3 on its own page

Question 4

+4 marksOne correct option

Consider a subspace of . Which of the following options describes a basis of ?

A
.
B
.
C
—
D
.

Show answer

Correct answer

A
.

Question 4 on its own page

Question 5

+4 marksOne correct option

Consider a subspace of . Which of the following options describes a basis of ?

A
.
B
.
C
—
D
.

Show answer

Correct answer

A
.

Question 5 on its own page

Question 6

+4 marksOne correct option

Consider a subspace of . Which of the following options describes a basis of ?

A
.
B
.
C
—
D
.

Show answer

Correct answer

A
.

Question 6 on its own page

Question 7

+4 marksOne or more correct options

Which of the following subsets are subspaces of under the usual addition and scalar multiplication?

Select all that apply.

A
.
B
.
C
.
D
.

Show answer

Correct answers

B
.
C
.

Question 7 on its own page

Question 8

+4 marksOne or more correct options

Which of the following subsets are subspaces of under the usual addition and scalar multiplication?

Select all that apply.

A
.
B
.
C
.
D
.

Show answer

Correct answers

B
.
C
.

Question 8 on its own page

Question 9

+4 marksOne or more correct options

Which of the following subsets are subspaces of under the usual addition and scalar multiplication?

Select all that apply.

A
.
B
.
C
.
D
.

Show answer

Correct answers

B
.
C
.

Question 9 on its own page

Question 10

+5 marksOne or more correct options

Let

where are distinct real numbers. Which of the following statements are correct?

Select all that apply.

A
If the sum of every row of is , then is .
B
changes sign if rows 2 and 4 are interchanged.
C
if any two of the numbers are equal.
D
changes sign if each row is multiplied by .

Show answer

Correct answers

A
If the sum of every row of is , then is .
B
changes sign if rows 2 and 4 are interchanged.
C
if any two of the numbers are equal.

Question 10 on its own page

Question 11

+5 marksOne or more correct options

Let

where are distinct real numbers. Which of the following statements are correct?

Select all that apply.

A
If the sum of every row of is , then is .
B
changes sign if rows 2 and 4 are interchanged.
C
if any two of the numbers are equal.
D
changes sign if each row is multiplied by .

Show answer

Correct answers

A
If the sum of every row of is , then is .
B
changes sign if rows 2 and 4 are interchanged.
C
if any two of the numbers are equal.

Question 11 on its own page

Question 12

+5 marksOne or more correct options

Let

where are distinct real numbers. Which of the following statements are correct?

Select all that apply.

A
If the sum of every row of is , then is .
B
changes sign if rows 2 and 4 are interchanged.
C
if any two of the numbers are equal.
D
changes sign if each row is multiplied by .

Show answer

Correct answers

A
If the sum of every row of is , then is .
B
changes sign if rows 2 and 4 are interchanged.
C
if any two of the numbers are equal.

Question 12 on its own page

Question 13

+5 marksOne or more correct options

If is a matrix and is a matrix, then choose the set of correct options.

Select all that apply.

A
If is the augmented matrix and is the matrix obtained from after a finite number of elementary row operations, then the system and the system have the same set of solutions.
B
If is the reduced row echelon form of , then the system has at least one solution.
C
If is the reduced row echelon form of , then is also in reduced row echelon form.
D
If is the reduced row echelon form of and there is no row such that the only non zero entry lies in the last column of , then the system has at least one solution.

Show answer

Correct answers

A
If is the augmented matrix and is the matrix obtained from after a finite number of elementary row operations, then the system and the system have the same set of solutions.
C
If is the reduced row echelon form of , then is also in reduced row echelon form.
D
If is the reduced row echelon form of and there is no row such that the only non zero entry lies in the last column of , then the system has at least one solution.

Question 13 on its own page

Question 14

+5 marksOne or more correct options

If is a matrix and is a matrix, then choose the set of correct options.

Select all that apply.

A
If is the augmented matrix and is the matrix obtained from after a finite number of elementary row operations, then the system and the system have the same set of solutions.
B
If is the reduced row echelon form of , then the system has at least one solution.
C
If is the reduced row echelon form of , then is also in reduced row echelon form.
D
If is the reduced row echelon form of and there is no row such that the only non zero entry lies in the last column of , then the system has at least one solution.

Show answer

Correct answers

A
If is the augmented matrix and is the matrix obtained from after a finite number of elementary row operations, then the system and the system have the same set of solutions.
C
If is the reduced row echelon form of , then is also in reduced row echelon form.
D
If is the reduced row echelon form of and there is no row such that the only non zero entry lies in the last column of , then the system has at least one solution.

Question 14 on its own page

Question 15

+5 marksOne or more correct options

If is a matrix and is a matrix, then choose the set of correct options.

Select all that apply.

A
If is the augmented matrix and is the matrix obtained from after a finite number of elementary row operations, then the system and the system have the same set of solutions.
B
If is the reduced row echelon form of , then the system has at least one solution.
C
If is the reduced row echelon form of , then is also in reduced row echelon form.
D
If is the reduced row echelon form of and there is no row such that the only non zero entry lies in the last column of , then the system has at least one solution.

Show answer

Correct answers

A
If is the augmented matrix and is the matrix obtained from after a finite number of elementary row operations, then the system and the system have the same set of solutions.
C
If is the reduced row echelon form of , then is also in reduced row echelon form.
D
If is the reduced row echelon form of and there is no row such that the only non zero entry lies in the last column of , then the system has at least one solution.

Question 15 on its own page

Question 16

+4 marksWritten answer

A company produces two types of gadgets, A and B. • Each gadget A requires 2 hours of assembly and 3 hours of testing. • Each gadget B requires 3 hours of assembly and 2 hours of testing. The company has 8 hours of assembly and 7 hours of testing available per week. The profit from gadget A is Rs 5, and from gadget B is Rs 4. Determine the total profit if the company uses all available assembly and testing hours.

Show answer

A written answer, not marked automatically.

Question 16 on its own page

Question 17

+4 marksWritten answer

A company produces two types of gadgets, A and B. • Each gadget A requires 2 hours of assembly and 3 hours of testing. • Each gadget B requires 3 hours of assembly and 2 hours of testing. The company has 8 hours of assembly and 7 hours of testing available per week. The profit from gadget A is Rs 5, and from gadget B is Rs 4. Determine the total profit if the company uses all available assembly and testing hours.

Show answer

A written answer, not marked automatically.

Question 17 on its own page

Question 18

+4 marksWritten answer

A company produces two types of gadgets, A and B. • Each gadget A requires 2 hours of assembly and 3 hours of testing. • Each gadget B requires 3 hours of assembly and 2 hours of testing. The company has 8 hours of assembly and 7 hours of testing available per week. The profit from gadget A is Rs 5, and from gadget B is Rs 4. Determine the total profit if the company uses all available assembly and testing hours.

Show answer

A written answer, not marked automatically.

Question 18 on its own page

Question 19

+4 marksWritten answer

Suppose and . Let be a vector defined as such that and . Find the value of .

Show answer

A written answer, not marked automatically.

Question 19 on its own page

Question 20

+4 marksWritten answer

Suppose and . Let be a vector defined as such that and . Find the value of .

Show answer

A written answer, not marked automatically.

Question 20 on its own page

Question 21

+4 marksWritten answer

Suppose and . Let be a vector defined as such that and . Find the value of .

Show answer

A written answer, not marked automatically.

Question 21 on its own page

Question 22

+4 marksWritten answer

Suppose the vectors , and in are linearly dependent. Find the value of .

Show answer

A written answer, not marked automatically.

Question 22 on its own page

Question 23

+4 marksWritten answer

Suppose the vectors , and in are linearly dependent. Find the value of .

Show answer

A written answer, not marked automatically.

Question 23 on its own page

Question 24

+4 marksWritten answer

Suppose the vectors , and in are linearly dependent. Find the value of .

Show answer

A written answer, not marked automatically.

Question 24 on its own page

Question 25

+4 marksWritten answer

Consider a shop that sells muffins, cookies, and cakes. The total sales on three consecutive days are as follows: • On Monday, 1 muffin, 2 cookies, and 3 cakes were sold for a total of 140. • On Tuesday, 2 muffins, 1 cookie, and 4 cakes were sold for a total of 160. • On Wednesday, 3 muffins, 3 cookies, and 5 cakes were sold for a total of 240. Let , , and denote the price of a muffin, a cookie, and a cake, respectively. Formulate a system of linear equations representing the above scenario and find the value of .

Show answer

A written answer, not marked automatically.

Question 25 on its own page

Question 26

+4 marksWritten answer

Consider a shop that sells muffins, cookies, and cakes. The total sales on three consecutive days are as follows: • On Monday, 1 muffin, 2 cookies, and 3 cakes were sold for a total of 140. • On Tuesday, 2 muffins, 1 cookie, and 4 cakes were sold for a total of 160. • On Wednesday, 3 muffins, 3 cookies, and 5 cakes were sold for a total of 240. Let , , and denote the price of a muffin, a cookie, and a cake, respectively. Formulate a system of linear equations representing the above scenario and find the value of .

Show answer

A written answer, not marked automatically.

Question 26 on its own page

Question 27

+4 marksWritten answer

Consider a shop that sells muffins, cookies, and cakes. The total sales on three consecutive days are as follows: • On Monday, 1 muffin, 2 cookies, and 3 cakes were sold for a total of 140. • On Tuesday, 2 muffins, 1 cookie, and 4 cakes were sold for a total of 160. • On Wednesday, 3 muffins, 3 cookies, and 5 cakes were sold for a total of 240. Let , , and denote the price of a muffin, a cookie, and a cake, respectively. Formulate a system of linear equations representing the above scenario and find the value of .

Show answer

A written answer, not marked automatically.

Question 27 on its own page

Question 28

+2 marksWritten answer

Suppose the rank of the matrix

is . Based on the above data, answer the given subquestions.

Find .

Show answer

A written answer, not marked automatically.

Question 28 on its own page

Question 29

+2 marksWritten answer

Suppose the rank of the matrix

is . Based on the above data, answer the given subquestions.

Find .

Show answer

A written answer, not marked automatically.

Question 29 on its own page

Question 30

+2 marksWritten answer

Suppose the rank of the matrix

is . Based on the above data, answer the given subquestions.

Find .

Show answer

A written answer, not marked automatically.

Question 30 on its own page

Question 31

+2 marksWritten answer

Suppose the rank of the matrix

is . Based on the above data, answer the given subquestions.

Find .

Show answer

A written answer, not marked automatically.

Question 31 on its own page

Question 32

+2 marksWritten answer

Suppose the rank of the matrix

is . Based on the above data, answer the given subquestions.

Find .

Show answer

A written answer, not marked automatically.

Question 32 on its own page

Question 33

+2 marksWritten answer

Suppose the rank of the matrix

is . Based on the above data, answer the given subquestions.

Find .

Show answer

A written answer, not marked automatically.

Question 33 on its own page

Question 34

+4 marksOne correct option

Consider a subset of . Based on the above data, answer the given subquestions.

Which of the following options is correct?

A
B
C
D

Show answer

Correct answer

C

Question 34 on its own page

Question 35

+4 marksOne correct option

Consider a subset of . Based on the above data, answer the given subquestions.

Which of the following options is correct?

A
B
C
D

Show answer

Correct answer

C

Question 35 on its own page

Question 36

+4 marksOne correct option

Consider a subset of . Based on the above data, answer the given subquestions.

Which of the following options is correct?

A
B
C
D

Show answer

Correct answer

C

Question 36 on its own page

Question 37

+4 marksWritten answer

Consider a subset of . Based on the above data, answer the given subquestions.

Consider the vector space with the addition and scalar multiplication operations from the correct option of the previous question. What is the dimension of the vector space?

Show answer

A written answer, not marked automatically.

Question 37 on its own page

Question 38

+4 marksWritten answer

Consider a subset of . Based on the above data, answer the given subquestions.

Consider the vector space with the addition and scalar multiplication operations from the correct option of the previous question. What is the dimension of the vector space?

Show answer

A written answer, not marked automatically.

Question 38 on its own page

Question 39

+4 marksWritten answer

Consider a subset of . Based on the above data, answer the given subquestions.

Consider the vector space with the addition and scalar multiplication operations from the correct option of the previous question. What is the dimension of the vector space?

Show answer

A written answer, not marked automatically.

Question 39 on its own page