Match the system of linear equations in Column A with their number of solutions in column B and their geometric representation in Column C. Table matching systems of linear equations, number of solutions and 3D plane plots (Table M2Q1:1) Choose the correct option from the following:

(D) i) → a → 2, ii) → b → 1.

(A) i) → b → 1, ii) → a → 2.

(B) i) → a → 1, ii) → b → 2.

(C) i) → b → 2, ii) → a → 1.

Figure from the original question paper

(A) Option figure from the original question paper

(B) Option figure from the original question paper

(C) Option figure from the original question paper

(D) Option figure from the original question paper

Figure from the original question paper

(B) W is closed under scalar multiplication.

(A) W is closed under addition.

Maths 2 Quiz 1 PYQ May 2023: 16 Jul 2023

Question 1

+2 marksOne correct option

Match the system of linear equations in Column A with their number of solutions in column B and their geometric representation in Column C.

Choose the correct option from the following:

A
i) → b → 1, ii) → a → 2.
B
i) → a → 1, ii) → b → 2.
C
i) → b → 2, ii) → a → 1.
D
i) → a → 2, ii) → b → 1.

Show answer

Correct answer

D
i) → a → 2, ii) → b → 1.

Question 1 on its own page

Question 2

+2 marksOne or more correct options

Which of the following matrices satisfy A*^(k)* = 0 for some natural number k?

Select all that apply.

A
B
C
D

Show answer

Correct answers

A
B

Question 2 on its own page

Question 3

+2 marksOne or more correct options

Select all that apply.

A
B
C
D

Show answer

Correct answers

A
B

Question 3 on its own page

Question 4

+2 marksOne or more correct options

Select the true statement(s).

Select all that apply.

A
Any subset of a linearly independent set is a linearly independent set.
B
Any superset of a spanning set is a spanning set.
C
Any subset of a basis is a basis.
D
Any superset of a subspace is a subspace.

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Correct answers

A
Any subset of a linearly independent set is a linearly independent set.
B
Any superset of a spanning set is a spanning set.

Question 4 on its own page

Question 5

+2 marksOne or more correct options

Select all that apply.

A
W is closed under addition.
B
W is closed under scalar multiplication.
C
W is a vector space.
D
W is not a vector space.

Show answer

Correct answers

B
W is closed under scalar multiplication.
D
W is not a vector space.

Question 5 on its own page

Question 6

+2 marksNumerical answer

Show answer

Correct answer: 505.5

Question 6 on its own page

Question 7

+3 marksNumerical answer

Show answer

Correct answer: 9

Question 7 on its own page

Question 8

+1 markNumerical answer

What is the dimension of vector spaces for the given subquestions.

Show answer

Correct answer: 1

Question 8 on its own page

Question 9

+2 marksNumerical answer

What is the dimension of vector spaces for the given subquestions.

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Correct answer: 5

Question 9 on its own page

Question 10

+1 markOne correct option

Shivani, Sruthi and Smriti enjoyed shopping on a Sunday. Shivani bought 2 shirts, a T-shirt and 2 pants, whereas Sruthi bought a T-shirt and a pant and Smriti bought 2 shirts and a pant. They paid Rs. 600, Rs. 400 and Rs. 300 respectively. Suppose $x_1$ is the price of a shirt, $x_2$ is the price of a T-shirt and $x_3$ is the price of a pant. Then the above information forms a system of linear equations. If $Ax = b$ is the matrix representation of the above system, where $x = \begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix}$ is the vector that represents the price of a shirt, T-shirt and pant respectively, answer the given subquestions.

Choose the correct option(s):

A
B
C
D

Show answer

Correct answer

B

Question 10 on its own page

Question 11

+2 marksNumerical answer

Shivani, Sruthi and Smriti enjoyed shopping on a Sunday. Shivani bought 2 shirts, a T-shirt and 2 pants, whereas Sruthi bought a T-shirt and a pant and Smriti bought 2 shirts and a pant. They paid Rs. 600, Rs. 400 and Rs. 300 respectively. Suppose $x_1$ is the price of a shirt, $x_2$ is the price of a T-shirt and $x_3$ is the price of a pant. Then the above information forms a system of linear equations. If $Ax = b$ is the matrix representation of the above system, where $x = \begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix}$ is the vector that represents the price of a shirt, T-shirt and pant respectively, answer the given subquestions.

How many solutions does the given system Ax = b have?

Show answer

Correct answer: 0

Question 11 on its own page

Question 12

+1 markNumerical answer

Shivani, Sruthi and Smriti enjoyed shopping on a Sunday. Shivani bought 2 shirts, a T-shirt and 2 pants, whereas Sruthi bought a T-shirt and a pant and Smriti bought 2 shirts and a pant. They paid Rs. 600, Rs. 400 and Rs. 300 respectively. Suppose $x_1$ is the price of a shirt, $x_2$ is the price of a T-shirt and $x_3$ is the price of a pant. Then the above information forms a system of linear equations. If $Ax = b$ is the matrix representation of the above system, where $x = \begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix}$ is the vector that represents the price of a shirt, T-shirt and pant respectively, answer the given subquestions.

Consider the set S of solutions of the system Ax = 0, where A is as given. Clearly, S is a vector space with respect to usual addition and scalar multiplication. What is the dimension of S?

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Correct answer: 1

Question 12 on its own page

Question 13

+2 marksOne correct option

Shivani, Sruthi and Smriti enjoyed shopping on a Sunday. Shivani bought 2 shirts, a T-shirt and 2 pants, whereas Sruthi bought a T-shirt and a pant and Smriti bought 2 shirts and a pant. They paid Rs. 600, Rs. 400 and Rs. 300 respectively. Suppose $x_1$ is the price of a shirt, $x_2$ is the price of a T-shirt and $x_3$ is the price of a pant. Then the above information forms a system of linear equations. If $Ax = b$ is the matrix representation of the above system, where $x = \begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix}$ is the vector that represents the price of a shirt, T-shirt and pant respectively, answer the given subquestions.

Which of the following forms a basis for S?

A
B
C
D

Show answer

Correct answer

B

Question 13 on its own page

Question 14

+1 markNumerical answer

Shivani, Sruthi and Smriti enjoyed shopping on a Sunday. Shivani bought 2 shirts, a T-shirt and 2 pants, whereas Sruthi bought a T-shirt and a pant and Smriti bought 2 shirts and a pant. They paid Rs. 600, Rs. 400 and Rs. 300 respectively. Suppose $x_1$ is the price of a shirt, $x_2$ is the price of a T-shirt and $x_3$ is the price of a pant. Then the above information forms a system of linear equations. If $Ax = b$ is the matrix representation of the above system, where $x = \begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix}$ is the vector that represents the price of a shirt, T-shirt and pant respectively, answer the given subquestions.

What is the rank of A?

Show answer

Correct answer: 2

Question 14 on its own page