Week 2 Mathematics 2 Questions | Prasnya

Prasnya

Continue with Google

Practice path

Qualifier / Quiz 1

Go to subjectMathematics 2 Go to chapterWeek 2

All questions

Give Mock Test Topic wise questions

Filters

Question type / Difficulty / Years (28)

Consider the system of equations in three variables

x,y,z

\begin{aligned}x+y+z&=3\\2x+3y+kz&=6\\3x+5y+(k+1)z&=9\end{aligned}

k

is a real parameter. Consider the following statements:

S_1

: The system has a unique solution if

k\ne 2

S_2

: The system has no solution if

k=2

S_3

: The system has infinitely many solutions for some value of

k

. Choose the correct option.

Single correctMARCH 15, 2026

A

3\times4

b

3\times1

matrix, then choose the set of correct options.

Multiple correctMARCH 15, 2026

A company produces two types of gadgets,

A

B

A

2

hours of assembly and

3

hours of testing. Each gadget

B

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

5

, and from gadget

B

4

. Determine the total profit if the company uses all available assembly and testing hours.

Integer answerMARCH 15, 2026

Consider a shop that sells muffins, cookies, and cakes. The total sales on three consecutive days are as follows: on Monday,

1

2

3

cakes were sold for a total of

140

2

1

4

cakes were sold for a total of

160

. On Wednesday,

3

3

5

cakes were sold for a total of

240

m,c,k

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

m+c+k

Integer answerMARCH 15, 2026

Consider the system of linear equations with unknowns

x,y,z

\begin{bmatrix}1&2&1\\3&0&-1\\1&8&5\end{bmatrix}\begin{bmatrix}x\\y\\z\end{bmatrix}=\begin{bmatrix}b_1\\b_2\\b_3\end{bmatrix},

b_1,b_2,b_3\in\mathbb{R}

. Choose the equation to be satisfied by

b_1,b_2,b_3

to ensure that the given system of equations has a solution.

Single correctOCTOBER 26, 2025

OCTOBER 26, 2025

Ax=b

be a system of linear equations with a square coefficient matrix

A

. Consider the following statements.

S_1

: If the RREF of

A

is the identity matrix, then the given system of equations has a solution.

S_2

: If the given system of equations has a solution, then the RREF of

A

is the identity matrix. Choose the correct option from the following.

Single correctOCTOBER 26, 2025

OCTOBER 26, 2025

Find the number of zero rows of

M

ComprehensionJULY 13, 2025

Suppose Shakti chooses some values for

a

b

such that multiple sets of values could represent the prices of

1

1

pen. What should the value of

a

ComprehensionJULY 13, 2025

Which of the following conditions is equivalent to having no solutions for the given system of equations?

ComprehensionFEBRUARY 23, 2025

FEBRUARY 23, 2025

Which of the following conditions is equivalent to having a unique solution for the given system of equations?

ComprehensionFEBRUARY 23, 2025

FEBRUARY 23, 2025

Consider the system of linear equations

Ax=b

. Choose all the options from the following which guarantee a unique solution.

Multiple correctOCTOBER 27, 2024

OCTOBER 27, 2024

Ax=b

be a system of linear equations, where

A=\begin{bmatrix}1&0&0&-2\\0&0&1&3\\0&0&0&1\end{bmatrix}

. Find the number of independent variables.

ComprehensionOCTOBER 27, 2024

OCTOBER 27, 2024

Consider the matrix

A=\begin{bmatrix}1&2&-3\\-2&1&-4\\1&0&1\end{bmatrix}

. Consider the system of linear equations

Ax=\begin{bmatrix}3\\b\\1\end{bmatrix}

. Find the value of

b

if the system has infinitely many solutions.

ComprehensionOCTOBER 27, 2024

OCTOBER 27, 2024

Consider the system of linear equations

Ax=b

A\in M_{n\times n}(\mathbb{R})

. Which of the following conditions guarantees that the system is consistent for any

b\in\mathbb{R}^n

? Select all true statements.

Multiple correctJULY 07, 2024

Ax=b

be a system of linear equations, where

A=\begin{bmatrix}1&0&0&-1\\0&0&1&5\\0&0&0&1\end{bmatrix}

x=\begin{bmatrix}x_1&x_2&x_3&x_4\end{bmatrix}^T

b\in\mathbb{R}^3

. Which of the following statements are true?

Multiple correctJULY 07, 2024

Does there exist an

a

such that the system has infinitely many solutions? If yes, find the value of

a

; else write the answer as

100

ComprehensionFEBRUARY 25, 2024

FEBRUARY 25, 2024

Select all true statements.

Multiple correctFEBRUARY 25, 2024

FEBRUARY 25, 2024

Find the values of

k

for which the system of equations has no solution.

ComprehensionOCTOBER 29, 2023

OCTOBER 29, 2023

Find the values of

k

for which the system of equations has infinitely many solutions.

ComprehensionOCTOBER 29, 2023

OCTOBER 29, 2023

If the system has a unique solution

(a,b)

a-b

ComprehensionOCTOBER 29, 2023

OCTOBER 29, 2023

Consider the system of linear equations represented in the matrix form

Ax=b

A=\begin{bmatrix}1&1&3\\1&2&4\\1&3&\alpha\end{bmatrix}

b=\begin{bmatrix}2\\3\\\beta\end{bmatrix}

. What is the value of

\alpha+\beta

if the above system has infinitely many solutions?

Integer answerJULY 16, 2023

How many solutions does the given system

Ax=b

ComprehensionJULY 16, 2023

t=2

the distribution vector is

X_2=\begin{bmatrix}\frac13&\frac12&\frac23\end{bmatrix}^T

. Which of the following options are true?

ComprehensionOCTOBER 16, 2022

OCTOBER 16, 2022

t=1

the distribution vector is

X_1=\begin{bmatrix}\frac12&\frac12&0\end{bmatrix}^T

. Which of the following options is true?

ComprehensionOCTOBER 16, 2022

OCTOBER 16, 2022

Choose the set of correct option(s).

ComprehensionOCTOBER 16, 2022

OCTOBER 16, 2022

If we try to find

x_1

x_2

x_3

using the appropriate matrix representation by taking

c=0.5

d=100

ComprehensionJUNE 05, 2022

If we try to find

x_1

x_2

x_3

using the appropriate matrix representation by taking

c=2

d\ne160

, then which option is always true?

ComprehensionJUNE 05, 2022

If we try to find

x_1

x_2

x_3

using the appropriate matrix representation by taking

c=3

d=100

, then which option is always true?

ComprehensionJUNE 05, 2022

Showing 28 questions.