CUET General Test Quantitative Reasoning > Linear Equation PYQs

Which of the following pair of linear equations is / are inconsistent? (A) $x - y = 5$; $3x - 3y = 10$ (B) $2x + 3y = 4$; $4x + 6y = 8$ (C) $9x + 6y = 6$; $3x + 2y = 3$ (D) $2x + 5y = 2$; $6x - 15y = 4$ Choose the correct answer from the options given below:

Which one of the following pair of linear equations is/are inconsistent? A. x – y = 8, 6x – 6y = 32 B. x + y = 5, 4x + 4y = 20 C. 4x– 6y = 16, 8x – 12y = 18 D. 4x – 4y – 4 = 0, 8x – 8y – 10 = 0 Choose the correct answer from the options given below:

Which of the following pair of linear equations has / have many infinite solutions? A. $9x + 3y + 12 = 0$; and $18x + 6y + 24 = 0$ B. $2x - 3y = 13$; and $7x - 2y = 20$ C. $x + y = 5$; and $2x + 2y = 10$ D. $3x + y - 3 = 0$; and $2x + \dfrac{2}{3}y = 2$ Choose the correct answer from the options given below:

Two lines x + y = 8 and 3x + y = 14 meet at the point:

The pair of equations x + 2y - 4 = 0 and 2x + 4y - 12 = 0 represents two lines, which are ?

Laxmi's father is 51 years old. He is three years older than three times Laxmi's age. The age of Laxmi is :

System of linear equations 2x + 4y +1 = 0 and 4x + 8y + 2 = 0 has/ have :

In the following system of linear equations $7x - 15y = 2$ and $x + 2y = 3$, the value of x and y is:

Which of the following pairs of linear equations is/are inconsistent? A. $x - y = 8; 3x - 3y = 16$ B. $3x + 2y = 5; 2x - 3y = 7.$ C. $2x - 2y - 2 = 0; 4x - 4y - 5 = 0.$ D. $2x - 3y = 8; 4x - 6y - 5 = 9$

If 2x + 3y = 18 and y = 2, then the value of x is:

Which of the following pair of linear equations has no solution? (A) $2x + 3y - 1 = 0$ and $4x + 6y - 4 = 0$ (B) $x - 2y = 0$ and $3x + 4y - 20 = 0$ (C) $x + 2y - 3 = 0$ and $5x + 10y + 7 = 0$ (D) $x + 2y - 4 = 0$ and $2x + 4y - 12 = 0$ Choose the **correct** answer from the options given below:

Which one of the following pair of linear equations is/are inconsistent? A. x − y = 6, x − y = 13 B. 2x − 10y = 15, 7x − 35y =25 C. x − y = 15, 5x - 5y = 75 D. 7x − 9y − 3 = 0, 14x − 18y − 8 = 0 Choose the correct answer from the options given below:

Which one of the following pairs of linear equations is/are inconsistent? (A) 7 x + 2 y = 3, 14 x + 4 y = 5 (B) 2 x - 3 y = 7, 4 x - 6 y = 12 (C) x - y = 10, 3 x - 3 y = 16 (D) 2 x - 2 y = 2, 4 x - 4 y = 5 Choose the correct answer from the options given below:

The distance between origin and the point of intersection of lines x + y – 5 = 0 and x – y + 1 = 0, is:

Which of the following pairs of linear equations is/are consistent? A. x + y – 5 = 0, 3x + 2y – 10 = 0 B. 3x – 2y – 6 = 0, 6x – 4y – 12 = 0 C. x – y – 9 = 0, 3x – 3y – 27 = 0 D. x + y – 4 = 0 , 3x + 3y – 12 = 0 Choose the correct option from the given below:

One says, "Give me a hundred rupees, friend! I shall then become twice as rich as you." The other replies, "If you give me ten rupees, I shall be six times as rich as you." What is the amount of their (respective) capital?

Five years ago, Sanjana was thrice as old as Sanjay. Ten years later, Sanjana will be twice as old as Sanjay. The age of Sanjay and Sanjana are respectively A. 20 B. 30 C. 40 D. 50 Choose the correct answer from the options given below:

Solve for $x$, if $4(x + 1) - 3(2x - 1) = x + 7$

Which of the following pairs of linear equations is/are consistent? A. $x + y = 5, 2x + 2y = 10$ B. $2x + y - 6 = 0, 4x - 2y - 4 = 0$ C. $x - y = 8, 3x - 3y = 16$ D. $x - 2y = 0, 3x + 4y - 20 = 0$ Choose the correct answer from the options given below:

Which one of the following pairs of linear equations is/are inconsistent? (A). $7x + y = 5, 14x + 2y = 10$ (B). $2x - 3y = 7, 4x - 6y = 12$ (C). $x - y = 10, 3x - 3y = 16$ (D). $2x - 2y - 2 = 0, 4x - 4y - 5 = 0$ Choose the correct option from the given below:

Solve the linear equation for $x$: $3x - 7 = 2x + 5$

The system of linear equations x + y + 1 = 0 and 2x + 2y + 7 = 0 has:

Which one of the following pair of linear equations is/are inconsistent? (A) 2x – 2y = 10, 3x – 3y = 15 (B) 3x – y = 7, 6x – 2y = 18 (C) x – y =15, 5x – 5y = 12 (D) 7x – 3y = 3, 14x – 6y = 8 Choose the correct answer from the options given below:

The system of linear equations 3x + y + 4 = 0 and 2x + y + 9 = 0 has:

Read the information given below carefully and answer the question that follows: Aditi, a salesgirl is appointed at a basic salary of ₹ 1200 per month. The condition of employment further stated that for every sale of ₹ 10000 or above she does, she will get 50 % of basic salary and 10 % of the sales as special incentive. However, this incentive scheme shall not work on the first ₹ 10000 of sales made. What should be the value of sales if Aditi wants to earn ₹ 7600 in a particular month?

Which one of the following pairs of linear equations has/ have infinite many solutions? (A) $9x + 3y + 12 = 0$, and $18x + 6y + 24 = 0$ (B) $2x - 3y = 13$, and $7x - 2y = 20$ (C) $x + y = 5$, $2x + 2y = 10$ (D) $3x + y - 3 = 0$ and $2x + \frac{2}{3}y = 2$ Choose the correct answer from the options given below:

Read the information given below carefully and answer the question that follows: **Question: How much does Ajay pay to his driver every month as Salary?** **Statements:** i. Rakesh pays 20% more per month, to his driver than Ajay as Rakesh's driver has a 15 year experience. Moreover, Ajay pays 30% more per month than Karan as Karan's driver has mere 5 years of experience. ii. As Karan would avail 10% discount on drivers's salary by paying for 6 months in advance, Karan paid his driver Rs 54000 for 6 months in advance. Determine which of the following is True in order to solve the asked question?

Rita purchased 9 pens and 7 pencils for ₹ 66. Megha also bought 5 pens and 11 pencils of the same kind for ₹ 58. What is the cost of 3 pencils?

If on dividing 26 into two parts, we find that three times the first and seven times the second part together equals to 122. Then, the ratio of first and second part shall be:

For what value of k, the system of equations $kx + 4y - k + 4 = 0$ and $16x + ky = k$ has an infinite number of solutions?

The system of equations $4x + 14y = 18$ and $6x + 21y = 33$ has

Which of the following pair of linear equations is inconsistent? (A) x - y = 5; 3x - 3y = 10 (B) 2x + 3y = 4; 4x + 6y = 8 (C) 9x + 6y = 6; 3x + 2y = 3 (D) 2x + 5y = 2; 6x - 15y = 4 Choose the correct answer from the options given below:

The present ratio of ages of P and Q is 2:7. Six years ago, this ratio was 1:5. Determine the present age of P?

The graphs of px + qy = r, mx + ny = s will be (A) intersecting, if the system has only one solution. (B) overlapping, if the system has a finite number of solutions. (C) parallel, if the system has infinite solutions Which of the statements below is/are incorrect?

Find the value of p for which the lines, $px + 3y + 5 = 0$ and $8x + 2y - 3 = 0$ are parallel.

The pair of linear equations mx + 2y + 3 = 0 and 3x + 6y + 2 = 0 intersect each other, if

For what value of k, the system of equations $3x - ky - 3 = 0$ and $2x - 3y - 4 = 0$ has no solution?

Seven chairs and three tables together cost ₹ 7400, three chairs and five tables together cost ₹ 5400. The total cost (in ₹) of 1 chair and 2 tables is:

The intersection point on the Y- axis of $5x - 3y = 9$ is

The equations: x + 4y - 3 = 0 and 2x + 8y - 6 = 0 have

The value of k, for which the system of equations 3x-ky-20 = 0, and 6x-10y+40 = 0 has no solution, is:

If 2x + 3y - 8 = 0 and 3x - 2y - 12 = 0, then $4x^2 + y^2 - 4x$ is equal to:

If $2^{(x+y)} = 64$ and $128^{(x-y)} = 2$, then what is the value of x?

In an examination which had 200 questions, students score 4 marks for every correct answer and lose 1 mark for every wrong answer. A student attempted all the 200 questions and scored 200 marks. The number of questions, student answered correctly in the examination, is:

If $6x - 10y = 10$ and $\frac{x}{x+y} = \frac{5}{7}$, then (x-y) is equal to:

In an examination, a student scores 3 marks for every correct answer and looses 1 marks for every wrong answer. A student attempted all the 120 questions and scored 320 marks. Find the number of questions, he answered incorrectly.

The sum of digits of a two-digit number is 14 and the difference between the two digits of the number is 2. The product of the two digits of the number is:

If 2x + 3y = 26 and y - x = 2, then the value of x + y is:

The pair of linear equations $kx + 3y + 1 = 0$ and $2x + y + 3 = 0$ intersect each other, if

Reena is twice as old as Sunita. Three years ago, Reena was three times as old as Sunita. What is present age of Reena?

The graphs of ax+by = c and dx+ey = f will be: (A) parallel, if the system has no solution. (B) coincident, if the system has finite numbers of solutions. (C) intersecting, if the system has only one solution. Which of the above statements is/ are correct? Choose the correct answer from the options given below:

Two water pipelines are represented by the equations $kx + 3y +1 = 0$ and $2x + y + 3 = 0$. For what value of k, the pipelines cross each other?

The present age of a father is 4 years more than double the age of his son. After 10 years, the father's age is 30 years more than his son. Then the present age of father is:

The present age of Harish is 8 times the sum of the ages of his two sons at present. After 8 years, his age will be 2 times the sum of the ages of his two sons. The present age of Harish (in years) is:

For which value of the k, the pair of linear equations has no solution $6x - 3y + 10 = 0$ and $kx - y + 9 = 0$ :

The difference between two numbers is 24. If one number is 2 times the second. Then the two numbers will be:

The difference between two numbers is 4 and there average is 6. The product of these numbers is:

The sum of the numerator and the denominator of a fraction is 11. If 1 is added to the numerator and 2 is subtracted from the denominator, it becomes $\frac{2}{3}$. The fraction is:

In a 2-digit number, the ten's digit is two times its unit's digit and the number is 12 less than two times the number obtained by interchanging its digits. Find the original number.

Linear equations $3x + 5y = 19$ and $10x - 3y = 24$ have solution $x = \frac{\alpha}{3}$ and $y = \frac{\beta}{2}$, then the value of $\alpha + \beta$ is:

An equation of the type $y = kx$ (k $\neq$ 0) represents a line :

The product of two positive numbers is 189 and their quotient is $\frac{3}{7}$. Find the sum of these numbers.

Match List - I with List - II. | List - I | List - II | | --- | --- | | (1) $14 - \frac{1}{10}(x+3) = \frac{5}{6}x$ | (I) 4 | | (2) $(x-5)^2 - (x+3)^2 = 48$ | (II) $-\frac{23}{2}$ | | (3) $6(x-4) = 4(x-3) - (3x-8)$ | (III) 61 | | (4) $(2x-1)(2x+3) = (2x-7)(2x+7)$ | (IV) $-2$ | Choose the correct answer from the options given below:

A railway half-ticket costs half the full ticket. However the reservation charge for all the tickets is constant. One full reserved ticket for a journey is Rs.525. If the cost of one full and one half reserved ticket for the same journey is Rs.850, then what is the reservation charge per ticket?

Match List I with List II | | LIST I (Equations) | | LIST II (Solutions) | |---|---|---|---| | A. | $2x - 4 = 2 - x$ | I. | $x = 3$ | | B. | $7 - 4x = 0$ | II. | $x = 2$ | | C. | $\frac{x}{2} - 3 = 0$ | III. | $x = \frac{7}{4}$ | | D. | $2x + 3 = x + 6$ | IV. | $x = 6$ | Choose the correct answer from the options given below:

Mohan's Mother is three times as old as Mohan. After 6 years, his mother will be two times as old as he will be them, find the age of Mohan.

If the cost of 4 pens and 6 note books is Rs 800, then find the cost of 6 pens and 9 note books.

The total age of P and Q is 18 years more than the total age of Q and R. R is how many years younger than P ?

When thrice of x is added to 7, we get 13, then the value of x is :

A father said to his child, "I was as old as you are at the time of your birth". If the father's age is 48 years now, the child's age six years back was:

The value of 'y' in the question $2x + 3y - 7 = 0$ if $x = -3/2$

The value of x in the equation $2x - 3 = 7 - 3x$