| Updated On - Nov 9, 2024
CAT 2023 Slot 1 QA Question Paper is available here for free download. CAT 2023 Slot 1 paper has been conducted on November 26 from 8.30 AM to 10.30 AM. CAT 2023 Slot 1 question paper QA comprises 22 questions to be attempted in 40 minutes. According to initial Students reaction, CAT 2023 Slot 1 QA was moderate to tough.
CAT 2023 Slot 1 QA Question Paper with Solutions PDF
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CAT 2023 Slot 1 QA Questions with Solution
| Q. No. | Question (with options) | Answer | Solution |
|---|---|---|---|
| 1 | If x and y are real numbers such that x² + (x − 2y − 1)² − 4y(x + y) = 0, then the value of x − 2y is: 1. 1 2. 2 3. -1 4. 0 |
Option 1 |
Given that x^2 + (x - 2y - 1)^2 - 4y(x + y) = 0, we need to find the value of x - 2y. Expanding and simplifying the expression might be complex, but observing patterns can help:
Upon simplifying, it turns out that x - 2y = 1 satisfies the equation. Answer: 1 |
| 2 | Let n be the least positive integer such that 168 is a factor of 1134n. If m is the least positive integer such that 1134n is a factor of 168m, then m + n equals: 1. 24 2. 12 3. 9 4. 15 |
Option 4 | By prime factorizing 1134... |
| 3 | If √5x + 9 + √5x − 9 = 3(2 + √2), then √10x + 9 is equal to: 1. 3√31 2. 2√7 3. 3√7/2 4. 4√5 |
Option 3 | Given √5x + 9 + √5x − 9 = 6 + 3√2... |
| 4 | If x and y are positive real numbers such that logy(x² + 12) = 4 and 3 logy x = 1, then x + y equals: 1. 10 2. 68 3. 20 4. 11 |
Option 1 | As it is given that logx(x² + 12) = 4... |
| 5 | The number of integer solutions of the equation 2|x|(x² + 1) = 5x² is: | 3 | Considering cases: x = 0, x > 0, and x < 0... |
| 6 | The equation x³ + (2r + 1)x² + (4r − 1)x + 2 = 0 has −2 as one of the roots. If the other two roots are real, then the minimum possible non-negative integer value of r is: | 2 | Using synthetic division and analyzing the discriminant... |
| 7 | Let α and β be the two distinct roots of the equation 2x² − 6x + k = 0, such that (α + β) and αβ are the distinct roots of the equation x² + px + p = 0. Then, the value of 8(k − p) is: | 6 | Applying Vieta’s formulas and substituting known values... |
| 8 | In an examination, the average marks of 4 girls and 6 boys is 24. Each of the girls has the same marks while each of the boys has the same marks. If the marks of any girl is at most double the marks of any boy, but not less than the marks of any boy, then the number of possible distinct integer values of the total marks of 2 girls and 6 boys is: | 21 | Setting up equations and evaluating the range for girls' marks... |
| 9 | The salaries of three friends Sita, Gita, and Mita are initially in the ratio 5 : 6 : 7, respectively. In the first year, they get salary hikes of 20%, 25%, and 20%, respectively. In the second year, Sita and Mita get salary hikes of 40% and 25%, respectively, and the salary of Gita becomes equal to the mean salary of the three friends. The salary hike of Gita in the second year is: | 26% | Applying successive percentage increases and calculating mean... |
| 10 | The minor angle between the hour hand and the minute hand of a clock was observed at 8:48 am. The minimum duration, in minutes, after 8:48 am when this angle increases by 50% is: | 24/11 | Calculating initial angle and applying relative speed of hands... |
| 11 | Brishti went on an 8-hour trip in a car. Before the trip, the car had travelled a total of x km till then, where x is a whole number and is palindromic. At the end of the trip, the car had travelled a total of 26862 km till then, this number again being palindromic. If Brishti never drove at more than 110 km/h, then the greatest possible average speed at which she drove during the trip, in km/h, was: | 100 | Testing values to find palindrome within speed constraints... |
| 12 | Gita sells two objects A and B at the same price such that she makes a profit of 20% on object A and a loss of 10% on object B. If she increases the selling price such that objects A and B are still sold at an equal price and a profit of 10% is made on object B, then the profit made on object A will be nearest to: | 47% | Calculating cost price and applying adjusted profit percentages... |
| 13 | A mixture P is formed by removing a certain amount of coffee from a coffee jar and replacing it with cocoa powder. The same amount is removed from mixture P and replaced with cocoa to form mixture Q. If the ratio of coffee and cocoa in Q is 16:9, find the ratio of cocoa in P to that in Q: | 5:9 | Using replacement ratios and solving for cocoa distribution... |
| 14 | Anil invests Rs. 22000 for 6 years in a scheme with 4% interest per annum, compounded half-yearly. Sunil invests in the same scheme for 5 years, then reinvests for one year at 10% simple interest. If both amounts are equal after 6 years, find Sunil's initial investment: | 20808 | Equating compound interest and simple interest earnings... |
| 15 | The amount of job Amal, Sunil, and Kamal can do in a day are in harmonic progression. Kamal takes twice as long as Amal to complete the job. If Amal and Sunil work for 4 and 9 days respectively, Kamal works for 16 days to complete the rest. How many days will Sunil take to finish alone? | 27 | Setting up equations based on harmonic progression ratios... |
| 16 | Arvind travels from town A to town B, and Surbhi from town B to town A, both starting at the same time along the same route. After meeting each other, Arvind takes 6 hours to reach town B while Surbhi takes 24 hours to reach town A. If Arvind travelled at a speed of 54 km/h, then the distance between town A and town B is: | 972 | Using relative speed calculations to find total distance... |
| 17 | A quadrilateral ABCD is inscribed in a circle such that AB : CD = 2 : 1 and BC : AD = 5 : 4. If AC and BD intersect at point E, then AE : CE equals: | 8 : 5 | Applying properties of cyclic quadrilaterals and similarity... |
| 18 | Let C be the circle given by x² + y² + 4x + 6y − 30 = 0, and let L be the locus of the point of intersection of a pair of tangents to C with an angle of 60°. Find the point at which L touches the line x = 6: | (6,3) | Using the locus equation and trigonometric relationships... |
| 19 | In a right-angled triangle △ABC, the altitude AB is 5 cm, and the base BC is 12 cm. P and Q are points on BC such that the areas of △ABP, △ABQ, and △ABC are in arithmetic progression. If the area of △ABC is 1.5 times that of △ABP, find the length of PQ: | 2 | Setting up area relationships based on arithmetic progression... |
| 20 | For some positive and distinct real numbers x, y, and z, if (1/√y + √xz) is the arithmetic mean of (1/√x + √yz) and (1/√z + √yx), then the relationship that always holds true is: | y, x, and z are in arithmetic progression | Testing arithmetic progression patterns for given conditions... |
| 21 | The number of all natural numbers up to 1000 with non-repeating digits is: | 738 | Counting unique digit combinations across 1-digit, 2-digit, and 3-digit numbers... |
| 22 | A lab experiment measures the number of organisms at 8 am every day. Starting with 2 organisms on the first day, the number of organisms each day is 3 more than twice the previous day's count. If the number of organisms on the nth day exceeds one million, find the lowest possible value of n: | 19 | Applying the recurrence relation and calculating terms until exceeding one million... |
CAT Questions
1. Let both the series \(a_1,a_2,a_3,....\) and \(b_1,b_2,b_3,....\) be in arithmetic progression such that the common differences of both the series are prime numbers. If \(a_5=b_9,a_{19}=b_{19}\) and \(b_2=0\) , then \(a_{11}\) equals
Let both the series \(a_1,a_2,a_3,....\) and \(b_1,b_2,b_3,....\) be in arithmetic progression such that the common differences of both the series are prime numbers. If \(a_5=b_9,a_{19}=b_{19}\) and \(b_2=0\) , then \(a_{11}\) equals
- 79
- 83
- 84
- 86
2. If \(x\) and \(y\) are positive real numbers such that \(log_x(x^2+12)=4\) and \(3\;log_yx=1\),then \(x+y\) equals
If \(x\) and \(y\) are positive real numbers such that \(log_x(x^2+12)=4\) and \(3\;log_yx=1\),then \(x+y\) equals
- 11
- 20
- 10
- 68
3. Anil borrows Rs 2 lakhs at an interest rate of 8% per annum, compounded half-yearly. He repays Rs 10320 at the end of the first year and closes the loan by paying the outstanding amount at the end of the third year. Then, the total interest, in rupees, paid over the three years is nearest to
Anil borrows Rs 2 lakhs at an interest rate of 8% per annum, compounded half-yearly. He repays Rs 10320 at the end of the first year and closes the loan by paying the outstanding amount at the end of the third year. Then, the total interest, in rupees, paid over the three years is nearest to
- 33130
- 40991
- 51311
- 51311
4. Average of 5 integers is 38 and all the numbers are between 0 and 50 (both inclusive). In these 5 numbers, a is the minimum. If exactly 3 of them are more than 32, find the difference between the minimum and the maximum value of a.
Average of 5 integers is 38 and all the numbers are between 0 and 50 (both inclusive). In these 5 numbers, a is the minimum. If exactly 3 of them are more than 32, find the difference between the minimum and the maximum value of a.
5. In a company, 20% of the employees work in the manufacturing department. If the total salary obtained by all the manufacturing employees is one-sixth of the total salary obtained by all the employees in the company, then the ratio of the average salary obtained by the manufacturing employees to the average salary obtained by the non-manufacturing employees is
In a company, 20% of the employees work in the manufacturing department. If the total salary obtained by all the manufacturing employees is one-sixth of the total salary obtained by all the employees in the company, then the ratio of the average salary obtained by the manufacturing employees to the average salary obtained by the non-manufacturing employees is
- 6 : 5
- 4 : 5
- 5 : 4
- 5 : 6
6. There is a sentence that is missing in the paragraph below. Look at the paragraph and decide where (option 1, 2, 3, or 4 ) the following sentence would best fit.
Sentence: This philosophical cut at one's core beliefs, values, and way of life is difficult enough.
Paragraph: The experience of reading philosophy is often disquieting. When reading philosophy, the values around which one has heretofore organised one's life may come to look provincial, flatly wrong, or even evil. __(1)_. When beliefs previously held as truths are rendered implausible, new beliefs, values, and ways of living may be required. _ (2) . What's worse, philosophers admonish each other to remain unsutured until such time as a defensible new answer is revealed or constructed. Sometimes philosophical writing is even strictly critical in that it does not even attempt to provide an alternative after tearing down a cultural or conceptual citadel. (3). The reader of philosophy must be prepared for the possibility of this experience. While reading philosophy can help one clarify one's values, and even make one self-conscious for the first time of the fact that there are good reasons for believing what one believes, it can also generate un-remediated doubt that is difficult to live with.
There is a sentence that is missing in the paragraph below. Look at the paragraph and decide where (option 1, 2, 3, or 4 ) the following sentence would best fit.
Sentence: This philosophical cut at one's core beliefs, values, and way of life is difficult enough.
Paragraph: The experience of reading philosophy is often disquieting. When reading philosophy, the values around which one has heretofore organised one's life may come to look provincial, flatly wrong, or even evil. __(1)_. When beliefs previously held as truths are rendered implausible, new beliefs, values, and ways of living may be required. _ (2) . What's worse, philosophers admonish each other to remain unsutured until such time as a defensible new answer is revealed or constructed. Sometimes philosophical writing is even strictly critical in that it does not even attempt to provide an alternative after tearing down a cultural or conceptual citadel. (3). The reader of philosophy must be prepared for the possibility of this experience. While reading philosophy can help one clarify one's values, and even make one self-conscious for the first time of the fact that there are good reasons for believing what one believes, it can also generate un-remediated doubt that is difficult to live with.
Sentence: This philosophical cut at one's core beliefs, values, and way of life is difficult enough.
Paragraph: The experience of reading philosophy is often disquieting. When reading philosophy, the values around which one has heretofore organised one's life may come to look provincial, flatly wrong, or even evil. __(1)_. When beliefs previously held as truths are rendered implausible, new beliefs, values, and ways of living may be required. _ (2) . What's worse, philosophers admonish each other to remain unsutured until such time as a defensible new answer is revealed or constructed. Sometimes philosophical writing is even strictly critical in that it does not even attempt to provide an alternative after tearing down a cultural or conceptual citadel. (3). The reader of philosophy must be prepared for the possibility of this experience. While reading philosophy can help one clarify one's values, and even make one self-conscious for the first time of the fact that there are good reasons for believing what one believes, it can also generate un-remediated doubt that is difficult to live with.
- Option 4
- Option 2
- Option 1
- Option 3
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