Algebra Topics for CAT
Algebra CAT Questions carry a good amount of weightage in the CAT Exam. In CAT 2021, it was seen that the maximum number of questions were asked from Arithmetic and Algebra topics. The Algebra Topics for CAT consist of various sub-topics. Algebra CAT questions comprise both MCQ as well as Non-MCQ questions. Go through the detailed CAT Syllabus to understand the topics to be covered.
The Algebra Topics for CAT are mentioned below:
- Inequalities and Modulus
- Functions and Graphs
- Linear and Quadratic Equations
- Polynomials
- Logarithms
- Algebraic Entities
- Maxima and Minima
The above-given topics should be practiced by the candidates thoroughly in order to solve the Algebra CAT Questions.
Weightage of Algebra CAT Questions
The candidates must have an idea about how many questions they should practice from each topic under Algebra. The candidates will get an idea about how many questions can be asked from each topic under the Algebra Section. According to CAT Exam Analysis 2021, the weightage of CAT Algebra Questions is given below.
Slots | Number Of Questions (Approx) |
Slot-1 | 7 |
Slot-2 | 9 |
Slot-3 | 6 |
Algebra CAT Questions PDF
The Algebra CAT Questions carry maximum weightage under the Quantitative Ability section of the CAT exam; therefore, the candidates are suggested to practice as many questions as possible on this topic. The candidates are advised to solve previous year's question papers and mocks so that they are well versed with the different pattern of questions asked on this section. Candidates can download the Algebra CAT Questions PDF given below:
☛ Algebra Questions for CAT- Download PDF
Types of Algebra CAT Questions
Given below are some of the sample questions of Algebra CAT Questions. The candidates can go through the below given Algebra CAT Questions to score well in the Quantitative Ability section of the CAT exam. CAT Quant Questions will help you practice and improve the accuracy and speed of solving questions.
The Algebra CAT Questions will give an overview of the type of questions asked on this topic.
Question: then the value of is
Answer: 1/16
Explanation:
Multiplying equations (1), (2) and (3), we get
Question: For which value of k does the following pair of equations yield a unique solution for x such that the solution is positive?
X2 – y2 = 0
(x-k)2 + y2 = 1
Answer:√2
Explanation:
Given: x ² = y ² and (x − k) ² + y ² = 1
Solving the two equations simultaneously, we get,
(x – k) ² + x ² = 1
∴x ² – 2kx + k ² + x ² = 1
∴2x ² – 2kx + (k ² – 1) = 0
If this equation has a unique solution for x, then discriminant = 0
∴4k ² – 8(k ² – 1) = 0
∴8 – 4k ² = 0
∴k ² = 2
Since k is positive the other solution is ruled out.
Hence k =
Question: The price of Darjeeling tea (in rupees per kilogram) is 100 + 0.10n, on the nth day of 2007 (n = 1, 2, 3,…., 100) and then remains constant. On the other hand, the price of Ooty tea (in rupees per kilogram) is 89 + 0.15n, on the nth day of 2007 (n = 1, 2,…., 365). On which date in 2007 will be prices of these two varieties of tea be equal?
Answer: 20th May
Explanation: Note that the price of Darjeeling tea remains constant after the 100th day (n=100)
If the prices of the two varieties of tea become equal before n=100, then 100 + 0.1 = 89 + 0.15 n
∴n =220, which is not possible. (since n is assumed to be less than 100)
∴The prices of the two varieties will be equal after n =100,
i.e., when the price of Darjeeling tea = 100 + 0.1 x 100 =110
∴ 89 + 0.15 n = 110
∴ n= 140
2007 is not a leap year. Number of days till 30th April 31+ 28 + 31 + 30 = 120
The prices of the two varieties will be equal on 20th May
Question: If a + b + c = 9, a3 + b3 + c3 – 3abc = 1026, then what is the value of ab + bc + ca?
Answer: -11
Explanation: Given, a3 + b3 + c3 – 3abc = 1026
We know that x3 + y3 + z3 – 3xyz = (x + y + z)[(x + y + z)2 – 3(xy + yz + zx)]
So, (a + b + c)[(a + b + c)2 – 3(ab + bc +ca)] = 1026
⇒ 9 × [(9)2 – 3(ab + bc + ca)] = 1026
⇒ 81 – 3(ab + bc + ca) = = 114
⇒ 3(ab + bc + ca) = 81 – 114 = -33
⇒ ab + bc + ca = = -11
Question: If xy = 96 and x2 + y2 = 208, then the value of (x + y) is:
Answer: ±20
Explanation: xy = 96 and x2 + y2 = 208
We know that (x+y)2 = x2 + y2 + 2xy
(x+y)2 = 208 + 192 = 400
x+y = ±20
How to Solve Algebra CAT Questions?
In order to solve Algebra CAT Questions, the candidates must have good knowledge of Arithmetic. Knowledge of basic arithmetic will help the candidates to solve Algebra CAT Questions accurately. Following are some of the tips to prepare for Algebra CAT Questions:
- The candidates can solve Algebra CAT Questions perfectly if they have a clear concept of Algebraic Identities.
- The candidates should regularly practice mocks and previous year's question papers and analyze them. This will help them to solve Algebra CAT Questions accurately.
- Candidates should have good knowledge of graphs in order to solve the questions on functions and graphs under Algebra CAT Questions.
Best Books to Prepare Algebra CAT Questions
The candidates often get confused about which books to choose in order to practice the Algebra CAT Questions. There are a variety of books available in the market for the aspirants who wish to prepare for the Quantitative Ability section of the CAT exam. The candidates can refer to BYJU'S Exam Prep study notes available on the App for Algebra CAT Questions.
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