The CAT DILR section requires good analysis skills, critical thinking, and attention to detail, along with a thorough understanding of the Geometry. This article provides a set of MCQs on Geometry to help you understand the topic and enhance your data interpretation and logical reasoning with the help of detailed solutions, which will help you in the CAT 2025 exam preparation.
Whether you're revising the basics or testing your knowledge, these MCQs will serve as a valuable practice resource.
The CAT 2025 exam is expected to follow a similar trend to the CAT 2024, with 24 questions from the VARC section out of a total of 68 questions.
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CAT MCQs on Geometry
1. In a triangle PQR, \(\angle PRQ = 90^\circ\). What is PR + RQ?
Statement A
A. The diameter of the incircle is 10.
Statement B
B. The diameter of the circumcircle is 18.
A. The diameter of the incircle is 10.
Statement B
B. The diameter of the circumcircle is 18.
A
The question can be answered by one of the statements alone but not by the other.
B
The question can be answered by using either statement alone.
C
The question can be answered by using both the statements together, but cannot be answered by using either statement alone.
D
The question cannot be answered even by using both statements together.
2. Two concentric circles have the same centre O. A chord on the outer circle AE intersects the inner circle in points B and D. C is a point on the segment BD. What is the ratio of AC to CE?
Statement A
A. Ratio of lengths of BC to CD is 1.
Statement B
B. A third circle intersects the inner circle at B and D. C is on the line joining the centres of the third and inner circle.
A. Ratio of lengths of BC to CD is 1.
Statement B
B. A third circle intersects the inner circle at B and D. C is on the line joining the centres of the third and inner circle.
A
The question can be answered by one of the statements alone but not by the other.
B
The question can be answered by using either statement alone.
C
The question can be answered by using both the statements together, but cannot be answered by using either statement alone.
D
The question cannot be answered even by using both statements together.
3. What are the ages of X and Y?
Statement A
A. The difference in their ages is 6.
Statement B
B. The product of their ages is divisible by 6.
A. The difference in their ages is 6.
Statement B
B. The product of their ages is divisible by 6.
A
The question can be answered by one of the statements alone but not by the other.
B
The question can be answered by using either statement alone.
C
The question can be answered by using both the statements together, but cannot be answered by using either statement alone.
D
The question cannot be answered even by using both statements together.
4. x is a real number. Is \(/(|x|<3\)?
Statement A
A. \(x(x+3)<0\)
Statement B
B. \(x(x-3)>0\)
A. \(x(x+3)<0\)
Statement B
B. \(x(x-3)>0\)
A
The question can be answered by one of the statements alone but not by the other.
B
The question can be answered by using either statement alone.
C
The question can be answered by using both the statements together, but cannot be answered by using either statement alone.
D
The question cannot be answered even by using both statements together.
5. \(a \oplus b = 1\) if a,b>0 or a,b<0; \quad \(a \oplus b = -1\) otherwise.
What is \((2 \oplus 0) \oplus (-5 \oplus -6)\)?
Statement A
A. \(a \oplus b = 0\) if $a=0$
Statement B
B. \(a \oplus b = b \oplus a\)
Statement A
A. \(a \oplus b = 0\) if $a=0$
Statement B
B. \(a \oplus b = b \oplus a\)
A
The question can be answered by one of the statements alone but not by the other.
B
The question can be answered by using either statement alone.
C
The question can be answered by using both the statements together, but cannot be answered by using either statement alone.
D
The question cannot be answered even by using both statements together.
6. Harshad bought shares of a certain company on one day and sold them the next day. He paid a brokerage of 1%. What was Harshad’s profit per rupee?
Statement A
A. His selling price was 1.05 times his purchase price.
Statement B
B. The number of shares he purchased was 100.
A. His selling price was 1.05 times his purchase price.
Statement B
B. The number of shares he purchased was 100.
A
The question can be answered by one of the statements alone but not by the other.
B
The question can be answered by using either statement alone.
C
The question can be answered by using both the statements together, but cannot be answered by using either statement alone.
D
The question cannot be answered even by using both statements together.
7.
How many people watch program P?
Statement A
A. The number watching Q is 1000; the number watching both P and Q is 100.
Statement B
B. The number of people watching either P or Q or both is 1500.
Statement A
A. The number watching Q is 1000; the number watching both P and Q is 100.
Statement B
B. The number of people watching either P or Q or both is 1500.
A
The question can be answered by one of the statements alone but not by the other.
B
The question can be answered by using either statement alone.
C
The question can be answered by using both the statements together, but cannot be answered by using either statement alone.
D
The question cannot be answered even by using both statements together.
8. Two lines are given by the equations ax + by = c and dx + ey = f. Do they intersect?
Statement A
A. a, b, c, d, e, f are distinct \& real.
Statement B
B. c \neq 0$ \& $f \neq 0$.
A. a, b, c, d, e, f are distinct \& real.
Statement B
B. c \neq 0$ \& $f \neq 0$.
A
The question can be answered by one of the statements alone but not by the other.
B
The question can be answered by using either statement alone.
C
The question can be answered by using both the statements together, but cannot be answered by using either statement alone.
D
The question cannot be answered even by using both statements together.
9. Ghosh flies to South Africa from Mumbai non-stop. His flight leaves Mumbai at 5 am on 10\textsuperscript{th} December 2000 as per Indian Standard Time. What is the local time in South Africa when Mr. Ghosh reaches there?
Statement A
A. The average speed of the plane during the flight is 700 km/h.
Statement B
B. The flight distance is 10,500 km.
A. The average speed of the plane during the flight is 700 km/h.
Statement B
B. The flight distance is 10,500 km.
A
The question can be answered by one of the statements alone but not by the other.
B
The question can be answered by using either statement alone.
C
The question can be answered by using both the statements together, but cannot be answered by using either statement alone.
D
The question cannot be answered even by using both statements together.
10. Is z the smallest of x, y, z?
Statement A
A. x is greater than at least one of y \& z.
Statement B
B. y is greater than at least one of x \& z.
A. x is greater than at least one of y \& z.
Statement B
B. y is greater than at least one of x \& z.
A
The question can be answered by one of the statements alone but not by the other.
B
The question can be answered by using either statement alone.
C
The question can be answered by using both the statements together, but cannot be answered by using either statement alone.
D
The question cannot be answered even by using both statements together.
11. A tractor travelled a distance 5 m. What is the radius of the rear wheel?
I. The front wheel rotates `N` times more than the rear wheel over this distance.
II. The circumference of the rear wheel is `r` times that of the front wheel.
II. The circumference of the rear wheel is `r` times that of the front wheel.
A
The question cannot be answered even with the help of both the statements taken together.
B
The question can be answered by any one of the statements
C
Each statement alone is sufficient to answer the question, but not the other one.
D
Both statements I and II together are needed to answer the question
12. What is the ratio of the two liquids A and B in the mixture finally, if these two liquids kept in three vessels are mixed together? (The containers are of equal volume.)
I. The ratio of liquid A to liquid B in the first and second vessel is 3:5 and 2:3 respectively.
II. The ratio of liquid A to liquid B in vessel 3 is 4:3.
II. The ratio of liquid A to liquid B in vessel 3 is 4:3.
A
The question cannot be answered even with the help of both the statements taken together.
B
The question can be answered by any one of the statements
C
Each statement alone is sufficient to answer the question, but not the other one.
D
Both statements I and II together are needed to answer the question
13. If a, b, c are integers, is (a-b+c)>(a+b-c)?
I. b is negative.
II. c is positive.
II. c is positive.
A
The question cannot be answered even with the help of both the statements taken together.
B
The question can be answered by any one of the statements
C
Each statement alone is sufficient to answer the question, but not the other one.
D
Both statements I and II together are needed to answer the question
14. If \(\alpha\) and \(\beta\) are the roots of the equation \(ax^2 + bx + c = 0\), then what is the value of \)(\alpha^2 + \beta^2)\)?
I. \(\alpha + \beta = -\left(\frac{b}{a}\right)\).
II. \(2\alpha\beta = \left(\frac{c}{a}\right)\).
II. \(2\alpha\beta = \left(\frac{c}{a}\right)\).
A
The question cannot be answered even with the help of both the statements taken together.
B
The question can be answered by any one of the statements
C
Each statement alone is sufficient to answer the question, but not the other one.
D
Both statements I and II together are needed to answer the question
15. What is the selling price of the article?
I. The profit on sales is 20%.
II. The profit on each unit is 25% and the cost price is Rs. 250.
II. The profit on each unit is 25% and the cost price is Rs. 250.
A
The question cannot be answered even with the help of both the statements taken together.
B
The question can be answered by any one of the statements
C
Each statement alone is sufficient to answer the question, but not the other one.
D
Both statements I and II together are needed to answer the question
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