All Courses
Get the App Signup / Login
Sign in Open App
CAT Exam  >  CAT Tests  >  CAT Practice Test: September 15 - CAT MCQ

CAT Practice Test: September 15 - CAT MCQ


Test Description

30 Questions MCQ Test - CAT Practice Test: September 15

CAT Practice Test: September 15 for CAT 2024 is part of CAT preparation. The CAT Practice Test: September 15 questions and answers have been prepared according to the CAT exam syllabus.The CAT Practice Test: September 15 MCQs are made for CAT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for CAT Practice Test: September 15 below.
Solutions of CAT Practice Test: September 15 questions in English are available as part of our course for CAT & CAT Practice Test: September 15 solutions in Hindi for CAT course. Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free. Attempt CAT Practice Test: September 15 | 60 questions in 120 minutes | Mock test for CAT preparation | Free important questions MCQ to study for CAT Exam | Download free PDF with solutions
CAT Practice Test: September 15 - Question 1
Save

What kind of a quadrilateral is formed by the vertices (0, 0), (4, 3), (3, 5) and (-1, 2)?

Detailed Solution for CAT Practice Test: September 15 - Question 1

Let the points be A(0, 0), B(4, 3), C(3, 5) and  D(-1, 2) 
Let A and B be the easy points then,

The sides are equal. So, the quadrilateral is at least a parallelogram.

and (AC)2 ≠ (AB)2 + (BC)2
Therefore, the quadrilateral is not rectangle.
So, the given quadrilateral is a parallelogram.

CAT Practice Test: September 15 - Question 2
Save

If a, b, c are in A.P. then the fixed point through which the straight line ax + 2by + c = 0 will always pass, is

Detailed Solution for CAT Practice Test: September 15 - Question 2

Since, a, b, c are in A.P.
So, 2b = a + c.
Now, only (1, -1) satisfies the equation.

1 Crore+ students have signed up on EduRev. Have you? Download the App
CAT Practice Test: September 15 - Question 3
Save

In the above figure, if O(0, 0) is the centre of the circle, then which of the following points lies outside the circle?

Detailed Solution for CAT Practice Test: September 15 - Question 3

A point will be outside the given circle if its distance from the centre, i.e. origin O, is more than 10.
Now, the distance of point (-7, -8) from O is , which is more than 10.
So, point (-7, -8) lies outside the given circle.
Hence, option (1) is correct.

CAT Practice Test: September 15 - Question 4
Save

Find the equation of a straight line which contains the point  with inclination 150o.
Detailed Solution for CAT Practice Test: September 15 - Question 4

Slope of the line, m = tan 150o = tan (90o + 60o) = -cot 60o = -1/√3
y = mx + c 

Line contains the point

CAT Practice Test: September 15 - Question 5
Save

Find the point which divides the line joining the points A (1, 3) and B (2, 7) in the ratio of 3 : 4 externally.
Detailed Solution for CAT Practice Test: September 15 - Question 5


CAT Practice Test: September 15 - Question 6
Save

If C is the centroid of the triangle PQR and the coordinates of points P, Q, R and C respectively are (x, 1), (0, y), (1/2, 0) and (1/2, 1/3), find the measure of angle PQR.
Detailed Solution for CAT Practice Test: September 15 - Question 6

The centroid of ΔPQR has coordinates (1/2, 1/3).
Therefore, 1/2 = (x + 0 + 1/2)/3 and 1/3 = (1 + y + 0)/3
So, x = 1 and y = 0
Angle PQR is equal to angle between line PQ and line QR.
Slope of PQ (m1)= (0 - 1)/(0 - 1) = 1
Slope of QR (m2)= (0 - 0)/((1/2) - 0) = 0
Angle between line PQ and line QR = tan θ = (m1 - m2)/(1 + m1m2) = (1 - 0)/(1 + (0)(1)) = 1
tan θ = 1
θ = 45°

CAT Practice Test: September 15 - Question 7
Save

In the xy-plane, which of the following points is the greatest distance from the origin?
Detailed Solution for CAT Practice Test: September 15 - Question 7

The square of the distance from the origin of (x, y) is x2 + y2.
This values for the different points given in options are 9, (4 + 9), (1 + 9) and 9, respectively. Among these, 4 + 9 is the greatest.

CAT Practice Test: September 15 - Question 8
Save

The projection (the foot of perpendicular) from (x, y) on the x-axis is
Detailed Solution for CAT Practice Test: September 15 - Question 8

The foot of perpendicular of a point on the x-axis always has abscissa equal to the perpendicular distance of the point from the y-axis and ordinate 0.
The projection or foot of perpendicular of (x, y) on the x-axis is (x, 0).

CAT Practice Test: September 15 - Question 9
Save

If a, b and c are the sides of a triangle, and a2 + b2 + c2 = ab + bc + ca, then the triangle is
Detailed Solution for CAT Practice Test: September 15 - Question 9

a2 + b2 + c2 = ab + bc + ac
(a - b)2 + (b - c)2 + (c - a)2 = 0  ...(1)
Since the sum of squares is zero, each term should be zero. 
⇒ (a - b)2 = 0, (b - c)2 = 0, (c - a)2 = 0   
⇒ a = b = c
Hence, the triangle is equilateral.

CAT Practice Test: September 15 - Question 10
Save

In the given figure, if PQ is parallel to OR, then what is the area of quadrilateral PQRO?
Detailed Solution for CAT Practice Test: September 15 - Question 10

Since ∠POR = 90° and ∠QOR = 45°, POQ is also equal to 45°.
So, ∠PQO = 45° and ∠QPO = 90°
Therefore, ΔQPO is an isosceles right-angled triangle.
So, OP = PQ = 4 units and OR = 5 units.
Now, OPQR is a trapezium with PQ and OR as its parallel sides.
So, area = ½(PQ + OR) × OP = ½ × (4 + 5) × 4 = 18 sq. units

CAT Practice Test: September 15 - Question 11
Save

Directions: Answer the question based on the following information.
A function has been defined for a variable x, where domain of F(x) and F1(x) ∈ [-2, 2].

Choose the correct option.
Detailed Solution for CAT Practice Test: September 15 - Question 11

F(2) = -2 and F1(-2) = -2
F(-2) = 0 and F1(2) = 0
So, according to this,
F(x) = F1(-x) or F1(x) = F(-x)

CAT Practice Test: September 15 - Question 12
Save

If f(x) = x3 + y3, g(x) = xy and h(x) = (x + y), then which of the following is the value of f(x)?
Detailed Solution for CAT Practice Test: September 15 - Question 12

x3 + y3 = (x + y)3 - 3xy (x + y)
= (x + y) [(x + y)2 - 3xy]
= h(x) [ {h(x)}2 - 3g(x) ]

CAT Practice Test: September 15 - Question 13
Save

An exponential function is given by f(x) = a3x. If the point  lies on the graph of this function, then the value of 'a' is
Detailed Solution for CAT Practice Test: September 15 - Question 13

Given function is f(x) = a3x
As point  lies on the given curve, it must satisfy the given equation.

a = 7

CAT Practice Test: September 15 - Question 14
Save

If f : R - {3} → R - {1} is defined by f(x) = , then f is
Detailed Solution for CAT Practice Test: September 15 - Question 14

Here, y = f(x)

Which is defined for y ∈ R - {1}
Hence f(x) is invertible.
∴ One - one and onto

CAT Practice Test: September 15 - Question 15
Save

Which of the following options is necessarily true if f(x) = x3 - 4x + p and f(0) and f(1) have opposite signs?
Detailed Solution for CAT Practice Test: September 15 - Question 15

f(x) = x3 - 4x + p
f(0) = p
f(1) = 1 - 4 + p = p - 3
∵ f(0) and f(1) have opposite signs
∴ f(0) and f(1) < 0
 p(p - 3) < 0
 0 < p < 3

CAT Practice Test: September 15 - Question 16
Save

If f(x) = ax2 + bx + c and c = then the graph of y = f(x) will certainly
Detailed Solution for CAT Practice Test: September 15 - Question 16


This shows that root of equation are real and equal. Thus, the graph touches the x-axis and is hence tangential to the x-axis.
Thus, answer option 3 is correct.

CAT Practice Test: September 15 - Question 17
Save

If f(x) = 3x - 5 and f(g(x)) = 2x, then g(x) equals
Detailed Solution for CAT Practice Test: September 15 - Question 17

Given: f(x) = 3x - 5 and f(g(x)) = 2(x)
f(g(x)) = 3g(x) - 5 = 2x
3g(x) - 5 = 2x
g(x) = (2x + 5)/3

CAT Practice Test: September 15 - Question 18
Save

If f(a, b) = a2 + b3, g(a, b) = a + b, then what is the value of f(3, g(3, 4))?
Detailed Solution for CAT Practice Test: September 15 - Question 18

f(a, b) = a2 + b3
g(a, b) = a + b
g(3, 4) = 7
f(3, g(3, 4)) = f(3, 7) = 32 + 73 = 352

CAT Practice Test: September 15 - Question 19
Save

When the curves y = log10 x and y = x-1 are drawn in the x - y plane, how many times do they intersect for the values x ≥ 1?
Detailed Solution for CAT Practice Test: September 15 - Question 19

It is given that y = log10x & y = 1/x
Draw their graphs approximately and check.

Here, we see the graph has only 1 intersection point.

CAT Practice Test: September 15 - Question 20
Save

Find the minimum value of x2 - 12x + 27.
Detailed Solution for CAT Practice Test: September 15 - Question 20

 f (x) = x2 - 12x + 27 = x2 - 12x + 36 - 9
= (x - 6)2 - 9.
Since (x - 6)2 ≥ 0, the minimum value of the expression is - 9.

CAT Practice Test: September 15 - Question 21
Save

Directions: Read the following information carefully and answer the question given below.

In a family there are six members and they are fashion designer, musician, neurologist, engineer, gynaecologist and cardiologist by profession. The cardiologist is the grandfather of F, who is a musician. A is married to B, the fashion designer. D who is a gynaecologist is married to the neurologist. C is the father of E and F. There are two married couples in this family.

Q. What is the profession of E?
Detailed Solution for CAT Practice Test: September 15 - Question 21

Here, '-' represents 'Female' and '+' represents 'Male'.

CAT Practice Test: September 15 - Question 22
Save

Directions: Study the following information carefully and answer the question that follows.

'A + B' means A is father of B.
'A # B' means A is sister of B.
'A - B' means A is husband of B.
'A @ B' means A is brother of B.
'A = B' means A is mother of B.

Q. If the expression 'N # S = X - C # H' is true, how is N related to C?
Detailed Solution for CAT Practice Test: September 15 - Question 22

'N # S = X - C # H' means N is the sister of S, who is the mother of X, who is the husband of C, who is the sister of H.

According to this, N is the aunt of C.

CAT Practice Test: September 15 - Question 23
Save

Directions: Read the following information carefully and answer the question given below.

In a family there are six members and they are fashion designer, musician, neurologist, engineer, gynaecologist and cardiologist by profession. The cardiologist is the grandfather of F, who is a musician. A is married to B, the fashion designer. D who is a gynaecologist is married to the neurologist. C is the father of E and F. There are two married couples in this family.

Q. How is F related to A?
Detailed Solution for CAT Practice Test: September 15 - Question 23

Here, '-' represents 'Female' and '+' represents 'Male'.

CAT Practice Test: September 15 - Question 24
Save

Directions: Study the following information carefully and answer the question that follows.

'A + B' means A is father of B.
'A # B' means A is sister of B.
'A - B' means A is husband of B.
'A @ B' means A is brother of B.
'A = B' means A is mother of B.

Q. If O = T # Y @ X - I, then which of the following is true?
Detailed Solution for CAT Practice Test: September 15 - Question 24

O = T # Y @ X - I, means O is the mother of T, who is the sister of Y, who is the brother of X, who is the husband of I.

According to this, O is the mother-in-law of I.

CAT Practice Test: September 15 - Question 25
Save

Directions: Read the following information carefully and answer the question given below.

In a family there are six members and they are fashion designer, musician, neurologist, engineer, gynaecologist and cardiologist by profession. The cardiologist is the grandfather of F, who is a musician. A is married to B, the fashion designer. D who is a gynaecologist is married to the neurologist. C is the father of E and F. There are two married couples in this family.

Q. Which of the following is a couple?
Detailed Solution for CAT Practice Test: September 15 - Question 25

Here, '-' represents 'Female' and '+' represents 'Male'.

CAT Practice Test: September 15 - Question 26
Save

Directions: Read the given information carefully and answer the following question.

Six family members Saksham, Lily, Thomas, Jack, Sanya and Julie are sitting in a row facing towards the south. Saksham who is the son-in-law of Julie is sitting second to the right of Sanya. There are only two persons who sit between Saksham and Jack. Sanya, who is the daughter of Julie but not the wife of Saksham sits at either of the corners. Lily is married to Saksham. Thomas who is sitting to the immediate right of Sanya is her nephew. Julie is the maternal grandmother of Jack and is sitting to the immediate left of her daughter. Jack is sitting third to the right of his father.

Q. How is Julie related to Jack?
Detailed Solution for CAT Practice Test: September 15 - Question 26

According to the question:

Jack is the son of Lily and Lily is the daughter of Julie.
So, Julie is the maternal grandmother of Jack.

CAT Practice Test: September 15 - Question 27
Save

Directions: Study the information given below and answer the question that follows.

A is the father of two children, B and D, who are of different sexes.
C is B's spouse.
E is of the same sex as D.
B and C have two children: F, who is of the same sex as B and G, who is of the same sex as C.
E's mother H, who is married to L, is the sister of D's mother, M.
E and E's spouse, I, have two children J and K, who are of the same sex as I.
No person has married more than once, and no children have been born out of wedlock.
The only restriction on marriage is that marriage to a sibling, to a direct descendant, or to more than one person at the same time is forbidden.

Q. According to the rules, D can marry
Detailed Solution for CAT Practice Test: September 15 - Question 27


We can draw the above diagram based on the information given in the question. If the gender of the person is known, it is denoted by the suffix m or f. If it is not known, then it is denoted by x or y. We know, for example, that G is of the same sex as C, so we can label both as x; B and therefore, F are of the opposite sex from C, so we can label both y, and so on. Horizontal lines indicate marriage, vertical or diagonal lines indicate children. 
D is an x, and can therefore, marry any unmarried y. So, he can marry F, J, or K. 
Hence, answer option (1) is correct.

CAT Practice Test: September 15 - Question 28
Save

Directions: Study the information given below and answer the question that follows.

A is the father of two children, B and D, who are of different sexes.
C is B's spouse.
E is of the same sex as D.
B and C have two children: F, who is of the same sex as B and G, who is of the same sex as C.
E's mother H, who is married to L, is the sister of D's mother, M.
E and E's spouse, I, have two children J and K, who are of the same sex as I.
No person has married more than once, and no children have been born out of wedlock.
The only restriction on marriage is that marriage to a sibling, to a direct descendant, or to more than one person at the same time is forbidden.

Q. F is
Detailed Solution for CAT Practice Test: September 15 - Question 28


We can draw the above diagram based on the information given in the question.
If the gender of the person is known, it is denoted by the suffix m or f. If it is not known, then it is denoted by x or y. We know, for example, that G is of the same sex as C, so we can label both as x; B and therefore, F are of the opposite sex from C, so we can label both y, and so on.
Horizontal lines indicate marriage, vertical or diagonal lines indicate children.  
This question orients you, in case you made an unwarranted assumption about the sexes. Since we do not know B's sex for sure, we cannot determine F's as well; this rules out all the wrong choices - including E, since we know H's sex.
Being the child of D's sibling, B, F is D's niece or nephew. 
Therefore, option 2 is the correct answer.

CAT Practice Test: September 15 - Question 29
Save

Directions: Study the following information carefully and answer the question given below.

'A + B' means 'A is the son of B.'
'A - B' means 'A is the father of B.'
'A x B' means 'A is the sister of B.'
'A * B' means 'A is the mother of B.'

Q. If P + Q * R x S _ T, then how is P related to T?
Detailed Solution for CAT Practice Test: September 15 - Question 29

P is the son of Q, Q is the mother of R, R is the sister of S, S is the father of T. P, S and R are the children of Q, and T is the child of S.
P and S are males, whereas R is a female. P is the paternal uncle of T.

CAT Practice Test: September 15 - Question 30
Save

Directions: Read the following information carefully and answer the question given below.

In a family there are six members and they are fashion designer, musician, neurologist, engineer, gynaecologist and cardiologist by profession. The cardiologist is the grandfather of F, who is a musician. A is married to B, the fashion designer. D who is a gynaecologist is married to the neurologist. C is the father of E and F. There are two married couples in this family.

Q. What is the profession of A?
Detailed Solution for CAT Practice Test: September 15 - Question 30

Here, '-' represents 'Female' and '+' represents 'Male'.

View more questions
Information about CAT Practice Test: September 15 Page
In this test you can find the Exam questions for CAT Practice Test: September 15 solved & explained in the simplest way possible. Besides giving Questions and answers for CAT Practice Test: September 15, EduRev gives you an ample number of Online tests for practice

Top Courses for CAT

Download as PDF

Top Courses for CAT

Important Questions for CAT Practice Test: September 15

Find all the important questions for CAT Practice Test: September 15 at EduRev.Get fully prepared for CAT Practice Test: September 15 with EduRev's comprehensive question bank and test resources. Our platform offers a diverse range of question papers covering various topics within the CAT Practice Test: September 15 syllabus. Whether you need to review specific subjects or assess your overall readiness, EduRev has you covered. The questions are designed to challenge you and help you gain confidence in tackling the actual exam. Maximize your chances of success by utilizing EduRev's extensive collection of CAT Practice Test: September 15 resources.

CAT Practice Test: September 15 MCQs with Answers

Prepare for the CAT Practice Test: September 15 within the CAT exam with comprehensive MCQs and answers at EduRev. Our platform offers a wide range of practice papers, question papers, and mock tests to familiarize you with the exam pattern and syllabus. Access the best books, study materials, and notes curated by toppers to enhance your preparation. Stay updated with the exam date and receive expert preparation tips and paper analysis. Visit EduRev's official website today and access a wealth of videos and coaching resources to excel in your exam.

Online Tests for CAT Practice Test: September 15

Practice with a wide array of question papers that follow the exam pattern and syllabus. Our platform offers a user-friendly interface, allowing you to track your progress and identify areas for improvement. Access detailed solutions and explanations for each test to enhance your understanding of concepts. With EduRev's Online Tests, you can build confidence, boost your performance, and ace CAT Practice Test: September 15 with ease. Join thousands of successful students who have benefited from our trusted online resources.
© EduRev
Education Revolution
Follow Us
Signup to see your scores go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup