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CAT Practice Test: September 15 - CAT MCQ


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30 Questions MCQ Test Daily Test for CAT Preparation - CAT Practice Test: September 15

CAT Practice Test: September 15 for CAT 2024 is part of Daily Test for CAT Preparation 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.
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CAT Practice Test: September 15 - Question 1
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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
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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.

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CAT Practice Test: September 15 - Question 3
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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'.

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