CAT 2019 QA Slot 2 Question Paper (Available) :Download Solution with Answer Key

CAT 2019 QA Question Paper for November 24 Evening Session (Slot 2) was rated moderate to difficult. There were 34 questions out of which 11 were TITA-type and carried no negative marking. Attempting 24 questions accurately was enough to get 99+ percentile. CAT QA section in slot 2 had the highest number of questions from Arithmetic (13).

VARC was the trickiest and the most time-consuming section. DILR question sets were easy to moderate with only a few time-consuming questions.

Candidates preparing for CAT 2025 can download the CAT QA question paper with the solution pdf for the Slot 1 exam conducted on November 24, 2019, to get a better idea about the type of questions asked in the paper and the difficulty level of questions.

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CAT 2019 QA Question Paper Slot 2- Nov 24, 2019

CAT 2019 QA Slot 2 Question APper with Answer Key	Download PDF	Check Solution

Question 1:

The real root of the equation \(26x + 23x^2 - 21 = 0\) is

(A) \( \log \frac{23}{3} \)
(B) \( \log 29 \)
(C) \( \log \frac{27}{3} \)
(D) \( \log 227 \)

Correct Answer: (B) \( \log 29 \)
View Solution

Question 2:

The average of 30 integers is 5. Among these, 20 do not exceed 5. What is the highest possible value of the average of these 20 integers?

(A) 4
(B) 5
(C) 4.5
(D) 3.5

Correct Answer: (C) 4.5
View Solution

Question 3:

Let \( a, b, x, y \) be real numbers such that \( a^2 + b^2 = 25 \), \( x^2 + y^2 = 169 \) and \( ax + by = 65 \). If \( k = ay - bx \), then

(A) \( k = 0 \)
(B) \( k > \frac{5}{13} \)
(C) \( k = \frac{5}{13} \)
(D) \( 0 < k \leq \frac{5}{13} \)

Correct Answer: (A) \( k = 0 \)
View Solution

Question 4:

In triangle ABC, medians AD and BE are perpendicular to each other, and have lengths 12 cm and 9 cm respectively. What is the area of triangle ABC (in cm\(^2\))?

(A) 80
(B) 68
(C) 72
(D) 78

Correct Answer: (C) 72
View Solution

Question 5:

Let \( a_1, a_2, a_3, \ldots \) be integers such that \[ a_1 - a_2 + a_3 - a_4 + \cdots + (-1)^{n-1}a_n = n \]
for all \( n \geq 1 \). What is the value of \( a_{51} + a_{52} + \cdots + a_{1023} \)?

(A) -1
(B) 1
(C) 0
(D) 10

Correct Answer: (C) 0
View Solution

Question 6:

How many factors of \( 24 \times 35 \times 104 \) are perfect squares which are greater than 1? (TITA)

Correct Answer: \boxed{26}
View Solution

Question 7:

Two circles, each of radius 4 cm, touch externally. Each of these circles is externally touched by a third circle. If all three have a common tangent, then the radius of the third circle (in cm) is:

(A) \( \frac{\pi}{3} \)
(B) 1
(C) \( \frac{1}{\sqrt{2}} \)
(D) \( \sqrt{2} \)

Correct Answer: (C) \( \frac{1}{\sqrt{2}} \)
View Solution

Question 8:

What is the largest positive integer such that \( \frac{n^2 + 7n + 12}{n - 12} \) is also a positive integer?

(A) 6
(B) 8
(C) 16
(D) 12

Correct Answer: (C) 16
View Solution

Question 9:

In 2010, a library contained 11500 books – fiction and non-fiction.
By 2015, the total number increased to 12760 with 10% increase in fiction and 12% in non-fiction.
How many fiction books were there in 2015?

(A) 6600
(B) 6160
(C) 6000
(D) 5500

Correct Answer: (B) 6160
View Solution

Question 10:

Let \( f(mn) = f(m) \cdot f(n) \) for all positive integers \( m, n \).
If \( f(1), f(2), f(3) \) are positive integers, and \[ f(1) < f(2), \quad f(24) = 54, \]
find \( f(18) \). (TITA)

Correct Answer: \boxed{36}
View Solution

Question 11:

Let A and B be regular polygons with \( a \) and \( b \) sides respectively. If \( b = 2a \) and
each interior angle of B is \( \frac{3}{2} \) times each interior angle of A, then
the interior angle (in degrees) of a regular polygon with \( a + b \) sides is: (TITA)

Correct Answer: \boxed{162}
View Solution

Question 12:

A cyclist leaves A at 10:00 am and reaches B at 11:00 am. Every minute after 10:01 am, a motorcycle leaves A and reaches B at constant speed. 45 such motorcycles reach B by 11:00 am. If the cyclist doubled speed, how many motorcycles would reach B before him?

(A) 22
(B) 20
(C) 15
(D) 23

Correct Answer: (A) 22
View Solution

Question 13:

Let \( A \) be a real number. The roots of \( x^2 - 4x - \log_2 A = 0 \) are real and distinct if and only if:

(A) \( A < 1/16 \)
(B) \( A > 1/8 \)
(C) \( A > 1/16 \)
(D) \( A < 1/8 \)

Correct Answer: (C) \( A > \frac{1}{16} \)
View Solution

Question 14:

John jogs on track A at 6 kmph and Mary jogs on track B at 7.5 kmph. The total length of tracks A and B is 325 m. While John makes 9 rounds of track A, Mary makes 5 rounds of track B. In how many seconds will Mary make one round of track A? (TITA)

Correct Answer: \boxed{39}
View Solution

Question 15:

Anil can do a job in 20 days, Sunil in 40. Anil works 3 days, Sunil joins. After few more days, Bimal joins. If Bimal has done 10% of the job, in how many total days was the work done?

(A) 13
(B) 12
(C) 15
(D) 14

Correct Answer: (D) 14
View Solution

Question 16:

Rama’s score was one-twelfth the sum of Mohan and Anjali’s scores.
After increasing each by 6, new ratio is 11:10:3 for Anjali:Mohan:Rama.
How much more did Anjali score than Rama?

(A) 26
(B) 32
(C) 24
(D) 35

Correct Answer: (C) 24
View Solution

Question 17:

A's score is 10% less than B. B is 25% more than C. C is 20% less than D.
If A = 72, find D. (TITA)

Correct Answer: \boxed{120}
View Solution

Question 18:

The base of a regular pyramid is a square and each of the other four sides is an equilateral triangle. Length of each side is 20 cm. Find the vertical height of the pyramid.

(A) \( 10\sqrt{2} \)
(B) \( 8\sqrt{3} \)
(C) 12
(D) \( 5\sqrt{5} \)

Correct Answer: (B) \( 8\sqrt{3} \)
View Solution

Question 19:

If \( x \) is a real number, then \( \sqrt{\log_e (4x - x^2)} \) is real if and only if?

(A) \( -3 \leq x \leq 3 \)
(B) \( 1 \leq x \leq 2 \)
(C) \( 1 \leq x \leq 3 \)
(D) \( -1 \leq x \leq 3 \)

Correct Answer: (B) \( 1 \leq x \leq 2 \)
View Solution

Question 20:

Let triangle ABC be right-angled with hypotenuse BC = 20 cm. If point P lies on BC such that AP is perpendicular to BC, what is the maximum length of AP?

(A) 10
(B) \( 8\sqrt{2} \)
(C) \( 6\sqrt{3} \)
(D) 5

Correct Answer: (A) 10
View Solution

Question 21:

Two ants A and B start from a point P on a circle at the same time, A moving clockwise and B anti-clockwise. They meet at 10:00 am when A has covered 60% of the track. If A returns to P at 10:12 am, when will B return to P?

(A) 10:27 am
(B) 10:25 am
(C) 10:45 am
(D) 10:18 am

Correct Answer: (A) 10:27 am
View Solution

Question 22:

How many positive integer pairs (m,n) satisfy the equation \( m^2 + 105 = n^2 \)? (TITA)

Correct Answer: \boxed{4}
View Solution

Question 23:

Salaries of Ramesh, Ganesh, Rajesh were in 6:5:7 in 2010 and in 3:4:3 in 2015. If Ramesh’s salary increased by 25%, what is approximate % increase in Rajesh’s salary?

(A) 7
(B) 8
(C) 9
(D) 10

Correct Answer: (C) 9
View Solution

Question 24:

A man uses 405 cc iron, 783 cc aluminium, 351 cc copper to make cylinders of same radius 3 cm and equal volume. Total surface area is?

(A) \( 1044(4 + \pi) \)
(B) \( 8464\pi \)
(C) \( 928\pi \)
(D) \( 1026(1 + \pi) \)

Correct Answer: (D) \( 1026(1 + \pi) \)
View Solution

Question 25:

Quadratic equation has roots 4a, 3a. What is a possible value of \( b^2 + c \)?

(A) 3721
(B) 549
(C) 361
(D) 427

Correct Answer: (A) 3721
View Solution

Question 26:

Six-digit number. Conditions:

(1) Sixth digit = sum of first 3 digits

(2) Fifth digit = sum of first 2 digits

(3) Third = first

(4) Second = twice first

(5) Fourth = fifth + sixth

A = ? (TITA)

Correct Answer: \boxed{9}
View Solution

Question 27:

Mukesh purchased 10 bicycles at the same price. He sold 6 at 25% profit and 4 at 25% loss. Total profit was Rs. 2000. What was the purchase price per bicycle?

(A) 2000
(B) 6000
(C) 8000
(D) 4000

Correct Answer: (D) 4000
View Solution

Question 28:

Find the number of common terms between these APs:

15, 19, 23, ..., 415 and 14, 19, 24, ..., 464

(A) 20
(B) 18
(C) 21
(D) 19

Correct Answer: (C) 21
View Solution

Question 29:

If \( (2n+1) + (2n+3) + \dots + (2n+47) = 5280 \), find \( 1 + 2 + \dots + n \)

Correct Answer: \boxed{820}
View Solution

Question 30:

500 ml each of 10%, 22%, and 32% salt solution in A, B, C.
100 ml from A → B, 100 from B → C, 100 from C → A.
Final strength in A = ?

(A) 15
(B) 12
(C) 13
(D) 14

Correct Answer: \boxed{13}
View Solution

Question 31:

Solve: \( 5x - 3y = 13438 \), \( 5x + 3y + 1 = 9686 \).
Then find \( x + y \)

Correct Answer: \boxed{2024}
View Solution

Question 32:

Amal invests Rs 12000 at 8% (compound annually) and Rs 10000 at 6% (compound semi-annually) for one year. Bimal invests at 7.5% simple interest for one year. Amal and Bimal earn equal interest. How much did Bimal invest?

Correct Answer: \boxed{1734}
View Solution

Question 33:

A shopkeeper sells two tables at cost \( p \) – one at 20% profit and one at 20% loss. Amal sells to Bimal at 30% profit; Asim sells to Barun at 30% loss.

Find \( \frac{x - y}{p} \) where x, y are amounts paid by Bimal and Barun.

(A) 1
(B) 1.2
(C) 0.7
(D) 0.50

Correct Answer: \boxed{1.2}
View Solution

Question 34:

John works 172 hours in total, with Rs. 57/hour regular and Rs. 114/hour overtime. Overtime income = 15% of regular income.

Find how many hours he worked overtime.

Correct Answer: \boxed{12}
View Solution

CAT 2019 Question Paper Slot 2 November 24: Sectional Analysis

CAT 2019 Slot 2 was conducted between 2.30 pm to 5:30 pm. The overall difficulty level of this slot was reported to be moderate to difficult. CAT 2019 QA Sectional Analysis is as follows:

In QA, there was a high number of questions from Arithmetic (14) and Algebra (11).
3 questions were based on Numbers and 6 questions were asked from Geometry.
The difficulty level of the QA section was similar to that of the previous years.

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CAT 2019 QA Slot 2 Question Paper (Available) :Download Solution with Answer Key

CAT 2019 QA Question Paper Slot 2- Nov 24, 2019

CAT 2019 Question Paper Slot 2 November 24: Sectional Analysis

CAT Question Papers of Other Years

Other MBA Exam Question Papers

CAT Questions

1.
The set of all real values of $x$ for which $(x^2 - |x+9| + x)>0$ is:

2.
A man takes a loan of 1000 and repays it by paying 530 at the end of the first year, and 594 at the end of the second year. Find the rate of interest per annum.

3.
The sum of all the digits of the number $(10^{50} + 10^{25} - 123)$, is

5.
In the set of consecutive odd numbers $\{1, 3, 5, \ldots, 57\}$, there is a number $k$ such that the sum of all the elements less than $k$ is equal to the sum of all the elements greater than $k$. Then, $k$ equals?

6.
For real values of $x$, the range of the function $f(x) = \dfrac{2x - 3}{2x^2 + 4x - 6}$ is

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CAT 2019 QA Question Paper Slot 2- Nov 24, 2019

CAT 2019 Question Paper Slot 2 November 24: Sectional Analysis

CAT Question Papers of Other Years

Other MBA Exam Question Papers

CAT Questions

1.The set of all real values of $x$ for which $(x^2 - |x+9| + x)>0$ is:

2.A man takes a loan of 1000 and repays it by paying 530 at the end of the first year, and 594 at the end of the second year. Find the rate of interest per annum.

3.The sum of all the digits of the number $(10^{50} + 10^{25} - 123)$, is

5.In the set of consecutive odd numbers $\{1, 3, 5, \ldots, 57\}$, there is a number $k$ such that the sum of all the elements less than $k$ is equal to the sum of all the elements greater than $k$. Then, $k$ equals?

6.For real values of $x$, the range of the function $f(x) = \dfrac{2x - 3}{2x^2 + 4x - 6}$ is

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1.
The set of all real values of $x$ for which $(x^2 - |x+9| + x)>0$ is:

2.
A man takes a loan of 1000 and repays it by paying 530 at the end of the first year, and 594 at the end of the second year. Find the rate of interest per annum.

3.
The sum of all the digits of the number $(10^{50} + 10^{25} - 123)$, is

5.
In the set of consecutive odd numbers $\{1, 3, 5, \ldots, 57\}$, there is a number $k$ such that the sum of all the elements less than $k$ is equal to the sum of all the elements greater than $k$. Then, $k$ equals?

6.
For real values of $x$, the range of the function $f(x) = \dfrac{2x - 3}{2x^2 + 4x - 6}$ is