CAT 2020 Question Paper-November 29 Morning Session (Slot 1) was rated from moderate to difficult in terms of overall difficulty. CAT QA was comparatively easier with 50% of questions based on various topics of Arithmetic. About 8 questions were asked from Algebra, while 3 questions each were asked from Geometry and Modern Maths.

  • CAT VARC was the trickiest and time-consuming. DILR question sets were of moderate difficulty with only a few time-consuming questions.

Candidates preparing for CAT 2025 can download CAT QA question paper with the answer key PDF for the Slot 1 exam conducted on November 29, 2020, to get a better idea about the type of questions asked in the paper and the difficulty level of questions.

Also Check:

CAT 2020 QA Slot 1 Question Paper with Solution PDF 

CAT 2020 QA Slot 1 Question Paper with Answer Key Download PDF Check Solutions 
CAT 2020 QA SLOT 1 QUESTION PAPER WITH SOLUTIONS
 

Question 1:

How many 3-digit numbers are there, for which the product of their digits is more than 2 but less than 7?


Question 2:

If \( f(5 + x) = f(5 - x) \) for every real \( x \) and \( f(x) = 0 \) has four distinct real roots, then the sum of the roots is

  • (A) 0
  • (B) 40
  • (C) 10
  • (D) 20

Question 3:

Veeru invested Rs 10000 at 5% simple annual interest, and exactly after two years, Joy invested Rs 8000 at 10% simple annual interest. How many years after Veeru’s investment, will their balances be equal?


Question 4:

A train traveled at one-third of its usual speed, reaching the destination 30 minutes late. On its return journey, it traveled at usual speed for 5 minutes but stopped for 4 minutes. The percentage increase in speed needed to reach on time is nearest to:

  • (A) 58
  • (B) 67
  • (C) 50
  • (D) 61

Question 5:

A straight road connects points A and B. Car 1 travels from A to B and Car 2 travels from B to A, both leaving at the same time. After meeting each other, they take 45 minutes and 20 minutes, respectively, to complete their journeys. If Car 1 travels at the speed of 60 km/hr, then the speed of Car 2, in km/hr, is

  • (A) 90
  • (B) 80
  • (C) 70
  • (D) 100
Correct Answer: (A) 90
View Solution

Question 6:

Let A, B, and C be three positive integers such that the sum of A and the mean of B and C is 5. In addition, the sum of B and the mean of A and C is 7. Then the sum of A and B is

  • (A) 6
  • (B) 4
  • (C) 7
  • (D) 5

Question 7:

The mean of all 4-digit even natural numbers of the form 'aabb', where \( a > 0 \), is

  • (A) 5544
  • (B) 4466
  • (C) 4864
  • (D) 5050

Question 8:

The number of distinct real roots of the equation \((x + 1/x)^2 - 3(x + 1/x) + 2 = 0\) equals:

  • (A) 0
  • (B) 1
  • (C) 2
  • (D) 3

Question 9:

A person spent Rs 50000 to purchase a desktop computer and a laptop computer. He sold the desktop at 20% profit and the laptop at 10% loss. If overall he made a 2% profit then the purchase price, in rupees, of the desktop is

  • (A) 20000
  • (B) 25000
  • (C) 30000
  • (D) 35000

Question 10:

Among 100 students, \( x_1 \) have birthdays in January, \( x_2 \) have birthdays in February, and so on. If \( x_0 = \max(x_1, x_2, \ldots, x_{12}) \), then the smallest possible value of \( x_0 \) is

  • (A) 8
  • (B) 10
  • (C) 12
  • (D) 9

Question 11:

Among 100 students, \( x_1 \) have birthdays in January, \( x_2 \) have birthdays in February, and so on. If \( x_0 = \max(x_1, x_2, \ldots, x_{12}) \), then the smallest possible value of \( x_0 \) is

  • (A) 8
  • (B) 10
  • (C) 12
  • (D) 9

Question 12:

How many distinct positive integer-valued solutions exist to the equation \( (x^2 - 7x + 11)^2 - 13x + 42 = 1 \)?

  • (A) 6
  • (B) 2
  • (C) 4
  • (D) 8

Question 13:

The area of the region satisfying the inequalities \( |x| - y \leq 1 \), \( y \geq 0 \), and \( y \leq 1 \) is

  • (A) 6
  • (B) 2
  • (C) 4
  • (D) 3

Question 14:

A solid right circular cone of height 27 cm is cut into 2 pieces along a plane parallel to its base at a height of 18 cm from the base. If the difference in the volume of the two pieces is 225 cc, the volume, in cc, of the original cone is

  • (A) 264
  • (B) 232
  • (C) 243
  • (D) 256

Question 15:

A circle is inscribed in a rhombus with diagonals 12 cm and 16 cm. The ratio of the area of the circle to the area of the rhombus is

  • (A) \( \frac{2\pi}{15} \)
  • (B) \( \frac{6\pi}{25} \)
  • (C) \( \frac{3\pi}{25} \)
  • (D) \( \frac{5\pi}{18} \)

Question 16:

Leaving home at the same time, Amal reaches office at 10:15 am if he travels at 8 kmph, and at 9:40 am if he travels at 15 kmph. Leaving home at 9:10 am, at what speed, in kmph, must he travel so as to reach office exactly at 10:00 am?

  • (A) 12
  • (B) 11
  • (C) 13
  • (D) 14

Question 17:

If \(a\), \(b\), and \(c\) are positive integers such that \(ab = 432\), \(bc = 96\) and \(c < 9\), then the smallest possible value of \(a + b + c\) is

  • (A) 56
  • (B) 49
  • (C) 46
  • (D) 59

Question 18:

If \( y \) is a negative number such that \( 2y^2 \log 3^5 = 5 \log 2^3 \), then \( y \) equals

  • (A) \( \log_2 \left( \frac{1}{3} \right) \)
  • (B) \( \log_2 \left( \frac{1}{5} \right) \)
  • (C) \( - \log_2 \left( \frac{1}{3} \right) \)
  • (D) \( - \log_2 \left( \frac{1}{5} \right) \)

Question 19:

On a rectangular metal sheet of area 135 sq in, a circle is painted such that the circle touches opposite two sides. If the area of the sheet left unpainted is two-thirds of the painted area, then the perimeter of the rectangle in inches is

  • (A) \( 3\pi(5 + \frac{12}{\pi}) \)
  • (B) \( 3\pi(4 + \frac{10}{\pi}) \)
  • (C) \( 4\pi(5 + \frac{13}{\pi}) \)
  • (D) \( 2\pi(5 + \frac{8}{\pi}) \)

Question 20:

An alloy is prepared by mixing metals A, B, C in the proportion \(3 : 4 : 7\) by volume. Weights of the same volume of metals A, B, C are in the ratio \(5 : 2 : 6\). In 130 kg of the alloy, the weight, in kg, of the metal C is

  • (A) 84
  • (B) 48
  • (C) 96
  • (D) 70

Question 21:

In 130 kg of the alloy, the weight, in kg, of the metal C is

  • (A) 84
  • (B) 48
  • (C) 96
  • (D) 70

Question 22:

A solution, of volume 40 litres, has dye and water in the proportion \(2 : 3\). Water is added to the solution to change this proportion to \(2 : 5\). If one-fourth of this diluted solution is taken out, how many litres of dye must be added to the remaining solution to bring the proportion back to \(2 : 3\)?

  • (A) 8
  • (B) 6
  • (C) 10
  • (D) 4

Question 23:

The number of real-valued solutions of the equation \(2^x + 2^{2x} = 2 - (x - 2)^2\) is

  • (A) infinite
  • (B) 0
  • (C) 1
  • (D) 2

Question 24:

If \(\log_4 5 = (\log_4 y) \cdot (\log_6 \sqrt{5})\), then \(y\) equals

  • (A) 36
  • (B) 25
  • (C) 16
  • (D) 64

Question 25:

In a group of people, 28% of the members are young while the rest are old. If 65% of the members are literates, and 25% of the literates are young, then the percentage of old people among the illiterates is nearest to

  • (A) 59
  • (B) 62
  • (C) 66
  • (D) 55


CAT 2020 Question Paper Nov 29: Sectional Analysis

CAT 2020 Slot 1 was conducted between 8.30 am to 10:30 am. The overall difficulty level of this slot was reported to be moderate to difficult.

  • QA section was slightly easier in terms of difficulty level and time consumed than VARC section
  • In total 2 Questions were asked from Numbers 
  • 8 Questions were asked from  Arithematic
  • 8 Questions were asked from Algebra
  • The remaining 3 Questions were asked from Modern Maths

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