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Mini Mock || CAT 2021 || 18 November

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Question 1

Direction: A sentence with two blanks is given, each blank indicating that something has been omitted. Choose the words that best fit the meaning of the sentence as a whole.

In the early 2000s, dozens of the world’s premier experts on sports-related concussions started meeting to _______ studies about concussions, with plans to issue a consensus set of guidelines on how best to _______ and deal with the condition.

Question 2

Direction: A sentence with two blanks is given, each blank indicating that something has been omitted. Choose the pair of words that best fits into the given blanks appropriately.

After more than 60 years of ____ of the Universal Declaration of Human Rights, we still have high ____ of child labor in some developing countries.

Question 3

Direction: A sentence with two blanks is given, each blank indicating that something has been omitted. Choose the pair of words that best fit the meaning of the sentence as a whole.

The tsunami and nuclear ____ in Fukushima, Japan, now threatens the ____ brains of children in Cambodia — but not for reasons that were ever expected.

Question 4

Direction: In the given question, a sentence with two blanks, each blank indicating that something has been omitted, is given. Choose the words that best fit the meaning of the sentence as a whole.

Cyber attacks _____ the general public or national and corporate organizations and are carried out through the spread of malicious programs (viruses), fake websites, and other means of _____ personal or institutional information from targets of attacks.

Question 5

Small Indian businesses and individuals continue to report being hit by the cyber-extortion ____ which has affected computers around the world, _____ essential services and forcing some to meet the unidentified hackers' ransom demands.

Question 6

A survey of 600 schools in India was conducted to gather information about their online teaching learning processes (OTLP). The following four facilities were studied.

F1: Own software for OTLP

F2: Trained teachers for OTLP

F3: Training materials for OTLP

F4: All students having Laptops

The following observations were summarized from the survey.

1. 80 schools did not have any of the four facilities – F1, F2, F3, F4

2. 40 schools had all four facilities.

3. The number of schools with only F1, only F2, only F3, and only F4 was 25, 30, 26 and 20 respectively.

4. The number of schools with exactly three of the facilities was the same irrespective of which three were considered.

5. 313 schools had F2

6. 26 schools had only F2 and F3 (but neither F1 nor F4).

7. Among the schools having F4, 24 had only F3, and 45 had only F2

8. 162 schools had both F1 and F2

9. The number of schools having F1 was the same as the number of schools having F4

What was the number of schools having only facilities F1 andF3?

Question 7

A survey of 600 schools in India was conducted to gather information about their online teaching learning processes (OTLP). The following four facilities were studied.

F1: Own software for OTLP

F2: Trained teachers for OTLP

F3: Training materials for OTLP

F4: All students having Laptops

The following observations were summarized from the survey.

1. 80 schools did not have any of the four facilities – F1, F2, F3, F4

2. 40 schools had all four facilities.

3. The number of schools with only F1, only F2, only F3, and only F4 was 25, 30, 26 and 20 respectively.

4. The number of schools with exactly three of the facilities was the same irrespective of which three were considered.

5. 313 schools had F2

6. 26 schools had only F2 and F3 (but neither F1 nor F4).

7. Among the schools having F4, 24 had only F3, and 45 had only F2

8. 162 schools had both F1 and F2

9. The number of schools having F1 was the same as the number of schools having F4

What was the number of schools having only facilities F1 andF4?

Question 8

A survey of 600 schools in India was conducted to gather information about their online teaching learning processes (OTLP). The following four facilities were studied.

F1: Own software for OTLP

F2: Trained teachers for OTLP

F3: Training materials for OTLP

F4: All students having Laptops

The following observations were summarized from the survey.

1. 80 schools did not have any of the four facilities – F1, F2, F3, F4

2. 40 schools had all four facilities.

3. The number of schools with only F1, only F2, only F3, and only F4 was 25, 30, 26 and 20 respectively.

4. The number of schools with exactly three of the facilities was the same irrespective of which three were considered.

5. 313 schools had F2

6. 26 schools had only F2 and F3 (but neither F1 nor F4).

7. Among the schools having F4, 24 had only F3, and 45 had only F2

8. 162 schools had both F1 and F2

9. The number of schools having F1 was the same as the number of schools having F4

What was the total number of schools having exactly three of the four facilities?

Question 9

A survey of 600 schools in India was conducted to gather information about their online teaching learning processes (OTLP). The following four facilities were studied.

F1: Own software for OTLP

F2: Trained teachers for OTLP

F3: Training materials for OTLP

F4: All students having Laptops

The following observations were summarized from the survey.

1. 80 schools did not have any of the four facilities – F1, F2, F3, F4

2. 40 schools had all four facilities.

3. The number of schools with only F1, only F2, only F3, and only F4 was 25, 30, 26 and 20 respectively.

4. The number of schools with exactly three of the facilities was the same irrespective of which three were considered.

5. 313 schools had F2

6. 26 schools had only F2 and F3 (but neither F1 nor F4).

7. Among the schools having F4, 24 had only F3, and 45 had only F2

8. 162 schools had both F1 and F2

9. The number of schools having F1 was the same as the number of schools having F4

What was the number of schools having facilities F2 and F4?

Question 10

Let

if x ≠ 1, – 1, and 1 if x = 1, – 1. Let

if x ≠ 1, and 3 if x = 1. What is the minimum possible value of

Question 11

Let m and n be positive integers, if x² + mx + 2n = 0 and x² + 2nx + m = 0 have real roots, then the smallest possible value of m + n is

Question 12

In how many ways can a pair of integers (x , A) be chosen such that x² − 2 |x| + |a − 2| = 0?

Question 13

If the roots of a quadratic equation

are α and β, whereas the roots of another equation

are (α + 2) and (β + 2), what is the value of a + b?

Question 14

If a, b and c are three distinct integers such that b + c – a = 0, then the roots of the quadratic equation (a + b – c) x² + 2(2a – b – c) x + (a – b + c) = 0 are

Question 15

Direction: Solve the following question and mark the best possible option.

Two different quadratic equations have a common root. Let the three unique roots of the two equations be A, B and C- all of them are positive integers. If (A + B + C) = 41 and the product of the roots of one of the equations is 35, which of the following options is definitely correct?

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