Q. What is the relationship between the sections of the CAT exam as described in the passage?
A.
They are independent and do not affect each other.
B.
They are interrelated and require a balanced approach.
C.
They focus solely on quantitative reasoning.
D.
They are designed to confuse the test-taker.
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Solution
The passage highlights that the sections are interrelated, necessitating a balanced preparation strategy.
Correct Answer:
B
— They are interrelated and require a balanced approach.
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Q. What is the relationship between the sides of a rhombus?
A.
All sides are equal.
B.
Opposite sides are equal.
C.
Adjacent sides are equal.
D.
No sides are equal.
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Solution
In a rhombus, all sides are equal in length.
Correct Answer:
A
— All sides are equal.
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Q. What is the relationship between the terms of a harmonic progression and their reciprocals?
A.
They are in geometric progression.
B.
They are in arithmetic progression.
C.
They are in quadratic progression.
D.
They are in exponential progression.
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Solution
The terms of a harmonic progression are the reciprocals of the terms of an arithmetic progression.
Correct Answer:
B
— They are in arithmetic progression.
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Q. What is the relationship between the two main concepts discussed in the passage?
A.
They are mutually exclusive.
B.
They complement each other.
C.
They are unrelated.
D.
They are contradictory.
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Solution
The two main concepts discussed in the passage complement each other, as they work together to address the issue.
Correct Answer:
B
— They complement each other.
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Q. What is the relationship between the two main ideas presented in the passage?
A.
They are contradictory.
B.
They complement each other.
C.
They are unrelated.
D.
They are sequential.
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Solution
The two main ideas in the passage complement each other, providing a holistic view of the topic discussed.
Correct Answer:
B
— They complement each other.
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Q. What is the relationship between the two studies mentioned in the passage?
A.
They are completely unrelated.
B.
One study supports the findings of the other.
C.
They contradict each other.
D.
They were conducted by the same researchers.
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Solution
The passage indicates that one study provides evidence that supports the findings of the other, establishing a relationship.
Correct Answer:
B
— One study supports the findings of the other.
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Q. What is the relationship between verbal ability and overall performance in the CAT exam as suggested in the passage?
A.
Verbal ability is secondary to quantitative skills.
B.
Verbal ability directly impacts overall performance.
C.
Verbal ability is irrelevant to the exam's success.
D.
Verbal ability is only important for certain sections.
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Solution
The passage suggests that strong verbal ability is crucial and directly influences overall performance in the CAT exam.
Correct Answer:
B
— Verbal ability directly impacts overall performance.
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Q. What is the remainder when 1000 is divided by 6?
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Solution
1000 divided by 6 gives a quotient of 166 and a remainder of 4.
Correct Answer:
A
— 4
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Q. What is the remainder when 1000 is divided by 9? (2023)
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Solution
1000 divided by 9 gives a remainder of 1 (1000 = 9*111 + 1).
Correct Answer:
B
— 2
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Q. What is the remainder when 123456 is divided by 10? (2023)
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Solution
The remainder when a number is divided by 10 is the last digit of the number, which is 6.
Correct Answer:
D
— 6
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Q. What is the remainder when 123456 is divided by 11? (2023)
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Solution
123456 mod 11 = 0, as 123456 is divisible by 11.
Correct Answer:
A
— 0
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Q. What is the remainder when 144 is divided by 11?
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Solution
144 divided by 11 gives a remainder of 1.
Correct Answer:
A
— 0
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Q. What is the remainder when 145 is divided by 12?
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Solution
145 divided by 12 gives a remainder of 1.
Correct Answer:
B
— 2
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Q. What is the remainder when 250 is divided by 7?
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Solution
250 divided by 7 gives a quotient of 35 and a remainder of 5.
Correct Answer:
A
— 1
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Q. What is the remainder when 256 is divided by 11?
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Solution
256 divided by 11 gives a quotient of 23 and a remainder of 3.
Correct Answer:
A
— 2
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Q. What is the remainder when 256 is divided by 7?
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Solution
256 divided by 7 gives a quotient of 36 and a remainder of 4.
Correct Answer:
B
— 4
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Q. What is the remainder when 256 is divided by 9?
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Solution
256 divided by 9 gives a quotient of 28 and a remainder of 4.
Correct Answer:
B
— 2
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Q. What is the remainder when 987654 is divided by 9?
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Solution
The sum of the digits of 987654 is 39, which is divisible by 9, hence the remainder is 0.
Correct Answer:
A
— 0
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Q. What is the remainder when 987654321 is divided by 9? (2023)
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Solution
The remainder when a number is divided by 9 can be found by summing its digits. The sum of the digits of 987654321 is 45, which is divisible by 9, hence the remainder is 0.
Correct Answer:
A
— 0
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Q. What is the result of (10 + 15) mod 7?
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Solution
(10 + 15) = 25; 25 mod 7 = 4.
Correct Answer:
B
— 2
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Q. What is the result of (15 + 10) mod 12?
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Solution
(15 + 10) = 25; 25 mod 12 = 1.
Correct Answer:
A
— 5
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Q. What is the result of (2^3)^2?
A.
2^5
B.
2^6
C.
2^7
D.
2^8
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Solution
Using the power of a power property, (a^m)^n = a^(m*n), we have (2^3)^2 = 2^(3*2) = 2^6.
Correct Answer:
B
— 2^6
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Q. What is the result of (3 * 4) mod 5?
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Solution
Calculating (3 * 4) = 12, and then 12 mod 5 = 2.
Correct Answer:
C
— 4
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Q. What is the result of 10 mod 3?
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Solution
10 divided by 3 gives a remainder of 1, so 10 mod 3 = 1.
Correct Answer:
B
— 2
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Q. What is the result of 5^2 * 5^(-3)? (2023)
A.
5^1
B.
5^(-1)
C.
5^0
D.
5^(-5)
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Solution
Using the property of exponents, we combine the exponents: 5^(2 + (-3)) = 5^(-1).
Correct Answer:
B
— 5^(-1)
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Q. What is the result of adding the binary numbers 1011 and 1101?
A.
11000
B.
10100
C.
10010
D.
11110
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Solution
Adding 1011 and 1101 in binary results in 11110.
Correct Answer:
D
— 11110
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Q. What is the result of adding the polynomials (2x^2 + 3x + 4) and (3x^2 - x + 2)?
A.
5x^2 + 2x + 6
B.
5x^2 + 4x + 6
C.
5x^2 + 3x + 6
D.
5x^2 + 3x + 4
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Solution
When adding the polynomials, combine like terms: (2x^2 + 3x + 4) + (3x^2 - x + 2) = 5x^2 + 2x + 6.
Correct Answer:
B
— 5x^2 + 4x + 6
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Q. What is the result of adding the polynomials (2x^2 + 3x - 4) and (x^2 - 5x + 6)?
A.
3x^2 - 2x + 2
B.
3x^2 - 2x - 2
C.
x^2 - 2x + 2
D.
3x^2 + 2x + 2
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Solution
When adding the polynomials, combine like terms: (2x^2 + x^2) + (3x - 5x) + (-4 + 6) = 3x^2 - 2x + 2.
Correct Answer:
A
— 3x^2 - 2x + 2
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Q. What is the result of adding the polynomials (3x^2 + 2x + 1) and (4x^2 - x + 5)?
A.
7x^2 + x + 6
B.
7x^2 + 3x + 6
C.
x^2 + x + 6
D.
7x^2 + 2x + 5
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Solution
Adding the two polynomials gives (3x^2 + 4x^2) + (2x - x) + (1 + 5) = 7x^2 + x + 6.
Correct Answer:
B
— 7x^2 + 3x + 6
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Q. What is the result of adding the polynomials (3x^2 + 2x - 1) and (4x^2 - 3x + 5)?
A.
7x^2 - x + 4
B.
7x^2 - x - 6
C.
x^2 - x + 4
D.
x^2 + 5
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Solution
Adding the two polynomials gives (3x^2 + 4x^2) + (2x - 3x) + (-1 + 5) = 7x^2 - x + 4.
Correct Answer:
A
— 7x^2 - x + 4
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