Select the option that is related to the third term in the same way as the second term is related to the first.
Error : Big mistake : : Deny : ?
The question asks us to find a word that shares the same relationship with "Deny" as "Big" shares with "Error". This is an analogy question, and we need to identify the type of relationship between the first pair of words and then apply the same relationship to the third word to find the fourth.
An "Error" is a mistake. A "Big mistake" is an intensified or more severe form of an error. So, the relationship is one of intensification or a more serious degree of the first term.
We need to find a word that represents an intensified or more severe form of "Deny".
Correct Option: D) Prohibition — "Prohibition" is a strong or official denial or forbidding of something, which is an intensified form of "Deny" (to refuse to admit or grant). This mirrors the relationship where a "Big mistake" is an intensified form of an "Error".
To find the Least Common Multiple (LCM) of two numbers, we can use the prime factorization method. This involves finding the prime factors of each number and then multiplying the highest powers of all common and uncommon prime factors.
First, we find the prime factors of 21.
\[ 21 = 3 \times 7 \]Next, we find the prime factors of 560.
\[ 560 = 10 \times 56 \]\[ 560 = (2 \times 5) \times (7 \times 8) \]\[ 560 = (2 \times 5) \times (7 \times 2^3) \]\[ 560 = 2^4 \times 5^1 \times 7^1 \]To find the LCM, we take the highest power of each prime factor present in either factorization.
Prime factors involved are 2, 3, 5, and 7.
Now, multiply these highest powers together:
\[ \text{LCM}(21, 560) = 2^4 \times 3^1 \times 5^1 \times 7^1 \]\[ \text{LCM}(21, 560) = 16 \times 3 \times 5 \times 7 \]\[ \text{LCM}(21, 560) = 48 \times 35 \]\[ \text{LCM}(21, 560) = 1680 \]B) 1680 is the least common multiple of 21 and 560.
This is a blood relation question. We need to deduce the relationship between X and Aamir by breaking down the given information step-by-step.
C) Uncle. X is the husband of Aamir's mother's sister, which means X is Aamir's maternal uncle.
Identify the odd:
The question asks to identify the odd one out from the given options, which are all units related to physical quantities. We need to determine the physical quantity each unit represents and find the one that is different from the others.
D) N is the odd one out because it is a unit of force, whereas options A, B, and C are all units of pressure.
The problem requires us to first arrange the letters of the word "ASTEROID" in alphabetical order. Then, we assign numerical values \(1, 2, 3, \dots\) to these alphabetically ordered letters. Finally, we identify the consonants among these letters and sum their assigned numerical values based on their positions from the left side in the alphabetically ordered sequence.
Identify the letters in the word "ASTEROID":
The letters are A, S, T, E, R, O, I, D.
Arrange the letters in alphabetical order:
D, E, I, O, R, S, T
Wait, the word is ASTEROID, which has 8 letters. Let's re-list them and sort carefully:
A, S, T, E, R, O, I, D
Alphabetical order: A, D, E, I, O, R, S, T
Assign numerical values to the alphabetically ordered letters:
A = 1
D = 2
E = 3
I = 4
O = 5
R = 6
S = 7
T = 8
Identify the consonants from the alphabetically ordered list:
The vowels are A, E, I, O, U. From our list, the vowels are A, E, I, O.
The consonants are the remaining letters: D, R, S, T.
Find the numerical values of the consonants:
D has a value of 2.
R has a value of 6.
S has a value of 7.
T has a value of 8.
Calculate the total value of the positions of the consonants:
Sum of the values of the consonants \( = 2 + 6 + 7 + 8 \)
\[ 2 + 6 + 7 + 8 = 23 \]
A) 23 is the correct sum of the numerical values assigned to the consonants (D, R, S, T) after arranging the letters of "ASTEROID" alphabetically and assigning values \(1, 2, 3, \dots\) to them.
This question asks us to evaluate the strength of two arguments regarding whether TV plays should be banned. We need to determine which argument provides a more logical and universally acceptable reason for or against the ban.
Correct Option: D) Only argument II is strong.
The question asks to identify the country that won the 2018 FIFA Fair Play Trophy. This requires knowledge of the results and awards from the 2018 FIFA World Cup.
C) Spain — Spain was awarded the FIFA Fair Play Trophy at the 2018 FIFA World Cup for having the best disciplinary record in the tournament.
What amount of water can reach a height of 10 m by a pump of 1 kW in a minute? (Take g = 10 m/s2)
This problem involves calculating the mass of water that can be lifted by a pump given its power, the height, and the time. We will use the relationship between power, work done, and potential energy. The work done by the pump is converted into the potential energy of the water lifted.
Identify the given values:
Calculate the total work done by the pump:
Power is defined as the rate at which work is done. So, Work Done = Power \(\times\) Time.
\[ \text{Work Done} = P \times t \] \[ \text{Work Done} = 1000 \text{ W} \times 60 \text{ s} \] \[ \text{Work Done} = 60000 \text{ J} \]Relate work done to potential energy:
The work done by the pump is used to increase the potential energy of the water. The potential energy (\(PE\)) of a mass \(m\) lifted to a height \(h\) is given by \(PE = mgh\).
Therefore, Work Done = Potential Energy gained by water.
\[ \text{Work Done} = mgh \] \[ 60000 \text{ J} = m \times 10 \text{ m/s}^2 \times 10 \text{ m} \]Solve for the mass (\(m\)) of the water:
\[ 60000 = m \times 100 \] \[ m = \frac{60000}{100} \] \[ m = 600 \text{ kg} \]Correct Option: D) 600 kg
The calculations show that the pump can lift 600 kg of water to a height of 10 m in one minute.
The question asks to identify the winner of the Man Booker International Award for the novel "A Horse Walks Into a Bar". This requires knowledge of literary awards and their recipients.
Correct Option: B) David Grossman
To find the number of factors of a given number, we first need to express the number as a product of its prime factors. Once we have the prime factorization in the form \(N = p_1^{a_1} \cdot p_2^{a_2} \cdot \dots \cdot p_k^{a_k}\), where \(p_1, p_2, \dots, p_k\) are distinct prime numbers and \(a_1, a_2, \dots, a_k\) are their respective positive integer exponents, the total number of factors is given by the product of one more than each exponent: \((a_1+1)(a_2+1)\dots(a_k+1)\).
We start by finding the prime factors of 4840.
\[ 4840 = 10 \times 484 \]\[ 4840 = (2 \times 5) \times (22 \times 22) \]\[ 4840 = (2 \times 5) \times (2 \times 11) \times (2 \times 11) \]\[ 4840 = 2 \times 2 \times 2 \times 5 \times 11 \times 11 \]\[ 4840 = 2^3 \times 5^1 \times 11^2 \]From the prime factorization \(2^3 \times 5^1 \times 11^2\), the exponents of the prime factors are:
Using the formula \((a_1+1)(a_2+1)(a_3+1)\), we get:
\[ \text{Number of factors} = (3+1)(1+1)(2+1) \]\[ \text{Number of factors} = (4)(2)(3) \]\[ \text{Number of factors} = 8 \times 3 \]\[ \text{Number of factors} = 24 \]Correct Option: C) 24
The number 4840 has 24 factors.