This question is based on identifying the odd number out using a mathematical relationship between digits. We need to examine the four three-digit numbers and determine which one does not follow the common pattern. The relationship is that the last two digits of each number represent the square of its first digit. Three numbers satisfy this condition, while one does not.
The four options are:
Each number contains three digits. We need to check whether the last two digits equal the square of the first digit.
The first digit is 9, and the last two digits form 81.
Calculate the square of 9:
\(9^2=81\)
The last two digits are 81, which matches the square of the first digit.
Therefore, 981 follows the pattern.
The first digit is 7, and the last two digits form 49.
Calculate the square of 7:
\(7^2=49\)
The last two digits are 49, which matches the square of the first digit.
Therefore, 749 follows the pattern.
The first digit is 6, and the last two digits form 36.
Calculate the square of 6:
\(6^2=36\)
The last two digits are 36, which matches the square of the first digit.
Therefore, 636 follows the pattern.
The first digit is 8, and the last two digits form 68.
Calculate the square of 8:
\(8^2=64\)
However, the last two digits are 68, not 64.
Therefore, 868 does not follow the pattern.
If it followed the same rule, the number would be 864 instead of 868.
Compare all four options:
Therefore, 868 is different from the remaining three numbers.
Correct Option: D) 868
In the numbers 981, 749 and 636, the last two digits are the squares of their respective first digits. However, in 868, the first digit is 8, whose square is 64, whereas the last two digits are 68. Therefore, 868 does not follow the common mathematical pattern and is the correct answer.
If x – y = 5 and xy = 15, then what is the value of x3 – y3?
The problem requires us to find the value of \(x^3 - y^3\) given the values of \(x - y\) and \(xy\). We can use the algebraic identity for the difference of cubes, which relates \(x^3 - y^3\) to \((x - y)\) and \(xy\).
A) The calculated value of \(x^3 - y^3\) is 350, which matches option A.
This is a logical reasoning problem involving matching five friends with their preferred car brands and colors. We will use a table to systematically fill in the information given in the clues and deduce the complete preferences for each person.
Let's create a table to organize the information:
| Friend | Brand | Color |
|---|---|---|
| A | ||
| B | ||
| C | ||
| D | ||
| E |
| Friend | Brand | Color |
|---|---|---|
| A | ||
| B | ||
| C | R | Blue |
| D | ||
| E |
| Friend | Brand | Color |
|---|---|---|
| A | (not T) | Black |
| B | ||
| C | R | Blue |
| D | ||
| E |
| Friend | Brand | Color |
|---|---|---|
| A | (not T) | Black |
| B | ||
| C | R | Blue |
| D | S | (not Silver) |
| E |
| Friend | Brand | Color |
|---|---|---|
| A | (not T) | Black |
| B | White | |
| C | R | Blue |
| D | S | (not Silver) |
| E |
| Friend | Brand | Color |
|---|---|---|
| A | (not T) | Black |
| B | White | |
| C | R | Blue |
| D | S | (not Silver) |
| E | Q | Silver |
The final table is:
| Friend | Brand | Color |
|---|---|---|
| A | P | Black |
| B | T | White |
| C | R | Blue |
| D | S | Grey |
| E | Q | Silver |
Correct Option: A) E
E likes Brand Q (Silver).
The question asks to identify the incorrect statement among the given options regarding the largest producers of certain agricultural commodities in India. We need to evaluate each statement based on current agricultural production data.
C) Punjab is the largest producer of wheat in India. This statement is incorrect. Uttar Pradesh holds the distinction of being the largest producer of wheat in India.
The question asks to identify the historical monument or significant feature depicted on the Indian 200-rupee note. This requires knowledge of the designs on current Indian currency notes.
Correct Option: D) The reverse side of the Indian 200-rupee note (Mahatma Gandhi New Series) depicts the Sanchi Stupa. The Sanchi Stupa is a Buddhist complex, famous for its Great Stupa, in Madhya Pradesh, India. It is one of the oldest stone structures in India and was originally commissioned by the Mauryan emperor Ashoka the Great in the 3rd century BCE.
The question asks to identify the Nobel laureate known for research on malaria transmission. This requires knowledge of significant contributions to medical science and the specific Nobel Prizes awarded for them.
Ronald Ross was a British medical doctor who received the Nobel Prize in Physiology or Medicine in 1902 for his work on malaria. He demonstrated that the malaria parasite is transmitted by mosquitoes, specifically identifying the role of the Anopheles mosquito in transmitting the disease to humans. His discovery was a crucial step in understanding and combating malaria.
To find the square root of 66049, we can use the long division method or estimation combined with checking the last digit. Since the options are provided, we can also use the last digit of the number to narrow down the possibilities and then verify by squaring the options.
D) 257 — Squaring 257 gives \(257 \times 257 = 66049\). Therefore, 257 is the square root of 66049.
To find the possible value of \(x\), we need to understand the properties of the Least Common Multiple (LCM). The LCM of a set of numbers is the smallest positive integer that is divisible by each of the numbers. We will find the prime factorization of the given numbers (6 and 9) and the LCM (72), and then use this to determine the possible prime factors of \(x\).
The LCM of 6, 9, and \(x\) is \(2^3 \times 3^2\). This means that the highest power of 2 present in any of the numbers (6, 9, or \(x\)) must be \(2^3\), and the highest power of 3 must be \(3^2\).
Based on the above, \(x\) must be of the form \(2^3 \times 3^k\), where \(k\) can be 0, 1, or 2. So, \(x\) must be a multiple of 8, and its prime factors can only be 2 and 3.
A) 24 — As shown in the step-by-step analysis, if \(x=24\), the LCM of 6, 9, and 24 is 72. This is because \(24 = 2^3 \times 3^1\), which provides the \(2^3\) factor needed for the LCM to be 72, while the \(3^2\) factor comes from 9.
The question asks to identify the incorrect statement among the given options regarding international organizations like the United Nations (UN), United Nations Security Council (UNSC), and the International Court of Justice (ICJ). We need to verify the factual accuracy of each statement.
Correct Option: D) The term of a judge in the International Court of Justice (ICJ) is five years. This statement is incorrect because ICJ judges serve a term of nine years.
The problem asks for the product of the Least Common Multiple (LCM) and the Highest Common Factor (HCF) of two numbers, 15 and 25. A fundamental property of numbers states that for any two positive integers, the product of their LCM and HCF is equal to the product of the numbers themselves.
Identify the given numbers: The two numbers are 15 and 25.
Recall the property of LCM and HCF: For any two positive integers \(a\) and \(b\), the following relationship holds:
\[ \text{LCM}(a, b) \times \text{HCF}(a, b) = a \times b \]Apply the property to the given numbers: Here, \(a = 15\) and \(b = 25\). So, the product of their LCM and HCF will be the product of 15 and 25.
Calculate the product of the numbers:
\[ 15 \times 25 \]Perform the multiplication:
\[ 15 \times 25 = 375 \]Alternatively, one could first find the HCF and LCM separately and then multiply them.
Find the prime factorization of each number:
\[ 15 = 3 \times 5 \]\[ 25 = 5 \times 5 = 5^2 \]Calculate the HCF: The HCF is the product of the common prime factors raised to the lowest power.
\[ \text{HCF}(15, 25) = 5^1 = 5 \]Calculate the LCM: The LCM is the product of all prime factors (common and uncommon) raised to the highest power.
\[ \text{LCM}(15, 25) = 3^1 \times 5^2 = 3 \times 25 = 75 \]Multiply the HCF and LCM:
\[ \text{HCF}(15, 25) \times \text{LCM}(15, 25) = 5 \times 75 = 375 \]Both methods yield the same result.
Correct Option: D) 375