Find the digit in the unit's place of 124n + 124(n+1), where n is any natural number.
To find the unit's digit of an expression, we only need to consider the unit's digits of the numbers involved. We will analyze the pattern of the unit's digit of powers of 4 and then apply it to the given expression.
A) 0 — As derived from both cases (n is odd or n is even), the unit's digit of the sum is always 0.
The question asks to identify the city in Punjab where the Rail Coach Factory (RCF) is located. This is a factual question related to Indian geography and public sector undertakings.
Correct Option: D) Kapurthala is the correct answer because the Rail Coach Factory (RCF), a major manufacturing unit for Indian Railways coaches, is located in Kapurthala, Punjab.
To simplify the given expression, we need to follow the order of operations, often remembered by the acronym PEMDAS/BODMAS. This rule states that operations should be performed in the following order: Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
In this expression, we only have division and multiplication. According to BODMAS/PEMDAS, division and multiplication have equal precedence and should be performed from left to right.
Thus, the simplified value of the expression is 25.
Correct Option: B) 25
This problem involves compound interest. We are given the final amount, the interest rate, and the time period. We need to find the original principal sum. We can use the compound interest formula to solve this.
Identify the given values:
Recall the compound interest formula:
The formula for the amount (\(A\)) when interest is compounded annually is:
\[ A = P \left(1 + \frac{R}{100}\right)^n \]Substitute the given values into the formula:
\[ 1815 = P \left(1 + \frac{10}{100}\right)^2 \]Simplify the term inside the parenthesis:
\[ 1815 = P \left(1 + 0.10\right)^2 \] \[ 1815 = P \left(1.10\right)^2 \]Calculate \((1.10)^2\):
\[ (1.10)^2 = 1.10 \times 1.10 = 1.21 \]Substitute this back into the equation:
\[ 1815 = P \times 1.21 \]Solve for \(P\):
Divide both sides by 1.21:
\[ P = \frac{1815}{1.21} \]To simplify the division, we can multiply the numerator and denominator by 100:
\[ P = \frac{181500}{121} \]Now, perform the division:
\(181500 \div 121 = 1500\)
So, \(P = 1500\).
Correct Option: D) ₹1,500.00
What is the LCM of \( \frac{3}{8} \), \( \frac{9}{20} \) and \( \frac{15}{16} \)?
\( \frac{45}{4} \)
\( \frac{16}{9} \)
\( \frac{3}{4} \)
\( \frac{9}{16} \)
To find the Least Common Multiple (LCM) of fractions, we use a specific formula: the LCM of fractions is equal to the LCM of their numerators divided by the HCF (Highest Common Factor) of their denominators.
Identify the fractions: We are given the fractions \( \frac{3}{8} \), \( \frac{9}{20} \), and \( \frac{15}{16} \).
Identify the numerators and denominators: Numerators are \(3, 9, 15\). Denominators are \(8, 20, 16\).
Calculate the LCM of the numerators: We need to find the LCM of \(3, 9, 15\). Prime factorization: \(3 = 3^1\) \(9 = 3^2\) \(15 = 3^1 \times 5^1\) To find the LCM, we take the highest power of each prime factor present: \[ \text{LCM}(3, 9, 15) = 3^2 \times 5^1 = 9 \times 5 = 45 \] So, the LCM of the numerators is \(45\).
Calculate the HCF of the denominators: We need to find the HCF of \(8, 20, 16\). Prime factorization: \(8 = 2^3\) \(20 = 2^2 \times 5^1\) \(16 = 2^4\) To find the HCF, we take the lowest power of the common prime factors: \[ \text{HCF}(8, 20, 16) = 2^2 = 4 \] So, the HCF of the denominators is \(4\).
Apply the formula for LCM of fractions: \[ \text{LCM of fractions} = \frac{\text{LCM of numerators}}{\text{HCF of denominators}} \] \[ \text{LCM} \left( \frac{3}{8}, \frac{9}{20}, \frac{15}{16} \right) = \frac{45}{4} \]
Correct Option: A) \( \frac{45}{4} \)
The problem asks us to identify the odd word-pair out of four given options. This is a classification type of analogy question where we need to find a common relationship among three pairs and then identify the pair that does not follow that relationship.
Correct Option: C) Fly : Swim
This pair is different because 'Fly' and 'Swim' are both verbs describing types of movement, but they are not antonyms. Flying is movement through the air, and swimming is movement through water. They represent different methods of locomotion rather than opposite states or actions.
The question asks for the full form of the acronym BIOS. This is a common computer term, and knowing its full form is fundamental to understanding how computers boot up and interact with hardware.
Correct Option: B) Basic Input/Output System is the correct full form of BIOS. BIOS is firmware used to perform hardware initialization during the booting process (power-on startup) and to provide runtime services for operating systems and programs.
The problem presents a series of alphanumeric terms. We need to identify the pattern in the letters and numbers separately to find the next term in the series. We will analyze the first letter, the number, and the last letter of each term.
The next term in the series will have 'T' as the first letter, '4' as the number, and 'S' as the last letter. So, the term is T4S.
Correct Option: C) T4S — This option matches the derived pattern for the first letter, the number, and the last letter.
The question asks about the primary diet of the Red Panda. To answer this, one needs to recall facts about the Red Panda's natural habitat and dietary preferences.
Correct Option: B) bamboo — Red Pandas primarily feed on bamboo shoots and leaves, making up a significant portion of their diet.
The question asks to identify the correctly matched pair among the given options, where each pair consists of a research institute and its location. This requires knowledge of the locations of prominent Indian research institutes.
Correct Option: C) Central Arid Zone Research Institute - Jodhpur