The question asks to identify the city known as the "city of pearls." This is a general knowledge question related to the geographical and historical epithets of Indian cities. We need to recall which city is historically associated with the pearl trade and processing.
Correct Option: C) Hyderabad is famously known as the "City of Pearls." This epithet originated from its historical role as a prominent trading center for pearls, especially during the rule of the Nizams. Even today, Hyderabad is a significant hub for pearl processing and trade.
Select the number that can replace the question mark (?) in the following equation.
? + \( \frac{18}{24} \) + 3 \( \frac{3}{4} \) = 23 \( \frac{13}{24} \)
19 \( \frac{13}{24} \)
19 \( \frac{11}{24} \)
1
19 \( \frac{1}{24} \)
To solve this problem, we need to find the value of the question mark (?) in the given equation. This involves isolating the unknown variable by performing arithmetic operations with fractions and mixed numbers. We will convert all mixed numbers to improper fractions or work with the whole and fractional parts separately, and then combine terms to find the solution.
Let the question mark be represented by \(x\). The given equation is:
\[ x + \frac{18}{24} + 3 \frac{3}{4} = 23 \frac{13}{24} \]Simplify the fraction \( \frac{18}{24} \) by dividing the numerator and denominator by their greatest common divisor, which is 6:
\[ \frac{18}{24} = \frac{18 \div 6}{24 \div 6} = \frac{3}{4} \]Convert the mixed numbers to improper fractions or separate the whole and fractional parts. It's often easier to work with whole numbers and fractions separately when possible. Let's rewrite the equation:
\[ x + \frac{3}{4} + 3 + \frac{3}{4} = 23 + \frac{13}{24} \]Combine the known whole numbers and fractions on the left side:
\[ x + (3) + \left( \frac{3}{4} + \frac{3}{4} \right) = 23 + \frac{13}{24} \]\[ x + 3 + \frac{6}{4} = 23 + \frac{13}{24} \]Simplify \( \frac{6}{4} \) to \( \frac{3}{2} \) or \( 1 \frac{1}{2} \):
\[ x + 3 + 1 \frac{1}{2} = 23 + \frac{13}{24} \]\[ x + 4 \frac{1}{2} = 23 + \frac{13}{24} \]Now, isolate \(x\) by subtracting \(4 \frac{1}{2}\) from both sides:
\[ x = 23 \frac{13}{24} - 4 \frac{1}{2} \]To subtract, find a common denominator for the fractions. The common denominator for 24 and 2 is 24. Convert \( \frac{1}{2} \) to an equivalent fraction with a denominator of 24:
\[ \frac{1}{2} = \frac{1 \times 12}{2 \times 12} = \frac{12}{24} \]Now perform the subtraction:
\[ x = 23 \frac{13}{24} - 4 \frac{12}{24} \]\[ x = (23 - 4) + \left( \frac{13}{24} - \frac{12}{24} \right) \]\[ x = 19 + \frac{1}{24} \]\[ x = 19 \frac{1}{24} \]D) \( 19 \frac{1}{24} \) is the correct answer, as derived from the step-by-step calculation.
To find the least number divisible by the first ten natural numbers, we need to find the Least Common Multiple (LCM) of these numbers. The first ten natural numbers are 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10.
C) 2520 is the least common multiple of the first ten natural numbers, meaning it is the smallest number divisible by all of them.
To determine if a number is divisible by 11, we use the divisibility rule for 11. This rule states that a number is divisible by 11 if the alternating sum of its digits is divisible by 11. The alternating sum is calculated by subtracting the sum of the digits at even places (from the right) from the sum of the digits at odd places (from the right).
Correct Option: D) 203456 is divisible by 11 because the alternating sum of its digits is 0.
The question asks about the mechanism that governs how different programs exchange data over the internet. This points to a protocol, which is a set of rules for communication. We need to identify which of the given options serves this purpose for internet data exchange.
http://, https://, ftp://), but it is not the protocol itself that governs data exchange.D) Hypertext transfer protocol — HTTP is the primary protocol used for transmitting data over the World Wide Web. It dictates the rules for how web clients (like browsers) and web servers communicate and exchange information, including text, images, videos, and other data, making it the correct answer for how different programs exchange data over the internet, especially in the context of web-based applications.
Find the HCF of (345 − 1) and (335 − 1).
To find the HCF (Highest Common Factor) of expressions of the form \((a^m - 1)\) and \((a^n - 1)\), we use the property that the HCF of \((a^m - 1)\) and \((a^n - 1)\) is \((a^{\text{HCF}(m, n)} - 1)\).
The given expressions are \((3^{45} - 1)\) and \((3^{35} - 1)\).
Here, the base \(a = 3\), and the exponents are \(m = 45\) and \(n = 35\).
We need to find \(\text{HCF}(45, 35)\).
The highest common factor of \(45\) and \(35\) is \(5\).
So, \(\text{HCF}(45, 35) = 5\).
Using the property \(\text{HCF}(a^m - 1, a^n - 1) = a^{\text{HCF}(m, n)} - 1\), we substitute the values:
\[ \text{HCF}(3^{45} - 1, 3^{35} - 1) = 3^{\text{HCF}(45, 35)} - 1 \]Substitute \(\text{HCF}(45, 35) = 5\):
\[ \text{HCF}(3^{45} - 1, 3^{35} - 1) = 3^5 - 1 \]Now, calculate \(3^5 - 1\):
\[ 3^5 = 3 \times 3 \times 3 \times 3 \times 3 = 243 \]So,
\[ 3^5 - 1 = 243 - 1 = 242 \]D) 242 is the HCF of \((3^{45} - 1)\) and \((3^{35} - 1)\).
The question asks to identify the Chief Justice of India (CJI) who served immediately before Justice S.A. Bobde. This requires knowledge of the chronological order of CJIs.
Correct Option: C) Ranjan Gogoi was the 46th Chief Justice of India and served immediately before Justice S.A. Bobde (the 47th CJI).
If the average of a1, a2, a3 and a4 is 19.5, a1 = 21 and the average of a1, a2 and a3 is equal to the average of a2, a3 and a4, then what will be the value of a4?
The problem provides information about the average of four numbers \(a_1, a_2, a_3, a_4\), the value of \(a_1\), and a relationship between the averages of two sets of three numbers. We need to use these pieces of information to find the value of \(a_4\).
Use the first average condition: The average of \(a_1, a_2, a_3, a_4\) is 19.5. The formula for average is the sum of numbers divided by the count of numbers.
\[ \frac{a_1 + a_2 + a_3 + a_4}{4} = 19.5 \]Multiply both sides by 4 to find the sum:
\[ a_1 + a_2 + a_3 + a_4 = 19.5 \times 4 = 78 \]We are given \(a_1 = 21\). Substitute this value into the equation:
\[ 21 + a_2 + a_3 + a_4 = 78 \] \[ a_2 + a_3 + a_4 = 78 - 21 = 57 \quad \text{(Equation 1)} \]Use the second average condition: The average of \(a_1, a_2, a_3\) is equal to the average of \(a_2, a_3, a_4\).
\[ \frac{a_1 + a_2 + a_3}{3} = \frac{a_2 + a_3 + a_4}{3} \]Since the denominators are the same, the numerators must be equal:
\[ a_1 + a_2 + a_3 = a_2 + a_3 + a_4 \]Simplify the equation from step 2: Subtract \(a_2\) and \(a_3\) from both sides of the equation:
\[ a_1 = a_4 \]Find the value of \(a_4\): Since we are given \(a_1 = 21\), and we found that \(a_1 = a_4\), it directly follows that:
\[ a_4 = 21 \]D) 21 — From the given conditions, we deduced that \(a_1 = a_4\). Since \(a_1\) is given as 21, \(a_4\) must also be 21.
The question asks to identify the Harappan site that is NOT associated with craft production. To answer this, we need to recall the primary activities and known crafts associated with each of the given Harappan sites.
Correct Option: D) Manda is the Harappan site that is NOT primarily associated with craft production. It was more of a northern outpost or trading station.
If we increase 50% of numerator and 80% of denominator of a fraction, then what fraction of the original will be the new fraction?
\( \frac{6}{5} \)
\( \frac{5}{6} \)
\( \frac{5}{8} \)
\( \frac{7}{9} \)
To solve this problem, we will first represent the original fraction algebraically. Then, we will calculate the new numerator and new denominator based on the given percentage increases. Finally, we will form the new fraction and express it as a fraction of the original fraction.
Let the original fraction be \( \frac{x}{y} \), where \(x\) is the numerator and \(y\) is the denominator.
The numerator is increased by 50%. This means the new numerator will be the original numerator plus 50% of the original numerator.
\[ \text{New Numerator} = x + 0.50x = 1.50x = \frac{3}{2}x \]The denominator is increased by 80%. This means the new denominator will be the original denominator plus 80% of the original denominator.
\[ \text{New Denominator} = y + 0.80y = 1.80y = \frac{9}{5}y \]Now, form the new fraction using the new numerator and new denominator.
\[ \text{New Fraction} = \frac{\text{New Numerator}}{\text{New Denominator}} = \frac{\frac{3}{2}x}{\frac{9}{5}y} \]Simplify the new fraction:
\[ \text{New Fraction} = \frac{3}{2}x \times \frac{5}{9y} = \frac{3 \times 5}{2 \times 9} \times \frac{x}{y} \]\[ \text{New Fraction} = \frac{15}{18} \times \frac{x}{y} \]\[ \text{New Fraction} = \frac{5}{6} \times \frac{x}{y} \]The new fraction is \( \frac{5}{6} \) times the original fraction \( \frac{x}{y} \).
Correct Option: B) \( \frac{5}{6} \)