This problem involves substituting given symbols with mathematical operators and then evaluating the expressions using the BODMAS/PEMDAS rule (Brackets, Orders/Exponents, Division, Multiplication, Addition, Subtraction) to find which expression results in 75.
Given the symbol-operator mapping:
We need to evaluate each option by replacing the letters with their corresponding operators and then performing the calculations according to the BODMAS rule.
Option A: \(84 \text{ B } 12 \text{ C } 76 \text{ D } 36 \text{ A } 4\)
Substitute the operators:
\[ 84 \times 12 + 76 - 36 \div 4 \]Perform division first:
\[ 84 \times 12 + 76 - 9 \]Perform multiplication:
\[ 1008 + 76 - 9 \]Perform addition:
\[ 1084 - 9 \]Perform subtraction:
\[ 1075 \]Option B: \(84 \text{ D } 12 \text{ A } 76 \text{ B } 36 \text{ C } 4\)
Substitute the operators:
\[ 84 - 12 \div 76 \times 36 + 4 \]Perform division:
\[ 84 - \frac{12}{76} \times 36 + 4 \] \[ 84 - \frac{3}{19} \times 36 + 4 \] \[ 84 - \frac{108}{19} + 4 \]This will not result in an integer, and certainly not 75.
Option C: \(84 \text{ A } 12 \text{ D } 76 \text{ C } 36 \text{ B } 4\)
Substitute the operators:
\[ 84 \div 12 - 76 + 36 \times 4 \]Perform division:
\[ 7 - 76 + 36 \times 4 \]Perform multiplication:
\[ 7 - 76 + 144 \]Perform addition/subtraction from left to right:
\[ -69 + 144 \] \[ 75 \]Option D: \(84 \text{ C } 12 \text{ D } 76 \text{ A } 36 \text{ B } 4\)
Substitute the operators:
\[ 84 + 12 - 76 \div 36 \times 4 \]Perform division:
\[ 84 + 12 - \frac{76}{36} \times 4 \] \[ 84 + 12 - \frac{19}{9} \times 4 \] \[ 84 + 12 - \frac{76}{9} \]This will not result in an integer, and certainly not 75.
Correct Option: C) \(84 \text{ A } 12 \text{ D } 76 \text{ C } 36 \text{ B } 4\)
As calculated above, this expression evaluates to 75.
The question asks to identify the tribal revolt whose origins were specifically tied to the British depriving tribals of their traditional rights over toddy trees. This requires knowledge of the specific causes and contexts of various tribal uprisings during the British colonial period in India.
Correct Option: D) The Koya revolt, particularly the Rampa Rebellion of 1879-80, was significantly fueled by the British government's imposition of taxes on toddy trees and the monopolization of forest produce, which directly infringed upon the traditional rights of the Koya tribals over these trees.
Given that 120.36 = x, 120.64 = y and xz = y4, then the value of z is close to:
The problem involves solving for an unknown variable \(z\) using given exponential and algebraic relationships. We need to first evaluate \(x\) and \(y\) using the given exponential expressions, then substitute these values into the equation relating \(x\), \(y\), and \(z\) to find \(z\).
Given \(x = 12^{0.36}\). We can use logarithms to simplify this, or directly calculate if a calculator is allowed. For competitive exams, approximations or properties of exponents might be needed. Let's keep it in exponential form for now.
Given \(y = 12^{0.64}\).
The third equation is \(x^z = y^4\).
Substitute the expressions for \(x\) and \(y\):
\[ (12^{0.36})^z = (12^{0.64})^4 \]To simplify the division, we can multiply the numerator and denominator by 100:
\[ z = \frac{256}{36} \]Both 256 and 36 are divisible by 4:
\[ z = \frac{256 \div 4}{36 \div 4} = \frac{64}{9} \]So, \(z\) is approximately 7.11.
Correct Option: A) 7.11
This problem involves substituting new meanings for mathematical operators and then evaluating the expression according to the order of operations (BODMAS/PEMDAS).
+ means -- means ×× means ÷÷ means +The original equation is: \(15 - 3 \div 5 + 18 \times 6 = ?\)
Applying the substitutions:
- becomes ×÷ becomes ++ becomes -× becomes ÷So, the new equation is: \(15 \times 3 + 5 - 18 \div 6 = ?\)
BODMAS/PEMDAS stands for Brackets/Parentheses, Orders/Exponents, Division, Multiplication, Addition, Subtraction. Operations are performed from left to right for division/multiplication and for addition/subtraction.
First, \(15 \times 3\):
\[ 15 \times 3 = 45 \]The equation becomes: \(45 + 5 - 18 \div 6 = ?\)
Next, \(18 \div 6\):
\[ 18 \div 6 = 3 \]The equation becomes: \(45 + 5 - 3 = ?\)
First, \(45 + 5\):
\[ 45 + 5 = 50 \]The equation becomes: \(50 - 3 = ?\)
Finally, \(50 - 3\):
\[ 50 - 3 = 47 \]Correct Option: D) 47
The question asks to identify the type of wave that a sound wave in air is. To answer this, we need to understand the fundamental characteristics of different wave types, specifically how the particles of the medium oscillate relative to the direction of wave propagation.
A) Longitudinal — Sound waves in air are longitudinal waves because the particles of the medium (air molecules) oscillate back and forth parallel to the direction in which the wave energy is traveling. This creates alternating regions of compression and rarefaction.
The question asks to identify the successor of Dhruvasena. This requires knowledge of the chronology of the Maitraka dynasty rulers, specifically their succession order.
Correct Option: A) Dharapatta succeeded Dhruvasena I. Dhruvasena I was the son of Bhatarka, the founder of the Maitraka dynasty. After Dhruvasena I, his younger brother Dharapatta ascended the throne.
Jon ranked 24th from the top and 16th from the bottom in his class. How many students are there in his class?
This problem involves determining the total number of students in a class given a person's rank from both the top and the bottom. The key is to understand that when a person's rank is counted from both ends, that person is counted twice. Therefore, to find the total number of students, we add the rank from the top and the rank from the bottom, and then subtract 1 (to account for the person being counted twice).
A) 39 is the correct answer. By adding Jon's rank from the top (24) and his rank from the bottom (16), we get 40. Since Jon is included in both counts, we subtract 1 to avoid double-counting him, resulting in 39 total students.
The problem asks us to identify the letter-cluster pair that does not follow the same pattern as the other three. We need to analyze the positional values of the letters in the English alphabet for each pair and find a consistent rule.
Let's analyze each option:
D) GJ - FK is the odd one out because the difference between the corresponding letters in the pairs is not consistently 2. For GJ - FK, the differences are -1 and +1, whereas for the other options, both differences are 2.
The sides of a rectangular field are 11 m and 14 m long. Its area is equal to the area of a circular field. What is the circumference (in m) of the circular field?
Take π = \( \frac{22}{7} \)
The problem requires us to find the circumference of a circular field given that its area is equal to the area of a rectangular field. First, we calculate the area of the rectangular field. Then, we use this area to find the radius of the circular field. Finally, we calculate the circumference of the circular field using its radius.
Calculate the area of the rectangular field:
The sides of the rectangular field are given as 11 m and 14 m.
\[ \text{Area of rectangle} = \text{length} \times \text{width} \] \[ \text{Area of rectangle} = 14 \text{ m} \times 11 \text{ m} \] \[ \text{Area of rectangle} = 154 \text{ m}^2 \]Determine the area of the circular field:
The problem states that the area of the circular field is equal to the area of the rectangular field.
\[ \text{Area of circular field} = 154 \text{ m}^2 \]Find the radius of the circular field:
The formula for the area of a circle is \( \pi r^2 \), where \( r \) is the radius. We are given \( \pi = \frac{22}{7} \).
\[ \pi r^2 = 154 \] \[ \frac{22}{7} \times r^2 = 154 \] \[ r^2 = 154 \times \frac{7}{22} \] \[ r^2 = 7 \times 7 \] \[ r^2 = 49 \] \[ r = \sqrt{49} \] \[ r = 7 \text{ m} \]Calculate the circumference of the circular field:
The formula for the circumference of a circle is \( 2 \pi r \).
\[ \text{Circumference} = 2 \times \frac{22}{7} \times 7 \] \[ \text{Circumference} = 2 \times 22 \] \[ \text{Circumference} = 44 \text{ m} \]B) 44 m is the calculated circumference of the circular field.
The question asks about the origin of the concept of Lok Adalat in India. To answer this, one needs to understand the historical context and foundational principles of Lok Adalats and compare them with various legal systems or dispute resolution mechanisms.
A) The concept of Lok Adalat draws inspiration from the ancient Indian dispute resolution mechanisms. These traditional systems, such as the Panchayat system, focused on resolving disputes through dialogue, mediation, and compromise within the community, which is the core principle behind Lok Adalats.