The problem requires us to evaluate a mathematical expression after interchanging certain operators. We need to replace '+' with '−', '−' with '+', '×' with '÷', and '÷' with '×'. After performing these substitutions, we will evaluate the new expression following the order of operations (BODMAS/PEMDAS).
Identify the original expression:
\[ 35 - 112 \times 84 \div 48 + 75 = ? \]
Apply the interchange rules:
Substitute the operators in the expression:
The original expression \(35 - 112 \times 84 \div 48 + 75\) becomes:
\[ 35 + 112 \div 84 \times 48 - 75 = ? \]
Evaluate the new expression using the order of operations (BODMAS/PEMDAS):
First, perform division and multiplication from left to right.
Division: \(112 \div 84\)
\[ 112 \div 84 = \frac{112}{84} = \frac{4 \times 28}{3 \times 28} = \frac{4}{3} \]
The expression becomes:
\[ 35 + \frac{4}{3} \times 48 - 75 \]
Multiplication: \(\frac{4}{3} \times 48\)
\[ \frac{4}{3} \times 48 = 4 \times \frac{48}{3} = 4 \times 16 = 64 \]
The expression becomes:
\[ 35 + 64 - 75 \]
Addition and Subtraction: Perform from left to right.
\[ 35 + 64 = 99 \]
The expression becomes:
\[ 99 - 75 \]
\[ 99 - 75 = 24 \]
Thus, the value of the expression after interchanging the operators is 24.
A) 24 is the correct answer, as calculated by applying the operator interchange rules and then following the order of operations.
This is a logical reasoning problem involving arrangement. We need to determine the floor on which each person lives based on the given clues and then find out how many people live below G.
A) Two — As determined in the step-by-step analysis, M and K live below G. Therefore, two people live below G.
We are given the compound interest (CI) for 2 years at a certain rate and need to find the simple interest (SI) for the same principal, rate, and time. We can use the formula for compound interest to find the principal amount first, and then calculate the simple interest.
The corresponding simple interest is \(\text{₹}100\).
C) 100
The question asks about the trend in the unemployment rate for urban areas (persons aged 15 and above) from FY23 to FY24, based on a Department of Economic Affairs report. To answer this, one needs to recall or refer to the latest economic survey or relevant government reports that provide these specific statistics.
Correct Option: A) Decreased from 5.4% to 5.1%
This option accurately reflects the reported trend of a decrease in the unemployment rate for persons aged 15 years and above in urban areas from FY23 to FY24, as per official economic reports.
The question asks about the primary purpose of the 'Save as Picture Presentation' option in MS PowerPoint. This feature is specifically designed to convert a presentation into a non-editable format, making it suitable for distribution where content modification is not desired.
Correct Option: B) To prevent any further editing of the presentation content
The given expression resembles the expansion of a cubic identity. We will first try to recognize the algebraic identity that matches the given expression. Once identified, we can substitute the given values of \(x\) and \(y\) into the simplified form of the expression to find the result.
The given expression is \( 64x^{3} + 27y^{3} + 144x^{2}y + 108xy^{2} \).
We can rewrite the terms as cubes:
\[ 64x^{3} = (4x)^{3} \] \[ 27y^{3} = (3y)^{3} \]Now, let's compare this with the identity \( (a+b)^{3} = a^{3} + b^{3} + 3a^{2}b + 3ab^{2} \).
If we let \( a = 4x \) and \( b = 3y \), then:
\[ a^{3} = (4x)^{3} = 64x^{3} \] \[ b^{3} = (3y)^{3} = 27y^{3} \] \[ 3a^{2}b = 3(4x)^{2}(3y) = 3(16x^{2})(3y) = 144x^{2}y \] \[ 3ab^{2} = 3(4x)(3y)^{2} = 3(4x)(9y^{2}) = 108xy^{2} \]Thus, the given expression is exactly the expansion of \( (4x + 3y)^{3} \).
We are given \( x = 5 \) and \( y = -5 \).
Substitute these values into the simplified expression \( (4x + 3y)^{3} \):
\[ (4(5) + 3(-5))^{3} \] \[ (20 - 15)^{3} \] \[ (5)^{3} \] \[ 5 \times 5 \times 5 = 125 \]Correct Option: B) 125
To solve this problem, we need to process each digit of the given number according to the specified rules: add 2 to odd digits and subtract 1 from even digits. After forming the new number, we will count how many distinct digits appear more than once.
A) Three — The digits 7, 3, and 5 each appear more than once in the new number 97135375. Thus, there are three such digits.
The problem presents a numerical series, and we need to find the next term. We will analyze the differences between consecutive terms to identify the pattern.
D) 1472 is the correct answer because it follows the established pattern of increasing differences.
The question asks to identify the founder of the Gurjara-Pratihara dynasty. This requires knowledge of the early rulers and origins of prominent medieval Indian dynasties.
Correct Option: C) Nagabhata I was the founder of the Gurjara-Pratihara dynasty. He ruled in the 8th century CE and is credited with establishing the Pratihara power in Malwa and parts of Rajasthan.
The question asks about the primary objective of the hyperloop test track launched by IIT Madras and Indian Railways. We need to identify the core goal of this project among the given options.
A) To revolutionise high-speed transportation and reduce travel time — This option accurately reflects the core purpose and most significant benefit of hyperloop technology. The entire concept is built around achieving unprecedented speeds for ground travel, which would fundamentally change how people move between cities.