This problem involves substituting given mathematical operator meanings into an expression and then evaluating the expression following the order of operations (BODMAS/PEMDAS).
The original expression is \( 25 + 18 - 3 \times 7 \div 3 \).
Applying the new meanings:
So, the new expression is \( 25 - 18 \div 3 + 7 \times 3 \).
BODMAS stands for Brackets, Orders (powers/roots), Division, Multiplication, Addition, Subtraction. PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. Division and Multiplication have the same precedence and are evaluated from left to right. Similarly, Addition and Subtraction have the same precedence and are evaluated from left to right.
The expression is \( 25 - 18 \div 3 + 7 \times 3 \).
\( 18 \div 3 = 6 \)
The expression becomes \( 25 - 6 + 7 \times 3 \).
\( 7 \times 3 = 21 \)
The expression becomes \( 25 - 6 + 21 \).
\( 25 - 6 = 19 \)
The expression becomes \( 19 + 21 \).
\( 19 + 21 = 40 \)
D) 40 is the correct answer after applying the operator changes and following the order of operations.
A man covers 1 km in 10 minutes. What is his speed in m/s?
To find the speed in meters per second (m/s), we need to convert the given distance from kilometers to meters and the given time from minutes to seconds. Then, we can apply the formula for speed: Speed = Distance / Time.
Convert distance from kilometers to meters:
Given distance = 1 km
We know that 1 km = 1000 meters.
So, Distance \( = 1 \text{ km} = 1 \times 1000 \text{ m} = 1000 \text{ m}\)
Convert time from minutes to seconds:
Given time = 10 minutes
We know that 1 minute = 60 seconds.
So, Time \( = 10 \text{ minutes} = 10 \times 60 \text{ seconds} = 600 \text{ seconds}\)
Calculate speed using the formula:
Speed \( = \frac{\text{Distance}}{\text{Time}}\)
Substitute the converted values:
\[ \text{Speed} = \frac{1000 \text{ m}}{600 \text{ s}} \]
\[ \text{Speed} = \frac{10}{6} \text{ m/s} \]
\[ \text{Speed} = \frac{5}{3} \text{ m/s} \]
\[ \text{Speed} \approx 1.666... \text{ m/s} \]
Rounding to two decimal places, Speed \( \approx 1.67 \text{ m/s}\).
Correct Option: C) 1.67
The calculated speed is approximately 1.67 m/s, which matches option C.
The ___ Five Year Plan of the Government of India (2012–17) is under drafting. (as of 2016)
The question asks to identify the Five Year Plan that was under drafting in 2016 and covered the period 2012-2017. This requires knowledge of the timeline and numbering of India's Five Year Plans.
A) 12th — The 12th Five Year Plan covered the period from 2012 to 2017. Therefore, in 2016, this plan would have been in its operational phase, and aspects of its implementation or subsequent plans might have been under drafting or review.
A man deposits Rs. 500 at the beginning of each year for 2 years at 10% p.a. compounded annually. Find the maturity value at the end of the 2nd year.
This problem involves calculating the maturity value of a series of deposits (an annuity) where interest is compounded annually. We need to calculate the future value of each deposit separately and then sum them up.
Correct Option: C) Rs. 1,155
The question asks to identify the ailment that is NOT related to the heart. We need to evaluate each option to determine its connection to cardiac health.
Based on these definitions, Diphtheria is the only option that is primarily an infectious disease of the throat and nose, with heart complications being secondary, rather than a primary heart ailment.
Correct Option: C) Diphtheria is a bacterial infection primarily affecting the throat and nose, though it can have serious complications, including effects on the heart, due to toxins. It is not fundamentally a heart disease itself.
If 'god is great' = 'cp an bo', 'great help done' = 'er cp fs' and 'he is great' = 'bo cp dq', then what represents 'he is god'?
This is a coding-decoding problem where words are assigned specific codes. We need to find the codes for individual words by comparing the given statements and then use these codes to form the code for the target phrase 'he is god'.
Compare Statement 1 and Statement 2. The common word is 'great'. The common code is 'cp'.
\[ \text{great} = \text{cp} \]Compare Statement 1 and Statement 3. The common word is 'is great'. We already know 'great' is 'cp'. The remaining common word is 'is'. The remaining common code is 'bo'.
\[ \text{is} = \text{bo} \]From Statement 1: 'god is great' = 'cp an bo'. We know 'great' = 'cp' and 'is' = 'bo'. Therefore, 'god' must be 'an'.
\[ \text{god} = \text{an} \]From Statement 3: 'he is great' = 'bo cp dq'. We know 'is' = 'bo' and 'great' = 'cp'. Therefore, 'he' must be 'dq'.
\[ \text{he} = \text{dq} \]Using the codes we found:
So, 'he is god' = 'dq bo an' (the order of codes might vary, but the set of codes must be present).
Correct Option: D) an bo dq
The codes for 'he', 'is', and 'god' are 'dq', 'bo', and 'an' respectively. Option D contains these three codes.
The question asks to identify the region or country for which 'Euro' is the currency. This requires knowledge of international currencies and economic blocs.
Correct Option: C) Euro Zone
The Euro is the official currency of 20 of the 27 member states of the European Union. These countries collectively form the Eurozone (also known as the euro area).
This problem involves understanding the properties of the arithmetic mean. When each number in a set is increased by a constant value, the mean of the new set of numbers also increases by the same constant value.
So, for the initial set:
\[ 35 = \frac{x_1 + x_2 + \ldots + x_{10}}{10} \]From this, we can find the sum of the original numbers:
\[ x_1 + x_2 + \ldots + x_{10} = 35 \times 10 = 350 \]This can be rewritten as:
\[ (x_1 + x_2 + \ldots + x_{10}) + (2 + 2 + \ldots + 2 \text{ (10 times)}) \]Substituting the sum of the original numbers:
\[ 350 + (10 \times 2) = 350 + 20 = 370 \]D) 37 is the correct answer. As shown by both the detailed calculation and the property of the mean, increasing each number by 2 increases the mean by 2.
The question asks about the primary composition of gunpowder. This requires knowledge of the historical and chemical composition of gunpowder.
Correct Option: B) Potassium nitrate is the main ingredient in gunpowder, acting as the oxidizer.
Replace # sign with the mathematical operators '+', '÷', '−' and '=' to get a balanced equation out of (27 # 15 # 2) # 10 # 4. Choose the right sequence from below.
The problem requires us to replace the '#' signs in the given expression with mathematical operators from the options to form a balanced equation. We need to test each option by substituting the operators into the expression and checking if the left-hand side (LHS) equals the right-hand side (RHS).
The given expression is \((27 \# 15 \# 2) \# 10 \# 4\).
We will substitute the operators from each option into the expression and evaluate it.
Let's check Option C: \((+, \-, \div, =)\)
Substitute the operators into the expression:
\[ (27 + 15 - 2) \div 10 = 4 \]Since the LHS equals the RHS, Option C provides the correct sequence of operators.
C) + − ÷ =
When we substitute these operators into the expression \((27 \# 15 \# 2) \# 10 \# 4\), we get:
\[ (27 + 15 - 2) \div 10 = 4 \]\[ (42 - 2) \div 10 = 4 \]\[ 40 \div 10 = 4 \]\[ 4 = 4 \]