The question asks us to evaluate an assertion and a reason statement regarding water. We need to determine if each statement is true or false independently, and then assess if the reason correctly explains the assertion.
Correct Option: D) Assertion is true but Reason is false.
Compute 7497 ÷ 147 - 8 = ?
-20
43
\( \frac{7497}{116} \)
\( \frac{7479}{116} \)
To solve this problem, we need to follow the order of operations, often remembered by the acronym PEMDAS/BODMAS (Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). In this case, we first perform the division and then the subtraction.
B) 43 — The calculation \(7497 \div 147 - 8\) correctly yields \(51 - 8 = 43\).
The question asks for the location of the Bhimbetka caves. This requires knowledge of Indian geography and historical sites.
B) Madhya Pradesh — The Bhimbetka Rock Shelters, a UNESCO World Heritage Site known for its prehistoric cave paintings, are situated in the Raisen District of Madhya Pradesh, India.
If ‘÷’ denotes ‘multiplication’, ‘−’ denotes ‘addition’, ‘+’ denotes ‘division’ and ‘×’ denotes ‘subtraction’, then which of the following is the value of the expression
19 ÷ 9 × 51 − 171 + 19
This problem involves substituting given symbol transformations into a mathematical expression and then evaluating the expression using the order of operations (BODMAS/PEMDAS).
The original expression is: \(19 \div 9 \times 51 - 171 + 19\)
Applying the transformations:
So, the new expression is: \(19 \times 9 - 51 + 171 \div 19\)
BODMAS stands for Brackets, Orders (powers/roots), Division, Multiplication, Addition, Subtraction. PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
First, perform Division:
\[ 171 \div 19 = 9 \]The expression becomes: \(19 \times 9 - 51 + 9\)
Next, perform Multiplication:
\[ 19 \times 9 = 171 \]The expression becomes: \(171 - 51 + 9\)
Next, perform Addition and Subtraction from left to right:
\[ 171 - 51 = 120 \]The expression becomes: \(120 + 9\)
Finally, perform the last Addition:
\[ 120 + 9 = 129 \]B) The calculated value of the expression after applying the symbol changes and following the order of operations is 129.
The question asks about the ownership/origin of the Hubble Space Telescope (HST) and its significant achievement of capturing the first-ever predicted supernova explosion. To answer this, one needs to recall general knowledge about major space observatories and the space agencies responsible for them.
Correct Option: A) USA
Which is the correct ascending order of the given numbers?
\( \frac{3}{7} \), 0.3,\( \frac{2}{7} \)
0.3, \( \frac{2}{7} \), \( \frac{3}{7} \)
\( \frac{2}{7} \), 0.3, \( \frac{3}{7} \)
\( \frac{2}{7} \), \( \frac{3}{7} \), 0.3
To arrange the given numbers in ascending order, we need to convert all numbers into a common format, either all decimals or all fractions with a common denominator. Converting them to decimals is often easier for comparison.
The given numbers are \( \frac{3}{7} \), 0.3, and \( \frac{2}{7} \).
First, convert the fractions to their decimal equivalents:
Now we have the numbers as:
Comparing the decimal values:
Arranging them in ascending order (from smallest to largest):
\( 0.2857 < 0.3000 < 0.4285 \)
Substitute the original numbers back into the ordered list:
\[\frac{2}{7} < 0.3 < \frac{3}{7}\]
C) \( \frac{2}{7} \), 0.3, \( \frac{3}{7} \) is the correct ascending order of the given numbers.
The question asks to identify the musical instrument played by the renowned musician Dr. L. Subramaniam. This is a factual question related to Indian classical music and famous personalities.
C) Violin — Dr. L. Subramaniam is a world-renowned Indian violinist, composer, and conductor, celebrated for his mastery of the Carnatic violin.
The question asks to identify the country with the lengthiest and most detailed constitution among the given democratic nations. This requires knowledge of the general characteristics of the constitutions of these countries.
Correct Option: D) India's Constitution is widely recognized as the lengthiest and most detailed written constitution in the world. It originally had 395 Articles, 22 Parts, and 8 Schedules. Currently, it consists of 448 Articles in 25 Parts and 12 Schedules, along with numerous amendments.
The problem involves calculating the total distance traveled when an equal distance is covered at three different speeds, and the total time taken is given. We will use the formula \(\text{Time} = \frac{\text{Distance}}{\text{Speed}}\) for each segment and sum the times to find the total distance.
Since speeds are in km/hr, we convert the total time from minutes to hours:
\[ T_{\text{total}} = 39.5 \text{ minutes} = \frac{39.5}{60} \text{ hours} = \frac{79}{120} \text{ hours} \]The sum of the times for each segment must equal the total time:
\[ t_1 + t_2 + t_3 = T_{\text{total}} \] \[ \frac{D}{3} + \frac{D}{5} + \frac{D}{8} = \frac{79}{120} \]Find a common denominator for 3, 5, and 8, which is 120.
\[ \frac{40D}{120} + \frac{24D}{120} + \frac{15D}{120} = \frac{79}{120} \] \[ \frac{(40 + 24 + 15)D}{120} = \frac{79}{120} \] \[ \frac{79D}{120} = \frac{79}{120} \]Multiply both sides by 120:
\[ 79D = 79 \] \[ D = \frac{79}{79} \] \[ D = 1 \text{ km} \]Since Monal Kumar traveled an equal distance \(D\) three times, the total distance is \(3D\).
\[ \text{Total Distance} = 3 \times D = 3 \times 1 \text{ km} = 3 \text{ km} \]Correct Option: D) 3
The problem requires us to interchange the mathematical signs '−' and '×', and the numbers '7' and '3' in each given option. After performing these interchanges, we need to evaluate each expression to find which one results in a correct mathematical equality.
We will apply the given interchanges to each option one by one:
Let's evaluate each option after applying the changes:
Option A: Original equation is \(20 \times 1 - 7 = 3\)
After interchanging signs and numbers:
\[ 20 - 1 \times 3 = 7 \]Now, evaluate the left side:
\[ 20 - (1 \times 3) = 20 - 3 = 17 \]Since \(17 \neq 7\), Option A is incorrect.
Option B: Original equation is \(1 \times 20 - 7 = 20\)
After interchanging signs and numbers:
\[ 1 - 20 \times 3 = 20 \]Now, evaluate the left side:
\[ 1 - (20 \times 3) = 1 - 60 = -59 \]Since \(-59 \neq 20\), Option B is incorrect.
Option C: Original equation is \(3 - 7 \times 1 = 20\)
After interchanging signs and numbers:
\[ 7 \times 3 - 1 = 20 \]Now, evaluate the left side:
\[ (7 \times 3) - 1 = 21 - 1 = 20 \]Since \(20 = 20\), Option C is correct.
Option D: Original equation is \(20 - 3 \times 1 = 7\)
After interchanging signs and numbers:
\[ 20 \times 7 - 1 = 3 \]Now, evaluate the left side:
\[ (20 \times 7) - 1 = 140 - 1 = 139 \]Since \(139 \neq 3\), Option D is incorrect.
Correct Option: C) \(3 - 7 \times 1 = 20\)
After interchanging '−' with '×', '×' with '−', '7' with '3', and '3' with '7', the equation becomes \(7 \times 3 - 1 = 20\). Evaluating the left side: \(21 - 1 = 20\), which is equal to the right side. Thus, this option is correct.