The question asks to identify the part of the alimentary canal where the complete digestion of carbohydrates, proteins, and fats occurs. This requires knowledge of the digestive processes in different organs of the human digestive system.
A) Small intestine — The small intestine is the main site where all three major macronutrients (carbohydrates, proteins, and fats) are completely broken down into their simplest absorbable forms with the help of various digestive enzymes from the pancreas and the intestinal wall itself.
The value of 39 ÷ {6 × (\( \frac{6}{7} \) of \( \frac{7}{8} \))} is:
\( \frac{25}{3} \)
\( \frac{28}{3} \)
\( \frac{26}{3} \)
\( \frac{23}{3} \)
To solve this problem, we need to follow the order of operations (BODMAS/PEMDAS). This means we first calculate the expression inside the curly braces, then perform the multiplication, and finally the division.
First, evaluate the expression inside the curly braces: \[6 \times (\frac{6}{7} \text{ of } \frac{7}{8})\].
The term "of" indicates multiplication. So, calculate \[\frac{6}{7} \text{ of } \frac{7}{8}\]:
\[ \frac{6}{7} \times \frac{7}{8} \]Multiply the numerators and the denominators:
\[ \frac{6 \times 7}{7 \times 8} = \frac{42}{56} \]Simplify the fraction by dividing both numerator and denominator by their greatest common divisor, which is 14:
\[ \frac{42 \div 14}{56 \div 14} = \frac{3}{4} \]Now, substitute this back into the expression inside the curly braces:
\[ 6 \times \frac{3}{4} \]Perform the multiplication:
\[ \frac{6 \times 3}{4} = \frac{18}{4} \]Simplify this fraction:
\[ \frac{18 \div 2}{4 \div 2} = \frac{9}{2} \]Finally, substitute this result back into the original expression:
\[ 39 \div \frac{9}{2} \]Dividing by a fraction is equivalent to multiplying by its reciprocal:
\[ 39 \times \frac{2}{9} \]Perform the multiplication:
\[ \frac{39 \times 2}{9} = \frac{78}{9} \]Simplify the fraction by dividing both numerator and denominator by their greatest common divisor, which is 3:
\[ \frac{78 \div 3}{9 \div 3} = \frac{26}{3} \]C) The calculated value is \( \frac{26}{3} \).
Which of the following statements is true about the nature of roots for the equation
2x2 − 9x + 15 = 0?
Both roots are imaginary or non-real
One root is positive real and one is negative real
Both roots are negative real
Both roots are positive real
To determine the nature of the roots of a quadratic equation of the form \(ax^2 + bx + c = 0\), we use the discriminant, \(\Delta = b^2 - 4ac\). The nature of the roots depends on the value of the discriminant:
The given quadratic equation is \(2x^2 - 9x + 15 = 0\).
Comparing this with the standard form \(ax^2 + bx + c = 0\), we have:
The discriminant \(\Delta\) is given by the formula \(\Delta = b^2 - 4ac\).
Substitute the values of \(a\), \(b\), and \(c\) into the formula:
\[ \Delta = (-9)^2 - 4(2)(15) \]\[ \Delta = 81 - 8(15) \]\[ \Delta = 81 - 120 \]\[ \Delta = -39 \]Since \(\Delta = -39\), which is less than 0 (\(\Delta < 0\)), the roots of the equation are imaginary (non-real) and distinct.
Correct Option: A) Both roots are imaginary or non-real
This is a logical reasoning problem involving the relative heights of six friends. We need to deduce the height order based on the given clues and identify the tallest person.
Correct Option: C) C
If the first and third digits of each number are interchanged and then the numbers are arranged in descending order, the position of how many numbers will NOT change?
7451, 3254, 7353, 3464, 1958
To solve this problem, we need to perform two main operations: first, interchange the first and third digits of each given number, and second, arrange the modified numbers in descending order. Finally, we will compare the positions of the original numbers with their positions after modification and reordering to find how many numbers retain their original position.
| Original Number | Modified Number | Position in Original Descending List | Position in Modified Descending List |
|---|---|---|---|
| 7451 | 5471 | 1st | 3rd |
| 3254 | 5234 | 4th | 5th |
| 7353 | 5373 | 2nd | 4th |
| 3464 | 6434 | 3rd | 1st |
| 1958 | 5918 | 5th | 2nd |
Correct Option: A) Zero
This problem involves setting up an algebraic equation based on the given present ages and the future ratio of their ages. We will define a variable for the number of years passed, express their ages after 'n' years, and then form a ratio equation to solve for 'n'.
Identify present ages:
The present age of the first person is 46 years.
The present age of the second person is 60 years.
Express ages after 'n' years:
After 'n' years, the age of the first person will be \( (46 + n) \) years.
After 'n' years, the age of the second person will be \( (60 + n) \) years.
Set up the ratio equation:
We are given that after 'n' years, the ratio of their ages is 4:5. So, we can write the equation:
\[ \frac{46 + n}{60 + n} = \frac{4}{5} \]Solve the equation for 'n':
Cross-multiply to eliminate the denominators:
\[ 5(46 + n) = 4(60 + n) \]Distribute the numbers:
\[ 230 + 5n = 240 + 4n \]Isolate 'n' terms on one side and constants on the other:
Subtract \(4n\) from both sides:
\[ 230 + 5n - 4n = 240 \]\[ 230 + n = 240 \]Solve for 'n':
Subtract 230 from both sides:
\[ n = 240 - 230 \]\[ n = 10 \]Thus, after 10 years, the ratio of their ages will be 4:5.
D) 10 — As calculated, the value of 'n' is 10 years.
Select the correct product when ethanol is heated at 443 K with excess concentrated sulphuric acid.
The question asks for the product formed when ethanol is heated with excess concentrated sulfuric acid at a specific temperature. This is a classic dehydration reaction of alcohols, where concentrated sulfuric acid acts as a dehydrating agent.
\[ \text{CH}_3\text{CH}_2\text{OH} \xrightarrow[\text{Conc. H}_2\text{SO}_4]{\text{443 K}} \text{CH}_2=\text{CH}_2 + \text{H}_2\text{O} \]
The product formed is ethene (\(\text{CH}_2=\text{CH}_2\)).
B) \(\text{CH}_2=\text{CH}_2\) is ethene, which is the product of the dehydration of ethanol at \(443 \text{ K}\) with concentrated sulfuric acid.
The question asks for the specific location where Gautama Buddha meditated for six years before achieving enlightenment at Bodhgaya. This requires knowledge of the historical and geographical details of Buddha's life.
A) Pragbodhi: This is the correct answer. Pragbodhi (also known as Dungeshwari Cave or Mahakala Cave) is the place where Siddhartha Gautama meditated for six years, undergoing severe ascetic practices, before he abandoned this path and proceeded to Bodhgaya for his final realization.
The problem asks us to identify a set of numbers that follows the same relationship as the given sets: (4, 6, 8) and (6, 9, 12). We need to find a pattern or rule that connects the three numbers within each set.
Let the numbers be \(a, b, c\). We observe the relationship between these numbers.
Let the numbers be \(a, b, c\). We apply the same observations.
Both sets follow the pattern where the numbers are in the ratio \(2:3:4\). This means if the first number is \(x\), the second number is \(\frac{3}{2}x\), and the third number is \(2x\).
Let's verify this rule for the given sets:
C) (8, 12, 16)
The set (8, 12, 16) follows the same pattern where the numbers are in the ratio \(2:3:4\).
To find the power supplied by the battery, we first need to calculate the total equivalent resistance of the circuit. Once the total resistance is known, we can find the total current flowing from the battery using Ohm's Law. Finally, the power supplied by the battery can be calculated using the formula \(P = V \times I\).
Two resistors, each of \(10 \ \Omega\), are connected in parallel. Let \(R_1 = 10 \ \Omega\) and \(R_2 = 10 \ \Omega\). The equivalent resistance for parallel connection (\(R_p\)) is given by:
\[ \frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2} \]\[ \frac{1}{R_p} = \frac{1}{10 \ \Omega} + \frac{1}{10 \ \Omega} \]\[ \frac{1}{R_p} = \frac{2}{10 \ \Omega} \]\[ R_p = \frac{10 \ \Omega}{2} \]\[ R_p = 5 \ \Omega \]The parallel combination (\(R_p = 5 \ \Omega\)) is connected in series with a third resistor (\(R_3 = 10 \ \Omega\)). The total equivalent resistance (\(R_{eq}\)) for a series connection is the sum of individual resistances:
\[ R_{eq} = R_p + R_3 \]\[ R_{eq} = 5 \ \Omega + 10 \ \Omega \]\[ R_{eq} = 15 \ \Omega \]The battery voltage (\(V\)) is \(6 \ \text{V}\). Using Ohm's Law (\(V = I \times R_{eq}\)), the total current (\(I\)) is:
\[ I = \frac{V}{R_{eq}} \]\[ I = \frac{6 \ \text{V}}{15 \ \Omega} \]\[ I = 0.4 \ \text{A} \]The power (\(P\)) supplied by the battery is given by the formula \(P = V \times I\):
\[ P = 6 \ \text{V} \times 0.4 \ \text{A} \]\[ P = 2.4 \ \text{W} \]D) 2.4 W is the calculated power supplied by the battery.