Who was honored with the 'Social Entrepreneur of the Year' award at the 7th Asian Awards in London?
The question asks to identify the recipient of the 'Social Entrepreneur of the Year' award at the 7th Asian Awards in London. This is a factual recall question related to current affairs or general knowledge about awards and recognitions.
Correct Option: D) Nisha Dutt was awarded the 'Social Entrepreneur of the Year' at the 7th Asian Awards in London. She is the CEO of Intellecap, a company focused on building and scaling enterprises that address social and environmental challenges.
The question asks for the location of Angel Falls. This is a direct factual question related to world geography. To answer this, one needs to recall the geographical location of famous natural landmarks.
Correct Option: A) Venezuela is the correct answer because Angel Falls is indeed located in Venezuela.
This is a syllogism problem. We can solve it using Venn diagrams or by applying rules of deduction. We will represent each statement as a relationship between sets and then check if the conclusions logically follow from these relationships.
A) Both 1 and 2 follow. As determined in the step-by-step analysis, both Conclusion 1 ("All glass is earth") and Conclusion 2 ("Some earth are sand") logically follow from the given statements.
Rationalise the denominator: \( \frac{1}{5+3\sqrt{2}} \) =?
\(\frac{5-2\sqrt{3}}{12}\)
\(\frac{5+2\sqrt{3}}{12}\)
\(\frac{5-3\sqrt{3}}{12}\)
\(\frac{5-3\sqrt{2}}{7}\)
To rationalize the denominator of a fraction involving a surd (irrational number), we multiply both the numerator and the denominator by the conjugate of the denominator. The conjugate of an expression of the form \(a+b\sqrt{c}\) is \(a-b\sqrt{c}\), and vice-versa. This method uses the algebraic identity \((x+y)(x-y) = x^2 - y^2\) to eliminate the square root from the denominator.
Identify the given expression:
\[ \frac{1}{5+3\sqrt{2}} \]Identify the denominator: \(5+3\sqrt{2}\). The conjugate of this denominator is \(5-3\sqrt{2}\).
Multiply both the numerator and the denominator by the conjugate:
\[ \frac{1}{5+3\sqrt{2}} \times \frac{5-3\sqrt{2}}{5-3\sqrt{2}} \]Multiply the numerators:
\[ 1 \times (5-3\sqrt{2}) = 5-3\sqrt{2} \]Multiply the denominators using the identity \((a+b)(a-b) = a^2 - b^2\), where \(a=5\) and \(b=3\sqrt{2}\):
\[ (5+3\sqrt{2})(5-3\sqrt{2}) = (5)^2 - (3\sqrt{2})^2 \] \[ = 25 - (3^2 \times (\sqrt{2})^2) \] \[ = 25 - (9 \times 2) \] \[ = 25 - 18 \] \[ = 7 \]Combine the simplified numerator and denominator:
\[ \frac{5-3\sqrt{2}}{7} \]This is the rationalized form of the given expression.
Correct Option: D) \(\frac{5-3\sqrt{2}}{7}\)
To answer this question, we need to recall the classification of the plant kingdom and the characteristics of each division, specifically where lichens are placed.
Correct Option: B) Thallophyta
We need to determine the time taken by the less efficient pipe alone to fill the tank. We'll use the concept of work rate, where the rate is the reciprocal of the time taken to complete a task. We'll set up equations based on the given efficiencies and combined working times, and then solve for the unknown time.
Let the time taken by the less efficient pipe (Pipe L) to fill the tank be \(x\) hours. Its filling rate is \(\frac{1}{x}\) tank per hour.
The other pipe (Pipe M) works 1.5 times as efficiently as Pipe L. So, its filling rate is \[1.5 \times \frac{1}{x} = \frac{1.5}{x} = \frac{3}{2x}\] tank per hour.
The discharge pipe (Pipe D) can empty the tank in 12 hours. Its emptying rate is \(\frac{1}{12}\) tank per hour.
When both filling pipes and the discharge pipe work together, the tank is filled in 28 hours. The combined filling rate is \(\frac{1}{28}\) tank per hour.
The combined rate can be expressed as the sum of the filling rates minus the emptying rate:
\[ \text{Rate}_{\text{L}} + \text{Rate}_{\text{M}} - \text{Rate}_{\text{D}} = \text{Combined Rate} \]\[ \frac{1}{x} + \frac{3}{2x} - \frac{1}{12} = \frac{1}{28} \]Now, solve the equation for \(x\):
\[ \frac{2}{2x} + \frac{3}{2x} = \frac{1}{28} + \frac{1}{12} \]\[ \frac{5}{2x} = \frac{3 + 7}{84} \]\[ \frac{5}{2x} = \frac{10}{84} \]\[ \frac{5}{2x} = \frac{5}{42} \]From the equation \[\frac{5}{2x} = \frac{5}{42}\], we can equate the denominators since the numerators are equal:
\[ 2x = 42 \]\[ x = \frac{42}{2} \]\[ x = 21 \]So, the less efficient pipe alone will fill the empty tank in 21 hours.
Correct Option: A) 21
The calculations show that the time taken by the less efficient pipe alone to fill the tank is 21 hours.
The force (F) is inversely proportional to the square of 'd', if the factor of 4 in 'd' is increased, then F becomes _______ times smaller.
\( \frac{1}{16} \)
\( \frac{1}{2} \)
\( \frac{1}{8} \)
\( \frac{1}{4} \)
The problem describes an inverse square relationship between force (F) and distance (d). We need to determine how the force changes when the distance is increased by a factor of 4. We will use the given proportionality to establish an equation and then substitute the new distance value to find the change in force.
Understand the proportionality: The problem states that the force (F) is inversely proportional to the square of 'd'. This can be written mathematically as:
\[ F \propto \frac{1}{d^2} \]Introduce a proportionality constant: To convert the proportionality into an equation, we introduce a constant 'k':
\[ F = \frac{k}{d^2} \quad \text{(Equation 1)} \]Here, 'k' is the constant of proportionality.
Consider the change in 'd': The problem states that 'd' is increased by a factor of 4. Let the new distance be \(d'\). Then:
\[ d' = 4d \]Calculate the new force (F'): Substitute \(d'\) into the proportionality equation:
\[ F' = \frac{k}{(d')^2} \] \[ F' = \frac{k}{(4d)^2} \] \[ F' = \frac{k}{16d^2} \]Compare the new force with the original force: We can rewrite the expression for \(F'\) by separating the constant term:
\[ F' = \frac{1}{16} \left( \frac{k}{d^2} \right) \]From Equation 1, we know that \(F = \frac{k}{d^2}\). Substitute F back into the equation for \(F'\):
\[ F' = \frac{1}{16} F \]Interpret the result: The new force \(F'\) is \(\frac{1}{16}\) times the original force F. This means the force becomes \(\frac{1}{16}\) times smaller.
A) \( \frac{1}{16} \) is the correct answer because when the distance 'd' is increased by a factor of 4, the force, being inversely proportional to the square of 'd', decreases by a factor of \(4^2 = 16\). Thus, the force becomes \(\frac{1}{16}\) times smaller.
To find the Least Common Multiple (LCM) of a set of numbers, we can use the prime factorization method. This involves finding the prime factors of each number and then taking the highest power of each prime factor that appears in any of the factorizations.
Thus, the LCM of 5, 180, and 24 is 360.
Correct Option: D) 360
This is a syllogism problem that can be solved using Venn diagrams or by analyzing the logical implications of the statements. We need to determine which conclusions logically follow from the given statements, treating them as true.
B) Both 1 and 2 follow.
This question tests knowledge about the relationship between atmospheric pressure changes and weather conditions. Barometric readings measure atmospheric pressure. A sudden decrease in barometric pressure is a key indicator of specific weather phenomena.
D) Will be very stormy. A sudden decrease in barometric pressure signifies the approach of a low-pressure system, which is typically associated with unstable atmospheric conditions, strong winds, and precipitation, leading to stormy weather.