The question asks for the theme of the 2018 World Sustainable Development Summit (WSDS 2018). This requires factual knowledge about past international conferences and their specific themes.
Correct Option: C) Partnerships for a Resilient Planet
This is a syllogism problem that can be solved using Venn diagrams or by applying rules of logical deduction. We need to determine which conclusions logically follow from the given statements.
Imagine three concentric circles. The innermost circle represents "Gifts". The next larger circle, enclosing "Gifts", represents "Dolls". The outermost circle, enclosing "Dolls" (and thus "Gifts"), represents "Toys".
Since all gifts are dolls, and all dolls are toys, it logically follows that all gifts must also be toys. If something is a gift, it's a doll, and if it's a doll, it's a toy. So, it must be a toy. This conclusion is valid.
If all gifts are toys (as established in Conclusion 1), then there must be at least some toys that are gifts. This is a direct consequence of the first conclusion. If the set of gifts is entirely inside the set of toys, then the intersection of toys and gifts is not empty, meaning some toys are indeed gifts. This conclusion is also valid.
B) Both (1) & (2) follow. Both conclusions are logically derived from the given statements.
The question asks to identify the type of plant tissue that is capable of cell division. This requires knowledge of the different types of plant tissues and their primary functions.
Correct Option: A) Meristematic tissue is composed of actively dividing cells and is responsible for the growth of the plant. These cells are undifferentiated and retain the capacity for continuous cell division throughout the plant's life.
If \( \frac{7}{16} \) of the weight of a brick is \( \frac{21}{8} \) kg, then \( \frac{5}{12} \) of the weight of the brick will be:
\( \frac{10}{3} \) kg
\( \frac{3}{5} \) kg
\( \frac{3}{10} \) kg
\( \frac{5}{2} \) kg
To solve this problem, we first need to find the total weight of the brick. We are given a fraction of the brick's weight and its corresponding value. From this, we can calculate the full weight. Once the total weight is known, we can then find the specified fraction of that total weight.
We are given that \( \frac{7}{16} \) of the weight of a brick is \( \frac{21}{8} \) kg.
So, we can write the equation:
\[ \frac{7}{16} \times W = \frac{21}{8} \]To find \(W\), we can multiply both sides of the equation by \( \frac{16}{7} \):
\[ W = \frac{21}{8} \times \frac{16}{7} \]We can cancel out common factors:
\[ W = \frac{21}{7} \times \frac{16}{8} \] \[ W = 3 \times 2 \] \[ W = 6 \text{ kg} \]Now that we know the total weight of the brick is 6 kg, we need to find \( \frac{5}{12} \) of this weight:
\[ \text{Required weight} = \frac{5}{12} \times 6 \]\[ \text{Required weight} = \frac{5 \times 6}{12} \] \[ \text{Required weight} = \frac{30}{12} \]
Divide both numerator and denominator by their greatest common divisor, which is 6:
\[ \text{Required weight} = \frac{30 \div 6}{12 \div 6} \] \[ \text{Required weight} = \frac{5}{2} \text{ kg} \]Correct Option: D) \( \frac{5}{2} \) kg
\(\frac{5^{0.25}\times(125)^{0.25}}{(256)^{0.1}\times(256)^{0.15}}\) =?
To solve this problem, we will simplify the numerator and the denominator separately using the properties of exponents. Specifically, we will use the rules \((a^m)^n = a^{mn}\) and \(a^m \times a^n = a^{m+n}\).
The numerator is \(5^{0.25} \times (125)^{0.25}\).
First, express 125 as a power of 5: \(125 = 5^3\).
Substitute this into the expression:
\[ 5^{0.25} \times (5^3)^{0.25} \]Apply the power rule \((a^m)^n = a^{mn}\):
\[ 5^{0.25} \times 5^{3 \times 0.25} = 5^{0.25} \times 5^{0.75} \]Apply the product rule \(a^m \times a^n = a^{m+n}\):
\[ 5^{0.25 + 0.75} = 5^{1.00} = 5 \]The denominator is \((256)^{0.1} \times (256)^{0.15}\).
Apply the product rule \(a^m \times a^n = a^{m+n}\):
\[ (256)^{0.1 + 0.15} = (256)^{0.25} \]Express 256 as a power of an integer. We know \(256 = 4^4\).
Substitute this into the expression:
\[ (4^4)^{0.25} \]Apply the power rule \((a^m)^n = a^{mn}\):
\[ 4^{4 \times 0.25} = 4^{1.00} = 4 \]Now, divide the simplified numerator by the simplified denominator:
\[ \frac{\text{Numerator}}{\text{Denominator}} = \frac{5}{4} \]D) \( \frac{5}{4} \) is the correct answer, as derived from the simplification of the given expression.
To find the Highest Common Factor (HCF) of a set of numbers, we can use the prime factorization method. This involves finding the prime factors of each number and then identifying the common prime factors raised to the lowest power they appear in any of the factorizations.
The prime factors of 64 are \(2^6\).
The prime factors of 28 are \(2^2 \times 7^1\).
The prime factors of 96 are \(2^5 \times 3^1\).
The only common prime factor among 64, 28, and 96 is 2.
The powers of 2 in the factorizations are \(2^6\), \(2^2\), and \(2^5\).
The lowest power of 2 among these is \(2^2\).
Correct Option: B) 4
The question asks to identify the CEO of Infosys as of July 2018. This requires knowledge of the leadership changes in major Indian IT companies, which is a common topic in current affairs sections of competitive exams.
Salil Parekh was appointed as the CEO and Managing Director of Infosys on January 2, 2018. Therefore, as of July 2018, he was indeed the CEO of Infosys.
A) Salil Parekh — Salil Parekh took over as the CEO and MD of Infosys on January 2, 2018, and continued in that role through July 2018 and beyond.
The problem presents a series of letter-number pairs. To find the next term, we need to identify the pattern in both the letters and the numbers separately.
Correct Option: A) N-14 is the correct answer because the letter sequence increases by 3 alphabetical positions (B+3=E, E+3=H, H+3=K, K+3=N) and the number sequence increases by 3 (2+3=5, 5+3=8, 8+3=11, 11+3=14).
The question asks to identify the sport associated with Amal Raj. This requires general knowledge about prominent Indian sportspersons and their respective fields.
A) Table Tennis — Amal Raj is a prominent Indian table tennis player. He has achieved significant success in the sport, including winning national championships and representing India at international events like the Commonwealth Games.
What will be the next term in this series?
DW,EV,FU___________
The problem presents a series of letter pairs. To find the next term, we need to identify the pattern in both the first and second letters of each pair.
A) GT — As determined by analyzing the patterns of both the first and second letters, the next term in the series is GT.