The question asks to identify the winner of the 2018–19 Vijay Hazare Trophy. This requires knowledge of the results of major Indian domestic cricket tournaments.
Correct Option: A) Mumbai
This question asks us to evaluate the strength of two arguments regarding the practice of shifting agriculture. A strong argument is one that is logical, factual, and directly relevant to the question, providing a compelling reason for or against the practice. We need to analyze each argument independently.
A) Only argument II is strong. Argument II presents a valid, comparative advantage (less expensive) which can be a reason for practicing shifting agriculture, making it a strong argument. Argument I is merely an unsubstantiated opinion.
The task is to evaluate the given conclusions based solely on the information provided in the statement. We must determine which conclusions logically follow from the statement without introducing outside knowledge.
Correct Option: D) Only conclusion II follows.
What is the missing term in the series?
YB25, WD23, ____, SH19
The problem presents a series of terms, each consisting of two letters and a number. To find the missing term, we need to identify the pattern in the letters and the numbers separately.
The first letters are Y, W, ___, S.
So, the first letter of the missing term is U.
The second letters are B, D, ___, H.
So, the second letter of the missing term is F.
The numbers are 25, 23, ___, 19.
So, the number in the missing term is 21.
The missing term consists of the first letter U, the second letter F, and the number 21. Therefore, the missing term is UF21.
Correct Option: B) UF21
A solid metallic hemisphere with radius r is melted and cast into a solid right circular cone with the radius of the base = r. What is the ratio of their curved surface areas?
\(\frac{5}{\sqrt{2}}\)
\(\frac{2}{\sqrt{5}}\)
\(\frac{3}{5}\)
\(\frac{5}{2}\)
The problem involves the transformation of a solid metallic hemisphere into a solid right circular cone. The key principle here is the conservation of volume. We will first calculate the volume of the hemisphere, then use this volume to find the height of the cone. Once the height of the cone is known, we can calculate the curved surface areas of both the hemisphere and the cone and then find their ratio.
Volume of the Hemisphere:
The radius of the hemisphere is given as \(r\). The volume of a hemisphere is given by the formula:
\[ V_{\text{hemisphere}} = \frac{2}{3} \pi r^3 \]Volume of the Cone:
The hemisphere is melted and recast into a cone with the base radius also \(r\). Let the height of the cone be \(h\). The volume of a cone is given by the formula:
\[ V_{\text{cone}} = \frac{1}{3} \pi r^2 h \]Equating Volumes to find the height of the cone:
Since the volume is conserved during melting and recasting:
\[ V_{\text{hemisphere}} = V_{\text{cone}} \]\[ \frac{2}{3} \pi r^3 = \frac{1}{3} \pi r^2 h \]Solve for \(h\):
Cancel out common terms \(\frac{1}{3} \pi r^2\) from both sides:
\[ 2r = h \]\[ h = 2r \]Curved Surface Area of the Hemisphere (CSA_hemisphere):
The curved surface area of a hemisphere is given by:
\[ \text{CSA}_{\text{hemisphere}} = 2 \pi r^2 \]Curved Surface Area of the Cone (CSA_cone):
The curved surface area of a cone is given by \(\pi r l\), where \(l\) is the slant height. We need to find \(l\). The slant height \(l\) can be found using the Pythagorean theorem:
\[ l = \sqrt{r^2 + h^2} \]Substitute \(h = 2r\) into the slant height formula:
\[ l = \sqrt{r^2 + (2r)^2} \]\[ l = \sqrt{r^2 + 4r^2} \]\[ l = \sqrt{5r^2} \]\[ l = r\sqrt{5} \]Calculate CSA_cone:
\[ \text{CSA}_{\text{cone}} = \pi r l = \pi r (r\sqrt{5}) = \pi r^2 \sqrt{5} \]Find the Ratio of their Curved Surface Areas:
The ratio of their curved surface areas is \[\frac{\text{CSA}_{\text{hemisphere}}}{\text{CSA}_{\text{cone}}}\]:
\[ \frac{\text{CSA}_{\text{hemisphere}}}{\text{CSA}_{\text{cone}}} = \frac{2 \pi r^2}{\pi r^2 \sqrt{5}} \]Simplify the ratio:
Cancel out \(\pi r^2\):
\[ \frac{\text{CSA}_{\text{hemisphere}}}{\text{CSA}_{\text{cone}}} = \frac{2}{\sqrt{5}} \]B) The ratio of their curved surface areas is \(\frac{2}{\sqrt{5}}\), as derived from the calculations.
The problem involves calculating averages. We are given the overall average of four numbers and the average of two of those numbers. We need to find the average of the remaining two numbers. The key concept is that the average is the sum of the numbers divided by their count.
The average of a set of numbers is given by:
\[ \text{Average} = \frac{\text{Sum of numbers}}{\text{Count of numbers}} \]We are given that the overall average of a, b, c, and d is 26.5. There are 4 numbers.
\[ \text{Sum}(a, b, c, d) = \text{Average} \times \text{Count} \]\[ a + b + c + d = 26.5 \times 4 \]\[ a + b + c + d = 106 \]We are given that the average of a and b is 20. There are 2 numbers.
\[ \text{Sum}(a, b) = \text{Average} \times \text{Count} \]\[ a + b = 20 \times 2 \]\[ a + b = 40 \]Substitute the sum of a and b into the equation for the sum of all four numbers:
\[ (a + b) + (c + d) = 106 \]\[ 40 + (c + d) = 106 \]\[ c + d = 106 - 40 \]\[ c + d = 66 \]Now that we have the sum of c and d, we can find their average. There are 2 numbers (c and d).
\[ \text{Average}(c, d) = \frac{\text{Sum}(c, d)}{\text{Count}} \]\[ \text{Average}(c, d) = \frac{66}{2} \]\[ \text{Average}(c, d) = 33 \]Correct Option: C) 33
The question asks about the state where assembly elections were held in 2018. To answer this, one needs to recall the election schedule for various Indian states around that year.
Correct Option: A) Meghalaya
Assembly elections in Meghalaya were indeed held in February 2018 to elect 59 of the 60 members of the Meghalaya Legislative Assembly.
Read the given statement and conclusions carefully and select which of the conclusions logically follow(s) from the statement.
Statement:
Some jaguars are cheetahs, some cheetahs are leopards. All leopards are panthers.
Conclusions:
1. All leopards are jaguars.
2. Some panthers are cheetahs.
Only conclusion 2 follows
Only conclusion 1 follows
Either 1 or 2 follows
Both 1 and 2 follow
This problem involves analyzing logical statements and deriving conclusions. We can use Venn diagrams to represent the relationships described in the statements to visually check the validity of the conclusions.
Represent the statements using Venn Diagrams:
Evaluate Conclusion 1: "All leopards are jaguars."
Evaluate Conclusion 2: "Some panthers are cheetahs."
Correct Option: A) Only conclusion 2 follows
To find the next term in the series, we need to identify the pattern in the numbers and the letters separately. Each term consists of a two-digit number, two letters, and another two-digit number.
Correct Option: B) 20TS19
The question asks about the authority responsible for approving major defence procurements in India. This falls under the domain of defence administration and policy-making bodies.
Correct Option: A) The Defence Acquisition Council (DAC) is the highest decision-making body in the Ministry of Defence for capital acquisitions. It approves proposals for new weapons systems, platforms, and equipment for the Indian armed forces. The approval of such a large procurement (111 utility helicopters for over Rs. 21,000 crores) falls directly under its purview.