The question asks about a specific cabinet appointment made in June 2024. To answer this, one needs to be aware of the recent ministerial changes and portfolio allocations in the Indian government.
C) Jagat Prakash Nadda was appointed as the Minister of Health and Family Welfare in June 2024, following the formation of the new Union Cabinet after the Lok Sabha elections.
The problem asks us to identify numbers in a given series that satisfy two conditions: they must be immediately preceded by another number and immediately followed by a symbol. We need to scan the series from left to right and check each number against these conditions.
B) Two
As identified in the step-by-step analysis, there are two numbers (8 and 7) that are immediately preceded by a number and immediately followed by a symbol.
This problem involves analyzing logical statements and deriving conclusions. We will use Venn diagrams to represent the relationships between the categories (Horses, Mirrors, Lizards) and then evaluate each conclusion based on these diagrams.
Statement 1: No horses are mirrors.
This means that the set of 'Horses' and the set of 'Mirrors' are completely separate. There is no overlap between them.
\[ \text{Horses} \cap \text{Mirrors} = \emptyset \]
Statement 2: Some lizards are horses.
This means there is an overlap between the set of 'Lizards' and the set of 'Horses'. Some lizards are definitely horses, and consequently, some horses are definitely lizards.
\[ \text{Lizards} \cap \text{Horses} \neq \emptyset \]
Evaluate Conclusion (I): Some horses are not lizards.
From Statement 2, we know that "Some lizards are horses." This implies that there is an intersection between Lizards and Horses. However, it does not necessarily mean that all horses are lizards, nor does it guarantee that some horses are NOT lizards. There could be a scenario where all horses are lizards (e.g., if the set of Horses is a subset of Lizards). Since this conclusion is not definitively true in all possible interpretations of the statements, it does not logically follow.
Evaluate Conclusion (II): Some lizards are not mirrors.
We know from Statement 2 that "Some lizards are horses." Let's call this group of lizards 'Lizards-that-are-horses'.
From Statement 1, we know that "No horses are mirrors." This means that any creature that is a horse cannot be a mirror.
Therefore, the 'Lizards-that-are-horses' (which are horses) cannot be mirrors. This directly implies that there are some lizards (specifically, those lizards that are horses) that are not mirrors. Hence, this conclusion logically follows.
Correct Option: C) Only conclusion (II) follows
To find the volume of a cube, we first need to determine the length of its side. We are given the perimeter of one face of the cube. Since a face of a cube is a square, we can use the perimeter formula for a square to find the side length. Once the side length is known, we can calculate the volume of the cube using the formula \(V = \text{side}^3\).
Correct Option: B) The volume of the cube is \(1728 \text{ cm}^3\).
If sec 4A = cosec (3A - 50°), where 4A and 3A are acute angles, find the value of cosec (A + 25°).
The problem involves trigonometric identities, specifically the complementary angle identity relating secant and cosecant functions. We are given an equation \(\text{sec } 4A = \text{cosec } (3A - 50^\circ)\) and asked to find the value of \(\text{cosec } (A + 25^\circ)\). We will use the identity \(\text{sec } \theta = \text{cosec } (90^\circ - \theta)\) to solve for A, and then substitute the value of A into the expression we need to evaluate.
Apply the complementary angle identity:
We know that \(\text{sec } \theta = \text{cosec } (90^\circ - \theta)\). Using this identity, we can rewrite \(\text{sec } 4A\) as \(\text{cosec } (90^\circ - 4A)\).
Set up the equation:
Given the equation \(\text{sec } 4A = \text{cosec } (3A - 50^\circ)\), substitute the identity from step 1:
Solve for A:
Since the cosecant values are equal, their angles must be equal (assuming they are acute angles, as stated in the problem, which ensures a unique solution within the relevant range):
Verify acute angles:
Given that \(4A\) and \(3A\) are acute angles:
For \(A = 20^\circ\), \(4A = 4 \times 20^\circ = 80^\circ\), which is acute.
For \(A = 20^\circ\), \(3A = 3 \times 20^\circ = 60^\circ\), which is acute.
Also, \(3A - 50^\circ = 60^\circ - 50^\circ = 10^\circ\), which is acute. The conditions are satisfied.
Evaluate the required expression:
We need to find the value of \(\text{cosec } (A + 25^\circ)\). Substitute \(A = 20^\circ\):
Recall the value of \(\text{cosec } 45^\circ\):
We know that \(\text{sin } 45^\circ = \frac{1}{\sqrt{2}}\). Since \(\text{cosec } \theta = \frac{1}{\text{sin } \theta}\):
Therefore, the value of \(\text{cosec } (A + 25^\circ)\) is \(\sqrt{2}\).
D) \(\sqrt{2}\) is the correct answer, as derived from the step-by-step solution.
The question asks to identify the type of chemical reaction that occurs when calcium oxide reacts with water to form slaked lime. We need to analyze the reactants and products to determine how they combine or break apart.
C) Combination reaction
A combination reaction is a type of chemical reaction in which two or more simple substances combine to form a more complex product. In this case, calcium oxide and water combine to form calcium hydroxide, fitting the definition perfectly.
The question asks for the increased funding allocated to the 'Sambal' scheme in the 2024-25 Indian Union Budget. This requires knowledge of specific budgetary allocations for the mentioned scheme.
According to the 2024-25 Interim Union Budget, the allocation for the 'Sambal' scheme (a sub-scheme under Mission Shakti) has been increased from ₹462 crore in the previous fiscal year to ₹629 crore.
D) ₹629 crore — This is the correct amount allocated to the 'Sambal' scheme in the 2024-25 Indian Union Budget, reflecting an increase from ₹462 crore in the previous fiscal year.
This problem involves analyzing logical statements and conclusions. We will use Venn diagrams to represent the given statements and then evaluate whether the conclusions logically follow from these diagrams.
Correct Option: C) Neither conclusion (I) nor (II) follows.
To find the share of A when a total amount is distributed between A and B in a given ratio, we first determine the total number of parts in the ratio. Then, we find the value of one part by dividing the total amount by the total number of parts. Finally, we multiply the value of one part by A's share in the ratio to get A's actual share.
Correct Option: A) ₹1,400 is the share of A.
To identify a heterogeneous mixture, we need to understand the definition of homogeneous and heterogeneous mixtures. A homogeneous mixture has a uniform composition throughout, meaning its components are evenly distributed and indistinguishable. A heterogeneous mixture, on the other hand, has a non-uniform composition, and its components remain distinct and can often be seen separately.
Correct Option: D) Oil mixed with water