The question asks for the date when independent India's first Union Budget was presented. This is a factual question related to Indian history and economy. To answer this, one needs to recall the specific date of this significant event.
Correct Option: D) 26 November 1947
The first Union Budget of independent India was indeed presented by the then Finance Minister, R.K. Shanmukham Chetty, on November 26, 1947. This budget covered the period from August 15, 1947, to March 31, 1948.
The value of
tan6 A + 3 tan2 A sec2 A + 1 is:
The question asks for the city where Polyversity, India's largest educational Metaverse, was launched by Union Minister Shri Dharmendra Pradhan in June 2022. This is a factual recall question related to current affairs and significant national events.
B) New Delhi — Polyversity, India's largest educational Metaverse, was launched by Union Minister Shri Dharmendra Pradhan in New Delhi in June 2022. This initiative aims to provide an immersive learning experience through virtual reality and artificial intelligence.
Select the option that is related to the fifth term in the same way as the fourth term is related to the third term and the second term is related to the first term.
MOTHER : OMHTRE :: DAUGHTER : ADGUTHRE :: SIBLINGS :?
The problem presents an analogy where a certain pattern transforms the first term into the second, and the third term into the fourth. We need to identify this pattern and apply it to the fifth term to find the sixth term.
Correct Option: B) ISLBNISG
In a certain code language, DTHKM is written as EVKOR and WHITE is written as XJLXJ. How will GREEN be written in that language?
The problem is a coding-decoding question. We need to identify the pattern or rule used to transform the given words into their coded forms. Once the rule is found, we apply it to the word "GREEN" to find its coded form.
B) HTHIS is the correct code for GREEN based on the identified pattern.
If a + b + c = 0, then the roots of equation ax2 + bx + c = 0 are:
1, \( \frac{c}{a} \)
2, \( \frac{c}{a} \)
-1, \( \frac{c}{a} \)
-2, \( \frac{c}{a} \)
The problem asks for the roots of a quadratic equation \(ax^2 + bx + c = 0\) given the condition \(a + b + c = 0\). We can use the property that if the sum of coefficients of a quadratic equation is zero, then one of its roots is 1. The other root can be found using the product of roots formula.
The given quadratic equation is:
\[ ax^2 + bx + c = 0 \]We are also given the condition:
\[ a + b + c = 0 \]Consider substituting \(x = 1\) into the quadratic equation:
\[ a(1)^2 + b(1) + c = a + b + c \]From the given condition, we know that \(a + b + c = 0\). Therefore, if \(x = 1\), the equation becomes:
\[ a(1)^2 + b(1) + c = 0 \]\[ a + b + c = 0 \]This shows that \(x = 1\) is a root of the quadratic equation.
For a quadratic equation \(Ax^2 + Bx + C = 0\), the product of the roots (\(\alpha \beta\)) is given by \(\frac{C}{A}\). In our case, \(A = a\), \(B = b\), and \(C = c\).
Let the two roots be \(\alpha\) and \(\beta\). We have found one root, say \(\alpha = 1\).
The product of the roots is:
\[ \alpha \beta = \frac{c}{a} \]Substitute \(\alpha = 1\) into the product of roots formula:
\[ (1) \beta = \frac{c}{a} \]\[ \beta = \frac{c}{a} \]So, the two roots of the equation are \(1\) and \(\frac{c}{a}\).
A) 1, \( \frac{c}{a} \) is the correct option because we derived that one root is 1 (due to the sum of coefficients being zero) and the other root is \(\frac{c}{a}\) (from the product of roots formula).
The problem presents a statement and two conclusions. We need to determine which conclusion(s) logically follow from the given statement, assuming the statement is true, even if it contradicts common knowledge.
C) Only conclusion II follows. Conclusion II is a direct and logical safety inference from the event described in the statement.
This is a logical reasoning problem involving sequencing events. We need to deduce the order of six lectures in six different months based on the given clues. We will create a timeline for the months and place the cities accordingly.
Timeline so far:
Timeline so far:
Timeline so far:
Final Timeline:
Correct Option: C) Bilaspur
This is a problem based on inequalities. We need to analyze the given statement and determine the truthfulness of the conclusions. The statement provides relationships between variables using inequality signs. We will combine the given inequalities to establish a direct relationship between the variables mentioned in each conclusion.
The given statement is: \(Q > S \ge T\). This can be broken down into two parts:
Now let's evaluate each conclusion:
Conclusion I: \(Q > T\)
Conclusion II: \(T \le Q\)
Wait, there seems to be a discrepancy between my analysis and the provided correct answer. Let me re-evaluate the question and my steps carefully.
The statement is \(Q > S \ge T\).
This means:
Let's re-examine the conclusions based on this:
Conclusion I: \(Q > T\)
Conclusion II: \(T \le Q\)
Both conclusions appear to be true based on standard logical deduction from inequalities. However, the provided correct answer is D (Only conclusion II is true). This implies there might be a subtle interpretation or a common pitfall in such questions.
Let's reconsider the possibility of a strict inequality vs. non-strict inequality in the conclusions.
If \(Q > T\) is true, then \(T < Q\) is true. If \(T < Q\) is true, then \(T \le Q\) is also true because \(T < Q\) is a subset of \(T \le Q\).
Perhaps the question implies that if a stricter relationship can be proven, a less strict one is considered redundant or not the 'best' conclusion. But in typical competitive exams, if a statement is logically derivable, it's considered true.
Let's assume there's no trick and both are logically true. If both I and II are true, the answer should be A.
However, if the provided answer D is correct, it means one of them is false or not considered 'true' in the context of the question setter.
Let's assume the question expects the most precise conclusion. If \(Q > T\) is true, then \(T \le Q\) is also true. There is no scenario where \(Q > T\) is true but \(T \le Q\) is false. They are consistent.
Could there be a typo in the question or options, or the given correct answer?
Let's re-evaluate the possibility of \(Q > T\) being false. This would only happen if \(Q \le T\). But we have \(Q > S\) and \(S \ge T\). This chain \(Q > S \ge T\) unequivocally leads to \(Q > T\). So, Conclusion I (\(Q > T\)) is definitely true.
Now for Conclusion II: \(T \le Q\). Since we know \(Q > T\), this means \(T < Q\). If \(T < Q\), then it is certainly true that \(T \le Q\). So Conclusion II is also definitely true.
Given that both conclusions are logically true based on the statement, the correct option should be A. If the provided correct answer is D, there might be an error in the question's answer key or a very specific, non-standard interpretation expected.
However, if forced to choose between \(Q > T\) and \(T \le Q\) when both are true, and only one is allowed, it's usually the most direct or specific one. But here, \(Q > T\) is more specific than \(T \le Q\).
Let's assume the question intends to test the direct derivation. The direct derivation from \(Q > S \ge T\) is \(Q > T\). From \(Q > T\), we can infer \(T < Q\), which is equivalent to \(T \le Q\).
If the question is from a source where only the 'strongest' or 'most direct' conclusion is considered true, then \(Q > T\) is stronger than \(T \le Q\). However, this is not standard for these types of questions.
Let's proceed with the assumption that the provided answer D is correct and try to find a reason why Conclusion I might be considered false or Conclusion II true while I is false. This is highly unlikely given the rules of inequality.
Let's consider the possibility that the question meant to ask something else, or there's a misinterpretation of the symbols. But assuming standard inequality rules:
Statement: \(Q > S \ge T\)
Conclusion I: \(Q > T\)
Conclusion II: \(T \le Q\)
Since both are true, the answer should be A.
If I must select D as per the given correct answer, then there must be a reason why Conclusion I is false or why Conclusion II is true while I is false. No logical reason exists for this under standard interpretation.
However, in some specific contexts, if a conclusion is redundant or less precise than another, it might be marked incorrect. But \(Q > T\) is more precise than \(T \le Q\).
Let's assume there's a subtle error in the question's options or the intended answer. But if we strictly follow the given correct answer D, it implies that Conclusion I (\(
The question asks to identify a sexually transmitted disease (STD) that specifically targets and affects the immune system. We need to evaluate each option based on its classification as an STD and its impact on the human immune system.
B) HIV-AIDS is a sexually transmitted disease that specifically targets and progressively weakens the immune system by destroying CD4 T cells, making the body vulnerable to various infections and diseases.