The question asks for the launch year of the 'Make in India' initiative. This is a factual question about a major government program. Recalling the year of its inception is key to answering correctly.
Correct Option: A) 2014 — The 'Make in India' initiative was launched in 2014.
The question asks to identify which statement is NOT an intended objective of the updated Defence Acquisition Procedure (DAP) 2024. This requires an understanding of the general goals and principles behind India's defence acquisition policies, particularly those aimed at boosting self-reliance (Aatmanirbhar Bharat) in defence manufacturing.
Correct Option: B) Eliminating all private sector participation in defence manufacturing
This problem involves decoding a set of relationships expressed through symbols and then determining the relationship between two individuals based on a given expression. We will break down the given expression step-by-step to establish the family tree and then find the relationship between Q and T.
Therefore, Q is the maternal uncle of S, and S is the father of T. This means Q is the brother of T's paternal grandmother (R) or, more directly, Q is the brother of S's mother (R), and S is T's father. So, Q is the brother of T's father's mother (R). In other words, Q is T's father's mother's brother.
C) Father's mother's brother. As derived, Q is the brother of R, and R is the mother of S, who is the father of T. Thus, Q is the brother of T's father's mother.
The problem presents a series of letter-number clusters. To find the missing cluster, we need to identify the pattern in the letters and the numbers separately.
E, F, G, H, ?
This is a simple alphabetical sequence. The next letter after H is I.
J, K, L, M, ?
This is also a simple alphabetical sequence. The next letter after M is N.
M, N, O, P, ?
This is another simple alphabetical sequence. The next letter after P is Q.
13, 15, 17, 19, ?
This is an arithmetic progression where each number increases by 2. The next number after 19 will be \(19 + 2 = 21\).
The next cluster will be composed of the letters I, N, Q, and the number 21. Thus, the cluster is INQ 21.
B) INQ 21 — This option correctly follows all the identified patterns for letters and numbers.
The question asks for the key combination primarily used to access the File menu in most Windows applications. This is a common keyboard shortcut for navigating application menus.
Correct Option: B) Alt + F is the standard keyboard shortcut to open the File menu in most Windows applications. The 'F' in 'File' is often underlined, indicating this shortcut.
The problem asks us to identify the letter-cluster pair that does not follow the same pattern as the others, based on the English alphabetical order. We need to find a consistent rule or relationship between the letters in each pair and then identify the pair that deviates from this rule.
The question asks for the correct sequence of steps to initiate a blank presentation in MS PowerPoint 2016 or later. This is a fundamental operation in PowerPoint, and understanding the menu navigation is key.
This sequence directly leads to the creation of a new, blank presentation.
Correct Option: A) File → New → Blank Presentation
The mean proportional between (9 + 4\(\sqrt{5}\)) and (18 − 8\(\sqrt{5}\)) is:
\(\sqrt{5}\)
\(\sqrt{15}\)
\(\sqrt{17}\)
\(\sqrt{2}\)
To find the mean proportional between two numbers, say \(a\) and \(b\), we use the formula \( \sqrt{a \times b} \). In this problem, we are given two expressions, \( (9 + 4\sqrt{5}) \) and \( (18 - 8\sqrt{5}) \). We will multiply these two expressions and then take the square root of the product.
Let the first number be \(a = 9 + 4\sqrt{5}\).
Let the second number be \(b = 18 - 8\sqrt{5}\).
The mean proportional \(M\) is given by \(M = \sqrt{a \times b}\).
\[ a \times b = (9 + 4\sqrt{5}) \times (18 - 8\sqrt{5}) \]
Factor out 2 from the second term \( (18 - 8\sqrt{5}) \):
\[ 18 - 8\sqrt{5} = 2(9 - 4\sqrt{5}) \]
Now, substitute this back into the product:
\[ a \times b = (9 + 4\sqrt{5}) \times 2(9 - 4\sqrt{5}) \]
\[ a \times b = 2 \times (9 + 4\sqrt{5}) \times (9 - 4\sqrt{5}) \]
Recognize the algebraic identity \( (x + y)(x - y) = x^2 - y^2 \). Here, \(x = 9\) and \(y = 4\sqrt{5}\).
\[ (9 + 4\sqrt{5})(9 - 4\sqrt{5}) = 9^2 - (4\sqrt{5})^2 \]
Calculate the squares:
\[ 9^2 = 81 \]
\[ (4\sqrt{5})^2 = 4^2 \times (\sqrt{5})^2 = 16 \times 5 = 80 \]
Substitute these values back:
\[ (9 + 4\sqrt{5})(9 - 4\sqrt{5}) = 81 - 80 = 1 \]
Now, substitute this result back into the product \(a \times b\):
\[ a \times b = 2 \times 1 = 2 \]
The mean proportional \(M = \sqrt{a \times b} = \sqrt{2}\).
Correct Option: D) \( \sqrt{2} \)
The surface area of a sphere is 25π cm². The volume of the sphere is:
\(\frac{509\pi}{3}\) cm³
\(\frac{125\pi}{3}\) cm³
\(\frac{500\pi}{3}\) cm³
\(\frac{125\pi}{6}\) cm³
To find the volume of the sphere, we first need to determine its radius. We can do this by using the given surface area of the sphere and the formula for the surface area of a sphere. Once the radius is found, we can then use the formula for the volume of a sphere to calculate the required volume.
The surface area (\(A\)) of a sphere with radius \(r\) is given by:
\[ A = 4\pi r^2 \]We are given that the surface area \(A = 25\pi \text{ cm}^2\). Substitute this into the formula:
\[ 25\pi = 4\pi r^2 \]Divide both sides by \(4\pi\):
\[ r^2 = \frac{25\pi}{4\pi} \]\[ r^2 = \frac{25}{4} \]\[ r = \sqrt{\frac{25}{4}} \]\[ r = \frac{5}{2} \text{ cm} \]The volume (\(V\)) of a sphere with radius \(r\) is given by:
\[ V = \frac{4}{3}\pi r^3 \]Substitute \(r = \frac{5}{2}\) cm into the volume formula:
\[ V = \frac{4}{3}\pi \left(\frac{5}{2}\right)^3 \]\[ V = \frac{4}{3}\pi \left(\frac{5^3}{2^3}\right) \]\[ V = \frac{4}{3}\pi \left(\frac{125}{8}\right) \]Multiply the terms:
\[ V = \frac{4 \times 125 \times \pi}{3 \times 8} \]\[ V = \frac{500\pi}{24} \]Divide the numerator and denominator by their greatest common divisor, which is 4:
\[ V = \frac{500\pi \div 4}{24 \div 4} \]\[ V = \frac{125\pi}{6} \text{ cm}^3 \]Correct Option: D) \(\frac{125\pi}{6}\) cm\(^3\)
The problem requires us to evaluate a mathematical expression after interchanging certain operators. We need to replace '+' with '−' and '−' with '+', and '×' with '÷' and '÷' with '×'. After performing these interchanges, we will evaluate the new expression following the order of operations (BODMAS/PEMDAS).
A) 516 is the correct answer, as calculated by interchanging the operators and then following the order of operations.