The problem asks us to find a pair of letter codes that follows the same pattern as the two given pairs. We need to identify the logical rule or transformation applied to the letters in the first code to get the letters in the second code for the given pairs. Once the pattern is identified, we apply it to the options to find the one that matches.
XBG : TCI
Since all three letters follow the \((-4, +1, +2)\) pattern, option A is the correct answer.
To find the equivalent ratio of 7:9, we need to identify which of the given options, when simplified to its lowest terms, results in the ratio 7:9. An equivalent ratio is obtained by multiplying or dividing both parts of the ratio by the same non-zero number.
Correct Option: D) 70 : 90
This is a blood relation question where symbols represent familial relationships. We need to decode the given expression 'P × Q ÷ R – S + T' step-by-step to determine the relationship between P and T.
A) Brother's wife – As derived, P is the wife of Q, and Q is the brother of T. Thus, P is T's brother's wife.
The numerical value of \(\frac{4}{\sec^2\theta}+\frac{3}{1+\cot^2\theta}+\sin^{2}\theta\) is:
To find the numerical value of the given trigonometric expression, we will use fundamental trigonometric identities to simplify each term. The key identities are:
\(\sec\theta = \frac{1}{\cos\theta}\)
\(\cot\theta = \frac{\cos\theta}{\sin\theta}\)
\(1 + \cot^2\theta = \csc^2\theta\)
\(\csc\theta = \frac{1}{\sin\theta}\)
\(\sin^2\theta + \cos^2\theta = 1\)
Let the given expression be \(E\):
\[ E = \frac{4}{\sec^2\theta} + \frac{3}{1+\cot^2\theta} + \sin^2\theta \]Simplify the first term, \(\frac{4}{\sec^2\theta}\):
Since \(\sec\theta = \frac{1}{\cos\theta}\), then \(\sec^2\theta = \frac{1}{\cos^2\theta}\).
So, \(\frac{4}{\sec^2\theta} = 4 \cos^2\theta\).
Simplify the second term, \(\frac{3}{1+\cot^2\theta}\):
Using the identity \(1 + \cot^2\theta = \csc^2\theta\), we get:
\[ \frac{3}{1+\cot^2\theta} = \frac{3}{\csc^2\theta} \]Since \(\csc\theta = \frac{1}{\sin\theta}\), then \(\csc^2\theta = \frac{1}{\sin^2\theta}\).
So, \(\frac{3}{\csc^2\theta} = 3 \sin^2\theta\).
Substitute the simplified terms back into the expression \(E\):
\[ E = 4 \cos^2\theta + 3 \sin^2\theta + \sin^2\theta \]Combine the \(\sin^2\theta\) terms:
\[ E = 4 \cos^2\theta + (3+1) \sin^2\theta \]\[ E = 4 \cos^2\theta + 4 \sin^2\theta \]Factor out 4:
\[ E = 4 (\cos^2\theta + \sin^2\theta) \]Apply the fundamental identity \(\sin^2\theta + \cos^2\theta = 1\):
\[ E = 4 (1) \]\[ E = 4 \]B) The numerical value of the given expression is 4.
The question asks to identify the place captured by Alfonso de Albuquerque in 1510 from the Sultan of Bijapur, which subsequently became the capital of the Portuguese eastern empire. This requires knowledge of key events in Portuguese colonial history in India.
Correct Option: A) Goa was captured by Alfonso de Albuquerque from the Sultan of Bijapur in 1510 and was subsequently made the capital of the Portuguese eastern empire.
This problem involves analyzing logical statements and drawing conclusions based on them. We can use Venn diagrams or direct logical deduction to determine which conclusions follow from the given statements.
Correct Option: C) Both conclusions (I) and (II) follow
The problem presents two pairs of letter groups (BGM : DEK and SVL : UTJ) that follow a specific pattern. We need to identify the same pattern and apply it to the given options to find the pair that matches.
The question asks to identify the court within the subordinate judiciary that possesses unlimited pecuniary jurisdiction in civil cases. This requires knowledge of the hierarchy and jurisdiction of civil courts in India.
Correct Option: B) Judge of District Court