The question asks to identify the individual or entity NOT associated with the White Revolution in India. We need to recall the key figures and organizations involved in this movement.
Correct Option: A) Norman Borlaug is associated with the Green Revolution, which focused on increasing crop production (especially wheat and rice), not the White Revolution (dairy production).
To find the ratio C : A, we first need to find a common ratio for A : B : C. We are given two separate ratios: A : B and B : C. We can combine these by making the common term 'B' equal in both ratios.
Write down the given ratios:
\[ A : B = 2 : 3 \] \[ B : C = 4 : 5 \]Find the least common multiple (LCM) of the 'B' values:
In the first ratio, \(B = 3\). In the second ratio, \(B = 4\).
The LCM of 3 and 4 is 12.
Adjust the first ratio (A : B) so that B becomes 12:
To change 3 to 12, we multiply by 4. So, we multiply both parts of the ratio \(A : B\) by 4.
Adjust the second ratio (B : C) so that B becomes 12:
To change 4 to 12, we multiply by 3. So, we multiply both parts of the ratio \(B : C\) by 3.
Combine the ratios to find A : B : C:
Now that the 'B' term is the same in both adjusted ratios, we can write:
Determine C : A:
From the combined ratio, \(A = 8\) and \(C = 15\).
Therefore, \(C : A = 15 : 8\).
Correct Option: D) 15 : 8
The problem requires finding the value of \(\theta\) given a trigonometric equation involving tangent and cotangent functions. We will use the trigonometric identity \(\cot A = \tan (90^\circ - A)\) to convert the cotangent term into a tangent term, allowing us to equate the angles.
The given equation is:
\[ \tan 2\theta = \cot(\theta + 6^\circ) \]Use the complementary angle identity \(\cot A = \tan (90^\circ - A)\). Here, \(A = \theta + 6^\circ\).
\[ \cot(\theta + 6^\circ) = \tan(90^\circ - (\theta + 6^\circ)) \]Simplify the expression inside the tangent function:
\[ \tan(90^\circ - \theta - 6^\circ) = \tan(84^\circ - \theta) \]Substitute this back into the original equation:
\[ \tan 2\theta = \tan(84^\circ - \theta) \]If \(\tan X = \tan Y\), then \(X = Y + n \cdot 180^\circ\) for integer \(n\). For acute angles or angles within the range \((0^\circ, 90^\circ)\), we can simply equate the angles:
\[ 2\theta = 84^\circ - \theta \]Solve for \(\theta\):
\[ 2\theta + \theta = 84^\circ \]\[ 3\theta = 84^\circ \]\[ \theta = \frac{84^\circ}{3} \]\[ \theta = 28^\circ \]Verify the angles: \(2\theta = 2(28^\circ) = 56^\circ\) and \(\theta + 6^\circ = 28^\circ + 6^\circ = 34^\circ\). Since \(\tan 56^\circ = \cot 34^\circ\) (because \(56^\circ + 34^\circ = 90^\circ\)), the solution is correct.
C) \(28^\circ\) is the correct value for \(\theta\) as derived from the trigonometric identity and algebraic manipulation.
The question asks to identify the state where slash and burn agriculture is known as 'Bewar'. This requires knowledge of the local names for shifting cultivation practiced in different regions of India.
Correct Option: A) Madhya Pradesh
In Madhya Pradesh, slash and burn agriculture is locally known as 'Bewar' or 'Dahiya', particularly by tribal communities.
The problem presents a numerical series, and we need to find the missing term. We will analyze the relationship between consecutive terms to identify the pattern and then apply it to find the missing number.
The differences are 7, 14, 28. It appears that each difference is double the previous difference:
Following this pattern, the next difference should be \(28 \times 2 = 56\).
The missing term is the previous term (54) plus the predicted difference (56):
\[ 54 + 56 = 110 \]If the missing term is 110, the next difference should be \(56 \times 2 = 112\).
Let's check if \(110 + 112 = 222\):
\[ 110 + 112 = 222 \]This matches the given term 222.
The next difference would be \(112 \times 2 = 224\).
Let's check if \(222 + 224 = 446\):
\[ 222 + 224 = 446 \]This also matches the given term 446. The pattern holds true.
Another way to look at the pattern is:
Applying this pattern to find the missing term:
\[ 54 \times 2 + 2 = 108 + 2 = 110 \]Verifying with the next term:
\[ 110 \times 2 + 2 = 220 + 2 = 222 \]This pattern also consistently yields 110 as the missing number.
Both methods confirm that the missing number is 110.
Correct Option: A) 110 is the number that replaces the question mark, following the identified pattern.
The question asks to categorize the Andaman Teal based on its geographical distribution and conservation status. Understanding the definitions of different species categories is crucial to answer this question.
Correct Option: C) Endemic species
The question asks for the definition of "Epigraphy." This is a direct knowledge-based question related to historical and archaeological terminology. We need to identify the correct field of study associated with this term.
C) Study of inscriptions
Epigraphy is the scientific study of epigraphs or inscriptions as writing; it is the study of such things as ancient writings, their deciphering, their interpretation, and their classification. It helps in understanding ancient cultures, languages, and historical events.
The question asks to identify the daughter of Chandragupta II, a prominent ruler of the Gupta Empire. This requires knowledge of the genealogical and matrimonial alliances of the Gupta dynasty.
D) Prabhavatigupta was the daughter of Chandragupta II and Dhruvadevi. She was married to Rudrasena II of the Vakataka dynasty, a significant political alliance for the Gupta Empire.
The question asks to identify the country where the Five-Hundred-Metre Aperture Spherical Telescope (FAST) was opened in 2020. This requires knowledge of major astronomical observatories and their locations.
D) China is the country where the Five-Hundred-Metre Aperture Spherical Telescope (FAST) is located and officially opened for operations in 2020.
The question asks to identify which of the given Grand Slam tennis tournaments is played on a clay court. This requires knowledge of the playing surfaces for each of the four major tennis tournaments.
Correct Option: A) Roland Garros is the only Grand Slam tournament played on clay courts. It is often referred to as the French Open.