The question asks to identify the Chinese scholar who visited Vijayawada to study Buddhist scriptures. This requires knowledge of prominent Chinese Buddhist pilgrims to India and their travel itineraries.
B) Xuan Zang — Xuanzang (also spelled Hiuen Tsang) was a renowned Chinese Buddhist monk who traveled to India in the 7th century CE. He spent many years studying Buddhism at various centers, including the famous Nalanda University. Historical records indicate that he also visited Dhanyakataka (Amaravati) and Vijayawada in present-day Andhra Pradesh, where he studied Buddhist scriptures and stayed for a significant period.
The problem requires finding the value of \(x\) given a trigonometric equation and a range for \(x\). We will use the fundamental trigonometric identity \(\sin^2x + \cos^2x = 1\) to express the equation in terms of a single trigonometric function, solve for that function, and then find \(x\).
Given the equation:
\[ 3\cos^2x - 2\sin^2x = -0.75 \]We know the identity \(\sin^2x + \cos^2x = 1\), which implies \(\sin^2x = 1 - \cos^2x\). Substitute this into the given equation:
\[ 3\cos^2x - 2(1 - \cos^2x) = -0.75 \]Expand and simplify the equation:
\[ 3\cos^2x - 2 + 2\cos^2x = -0.75 \]\[ 5\cos^2x - 2 = -0.75 \]Isolate the \(\cos^2x\) term:
\[ 5\cos^2x = 2 - 0.75 \]\[ 5\cos^2x = 1.25 \]Solve for \(\cos^2x\):
\[ \cos^2x = \frac{1.25}{5} \]\[ \cos^2x = \frac{5}{4 \times 5} \]\[ \cos^2x = \frac{1}{4} \]Take the square root of both sides to find \(\cos x\):
\[ \cos x = \pm\sqrt{\frac{1}{4}} \]\[ \cos x = \pm\frac{1}{2} \]Given the range \(0^\circ \le x \le 90^\circ\), cosine values are non-negative. Therefore, we take the positive value:
\[ \cos x = \frac{1}{2} \]Recall the standard trigonometric values. For \(\cos x = \frac{1}{2}\), the value of \(x\) is \(60^\circ\).
This value \(60^\circ\) lies within the given range \(0^\circ \le x \le 90^\circ\).
Correct Option: A) \(60^\circ\)
This question tests logical reasoning, specifically the ability to infer conclusions from a given statement. We need to determine if the conclusions logically and necessarily follow from the statement, without introducing outside information or making assumptions.
Correct Option: C) Neither conclusion I nor II follows
The question asks to identify the first bank in India to introduce the Iris Scan Authentication feature for Aadhaar-based transactions. This is a factual question related to banking technology and innovation in India.
Correct Option: B) Axis Bank was the first bank in India to introduce the Iris Scan Authentication feature for Aadhaar-based transactions. This initiative aimed to enhance security and convenience for customers using their Aadhaar identity for banking services.
The question asks about the mode of reproduction in Amoeba. Amoeba is a single-celled organism, and its reproduction method is a common topic in biology. We need to identify the correct asexual reproduction method it employs.
Correct Option: A) Binary fission is the most common method of asexual reproduction in Amoeba, where the parent cell divides into two identical daughter cells.
To solve this problem, we need to follow the order of operations, often remembered by the acronym PEMDAS/BODMAS (Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).
The expression is \(8 \times (7 - (-2) \times (-4))\).
Inside the parentheses, we have \(7 - (-2) \times (-4)\). According to the order of operations, multiplication comes before subtraction.
Calculate the product of \((-2)\) and \((-4)\):
\[ (-2) \times (-4) = 8 \]Now the expression inside the parentheses becomes:
\[ 7 - 8 \]The original expression now simplifies to:
\[ 8 \times (-1) \]Therefore, the value of the expression is \(-8\).
Correct Option: D) -8
The problem provides the percentage distribution of expenses for a small-scale business and the actual amount spent on employees' salaries. We need to find the maintenance expense. We can determine the total expenses by using the given salary amount and its corresponding percentage. Once the total expenses are known, we can calculate the maintenance expense using its percentage.
Identify the given percentages of expenses:
Identify the given actual expense:
Let the total expenses of the business be \(X\). We know that the employees' salary is \(25\%\) of the total expenses.
\[ 25\% \text{ of } X = \text{₹}2,00,000 \]Convert the percentage to a decimal or fraction:
\[ \frac{25}{100} \times X = \text{₹}2,00,000 \]\[ 0.25 \times X = \text{₹}2,00,000 \]Calculate the total expenses \(X\):
\[ X = \frac{\text{₹}2,00,000}{0.25} \]\[ X = \text{₹}2,00,000 \times 4 \]\[ X = \text{₹}8,00,000 \]Now that we have the total expenses, we can calculate the maintenance expense, which is \(50\%\) of the total expenses.
\[ \text{Maintenance Expense} = 50\% \text{ of } \text{₹}8,00,000 \]\[ \text{Maintenance Expense} = \frac{50}{100} \times \text{₹}8,00,000 \]\[ \text{Maintenance Expense} = 0.50 \times \text{₹}8,00,000 \]\[ \text{Maintenance Expense} = \text{₹}4,00,000 \]B) The maintenance expense is ₹4,00,000.
The work done to change the velocity of an object is equal to the change in its kinetic energy. This is known as the work-energy theorem. We need to calculate the initial and final kinetic energies and then find their difference.
The formula for kinetic energy is \(KE = \frac{1}{2}mv^2\).
\[ KE_i = \frac{1}{2}mu^2 = \frac{1}{2} \times 800 \, \text{kg} \times (5 \, \text{m/s})^2 \]\[ KE_i = 400 \, \text{kg} \times 25 \, (\text{m/s})^2 = 10000 \, \text{J} = 10 \, \text{kJ} \]According to the work-energy theorem, the work done is the change in kinetic energy:
\[ W = KE_f - KE_i \]\[ W = 40000 \, \text{J} - 10000 \, \text{J} = 30000 \, \text{J} \]\[ W = 30 \, \text{kJ} \]Correct Option: A) 30 kJ
The problem involves a coding-decoding pattern where letters are assigned numerical values. We need to identify the pattern used to convert "POT" into "151419" and then apply the same pattern to decode "OUGHT". Typically, in such problems, letters are assigned their alphabetical positions (A=1, B=2, ..., Z=26).
14206719
Correct Option: B) 14206719 is the code derived by applying the pattern (alphabetical position - 1) to each letter of "OUGHT" and concatenating the results.
The question asks to identify which of the given options is NOT a part of the male reproductive system in human beings. To answer this, we need to recall the primary organs of both male and female reproductive systems.
Correct Option: D) Ovary — The ovary is a primary reproductive organ in females, responsible for producing eggs and female hormones. It is not a component of the male reproductive system.