This problem involves compound interest. We are given the initial principal, the time it takes for the sum to double, and we need to find the amount after a longer period. The key property of compound interest is that if a sum doubles in a certain period, it will double again in the same period, and so on. This forms a geometric progression.
Identify the initial principal and doubling period:
Initial Principal \((P)\) = ₹12,000.00
The sum doubles at the end of 5 years. This means after 5 years, the amount becomes \(2P\).
Determine the amount after successive doubling periods:
Since the sum doubles every 5 years:
After 5 years, the amount will be \(2 \times P = 2 \times \text{₹}12,000 = \text{₹}24,000\).
After another 5 years (total 10 years), the amount will double again: \(2 \times (2P) = 4P = 4 \times \text{₹}12,000 = \text{₹}48,000\).
After another 5 years (total 15 years), the amount will double yet again: \(2 \times (4P) = 8P = 8 \times \text{₹}12,000\).
Calculate the final amount after 15 years:
\[ \text{Amount after 15 years} = 8 \times \text{₹}12,000 = \text{₹}96,000 \]D) ₹96,000.00 is the correct amount after 15 years.
The problem asks us to identify consonants in a given arrangement that satisfy two conditions: they must be immediately followed by a vowel, and they must NOT be immediately preceded by a number. We will systematically scan the arrangement and check each consonant against these conditions.
D) One. Only the consonant 'L' in the sequence 'LAB' satisfies both conditions: it is immediately followed by a vowel ('A') and not immediately preceded by a number ('@' is a symbol, not a number).
A circle touches the side BC of triangle ABC at P. Side AB and AC are produced to touch the circle at points Q and R respectively. The length of AQ is:
\( \frac{1}{2} \) (BC + CA + AB)
\( \frac{1}{2} \) (2BC + 2CA + 2AB)
\( \frac{1}{3} \) (BC + CA + AB)
\( \frac{1}{4} \) (BC + CA + AB)
This problem involves properties of tangents drawn from an external point to a circle. We will use the fact that the lengths of tangents drawn from an external point to a circle are equal. We will relate the length of AQ to the perimeter of the triangle ABC.
Correct Option: A) \( \frac{1}{2} \) (BC + CA + AB)
The question asks to identify the busiest sea route in the world. This requires knowledge of major global shipping lanes and their economic significance.
Correct Option: C) The North Atlantic sea route. This route connects the highly industrialized and economically powerful regions of North America and Western Europe, making it the busiest in terms of shipping traffic and trade volume.
The question asks to identify an allotropic form of carbon from the given options. Allotropes are different structural forms of the same element in the same physical state. They exhibit different physical properties but similar chemical properties.
D) Diamond — Diamond is a crystalline allotrope of carbon, known for its extreme hardness and high refractive index. Its structure consists of carbon atoms covalently bonded in a tetrahedral lattice.
This problem involves setting up and solving a system of equations based on the given ratios. We will represent the numbers using a common multiple and then form an equation when 4 is added to them, allowing us to find the value of the common multiple and subsequently the numbers themselves. Finally, we will calculate the difference between these numbers.
Represent the numbers: Let the two numbers be \(2x\) and \(3x\), since their ratio is given as \(2:3\).
Formulate the equation after adding 4: When 4 is added to each number, the new numbers become \((2x + 4)\) and \((3x + 4)\). The new ratio is given as \(7:10\). So, we can write the equation:
\[ \frac{2x + 4}{3x + 4} = \frac{7}{10} \]Solve the equation for \(x\): Cross-multiply to solve for \(x\):
\[ 10(2x + 4) = 7(3x + 4) \] \[ 20x + 40 = 21x + 28 \]Rearrange the terms to isolate \(x\):
\[ 40 - 28 = 21x - 20x \] \[ 12 = x \]So, the value of \(x\) is 12.
Find the original numbers: Substitute \(x = 12\) back into our expressions for the numbers:
First number \( = 2x = 2 \times 12 = 24 \)
Second number \( = 3x = 3 \times 12 = 36 \)
The two numbers are 24 and 36.
Calculate the difference between the numbers: Difference \( = 36 - 24 = 12 \)
Correct Option: A) 12
The problem presents a series of letters: Y, V, Q, J, ?. We need to identify the pattern in the series to find the missing letter. This type of problem usually involves finding the difference in alphabetical positions between consecutive letters.
A) The pattern of differences between consecutive letters is an increasing series of odd numbers (3, 5, 7, ...). The next difference is 9. Subtracting 9 from the position of J (10) gives 1, which corresponds to the letter A.
To solve this problem, we need to first identify the first five composite numbers and the first five prime numbers. Then, we will calculate the mean of each set of numbers. Finally, we will find the difference between these two means.
A composite number is a positive integer that has at least one divisor other than 1 and itself. The first few natural numbers are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ...
So, the first five composite numbers are \(4, 6, 8, 9, 10\).
The mean is the sum of the numbers divided by the count of the numbers.
\[ \text{Mean of composite numbers} = \frac{4 + 6 + 8 + 9 + 10}{5} = \frac{37}{5} = 7.4 \]A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.
The first five prime numbers are \(2, 3, 5, 7, 11\).
The difference between the mean of the first 5 composite numbers and the mean of the first five prime numbers is \(1.8\).
A) 1.8 — This matches our calculated difference.
The question asks to identify the country that topped the medal tally at the 2018 Asian Games held in Jakarta and Palembang, Indonesia. This requires knowledge of the results of major international sporting events, which is a common topic in general awareness sections of competitive exams.
D) China — China consistently performs exceptionally well in the Asian Games and topped the medal tally in the 2018 Jakarta Games.