To solve this problem, we need to identify consonants that fit a specific pattern: they must be immediately preceded by a vowel and immediately followed by a vowel. We will first list all vowels and consonants, then systematically scan the given series to find such combinations.
B) Four. There are four such consonants (S, K, W, T) in the series, each immediately preceded by a vowel and immediately followed by a vowel.
To solve this problem, we will assume an initial salary for Ravi. Then, we will calculate the salary after a 50% reduction and subsequently calculate the salary after a 50% raise on the reduced amount. Finally, we will compare the final salary with the initial salary to find the percentage decrease.
Assume an Initial Salary: Let Ravi's initial salary be \(₹100\).
Calculate Salary after 50% Reduction: A 50% reduction means the salary becomes \(100\% - 50\% = 50\%\) of the original salary.
\[ \text{Reduced Salary} = \text{Initial Salary} \times (1 - 0.50) \\ \text{Reduced Salary} = ₹100 \times 0.50 = ₹50 \]Calculate Salary after 50% Raise: The raise is applied to the reduced salary (\(₹50\)). A 50% raise means the salary increases by 50% of the reduced salary.
\[ \text{Amount of Raise} = \text{Reduced Salary} \times 0.50 \\ \text{Amount of Raise} = ₹50 \times 0.50 = ₹25 \]So, the final salary is:
\[ \text{Final Salary} = \text{Reduced Salary} + \text{Amount of Raise} \\ \text{Final Salary} = ₹50 + ₹25 = ₹75 \]Compare Final Salary to Initial Salary: Initial Salary = \(₹100\) Final Salary = \(₹75\)
The decrease in salary is:
\[ \text{Decrease} = \text{Initial Salary} - \text{Final Salary} \\ \text{Decrease} = ₹100 - ₹75 = ₹25 \]Calculate Percentage Lower: The percentage lower is calculated with respect to the initial salary.
\[ \text{Percentage Lower} = \frac{\text{Decrease}}{\text{Initial Salary}} \times 100\% \\ \text{Percentage Lower} = \frac{₹25}{₹100} \times 100\% \\ \text{Percentage Lower} = 0.25 \times 100\% = 25\% \]Correct Option: A) 25%
The question asks about the basis for the early classification of elements. Early chemists observed and categorized elements based on their observable characteristics and how they behaved in reactions.
Correct Option: A) properties
Early classification systems, such as those proposed by Dobereiner, Newlands, and Mendeleev, were fundamentally based on the observed physical and chemical properties of elements. Elements with similar properties were grouped together.
In an electric circuit, where 5 lamps are connected in series, if the power, voltage, current and resistance are represented by P, V, I and R, respectively, then which of the following relations holds true?
This question asks to identify the correct relationship for electrical power (P) in terms of voltage (V), current (I), and resistance (R). We will use the fundamental formulas for electrical power and Ohm's Law to derive the correct expression.
B) P = I2 R
As derived in step 3, this is a correct formula for electrical power, expressing power in terms of current and resistance.
An object is placed in front of a concave lens at a distance d. An erect image of the object is formed at \( \frac{d}{3} \). If the focal length of the lens is 15 cm, then d is equal to:
This problem involves a concave lens and image formation. We need to use the lens formula and the magnification formula, along with the sign conventions for lenses, to find the object distance 'd'.
Identify the given information and sign conventions:
Apply the lens formula:
The lens formula is given by:
\[ \frac{1}{v} - \frac{1}{u} = \frac{1}{f} \]Substitute the values into the lens formula:
\[ \frac{1}{(-\frac{d}{3})} - \frac{1}{(-d)} = \frac{1}{-15} \]\[ -\frac{3}{d} + \frac{1}{d} = -\frac{1}{15} \]Simplify the equation:
\[ \frac{-3 + 1}{d} = -\frac{1}{15} \]\[ \frac{-2}{d} = -\frac{1}{15} \]Solve for \(d\):
Multiply both sides by \(-1\):
\[ \frac{2}{d} = \frac{1}{15} \]\[ d = 2 \times 15 \]\[ d = 30 \text{ cm} \]D) 30 cm is the correct answer. The calculation using the lens formula and proper sign conventions yields \(d = 30 \text{ cm}\).
To find the Least Common Multiple (LCM) of the given marks (20, 28, and 42), we can use the prime factorization method. This involves finding the prime factors of each number and then taking the highest power of each prime factor that appears in any of the factorizations.
The unique prime factors involved are 2, 3, 5, and 7.
Correct Option: C) 420
Aman deposits Rs 8,000 at 10% rate of simple interest per annum. The total amount he will get at the end of 2 years is:
This problem involves calculating simple interest and then finding the total amount received at the end of a specific period. We will use the formula for simple interest and then add it to the principal amount to find the total amount.
Correct Option: D) 9,600
The question asks about the percentage of post offices expected to be under the core banking system in India by the year 2022. This is a factual question related to government initiatives and financial inclusion, specifically concerning the Department of Posts.
Correct Option: B) 100% — As per government plans and announcements, all 1.5 lakh post offices were targeted to be brought under the core banking system by 2022 to facilitate financial inclusion and offer modern banking services.
This problem involves calculating the total weight from an average and then determining the weight of a new item when the average changes. We will use the formula: Total Weight = Average Weight \(\times\) Number of Items.
Given that the average weight of 32 parcels is 96 kg.
\[ \text{Initial Total Weight} = \text{Average Weight} \times \text{Number of Parcels} \\ \text{Initial Total Weight} = 96 \text{ kg} \times 32 \\ \text{Initial Total Weight} = 3072 \text{ kg} \]One more parcel is included, and the average increases by 2 kg.
\[ \text{New Average Weight} = \text{Initial Average Weight} + 2 \text{ kg} \\ \text{New Average Weight} = 96 \text{ kg} + 2 \text{ kg} \\ \text{New Average Weight} = 98 \text{ kg} \]One more parcel is added to the initial 32 parcels.
\[ \text{New Number of Parcels} = 32 + 1 \\ \text{New Number of Parcels} = 33 \]Using the new average and new number of parcels.
\[ \text{New Total Weight} = \text{New Average Weight} \times \text{New Number of Parcels} \\ \text{New Total Weight} = 98 \text{ kg} \times 33 \\ \text{New Total Weight} = 3234 \text{ kg} \]The weight of the new parcel is the difference between the new total weight and the initial total weight.
\[ \text{Weight of New Parcel} = \text{New Total Weight} - \text{Initial Total Weight} \\ \text{Weight of New Parcel} = 3234 \text{ kg} - 3072 \text{ kg} \\ \text{Weight of New Parcel} = 162 \text{ kg} \]B) 162 kg — As calculated in the step-by-step solution, the weight of the new parcel is 162 kg.