The problem presents a coding-decoding question where words are encoded using a specific pattern. We need to identify this pattern by analyzing the given examples and then apply it to encode the target word 'CURVE'. The pattern usually involves shifts in letter positions in the alphabet, either forward or backward, or a combination of both.
Correct Option: A) HAYDN
To find the difference between compound interest (CI) and simple interest (SI) for a given principal, rate, and time, we will calculate both SI and CI separately and then find their difference. Alternatively, for 2 years, there's a direct formula for the difference between CI and SI.
Given:
The formula for Simple Interest is:
\[ \text{SI} = \frac{P \times R \times T}{100} \]\[ \text{SI} = \frac{10000 \times 5 \times 2}{100} \]\[ \text{SI} = \frac{100000}{100} \]\[ \text{SI} = \text{Rs } 1000 \]The formula for the Amount \((A)\) when interest is compounded annually is:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]\[ A = 10000 \left(1 + \frac{5}{100}\right)^2 \]\[ A = 10000 \left(1 + \frac{1}{20}\right)^2 \]\[ A = 10000 \left(\frac{21}{20}\right)^2 \]\[ A = 10000 \times \frac{21 \times 21}{20 \times 20} \]\[ A = 10000 \times \frac{441}{400} \]\[ A = \frac{10000}{400} \times 441 \]\[ A = 25 \times 441 \]\[ A = \text{Rs } 11025 \]Now, calculate Compound Interest (CI):
\[ \text{CI} = A - P \]\[ \text{CI} = 11025 - 10000 \]\[ \text{CI} = \text{Rs } 1025 \]The difference between CI and SI for 2 years is given by:
\[ \text{Difference} = P \left(\frac{R}{100}\right)^2 \]\[ \text{Difference} = 10000 \left(\frac{5}{100}\right)^2 \]\[ \text{Difference} = 10000 \left(\frac{1}{20}\right)^2 \]\[ \text{Difference} = 10000 \times \frac{1}{400} \]\[ \text{Difference} = \frac{10000}{400} \]\[ \text{Difference} = 25 \]The difference between CI and SI is:
\[ \text{Difference} = \text{CI} - \text{SI} \]\[ \text{Difference} = 1025 - 1000 \]\[ \text{Difference} = \text{Rs } 25 \]A) 25 — The calculated difference between the compound interest and simple interest is Rs 25.
The question asks to identify the Five-Year Plan in which the removal of poverty and attainment of self-reliance were the primary objectives. This requires knowledge of the main goals and characteristics of India's various Five-Year Plans.
B) Fifth Five-Year Plan (1974-1979) had the twin objectives of 'Garibi Hatao' (removal of poverty) and attainment of self-reliance. This plan was drafted by D.P. Dhar and was launched during a period of economic crisis due to the 1971 war and the oil shock.
To solve this problem, we need to identify all prime numbers within the given ranges, calculate their sums, and then find the positive difference between these two sums.
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.
The prime numbers between 11 and 20 are 11, 13, 17, 19.
The prime numbers between 30 and 50 are 31, 37, 41, 43, 47.
Positive difference \( = |S_2 - S_1| \)
\[ \text{Difference} = |199 - 60| = 139 \]D) 139 is the positive difference between the sum of prime numbers between 11 and 20 and the sum of prime numbers between 30 and 50.
This problem requires the application of the empirical relationship between mean, median, and mode for a moderately skewed distribution. The empirical formula states that for such distributions, the difference between the mode and the mean is approximately three times the difference between the mean and the median.
A) 39 — By applying the empirical formula relating mode, median, and mean, and substituting the given values, the mean is calculated to be 39.
To find the simple interest rate at which a sum of money doubles in a given time, we use the simple interest formula. When the sum doubles, the simple interest earned is equal to the principal amount.
Let the principal amount be \(P\).
If the sum of money doubles, the Amount (\(A\)) becomes \(2P\).
The Simple Interest (\(SI\)) earned is the difference between the Amount and the Principal:
\[ SI = A - P = 2P - P = P \]The time period (\(T\)) given is 10 years.
The formula for Simple Interest is:
\[ SI = \frac{P \times R \times T}{100} \]Substitute the known values into the formula:
\[ P = \frac{P \times R \times 10}{100} \]Now, we need to solve for \(R\), the rate of interest per annum.
Divide both sides by \(P\) (assuming \(P \neq 0\)):
\[ 1 = \frac{R \times 10}{100} \]Simplify the equation:
\[ 1 = \frac{R}{10} \]Multiply both sides by 10 to find \(R\):
\[ R = 1 \times 10 \]\[ R = 10\% \]D) 10% is the correct rate of simple interest per annum for the sum to double in 10 years.
A) 8.50% — If the rate were 8.50%, the interest earned in 10 years would be \(P \times 0.085 \times 10 = 0.85P\). The total amount would be \(P + 0.85P = 1.85P\), which is less than double.
B) 15% — If the rate were 15%, the interest earned in 10 years would be \(P \times 0.15 \times 10 = 1.5P\). The total amount would be \(P + 1.5P = 2.5P\), which is more than double.
C) 20% — If the rate were 20%, the interest earned in 10 years would be \(P \times 0.20 \times 10 = 2P\). The total amount would be \(P + 2P = 3P\), which is triple, not double.
In this question, a group of numbers/symbols is coded using letters as per the table given below and the conditions which follow. The correct combination of codes following the condition is your answer.
| Number/Symbol | 2 | 6 | % | @ | ? | 4 | < | 3 | 7 | = | ! | & | 9 | 8 |
| Code | K | S | R | T | U | M | W | Y | A | V | C | X | E | B |
Conditions:
(i) If the first element is a number and the last a symbol, the codes for these two are to be interchanged.
(ii) If the first element is an even number and the last an odd number, the first and the last elements are to be coded as O.
(iii) If both the second and third elements are perfect squares, the third element is to be coded as the code for the second element.
How will ‘3 = 7 4 %’ be coded?
The problem requires us to code a given sequence of numbers/symbols based on a provided table and a set of conditions. We need to first find the direct codes for each element in the sequence and then apply the conditions in the given order to determine the final coded sequence.
A) RVAMY is the correctly derived code after applying the conditions.
This is a seating arrangement puzzle. We need to deduce the positions of eight people (P, Q, R, S, T, X, Y, Z) sitting around a square table based on the given clues. Some are at corners, and some are at the exact center of the sides. All are facing the center. We will use a step-by-step method to place them and then answer the question.
Identify positions: There are 8 people around a square table. This means 4 people are at the corners and 4 people are at the exact center of the sides.
Clue 1: "S, T, Y and Z are sitting at the exact centre of the sides of the table."
This means P, Q, R, X must be sitting at the corners.
Clue 2: "Z who is to the immediate left of R, has P as immediate neighbour."
Since Z is at the center of a side and R is at a corner, R's immediate left will be a side position. So, Z is to the immediate left of R. Also, P is an immediate neighbour of Z. Since Z is at a side, its neighbours are two corners. One corner is R, so the other corner must be P. This means R, Z, P are in sequence. Let's place them: If R is at a corner, Z is to its immediate left (side position), and P is to Z's immediate left (corner position).
Clue 3: "S is the immediate neighbour of Q and X."
S is at a side position. Its neighbours must be corners. So, Q and X are at corners. This is consistent with P, Q, R, X being at corners.
Clue 4: "Y does not have X and P as his immediate neighbours."
Y is at a side position. Its neighbours are corners. So, the two corners adjacent to Y are not X and not P.
Combine and deduce:
Final Arrangement (clockwise from top-left corner):
P (corner), Z (side), R (corner), T (side), X (corner), S (side), Q (corner), Y (side).
Answer the question: "who is sitting to the immediate right of X?"
Looking at the arrangement, to the immediate right of X (which is at the bottom-right corner) is S (at the bottom side). Wait, let's re-check the direction. All are facing the center. So, if X is at the bottom-right corner, facing the center, its immediate right is the person at the right side. In our arrangement, T is at the right side. Let's re-verify the full arrangement.
Let's draw it:
P --- Z --- R
| |
Y T
| |
Q --- S --- X
Let's re-verify the conditions with this arrangement:
Now, let's find the person to the immediate right of X. X is at the bottom-right corner, facing the center. Its immediate right is T (at the right side).
A) T is sitting to the immediate right of X.
The question asks about the fundamental function of an electric motor. To answer this, we need to recall the basic principle of how an electric motor operates and what energy conversion it performs.
A) electrical energy into mechanical energy
This is the precise definition and function of an electric motor. It takes electricity (electrical energy) and converts it into rotational motion (mechanical energy) to perform work.
To find the electric power consumed by the bulbs, we first need to calculate the total resistance of the circuit since the bulbs are connected in series. Then, we can find the total current flowing through the circuit using Ohm's Law. Finally, we can calculate the total power consumed using the formula \(P = I^2 R_{\text{total}}\) or \(P = V I\).
For components connected in series, the total resistance is the sum of individual resistances.
\[ R_{\text{total}} = R_1 + R_2 \]\[ R_{\text{total}} = 5 \, \Omega + 5 \, \Omega \]\[ R_{\text{total}} = 10 \, \Omega \]Using Ohm's Law, \(V = I R_{\text{total}}\), we can find the current \(I\).
\[ I = \frac{V}{R_{\text{total}}} \]\[ I = \frac{3 \, \text{V}}{10 \, \Omega} \]\[ I = 0.3 \, \text{A} \]The power consumed can be calculated using the formula \(P = V I\).
\[ P = V I \]\[ P = (3 \, \text{V}) \times (0.3 \, \text{A}) \]\[ P = 0.9 \, \text{W} \]Alternatively, using \(P = I^2 R_{\text{total}}\):\[ P = (0.3 \, \text{A})^2 \times (10 \, \Omega) \]\[ P = 0.09 \, \text{A}^2 \times 10 \, \Omega \]\[ P = 0.9 \, \text{W} \]C) The calculated power consumed is \(0.9 \, \text{W}\).