The question asks to identify the state where the Jantar Mantar, a UNESCO World Heritage Site and an astronomical observation site, is located. This requires knowledge of prominent historical and cultural sites in India.
A) Rajasthan — The Jantar Mantar in Jaipur, Rajasthan, is a collection of nineteen architectural astronomical instruments built by the Rajput king Sawai Jai Singh II, and it is a UNESCO World Heritage Site.
The problem asks us to find the missing letter-clusters, # and %, by identifying the pattern and relationship between the given letter-cluster pairs. We need to analyze the transformation from one cluster to another in the first pair (XFL) and apply the same logic to find # and %.
C) # = SAG, % = PXD
This is a coding-decoding problem where letters are assigned numerical codes. We need to identify the pattern or direct mapping between letters and numbers from the given examples and then apply it to find the code for the specific letter 'D'.
A) 1. Based on the coding of 'CARD' as '4681', the letter 'D' corresponds to the digit '1'. Although 'D' is coded as '3' in 'DOGS', if option 'A' (1) is the correct answer, it implies that the code for 'D' is derived from the first example provided, 'CARD'.
A group of numbers and symbols is coded using letter codes as per the codes given below and the conditions that follow. Study the given codes and conditions and answer the question that follows.
Note: If none of the conditions apply, then codes for the respective number/symbol are to be followed directly as given in the table.
| Number/Symbols | 4 | # | $ | 7 | 9 | 2 | 6 | @ | 3 | & | 5 | + |
| Code | B | W | Q | C | A | T | J | N | P | D | G | E |
Conditions:
(i) If the first element is a number and the last element is a symbol, then the codes for the first and last elements are to be interchanged.
(ii) If the first element is divisible by 2 and the last element is divisible by 3, then the first and last elements are to be coded as *
(iii) If the first element is a symbol and the last element is an even number, then their codes (i.e. first and last element) are to be changed to the code for 3.
Identify the code for the following.
56#4+
The problem requires us to decode a given sequence of numbers and symbols based on a provided coding table and a set of conditions. We need to first identify the codes for each element in the sequence and then check if any of the given conditions apply. If a condition applies, we modify the codes accordingly. If no condition applies, we use the direct codes from the table.
A) EJWBG is incorrect. This option seems to have swapped the first and last codes but used the original codes for 5 and + instead of the swapped ones. The correct application of condition (i) results in G for the first element and E for the last element.
B) GJWBG is incorrect. The last element's code is incorrect. It should be E, not G.
C) GJWBE is the correct code derived from applying condition (i) and direct coding for the rest.
D) EJGBE is incorrect. This option has multiple errors in the codes for the middle elements and the first element.
We are given two equations representing the cost of chairs and tables. We need to find the cost of a specific combination of chairs and tables. We can solve this by finding the cost of one table and then using that information to find the required cost.
Let the cost of one chair be \(C\) and the cost of one table be \(T\).
From the first statement, "18 chairs and 4 tables cost ₹7,100", we can form the equation:
\[ 18C + 4T = 7100 \quad \text{(Equation 1)} \]From the second statement, "18 chairs and 7 tables cost ₹7,700", we can form the equation:
\[ 18C + 7T = 7700 \quad \text{(Equation 2)} \]To find the cost of one table, subtract Equation 1 from Equation 2:
\[ (18C + 7T) - (18C + 4T) = 7700 - 7100 \]\[ 18C + 7T - 18C - 4T = 600 \]\[ 3T = 600 \]Now, solve for \(T\):
\[ T = \frac{600}{3} \]\[ T = 200 \]So, the cost of one table is ₹200.
We need to find the cost of 18 chairs and 5 tables. We can express this as \(18C + 5T\).
Notice that the required expression \(18C + 5T\) is exactly in the middle of the two given expressions in terms of the number of tables (4 tables, 5 tables, 7 tables). Specifically, it's one table more than the first scenario and two tables less than the second scenario.
We can add the cost of one table to the first scenario (18 chairs and 4 tables) to get the cost of 18 chairs and 5 tables:
\[ \text{Cost of (18 chairs + 5 tables)} = \text{Cost of (18 chairs + 4 tables)} + \text{Cost of 1 table} \]\[ \text{Cost} = 7100 + 200 \]\[ \text{Cost} = 7300 \]Alternatively, we could subtract the cost of two tables from the second scenario (18 chairs and 7 tables):
\[ \text{Cost of (18 chairs + 5 tables)} = \text{Cost of (18 chairs + 7 tables)} - \text{Cost of 2 tables} \]\[ \text{Cost} = 7700 - (2 \times 200) \]\[ \text{Cost} = 7700 - 400 \]\[ \text{Cost} = 7300 \]C) ₹7,300 is the correct cost for 18 chairs and 5 tables.
To find Amit's total savings in a year, we first need to calculate his monthly savings. Then, we account for the month when he spends his entire savings on his birthday celebration, meaning he saves nothing in that particular month. Finally, we multiply his monthly savings by the number of months he actually saves.
Amit's expenses include house rent and bills.
\[ \text{Total Monthly Expenses} = \text{House Rent} + \text{Bills} \\ \text{Total Monthly Expenses} = \text{₹}4,000 + \text{₹}2,000 \\ \text{Total Monthly Expenses} = \text{₹}6,000 \]Monthly savings are the salary minus total monthly expenses.
\[ \text{Monthly Savings} = \text{Monthly Salary} - \text{Total Monthly Expenses} \\ \text{Monthly Savings} = \text{₹}13,000 - \text{₹}6,000 \\ \text{Monthly Savings} = \text{₹}7,000 \]In the month of his birthday, Amit spends his complete monthly savings. This means he saves ₹0 in that month. Therefore, he saves for only 11 months in a year.
Multiply the monthly savings by the number of months he actually saves.
\[ \text{Annual Savings} = \text{Monthly Savings} \times \text{Number of Saving Months} \\ \text{Annual Savings} = \text{₹}7,000 \times 11 \\ \text{Annual Savings} = \text{₹}77,000 \]Correct Option: B) 77,000
To find the marked price, we first need to calculate the selling price using the cost price and the profit percentage. Once we have the selling price, we can use the discount percentage to work backward and find the marked price.
Correct Option: D) ₹1,507
To find the height of the cone, we will use the given curved surface area and the diameter of the base. First, we'll calculate the radius from the diameter. Then, using the formula for the curved surface area of a cone, we'll find the slant height. Finally, we'll use the Pythagorean theorem, which relates the radius, height, and slant height, to determine the height of the cone.
The radius (\(r\)) is half of the diameter.
\[ r = \frac{d}{2} = \frac{44 \text{ cm}}{2} = 22 \text{ cm} \]The formula for the curved surface area of a right circular cone is \(CSA = \pi r l\), where \(l\) is the slant height.
\[ 2684\pi = \pi \times 22 \times l \]Divide both sides by \(22\pi\):
\[ l = \frac{2684\pi}{22\pi} \]\[ l = \frac{2684}{22} \]\[ l = 122 \text{ cm} \]For a right circular cone, the radius (\(r\)), height (\(h\)), and slant height (\(l\)) are related by the Pythagorean theorem:
\[ l^2 = r^2 + h^2 \]Thus, the height of the cone is \(120\) cm.
D) 120 — The calculated height of the cone is 120 cm, which matches this option.
The problem asks us to identify the fourth element from the right in a given series after removing all symbols. We need to first filter out the symbols from the original series and then count from the right end of the modified series.
D) The fourth element from the right in the modified series is 7.
The problem asks us to identify the letter-cluster pair that does not follow the same pattern as the others, based on the English alphabetical order. We need to find the relationship between the letters within each pair and between the two letters of the pair.
Let's assign numerical positions to each letter in the English alphabet (A=1, B=2, ..., Z=26) and analyze each option:
Let the pair be \(L_1L_2 - L_3L_4\). We often look for patterns like \(L_1 \to L_3\) and \(L_2 \to L_4\).
Comparing the patterns:
It is clear that options A, C, and D follow the pattern of adding 2 to the first letter and adding 6 to the second letter (cyclically, if needed) to get the corresponding letters in the second cluster. Option B deviates from this pattern with (+3, +6).
B) GK – JQ — This pair follows the pattern of (+3, +6) for its letters, while the other three pairs follow the pattern of (+2, +6).