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 then compare these relationships across all options.
A) PK - MJ
In options B, C, and D, the letters within each cluster are consecutive (e.g., NO, FG, JK, IJ, AB, EF). Also, the first letter of the first cluster is 5 positions ahead of the first letter of the second cluster, and the second letter of the first cluster is 5 positions ahead of the second letter of the second cluster. For example, in NO - IJ: N is 5 positions after I, and O is 5 positions after J. In PK - MJ, the letters within the clusters are not consecutive (P and K have 4 letters in between; M and J have 2 letters in between). Therefore, PK - MJ does not belong to the group.
To find the mean proportional between two numbers, say \(a\) and \(b\), we use the formula \(\sqrt{a \times b}\). This is derived from the concept of continued proportion where if \(a, x, b\) are in continued proportion, then \[\frac{a}{x} = \frac{x}{b}\], which implies \(x^2 = ab\), and thus \(x = \sqrt{ab}\).
B) 0.6 is the correct answer because the mean proportional between 0.06 and 6 is calculated as \(\sqrt{0.06 \times 6} = \sqrt{0.36} = 0.6\).
The question asks for the Chief Minister of Delhi as of March 2025 and their constituency in the 2025 Delhi Assembly elections. This is a hypothetical scenario as the 2025 elections have not occurred yet. Therefore, the answer must be based on a fictional outcome or a scenario where a new Chief Minister is projected.
B) Rekha Gupta from Shalimar Bagh. This option presents a hypothetical but plausible scenario where Rekha Gupta, a prominent BJP leader, becomes the Chief Minister of Delhi after the 2025 elections, winning from the Shalimar Bagh constituency. This implies a change in government from the current AAP government.
To simplify the given expression, we need to follow the order of operations, commonly known as BODMAS/PEMDAS. This acronym stands for Brackets/Parentheses, Orders/Exponents, Division, Multiplication, Addition, and Subtraction. We will perform operations in this specific order from left to right.
The given expression is:
\[ 66 - 4 \times (30 + 3) + 40 \]First, perform the operation inside the parentheses (Brackets):
\[ (30 + 3) = 33 \]Substitute this value back into the expression:
\[ 66 - 4 \times 33 + 40 \]Next, perform the Multiplication:
\[ 4 \times 33 = 132 \]Substitute this value back into the expression:
\[ 66 - 132 + 40 \]Now, perform Addition and Subtraction from left to right. First, perform the Subtraction:
\[ 66 - 132 = -66 \]Finally, perform the Addition:
\[ -66 + 40 = -26 \]A) The simplified value of the expression is \(-26\).
The question asks for the year in which the Swadeshi Movement began. This movement was a direct response to the British government's decision to partition Bengal.
Correct Option: D) 1905
To find the correct average, we first need to calculate the original (incorrect) sum of observations. Then, we adjust this sum by subtracting the misread value and adding the correct value. Finally, we divide the corrected sum by the total number of observations to get the correct average.
The average of 10 observations is given as 40.
\[ \text{Average} = \frac{\text{Sum of observations}}{\text{Number of observations}} \]So, the incorrect sum of observations is:
\[ \text{Incorrect Sum} = \text{Average} \times \text{Number of observations} \] \[ \text{Incorrect Sum} = 40 \times 10 = 400 \]An observation was misread as 34 instead of 43. To correct the sum, we need to subtract the incorrect value (34) and add the correct value (43).
\[ \text{Correct Sum} = \text{Incorrect Sum} - \text{Misread Value} + \text{Correct Value} \] \[ \text{Correct Sum} = 400 - 34 + 43 \] \[ \text{Correct Sum} = 366 + 43 \] \[ \text{Correct Sum} = 409 \]Now, divide the correct sum by the number of observations (which remains 10).
\[ \text{Correct Average} = \frac{\text{Correct Sum}}{\text{Number of observations}} \] \[ \text{Correct Average} = \frac{409}{10} \] \[ \text{Correct Average} = 40.9 \]Correct Option: D) 40.9
The problem presents a series of three-letter combinations. We need to identify the pattern in the alphabetical positions of the letters within each combination and between consecutive combinations to find the missing term.
L (12) \(\rightarrow\) N (14) \(\rightarrow\) P (16) \(\rightarrow\) R (18)
The pattern for the first letter is an increment of 2. So, the first letter of the next term will be \(R + 2 = T (20)\).
J (10) \(\rightarrow\) L (12) \(\rightarrow\) N (14) \(\rightarrow\) P (16)
The pattern for the second letter is also an increment of 2. So, the second letter of the next term will be \(P + 2 = R (18)\).
Q (17) \(\rightarrow\) S (19) \(\rightarrow\) U (21) \(\rightarrow\) W (23)
The pattern for the third letter is also an increment of 2. So, the third letter of the next term will be \(W + 2 = Y (25)\).
The next term in the series will be formed by combining the letters found in steps 1, 2, and 3: T R Y.
Correct Option: B) TRY is the correct term that follows the established pattern for all three letters.
This problem involves arranging six people (A, B, C, D, E, F) on six different floors (1 to 6) based on given conditions. We will use a systematic approach to deduce the floor for each person and then answer the question about the number of people between A and E.
The problem asks us to identify numbers in a given series that are immediately preceded by a number and immediately followed by a number. We need to scan the series from left to right and apply this condition to each number.
A) There are 2 such numbers (6 and 8) in the series that are immediately preceded by a number and immediately followed by a number.
The question asks about a specific appointment to a high-profile position (Chairman of ISRO) in a future month (January 2025). Such questions test general knowledge and awareness of current affairs, particularly concerning significant governmental and scientific appointments. To answer correctly, one needs to recall or be aware of recent or upcoming appointments in key national organizations.
C) Dr. V Narayanan. While S. Somanath is the current Chairman of ISRO, the question specifically asks about an appointment in January 2025. In the context of competitive exams, if such a question is posed with a specific correct answer, it implies that Dr. V Narayanan is the designated individual for this hypothetical future appointment as per the question setter's information or scenario. Dr. V Narayanan is a distinguished scientist and Director of the Liquid Propulsion Systems Centre (LPSC), a unit of ISRO, making him a plausible candidate for such a high-ranking position in the future.