This is a coding-decoding problem where letters are assigned numerical codes. We need to find the code for a specific letter by comparing the given coded words.
Correct Option: D) 4
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.
1 @ 2 2 7 © & 8 6 * # 9 3 6 & 6 # & * © @ 81 @ 2: '2' is preceded by '@' (symbol), not a number.@ 2 2: The first '2' is preceded by '@' (symbol), not a number.2 2 7: The second '2' is preceded by '2' (number) and followed by '7' (number). This is a match! (2 2 7)2 7 ©: '7' is preceded by '2' (number) but followed by '©' (symbol), not a number.7 © &: '©' is a symbol, not a number.© & 8: '&' is a symbol, not a number.& 8 6: '8' is preceded by '&' (symbol), not a number.8 6 *: '6' is preceded by '8' (number) but followed by '*' (symbol), not a number.6 * #: '*' is a symbol, not a number.* # 9: '#' is a symbol, not a number.# 9 3: '9' is preceded by '#' (symbol), not a number.9 3 6: '3' is preceded by '9' (number) and followed by '6' (number). This is a match! (9 3 6)3 6 &: '6' is preceded by '3' (number) but followed by '&' (symbol), not a number.6 & 6: '&' is a symbol, not a number.& 6 #: '6' is preceded by '&' (symbol), not a number.6 # &: '#' is a symbol, not a number.# & *: '&' is a symbol, not a number.& * ©: '*' is a symbol, not a number.* © @: '©' is a symbol, not a number.© @ 8: '@' is a symbol, not a number.C) 2
The question asks about the fabrication technology used for the Vikram 3201 microprocessor, which is a specific detail related to India's indigenous microprocessor development program. To answer this, one needs to recall the publicly available information regarding the specifications of this particular microprocessor.
Correct Option: C) 180nm CMOS technology
The question asks to identify the dance form that depicts a mock fight between Goddess Durga and the demon Mahishasura. This requires knowledge of various Indian folk dances and their associated cultural or mythological themes.
Correct Option: B) Dandiya Raas is a traditional folk dance from Gujarat, primarily performed during the Navaratri festival. The dance involves men and women dancing in circles with two sticks (dandiyas) in their hands, striking them together. This striking of sticks symbolizes the mock fight between Goddess Durga and the demon Mahishasura, representing the triumph of good over evil. The dance is an integral part of the Navaratri celebrations, which commemorate Durga's victory.
To find the standard deviation of a given set of data, we need to follow these steps: calculate the mean, find the deviation of each data point from the mean, square these deviations, find the average of the squared deviations (variance), and finally take the square root of the variance.
List the data points:
\(X = \{65, 47, 59, 75, 82, 91, 55, 78\}\)
The number of data points, \(n = 8\).
Calculate the mean (\(\bar{X}\)):
The mean is the sum of all data points divided by the number of data points.
\[ \bar{X} = \frac{\sum X}{n} = \frac{65 + 47 + 59 + 75 + 82 + 91 + 55 + 78}{8} \] \[ \bar{X} = \frac{552}{8} = 69 \]Calculate the deviation of each data point from the mean (\(X - \bar{X}\)):
Square each deviation (\((X - \bar{X})^2\)):
Sum the squared deviations (\(\sum (X - \bar{X})^2\)):
\[ \sum (X - \bar{X})^2 = 16 + 484 + 100 + 36 + 169 + 484 + 196 + 81 = 1566 \]Calculate the variance (\(\sigma^2\)):
The variance is the average of the squared deviations. For a population, it's divided by \(n\). For a sample, it's divided by \(n-1\). In competitive exams, if not specified, assume population standard deviation unless it's a small sample where sample standard deviation is explicitly mentioned or implied. Here, we'll use \(n\).
\[ \sigma^2 = \frac{\sum (X - \bar{X})^2}{n} = \frac{1566}{8} = 195.75 \]Calculate the standard deviation (\(\sigma\)):
The standard deviation is the square root of the variance.
\[ \sigma = \sqrt{\sigma^2} = \sqrt{195.75} \approx 13.991068 \]Rounding off to 2 decimal places, the standard deviation is \(13.99\).
Correct Option: B) 13.99
The problem asks us to identify the highest and lowest numbers from a given set of three-digit numbers. Then, we need to extract specific digits from these identified numbers and perform an addition operation as specified.
Correct Option: D) 1
The given expression is a quadratic trinomial. We need to factorise it into the square of a binomial. This can be done by recognizing the pattern of a perfect square trinomial, which is of the form \( (x+y)^2 = x^2 + 2xy + y^2 \) or \( (x-y)^2 = x^2 - 2xy + y^2 \).
Identify the given expression: \( 100a^{2} + 300ab + 225b^{2} \).
Compare this expression with the general form of a perfect square trinomial, \( x^2 + 2xy + y^2 \). We need to find \(x\) and \(y\) such that the given expression matches this form.
Find the square root of the first term, \( 100a^{2} \).
\[ \sqrt{100a^{2}} = \sqrt{100} \times \sqrt{a^{2}} = 10a \]
So, we can consider \( x = 10a \).
Find the square root of the third term, \( 225b^{2} \).
\[ \sqrt{225b^{2}} = \sqrt{225} \times \sqrt{b^{2}} = 15b \]
So, we can consider \( y = 15b \).
Now, check if the middle term, \( 300ab \), matches \( 2xy \).
Calculate \( 2xy \) using the values of \( x \) and \( y \) we found:
\[ 2xy = 2 \times (10a) \times (15b) = 20a \times 15b = 300ab \]
Since \( 2xy = 300ab \), which matches the middle term of the given expression, the expression is indeed a perfect square trinomial of the form \( (x+y)^2 \).
Substitute the values of \( x \) and \( y \) back into the formula \( (x+y)^2 \):
\[ (10a + 15b)^2 \]
C) \( (10a + 15b)^{2} \) is the correct factorization because it matches the perfect square trinomial form \( (x+y)^2 = x^2 + 2xy + y^2 \) where \( x = 10a \) and \( y = 15b \).
In this question, a group of letters is coded by using numbers and symbols as per the table given below and the conditions which follow.
| Letter | U | M | S | J | P | T | F | A |
| Code | 7 | 4 | @ | $ | % | * | 6 | 3 |
Conditions:
1. If the 1st letter is a vowel and the 3rd letter is a consonant, both are to be coded as the code for that 3rd letter consonant.
2. If the 1st and last letters are vowels, both are to be coded as 'N'.
3. If the 2nd and last letters are vowels, their codes are to be interchanged.
What is the correct combination of codes (by following only the applicable condition(s)) for the following letters?
AJSPT
The problem requires us to code a given sequence of letters (AJSPT) based on a provided table and a set of conditions. We need to apply the conditions sequentially and only if they are applicable. The key is to identify the letters as vowels or consonants and their positions (1st, 2nd, 3rd, last) to determine which condition(s) apply.
Identify the letters and their standard codes:
So, the initial code for AJSPT is 3 \) @ % *.
Analyze the given word: AJSPT
Check Condition 1: "If the 1st letter is a vowel and the 3rd letter is a consonant, both are to be coded as the code for that 3rd letter consonant."
Since both conditions are met, Condition 1 applies.
According to Condition 1, the 1st letter (A) and the 3rd letter (S) should both be coded as the code for the 3rd letter (S). The code for S is '@'.
So, the new code becomes: @ \( @ % *.
Check Condition 2: "If the 1st and last letters are vowels, both are to be coded as 'N'."
Since the last letter is not a vowel, Condition 2 does not apply.
Check Condition 3: "If the 2nd and last letters are vowels, their codes are to be interchanged."
Since neither the 2nd nor the last letter is a vowel, Condition 3 does not apply.
Final Code: Only Condition 1 applied. The code derived after applying Condition 1 is @ \) @ % *.
D) @ \( @ % *
This matches the code obtained after applying the applicable condition.
A) 3 \) % @ * — This option incorrectly applies the code for P (%) to S and the code for S (@) to P, and does not apply Condition 1 correctly to the first letter.
B) 3 \( @ % * — This is the initial code without applying any conditions. Condition 1 is applicable, so this option is incorrect.
C) 3 \) 3 % * — This option incorrectly codes the 3rd letter as the 1st letter's code (3) and does not apply Condition 1 correctly to the first letter.
The question asks to identify the members of India's recurve men's archery team that won a silver medal in the World Cup Stage 1, 2025. This is a factual recall question related to recent sports achievements. Candidates need to be aware of current events in sports.
Based on reports from the Archery World Cup Stage 1, 2025, the Indian men's recurve team comprising Dhiraj Bommadevara, Atanu Das, and Tarundeep Rai secured a silver medal.
D) Dhiraj Bommadevara, Atanu Das and Tarundeep Rai are indeed the members of the Indian men's recurve team that won a silver medal at the World Cup Stage 1, 2025.
The question asks about a specific policy document related to defence procurement in India where a fast-track clause was introduced in 2024 to reduce acquisition delays. Identifying the primary policy governing defence acquisitions is key to answering this question.
Correct Option: A) Defence Acquisition Procedure — The Defence Acquisition Procedure (DAP) is the comprehensive policy document that governs all capital acquisitions of the Indian Armed Forces. In 2024, a new fast-track procurement clause was indeed introduced into the DAP to reduce acquisition delays for urgent requirements.