The problem asks us to identify the letter-cluster pair that does not follow the same pattern as the others, based on English alphabetical order. We need to find the relationship between the letters within each cluster and between the two clusters in each pair.
In option A (FI-NS), the jump from F to N is +8, and from I to S is +10. This deviates from the pattern observed in options B, C, and D where the jumps are +7 and +10 respectively.
The question asks for the number of girls Space Kidz India aims to train for its ShakthiSAT mission. This is a factual recall question related to current affairs and space technology initiatives.
Correct Option: A) 12,000
Space Kidz India's ShakthiSAT mission specifically targets training 12,000 girls aged 14-18 from 108 countries in space technology. This number is a key detail of the initiative.
The mean marks of the following distribution is:
| Marks Obtained | No. of Students |
| 83 | 9 |
| 73 | 5 |
| 20 | 18 |
| 82 | 16 |
To find the mean marks of a given distribution, we use the formula for the mean of a grouped data set. This involves calculating the sum of the product of each mark and its corresponding number of students (frequency), and then dividing this sum by the total number of students.
Let \(x_i\) be the marks obtained and \(f_i\) be the number of students (frequency).
| Marks (\(x_i\)) | No. of Students (\(f_i\)) | \(f_i \times x_i\) |
|---|---|---|
| 83 | 9 | \(83 \times 9 = 747\) |
| 73 | 5 | \(73 \times 5 = 365\) |
| 20 | 18 | \(20 \times 18 = 360\) |
| 82 | 16 | \(82 \times 16 = 1312\) |
The formula for the mean is:
\[ \bar{x} = \frac{\Sigma f_i x_i}{\Sigma f_i} \]Substitute the calculated values:
\[ \bar{x} = \frac{2784}{48} \] \[ \bar{x} = 58 \]Correct Option: D) 58
To determine the correct sequence of mountain ranges from north to south, we need to recall their geographical locations within India. Visualizing a map of India and identifying the relative positions of the Aravalli, Vindhya, Satpura, and Ajanta ranges is crucial for solving this question.
Based on their geographical positions, the sequence from north to south is: Aravalli Range, Vindhya Range, Satpura Range, and Ajanta Range.
Thus, the correct sequence is 2, 1, 4, 3.
C) 2, 1, 4, 3 is the correct sequence from north to south, placing the Aravalli Range first, followed by the Vindhya Range, then the Satpura Range, and finally the Ajanta Range.
The problem asks us to identify the third element from the left in a given series after all symbols are removed. We need to first filter out the symbols and then count the remaining elements from left to right.
Therefore, the third element from the left after removing all symbols is 2.
Correct Option: A) 2
The question asks about the relationship between current and resistance in a resistor. This relationship is fundamental in electrical circuits and is described by Ohm's Law.
B) inversely proportional to the resistance — As derived from Ohm's Law (\(I = V/R\)), current is inversely proportional to resistance when voltage is constant.
The problem requires us to evaluate an expression after interchanging certain mathematical operators. We need to replace '+' with '−' and '−' with '+', and similarly '÷' with '×' and '×' with '÷'. After the interchange, we will apply the BODMAS/PEMDAS rule to solve the new expression.
C) The final calculated value after interchanging the operators and applying BODMAS/PEMDAS is \(64\).
The question asks to identify the metal least likely to corrode in moist air. Corrosion is a redox process where metals react with substances in their environment, typically oxygen and water, to form more stable compounds like oxides or hydroxides. The likelihood of a metal corroding is related to its position in the reactivity series (also known as the electrochemical series).
Copper is positioned lower in the reactivity series compared to Zinc, Iron, and Magnesium. This indicates that copper is less reactive and therefore less prone to oxidation (corrosion) when exposed to moist air.
The problem presents a series of letter groups. We need to identify the pattern in the progression of letters within each group and between consecutive groups to determine the next group in the series.
Correct Option: C) OVS is the correct option because it follows the established pattern where each corresponding letter in consecutive groups advances by two positions in the English alphabetical order.
The question asks about the typical positioning of the centres of curvature relative to the optical centre in a thin lens. Understanding the definition of a lens and its constituent spherical surfaces is key to answering this question.
A) They are equidistant from the optical centre. This is true for a symmetrical thin lens, where the optical centre lies exactly midway between the two centres of curvature. In general, for any thin lens, the centres of curvature are located on the principal axis on opposite sides of the optical centre, and for symmetrical lenses, they are equidistant.