Find the arithmetic mean of the following data.
| x | 6 | 10 | 18 | 24 | 30 | 36 |
| f | 4 | 3 | 4 | 2 | 1 | 1 |
To find the arithmetic mean of a given frequency distribution, we use the formula for the mean of grouped data. This involves multiplying each data point (x) by its corresponding frequency (f), summing these products, and then dividing by the total sum of frequencies.
B) 16 — The arithmetic mean calculated by summing the products of each value and its frequency, and then dividing by the total frequency, is 16.
Eight friends are sitting around a square table facing the centre. Four of them are sitting at the corners and the remaining four are sitting at the exact middle of the four sides. Only Charu is sitting between Karan and Hitesh. Jay is sitting fourth to the left of Laxshita. Alok is sitting second to the left of Laxshita. Siya is sitting to the immediate right of Jay. Karan is sitting fourth to the left of Siya. Rashmi is sitting fourth to the right of Hitesh. Who is sitting to the immediate right of Alok?
This is a seating arrangement puzzle. We need to deduce the positions of eight friends sitting around a square table based on the given clues. We will start by drawing a square table and placing individuals as per the definite clues, then use relative positions to fill in the rest.
A) Rashmi is sitting to the immediate right of Alok, as determined by the seating arrangement.
Find the resistance of the conductor using the given graph 
To find the resistance of the conductor, we use Ohm's Law, which states that the resistance \( R \) is the ratio of voltage \( V \) to current \( I \). The graph provided shows a linear relationship between voltage and current.
Correct Option: D) 60 ohm
The question asks for the venue of the World Athletics Championships 2022 where Neeraj Chopra won a silver medal. This requires knowledge of major international sporting event locations.
Correct Option: C) United States of America
If a = 28 - 5\(\sqrt{12}\) and b = 2 + \(\sqrt{3}\), find the value of (a\(\sqrt{3}\) + b).
31 - 8\(\sqrt{3}\)
32 + 27\(\sqrt{3}\)
-30 + 30\(\sqrt{3}\)
-28 + 29\(\sqrt{3}\)
To find the value of \((a\sqrt{3} + b)\), we first need to simplify the expression for \(a\) by simplifying the square root term. Then, we substitute the simplified \(a\) and the given \(b\) into the expression and perform the necessary arithmetic operations, combining like terms (rational numbers and terms involving \(\sqrt{3}\)).
We know that \(12 = 4 \times 3\). So, \(\sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3}\).
Given \(a = 28 - 5\sqrt{12}\).
Substitute \(\sqrt{12} = 2\sqrt{3}\):
\[ a = 28 - 5(2\sqrt{3}) \]Simplify:
\[ a = 28 - 10\sqrt{3} \]Given \(b = 2 + \sqrt{3}\).
Since \(\sqrt{3} \times \sqrt{3} = 3\):
\[ 28\sqrt{3} - 10(3) = 28\sqrt{3} - 30 \]Simplify:
\[ -28 + (28 + 1)\sqrt{3} \]Final result:
\[ -28 + 29\sqrt{3} \]D) \(-28 + 29\sqrt{3}\) is the correct answer, as derived from the step-by-step calculation.
Which of the following options is the closest approximate value which will come in place of the question mark (?) in the following equation? 2.59 × 1.3 - 4 + 3 =?
To find the approximate value, we will first round off the numbers to their nearest whole numbers or to one decimal place if necessary. Then, we will perform the operations following the order of operations (BODMAS/PEMDAS: Brackets, Orders/Exponents, Division/Multiplication, Addition/Subtraction).
The number \(2.59\) can be approximated to \(2.6\) or \(3\). Since the other number is \(1.3\), approximating \(2.59\) to \(2.6\) will give a more accurate result than rounding to \(3\). Let's use \(2.6\).
The number \(1.3\) is already a simple decimal, so we'll keep it as \(1.3\).
The equation is \(2.59 \times 1.3 - 4 + 3 = ?\)
Using the approximated values:
\[ 2.6 \times 1.3 \]\[ 2.6 \times 1.3 = 3.38 \]The equation becomes:
\[ 3.38 - 4 + 3 \]First, \(3.38 - 4\):
\[ 3.38 - 4 = -0.62 \]\[ -0.62 + 3 = 2.38 \]
The calculated value is \(2.38\). We need to find the option closest to \(2.38\).
Comparing \(2.38\) with the options:
The closest value to \(2.38\) is \(2\).
C) The calculated approximate value is \(2.38\), which is closest to \(2\).
The question asks about the chemical compound responsible for the shiny finish on walls after whitewashing with slaked lime. This involves understanding the chemical reactions that occur when slaked lime is applied to walls and exposed to the atmosphere.
Correct Option: D) Calcium carbonate
The shiny finish on walls after whitewashing with slaked lime is due to the formation of calcium carbonate \(( \text{CaCO}_3 )\) through a reaction between calcium hydroxide and atmospheric carbon dioxide.
The problem involves decoding a pattern in a given code language. We need to identify the rule applied to transform the letters of the original word into the coded word. Once the rule is established, we apply it to the target word 'CHAIR' to find its coded form.
Thus, 'CHAIR' will be written as 'DKBLS'.
A) DKBLS is the correct code for 'CHAIR' based on the identified \(+1, +3, +1, +3, +1\) pattern.
The question asks about the Hindu calendar month during which Buddha Purnima is celebrated. This requires knowledge of the Hindu calendar and the specific date of Buddha Purnima.
Correct Option: D) Vaishakha — Buddha Purnima is celebrated on the full moon day of the Vaishakha month in the Hindu calendar.
The question asks to identify the correct objectives of the National Informatics Centre (NIC) from the given options. We need to evaluate each statement based on the known functions and roles of the NIC.
Correct Option: B) A and C