We are given the mean of the 5 smallest numbers and the mean of all 13 numbers in a group. We need to find the mean of the remaining 8 largest numbers. We will use the definition of the mean (average) to calculate the sum of numbers in each group and then find the sum of the 8 largest numbers, from which we can calculate their mean.
Correct Option: D) 21.25
To solve this problem, we need to follow the order of operations, often remembered by the acronym PEMDAS/BODMAS (Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). We will work from the innermost brackets outwards.
First, evaluate the innermost parenthesis: \((89 - 72 \div 9 \times 6)\).
Inside this, we perform division and multiplication from left to right.
\[ 72 \div 9 = 8 \]\[ 8 \times 6 = 48 \]Substitute this value back into the parenthesis:
\[ 89 - 48 = 41 \]Now, substitute this result back into the curly braces: \({53 - (41)}\).
\[ 53 - 41 = 12 \]Next, substitute this result back into the square brackets: \([35 - {12}]\).
\[ 35 - 12 = 23 \]Finally, perform the division operation:
\[ 138 \div 23 \]\[ 138 \div 23 = 6 \]B) The final calculated value is 6.
The question asks about the factors affecting the resistivity of a conductor. Resistivity is an intrinsic property of a material, meaning it depends on the fundamental nature of the substance itself rather than its physical dimensions.
A) Material β Resistivity is an intrinsic property of the material itself. Different materials have different resistivities due to their atomic structure and electron availability.
The problem involves simple interest calculations. We are given two scenarios for the amount received after 5 years, differing only by a 2% increase in the annual simple interest rate. We need to find the original principal sum. We will use the formula for simple interest and amount to set up equations and solve for the principal.
Let the original principal be \(P\), the time be \(T = 5\) years, and the original simple interest rate be \(R\) percent per annum.
The formula for simple interest is:
\[ \text{Simple Interest (SI)} = \frac{P \times R \times T}{100} \]The formula for the amount is:
\[ \text{Amount (A)} = P + \text{SI} = P + \frac{P \times R \times T}{100} = P \left(1 + \frac{R \times T}{100}\right) \]In the first scenario, the amount after 5 years is Rs. 5,250. So, we have:
\[ 5250 = P \left(1 + \frac{R \times 5}{100}\right) \]\[ 5250 = P \left(1 + \frac{5R}{100}\right) \quad \text{(Equation 1)} \]In the second scenario, the simple interest rate is \(R + 2\) percent per annum, and the amount is Rs. 5,600. So, we have:
\[ 5600 = P \left(1 + \frac{(R+2) \times 5}{100}\right) \]\[ 5600 = P \left(1 + \frac{5R + 10}{100}\right) \quad \text{(Equation 2)} \]Now, let's expand Equation 2:
\[ 5600 = P \left(1 + \frac{5R}{100} + \frac{10}{100}\right) \]\[ 5600 = P \left(1 + \frac{5R}{100}\right) + P \left(\frac{10}{100}\right) \]From Equation 1, we know that \(P \left(1 + \frac{5R}{100}\right) = 5250\). Substitute this into the expanded Equation 2:
\[ 5600 = 5250 + P \left(\frac{10}{100}\right) \]\[ 5600 - 5250 = P \left(\frac{10}{100}\right) \]\[ 350 = P \left(\frac{1}{10}\right) \]Solve for \(P\):
\[ P = 350 \times 10 \]\[ P = 3500 \]Thus, the original sum invested was Rs. 3,500.
D) 3,500
The question asks for the specific biological process where sperm and ova fuse to form a zygote. We need to identify the term that precisely describes this event from the given options.
Correct Option: B) Fertilisation
Fertilisation is the process by which male and female gametes (sperm and ova) fuse to form a single cell called a zygote. This is a crucial step in sexual reproduction, initiating the development of a new organism.
The given sequence is an arithmetic progression (AP). We need to find the sum of the first 10 terms. We will first identify the first term and the common difference, and then use the formula for the sum of the first \(n\) terms of an AP.
Identify the first term (\(a\)) and common difference (\(d\)):
The given sequence is \(-3, -8, -13, -18, \dots\)
The first term is \(a = -3\).
The common difference \(d\) is the difference between any term and its preceding term:
\[ d = -8 - (-3) = -8 + 3 = -5 \]\[ d = -13 - (-8) = -13 + 8 = -5 \]\[ d = -18 - (-13) = -18 + 13 = -5 \]Identify the number of terms (\(n\)):
We need to find the sum of the first 10 terms, so \(n = 10\).
Use the formula for the sum of the first \(n\) terms of an AP:
The formula for the sum of the first \(n\) terms of an arithmetic progression is:
\[ S_n = \frac{n}{2} [2a + (n-1)d] \]Substitute the values into the formula:
Substitute \(a = -3\), \(d = -5\), and \(n = 10\) into the formula:
\[ S_{10} = \frac{10}{2} [2(-3) + (10-1)(-5)] \]\[ S_{10} = 5 [-6 + (9)(-5)] \]\[ S_{10} = 5 [-6 - 45] \]\[ S_{10} = 5 [-51] \]\[ S_{10} = -255 \]C) -255 is the correct sum of the first 10 terms of the given arithmetic progression.
This is a problem involving inverse proportion. The total amount of wheat available is fixed. The consumption rate depends on the number of students. When the number of students increases, the number of days the remaining wheat will last decreases. We will first calculate the total wheat consumed in the initial period, then find the remaining wheat. Finally, we will calculate how many days this remaining wheat will last for the increased number of students.
Correct Option: B) 15 days is the correct answer. The balance wheat will feed the students for 15 days.
Who took oath on 23rd January 2018 as the Governor of Madhya Pradesh?
Om Prakash Kohli
Kumud Ben Joshi
Ram Naresh Yadav
Anandiben Patel
The question asks to identify the Governor of Madhya Pradesh who took office on January 23, 2018. This requires knowledge of political appointments and current affairs relevant to that period.
On January 23, 2018, Anandiben Patel was sworn in as the Governor of Madhya Pradesh. She succeeded Om Prakash Kohli, who was holding additional charge of the state.
D) Anandiben Patel β She took oath as the Governor of Madhya Pradesh on January 23, 2018.
The question asks for the term used to describe sound generated by a single frequency. We need to understand the basic definitions of sound properties.
Correct Option: A) A tone is a sound characterized by a single, definite frequency. When a sound wave consists of only one frequency, it is referred to as a pure tone.
The question asks to identify the recipient of the Saraswati Samman Award for the year 2016. This is a factual question related to awards and honors, which requires knowledge of current affairs and literary awards.
C) Mahabaleshwar Sail β Mahabaleshwar Sail, a prominent Konkani writer, was awarded the Saraswati Samman for 2016 for his novel 'Hawthan'.