In a class test, a certain number of students got different ranks based on their marks. Anshu is ranked 19th from the top. 6 students are ranked after Anshu. How many total students gave the test?
To find the total number of students, we need to sum the number of students ranked before Anshu, Anshu herself, and the number of students ranked after Anshu.
Let \(N_{\text{before}}\) be the number of students before Anshu.
Let \(N_{\text{after}}\) be the number of students after Anshu.
Let \(N_{\text{Anshu}}\) be Anshu herself (which is 1).
The total number of students (\(N_{\text{total}}\)) is given by:
\[ N_{\text{total}} = N_{\text{before}} + N_{\text{Anshu}} + N_{\text{after}} \]
From the problem statement:
Substitute these values into the formula:
\[ N_{\text{total}} = 18 + 1 + 6 \]\[ N_{\text{total}} = 19 + 6 \]\[ N_{\text{total}} = 25 \]
Therefore, there are 25 total students who gave the test.
Correct Option: D) 25
Study the given line graph and answer the following question.
The given line graph depicts the number of boys and girls in three schools (P, Q and R).
What is the average number of boys in the given three schools?
To find the average number of boys in the three schools, we need to sum the number of boys in each school and divide by the total number of schools.
\[ \text{Total boys} = 200 + 90 + 190 = 480 \]
\[ \text{Average boys} = \frac{\text{Total boys}}{\text{Number of schools}} = \frac{480}{3} = 160 \]
The average number of boys in the three schools is 160.
Correct Option: A) 160
Simplify
(3x+4)2+(3x−4)2+(3x+4)(3x−4)
27x2 - 24x + 16
27x2 + 16
27x2 + 48x + 32
27x2 - 16
To simplify the given algebraic expression, we will use the algebraic identities for squares of binomials and the difference of squares. Specifically, we will use:
We will apply these identities to each term in the expression and then combine like terms.
The given expression is:
\[ (3x+4)^2 + (3x-4)^2 + (3x+4)(3x-4) \]Step 1: Simplify the first term \((3x+4)^2\).
Using the identity \((a+b)^2 = a^2 + 2ab + b^2\) with \(a=3x\) and \(b=4\):
\[ (3x+4)^2 = (3x)^2 + 2(3x)(4) + (4)^2 \]\[ = 9x^2 + 24x + 16 \]Step 2: Simplify the second term \((3x-4)^2\).
Using the identity \((a-b)^2 = a^2 - 2ab + b^2\) with \(a=3x\) and \(b=4\):
\[ (3x-4)^2 = (3x)^2 - 2(3x)(4) + (4)^2 \]\[ = 9x^2 - 24x + 16 \]Step 3: Simplify the third term \((3x+4)(3x-4)\).
Using the identity \((a+b)(a-b) = a^2 - b^2\) with \(a=3x\) and \(b=4\):
\[ (3x+4)(3x-4) = (3x)^2 - (4)^2 \]\[ = 9x^2 - 16 \]Step 4: Combine all the simplified terms.
Substitute the simplified terms back into the original expression:
\[ (9x^2 + 24x + 16) + (9x^2 - 24x + 16) + (9x^2 - 16) \]Now, combine the like terms:
Combine \(x^2\) terms:
\[ 9x^2 + 9x^2 + 9x^2 = 27x^2 \]Combine \(x\) terms:
\[ 24x - 24x = 0x = 0 \]Combine constant terms:
\[ 16 + 16 - 16 = 16 \]So, the simplified expression is:
\[ 27x^2 + 0 + 16 = 27x^2 + 16 \]B) \(27x^2 + 16\) is the correct simplification of the given expression.
Double displacement reaction takes place with:
i) Precipitates are formed.
ii) Evolution of a gas
iii) Change in colour
The question asks about the characteristics of a double displacement reaction. We need to identify which of the given observations (formation of precipitates, evolution of gas, change in colour) are typical outcomes of such reactions.
D) Only i and ii — Double displacement reactions are characterized by the formation of precipitates and/or the evolution of a gas. A change in colour can happen but is not a universal characteristic that defines these reactions.
The element ‘x’ in modern periodic table has an electronic configuration 2, 8, 8. The element ‘x’ is placed in the:
To determine the group of an element in the modern periodic table, we need to know its electronic configuration. The group number is primarily determined by the number of valence electrons (electrons in the outermost shell) for main group elements. For elements with completely filled outermost shells, they belong to the noble gas group.
C) 18th group. The electronic configuration 2, 8, 8 indicates that the outermost shell has 8 electrons, which is a stable octet. Elements with a stable octet in their outermost shell (except Helium) are noble gases, and they are placed in the 18th group of the modern periodic table.
The question asks to identify the Chairman of the National Planning Committee set up by Subhash Chandra Bose in 1938. This is a factual question related to Indian history, specifically the pre-independence era and the Indian National Congress.
Correct Option: A) Jawaharlal Nehru was indeed the Chairman of the National Planning Committee established by Subhash Chandra Bose in 1938. Nehru was a strong proponent of economic planning and played a crucial role in shaping India's post-independence economic policies.
Find the median of the given frequency distribution.
| Class Interval | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 |
| f | 8 | 7 | 9 | 12 | 11 |
\( \frac{215}{9} \)
\( \frac{85}{3} \)
\(\frac{265}{9}\)
\(\frac{88}{3}\)
To find the median of a grouped frequency distribution, we first need to calculate the cumulative frequencies. Then, we identify the median class, which is the class interval containing the \((N/2)\)-th observation. Finally, we use the median formula for grouped data.
| Class Interval | Frequency (f) | Cumulative Frequency (cf) |
|---|---|---|
| 0-10 | 8 | 8 |
| 10-20 | 7 | 8 + 7 = 15 |
| 20-30 | 9 | 15 + 9 = 24 |
| 30-40 | 12 | 24 + 12 = 36 |
| 40-50 | 11 | 36 + 11 = 47 |
Correct Option: C) \( \frac{265}{9} \)
Study the given letter series and answer the question that follows.
(Left) H A D W V Q T S P E R S T K E L M T (Right)
How many such vowels are there each of which is immediately preceded by a consonant and also immediately followed by a consonant?
The problem asks us to count the number of vowels in a given letter series that satisfy two conditions: they must be immediately preceded by a consonant and immediately followed by a consonant. We need to systematically scan the series, identify vowels, and then check their preceding and succeeding letters.
H A D (C-V-C) - Count = 1
W V Q T S P E R S (C-V-C) - Count = 2
T K E L M (C-V-C) - Count = 3
The other vowels in the series are 'A' (in HAD), 'E' (in PERS), and 'E' (in KELM). All these instances fit the criteria.
Therefore, there are 3 such vowels.
B) 3 is the correct answer because we found three instances where a vowel is immediately preceded by a consonant and immediately followed by a consonant.
As per Reserve Bank of India (Regulatory Framework for Microfinance Loans) Directions, 2022, a microfinance loan is defined as a collateral-free loan given to a household having annual household income up to ________. For this purpose, the household shall mean an individual family unit, i.e., husband, wife, and their unmarried children
The question asks for the annual household income limit for a microfinance loan as per the RBI (Regulatory Framework for Microfinance Loans) Directions, 2022. This requires knowledge of the specific guidelines issued by the Reserve Bank of India.
D) Rs 3,00,000 is the correct annual household income limit for a microfinance loan as per the RBI (Regulatory Framework for Microfinance Loans) Directions, 2022.
In February 2022, which of the following became the 1st state in the country to launch night navigation mobile app in rivers?
The question asks to identify the first state in India to launch a night navigation mobile app for rivers in February 2022. This is a factual question related to current affairs and technological advancements in state administration.
B) Assam — Assam launched the night navigation mobile app for ferry services on the Brahmaputra River in February 2022, making it the first state in the country to do so. The app aims to prevent collisions and improve safety during night-time navigation on rivers.