This is a logical reasoning problem involving arrangement based on given conditions. We need to determine the travel month for each person to find out who travelled in July. We will use a table to map persons to months and deduce the arrangement step-by-step.
| Month | Person |
|---|---|
| January | |
| February | |
| March | |
| July | |
| September | |
| December |
| Month | Person |
|---|---|
| January | |
| February | |
| March | |
| July | |
| September | Prem |
| December |
| Month | Person |
|---|---|
| January | |
| February | |
| March | |
| July | Uma |
| September | Prem |
| December |
| Month | Person |
|---|---|
| January | |
| February | |
| March | |
| July | |
| September | Prem |
| December | Uma |
| Month | Person |
|---|---|
| January | |
| February | |
| March | |
| July | Uma |
| September | Prem |
| December |
| Month | Person |
|---|---|
| January | Tarun |
| February | Amit |
| March | |
| July | Uma |
| September | Prem |
| December |
| Month | Person |
|---|---|
| January | Tarun |
| February | Amit |
| March | Shyam |
| July | Uma |
| September | Prem |
| December | Ram |
| Month | Person |
|---|---|
| January | |
| February | Tarun |
| March | Amit |
| July | Uma |
| September | Prem |
| December |
| Month | Person |
|---|---|
| January | |
| February | |
| March | |
| July | |
| September | Prem |
| December | Uma |
| Month | Person |
|---|---|
| January | Tarun |
| February | Amit |
| March | |
| July | |
| September | Prem |
| December | Uma |
| Month | Person |
|---|---|
| January | |
| February | Tarun |
| March | Amit |
| July | |
| September | Prem |
| December | Uma |
| Month | Person |
|---|---|
| January | Tarun |
| February | Amit |
| March | Shyam |
| July | Uma |
| September | Prem |
| December | Ram |
A) Shyam — Shyam travelled in March, not July.
The question asks for the definition of the focal length of a spherical mirror. We need to recall the standard definitions of key terms associated with spherical mirrors, such as pole, principal focus, and centre of curvature.
C) pole and principal focus. This is the standard definition of focal length for a spherical mirror. The distance between the pole (P) and the principal focus (F) is called the focal length (\(f\)).
The question asks to identify the incorrect statement regarding magnetic field lines outside a bar magnet. We need to recall the fundamental properties of magnetic field lines to evaluate each option.
The question asks for the INCORRECT statement.
Correct Option: C) Field lines intersect each other. — This statement is incorrect because magnetic field lines never intersect. If they did, it would imply two directions for the magnetic field at a single point, which is impossible.
To find the initial word/cluster that appears exactly in the middle, we need to follow two steps:
EIKL, EILV, ELOV, EILM, CKLU
Comparing the clusters letter by letter:
So, the alphabetically sorted list of new clusters is:
There are 5 words in the list. The middle word will be the \(\left(\frac{5+1}{2}\right)^{\text{th}}\) word, which is the 3rd word.
The 3rd word in the sorted list is EILM.
The cluster EILM was formed from the original word LIME.
B) LIME is the initial word whose rearranged cluster (EILM) appears exactly in the middle of the alphabetically sorted list of new clusters.
The question asks about the normal breathing rate of an adult human at rest. This is a factual question related to human physiology. We need to recall the typical range for respiratory rate.
C) 15–18. This range is considered normal for an adult human breathing at rest. A respiratory rate between 12 and 20 breaths per minute is generally accepted as healthy for adults.
To determine which element has the highest atomic radius among the given options, we need to understand the trends of atomic radius in the periodic table. Atomic radius generally decreases across a period from left to right and increases down a group.
Atomic radius generally decreases as we move from left to right across a period. This is because the number of protons (nuclear charge) increases, pulling the valence electrons closer to the nucleus, while the number of electron shells remains the same. The order of elements in Period 2 from left to right is Li, Be, N, O.
Based on the trend, Lithium (Li) is the leftmost element among the given options in Period 2. Therefore, it will have the largest atomic radius.
The atomic radius decreases in the order: Li > Be > N > O.
C) Li has the highest atomic radius among the given options because it is the leftmost element in Period 2, where atomic radius decreases from left to right.
Roots of the equation x² = 24 – 10x are:
To find the roots of the given quadratic equation, we first need to rearrange it into the standard form \(ax^2 + bx + c = 0\). Once in standard form, we can solve for the roots using either factorization (splitting the middle term) or the quadratic formula.
The given equation is \(x^2 = 24 - 10x\). To bring it to the standard quadratic form \(ax^2 + bx + c = 0\), move all terms to one side:
\[ x^2 + 10x - 24 = 0 \]Here, \(a=1\), \(b=10\), and \(c=-24\).
We need to find two numbers that multiply to \(ac = 1 \times (-24) = -24\) and add up to \(b = 10\). These numbers are \(12\) and \(-2\) because \(12 \times (-2) = -24\) and \(12 + (-2) = 10\).
Now, split the middle term (\(10x\)) using these numbers:
\[ x^2 + 12x - 2x - 24 = 0 \]Group the terms and factor out common factors:
\[ (x^2 + 12x) - (2x + 24) = 0 \] \[ x(x + 12) - 2(x + 12) = 0 \]Now, factor out \((x + 12)\):
\[ (x + 12)(x - 2) = 0 \]For the product of two factors to be zero, at least one of the factors must be zero.
\[ x + 12 = 0 \quad \text{or} \quad x - 2 = 0 \] \[ x = -12 \quad \text{or} \quad x = 2 \]Thus, the roots of the equation are \(2\) and \(-12\).
Correct Option: A) 2, –12
The question asks to identify the committee constituted by the RBI in the wake of the 2010 Andhra Pradesh microfinance crisis to address issues in the Microfinance Institutions (MFI) sector. This requires knowledge of significant committees and their mandates related to financial regulation in India.
B) Malegam Committee — The Reserve Bank of India (RBI) constituted a Sub-Committee of its Central Board, chaired by Mr. Y.H. Malegam, in October 2010. This committee was tasked with studying issues and concerns in the Microfinance Institutions (MFI) sector in India, particularly in the aftermath of the Andhra Pradesh microfinance crisis. Its recommendations were crucial in shaping the regulatory framework for MFIs.
This problem can be solved by using the algebraic identity for \((a-b)^2\), which relates \((a-b)\), \((a^2+b^2)\), and \(ab\). We are given the values of \((a-b)\) and \((a^2+b^2)\), and we need to find the value of \(ab\).
The relevant algebraic identity is:
\[ (a - b)^2 = a^2 + b^2 - 2ab \]We are given \((a - b) = 8\) and \((a^2 + b^2) = 160\). Substitute these values into the identity:
\[ (8)^2 = 160 - 2ab \]Calculate the square of 8:
\[ 64 = 160 - 2ab \]Move the term \(2ab\) to one side and the constants to the other:
\[ 2ab = 160 - 64 \]\[ 2ab = 96 \]Divide both sides by 2 to find the value of \(ab\):
\[ ab = \frac{96}{2} \]\[ ab = 48 \]Correct Option: D) 48
The question asks to identify the committee specifically constituted for the promotion of small scale industries in India. This requires knowledge of various committees formed by the Indian government and their respective mandates.
D) Karve Committee
The Karve Committee, also known as the Village and Small Scale Industries Committee, was constituted in 1955. Its primary objective was to suggest measures for the promotion and development of village and small-scale industries. The recommendations of this committee were instrumental in shaping India's Second Five Year Plan (1956-1961) with a strong emphasis on the growth of small-scale industries to generate employment and ensure equitable distribution of wealth.