‘Emotional intelligence’ (EI) refers to the ability to recognize, understand, and manage one’s own emotions, as well as the emotions of others. It encompasses skills such as emotional awareness, empathy, and effective communication, distinguishing it from cognitive intelligence (IQ).

The utility of emotional intelligence is significant across various domains. In personal relationships, EI enhances communication and fosters empathy, leading to stronger connections. In the workplace, individuals with high EI are often better leaders, as they can motivate teams, resolve conflicts, and create a positive work environment. Additionally, EI contributes to mental well-being, enabling individuals to manage stress and navigate challenges effectively. Overall, emotional intelligence is crucial for personal growth and professional success, as it enhances interpersonal interactions and emotional regulation.

In contemporary administration, transparency is crucial for fostering trust between the government and citizens. It ensures that processes, decisions, and policies are clear and accessible, reducing opportunities for corruption and misuse of power. When administrative actions are open to scrutiny, public accountability increases, empowering citizens to participate actively in governance.

For instance, initiatives like the Right to Information (RTI) Act allow citizens to request information, enhancing governmental openness. Transparency also facilitates informed decision-making by citizens, as they can understand the rationale behind policies. Moreover, transparent governance contributes to a more effective administration by promoting efficiency and ethical behavior. Ultimately, transparency strengthens democracy by ensuring that public officials remain answerable to the populace.

The total amount of ₹ 15,02,000 is divided among A, B, and C in the ratio $5:7:85:7:8$5:7:8.

1. Calculating Individual Shares:
   • Total parts = $5+7+8=205\; +\; 7\; +\; 8\; =\; 20$5+7+8=20
   • Amount for $AA$A: $A=\frac{5}{20}\times 15,02,000=₹3,75,500A\; =\; \backslash frac\{5\}\{20\}\; \backslash times\; 15,02,000\; =\; ₹\; 3,75,500$A=205​×15,02,000=₹3,75,500
   • Amount for $CC$C: $C=\frac{8}{20}\times 15,02,000=₹6,00,800C\; =\; \backslash frac\{8\}\{20\}\; \backslash times\; 15,02,000\; =\; ₹\; 6,00,800$C=208​×15,02,000=₹6,00,800
2. Calculating Simple Interest:
   • For A (4% for 2 years):

     $A_{}=\frac{P\times r\times t}{100}=\frac{3,75,500\times 4\times 2}{100}=₹3,006\backslash text\{SI\}\_A\; =\; \backslash frac\{P\; \backslash times\; r\; \backslash times\; t\}\{100\}\; =\; \backslash frac\{3,75,500\; \backslash times\; 4\; \backslash times\; 2\}\{100\}\; =\; ₹\; 3,006$SIA​=100P×r×t​=1003,75,500×4×2​=₹3,006

   • For C (6% for 5 years):

     $C_{}=\frac{P\times r\times t}{100}=\frac{6,00,800\times 6\times 5}{100}=₹1,80,240\backslash text\{SI\}\_C\; =\; \backslash frac\{P\; \backslash times\; r\; \backslash times\; t\}\{100\}\; =\; \backslash frac\{6,00,800\; \backslash times\; 6\; \backslash times\; 5\}\{100\}\; =\; ₹\; 1,80,240$SIC​=100P×r×t​=1006,00,800×6×5​=₹1,80,240

Conclusion: The simple interest obtained by A is ₹ 3,006, and by C is ₹ 1,80,240.

To find the coordinates of point $DD$D that divides the line segment $ACAC$AC in the ratio $1:31:3$1:3:

Using the section formula, the coordinates of $DD$D are:

$D(\frac{1\cdot 6+3\cdot 0}{1+3},\frac{1\cdot 0+3\cdot 4}{1+3})=D(\frac{6}{4},\frac{12}{4})=D(1.5,3)D\backslash left(\; \backslash frac\{1\; \backslash cdot\; 6\; +\; 3\; \backslash cdot\; 0\}\{1\; +\; 3\},\; \backslash frac\{1\; \backslash cdot\; 0\; +\; 3\; \backslash cdot\; 4\}\{1\; +\; 3\}\; \backslash right)\; =\; D\backslash left(\; \backslash frac\{6\}\{4\},\; \backslash frac\{12\}\{4\}\; \backslash right)\; =\; D(1.5,\; 3)$D(1+31⋅6+3⋅0​,1+31⋅0+3⋅4​)=D(46​,412​)=D(1.5,3)

Next, we calculate the area of triangles $ABDABD$ABD and $ABCABC$ABC:

1. Area of triangle $ABCABC$ABC:

${ABC}_{}=\frac{1}{2}\mid 0(3-0)+1(0-4)+6(4-3)\mid =\frac{1}{2}\mid 0-4+6\mid =\frac{1}{2}\times 2=1\backslash text\{Area\}\_\{ABC\}\; =\; \backslash frac\{1\}\{2\}\; \backslash left|\; 0(3-0)\; +\; 1(0-4)\; +\; 6(4-3)\; \backslash right|\; =\; \backslash frac\{1\}\{2\}\; \backslash left|\; 0\; –\; 4\; +\; 6\; \backslash right|\; =\; \backslash frac\{1\}\{2\}\; \backslash times\; 2\; =\; 1$AreaABC​=21​∣0(3−0)+1(0−4)+6(4−3)∣=21​∣0−4+6∣=21​×2=1

1. Area of triangle $ABDABD$ABD:

${ABD}_{}=\frac{1}{2}\mid 0(3-3)+1(3-4)+1.5(4-3)\mid =\frac{1}{2}\mid 0-1+1.5\mid =\frac{1}{2}\times 0.5=0.25\backslash text\{Area\}\_\{ABD\}\; =\; \backslash frac\{1\}\{2\}\; \backslash left|\; 0(3-3)\; +\; 1(3-4)\; +\; 1.5(4-3)\; \backslash right|\; =\; \backslash frac\{1\}\{2\}\; \backslash left|\; 0\; –\; 1\; +\; 1.5\; \backslash right|\; =\; \backslash frac\{1\}\{2\}\; \backslash times\; 0.5\; =\; 0.25$AreaABD​=21​∣0(3−3)+1(3−4)+1.5(4−3)∣=21​∣0−1+1.5∣=21​×0.5=0.25

Thus, the ratio of the areas is:

${ABD}_{}:{ABC}_{}=0.25:1=1:4\backslash text\{Area\}\_\{ABD\}\; :\; \backslash text\{Area\}\_\{ABC\}\; =\; 0.25\; :\; 1\; =\; 1\; :\; 4$AreaABD​:AreaABC​=0.25:1=1:4

Conclusion: The coordinates of point $DD$D are $(1.5,3)(1.5,\; 3)$(1.5,3), and the area ratio of triangle $ABDABD$ABD to triangle $ABCABC$ABC is $1:41:4$1:4.