A और B की कार्य क्षमता निम्नलिखित है:

A अकेले 7 दिन में पूरा करता है, इसलिए A की कार्य क्षमता =
1
7
7
1
​
कार्य/दिन।
B अकेले 14 दिन में पूरा करता है, इसलिए B की कार्य क्षमता =
1
14
14
1
​
कार्य/दिन।
दोनों मिलकर दो दिन काम करते हैं:

A + B की संयुक्त कार्य क्षमता
=
1
7
+
1
14
=
2
14
+
1
14
=
3
14
कार्य/दिन
A + B की संयुक्त कार्य क्षमता=
7
1
​
+
14
1
​
=
14
2
​
+
14
1
​
=
14
3
​
कार्य/दिन
दो दिन काम करने पर:

कुल कार्य
=
2
×
3
14
=
6
14
=
3
7
कुल कार्य=2×
14
3
​
=
14
6
​
=
7
3
​

बचे हुए कार्य =
1
−
3
7
=
4
7
1−
7
3
​
=
7
4
​

अब C कार्य में शामिल होता है और तीनों मिलकर कार्य को पूरा करते हैं। मान लीजिए C की कार्य क्षमता
1
𝑥
x
1
​
कार्य/दिन है।

अतः:

3
14
+
1
𝑥
=
1
1
(एक दिन में पूरा)
14
3
​
+
x
1
​
=
1
1
​
(एक दिन में पूरा)
1
𝑥
=
1
−
3
14
=
11
14
x
1
​
=1−
14
3
​
=
14
11
​

तो,

𝑥
=
14
11
दिन
x=
11
14
​
दिन
इसलिए, C अकेले
14
11
11
14
​
दिन में कार्य पूरा करेगा।

To solve this problem using a Venn diagram:

Define the Sets:

𝑀
M: Students studying Maths (270)
𝐹
F: Students studying French (300)
𝐵
B: Students studying Business Studies (50)
Given Data:

All Maths students also study French:
∣
𝑀
∩
𝐹
∣
=
270
∣M∩F∣=270
Students studying both Maths and Business Studies:
∣
𝑀
∩
𝐵
∣
=
20
∣M∩B∣=20
Students studying both French and Business Studies:
∣
𝐹
∩
𝐵
∣
=
35
∣F∩B∣=35
Calculate Intersections:

Students studying all three subjects:
∣
𝑀
∩
𝐹
∩
𝐵
∣
=
20
∣M∩F∩B∣=20
Students studying only French and Business Studies:
∣
𝐹
∩
𝐵
∣
−
∣
𝑀
∩
𝐹
∩
𝐵
∣
=
35
−
20
=
15
∣F∩B∣−∣M∩F∩B∣=35−20=15
Students studying only French:

Total studying French:
300
−
270
−
15
=
15
300−270−15=15
Probability:

Students studying only French = 15
Total students = 400
𝑃
(
only French
)
=
15
400
=
3
80
P(only French)=
400
15
​
=
80
3
​

Thus, the probability that the selected student studies French but neither Maths nor Business Studies is
3
80
80
3
​
.

त्रिभुज ABC का क्षेत्रफल
1
2
×
base
×
height
2
1
​
×base×height से दिया जाता है।

बिंदु B(1, 2) और C(2, 3) के बीच की दूरी =
(
2
−
1
)
2
+
(
3
−
2
)
2
=
2
(2−1)
2
+(3−2)
2

​
=
2
​
.

क्षेत्रफल = 4 वर्ग इकाई, तो:

1
2
×
2
×
ℎ
=
4
  
⟹
  
ℎ
=
8
2
=
4
2
.
2
1
​
×
2
​
×h=4⟹h=
2
​

8
​
=4
2
​
.
चूंकि A रेखा
2
𝑥
+
𝑦
−
2
=
0
2x+y−2=0 पर है, इसे
𝑦
=
−
2
𝑥
+
2
y=−2x+2 में व्यक्त किया जा सकता है।

इससे
ℎ
=
∣
𝐴
𝑥
1
+
𝐵
𝑦
1
+
𝐶
∣
/
𝐴
2
+
𝐵
2
h=∣Ax
1
​
+By
1
​
+C∣/
A
2
+B
2

​
से
𝐴
A के निर्देशांक मिलेंगे।

समीकरण हल करने पर
𝐴
(
0
,
2
)
A(0,2) या
𝐴
(
1
,
0
)
A(1,0) मिलते हैं।

अतः शीर्ष A के निर्देशांक हैं (0, 2) और (1, 0)।

मान लीजिए, एक कमीज का खरीद मूल्य
𝐶
C है।

तो, 150 कमीजों का खरीद मूल्य:
150
𝐶
150C

यदि 120 कमीजों का विक्रय मूल्य
𝑆
S है, तो:

𝑆
=
150
𝐶
120
=
1.25
𝐶
(
एक कमीज के लिए
)
S=
120
150C
​
=1.25C(एक कमीज के लिए)
लाभ = विक्रय मूल्य – खरीद मूल्य =
1.25
𝐶
−
𝐶
=
0.25
𝐶
1.25C−C=0.25C

लाभ प्रतिशत =
0.25
𝐶
𝐶
×
100
=
25
%
C
0.25C
​
×100=25%

इसलिए, लाभ 25% है।

Communal tensions had a profound impact on the constitutional development and political landscape in India during the late 19th and early 20th centuries. Here are several key ways these tensions influenced the situation:

1. Separate Electorates

• Institutionalization of Division: The introduction of separate electorates for Muslims in the Government of India Act of 1909 and subsequently for other communities institutionalized communal divisions in the political process. This reinforced the notion of communal identities over national unity, leading to further polarization.
• Political Fragmentation: The separate electorates fostered a fragmented political landscape, encouraging parties to cater to specific communal interests rather than pursuing a unified national agenda. This made it difficult to build coalitions that could represent broader Indian interests.

2. Influence on Political Parties

• Rise of the Muslim League: The increasing communal tensions contributed to the strengthening of the All India Muslim League, which advocated for Muslim political rights and ultimately led to the demand for a separate nation. This shift created a competitive and adversarial political environment.
• Diminishing INC Unity: The Indian National Congress (INC), initially a broad-based national party, faced challenges in maintaining cohesion as communal tensions escalated. The INC’s attempts to appeal to both Hindus and Muslims often resulted in internal conflicts and weakened its overall influence.

3. Constitutional Reforms and Compromises

• Failure of Inclusive Reforms: Efforts to create a unified constitutional framework often failed due to communal tensions. For example, the Cripps Mission in 1942 proposed constitutional changes but could not adequately address the concerns of both the INC and the Muslim League, leading to its rejection.
• Communal Riots and Reactions: Major communal riots, such as those in the 1940s, further entrenched divisions and made British authorities hesitant to implement reforms that might escalate tensions. This led to a cautious approach to constitutional development, often prioritizing stability over genuine representation.

4. Impact on Nationalist Movements

• Diversion of Focus: The rise of communal politics diverted attention from anti-colonial struggles, as parties focused more on communal issues than on a united fight for independence. This often resulted in a fragmented nationalist movement.
• Demand for Partition: Communal tensions culminated in the demand for partition, as the Muslim League’s call for a separate state grew stronger. This was a direct response to perceived inadequacies in representing Muslim interests within a unified India.

5. Role of Colonial Administration

• Divide and Rule Policy: The British colonial government often exacerbated communal tensions through a “divide and rule” strategy, manipulating divisions for political gain. This approach reinforced communal identities and weakened nationalist unity.
• Communal Representation: British policies that favored certain communities over others further entrenched communal identities in the political landscape, making it challenging to foster a sense of Indian nationalism.

6. Constitutional Framework Post-Independence

• Communal Violence and Partition: The legacy of communal tensions directly influenced the constitutional framework adopted post-independence. The partition of India in 1947, marked by widespread communal violence, necessitated a complex approach to governance that sought to address communal identities.
• Secularism and Minority Rights: The new Indian constitution enshrined secularism and minority rights as a response to communal tensions, reflecting an attempt to create a framework that could accommodate India’s diverse population while promoting national unity.

Conclusion

Communal tensions significantly affected constitutional development and the political landscape in India by fostering divisions, influencing party dynamics, and complicating the path to independence. These tensions not only shaped the nature of political negotiations and reforms but also had lasting implications for the formation of independent India, including the challenges of communal violence and the need for a secular and inclusive constitutional framework.