तुलसीदास की भक्ति में प्रेम के महत्व की विवेचना कीजिए।

निम्नलिखित पद्यांशों की ससंदर्भ व्याख्या कीजिए: 
(क) गोरी सोवै सेज पर मुख पर डारे केस।
चल खुसरो घर आपने रैन भई चहुँ देस।।
[खुसरो रैन सोहाग की, जागी पी के संग।
तन मेरो मन पिऊ को दोऊ भए एक रंग।।
(ख) हम न मरें मरिहैं संसारा।
हमको मिला जिआबनहारा।।
साकत मरिहैं संत जन जीवहिं, भरि भरि राम रसायन पीवहिं।
हरि मरिहैं तो हमहुँ मरिहैं, हरि न मरै हम काहे को मरिहैं।
कहे कबीर मन मनहिं मिलावा अमर भया सुखसागर पावां।।
(ग) अंखियां हरि–दरसन की प्यासी।
देखो चाहत कमलनैन को, निसि–दिन रहति उदासी।।
आए जूठी फिरि गए आंगन, डारि गए फांसी।
केसरि तिलक मोतिन की माला, वृन्दावन के बासी।
काहू के मन कोउ न जानत, लोगन के मन हांसी।
सूरदास प्रभु तुम्हरे दरस को करवत लैहौं कासी।।

(घ) खेती न किसान को, भिखारी को न भीख, बलि,
बनिक को बनिज, न चाकर को चाकरी।
जीविका विहीन लोग सीदमान सोच बस,
कहँ एक एकन सों, 'कहाँ जाई, का करी?
बेदहूँ पुरान कही, लोकहूँ बिलोकिअत,
साँ सबै पै, राम! रावर कृपा करी।

दारिद–दसानन दबाई दुनी, दीनबंधु!
दुरित–दहन देखि तुलसी हाहा करी।।

The following table shows the concentration of a new antibiotic, the total number of infected subjects, and the number of subjects who showed complete recovery:

(i) Fit a logistic regression model considering ẞ=-2.148 and ẞ = 0.36, as the initial values of the parameters. Perform calculations for only one iteration using the Newton-Raphson method.

(ii) Test the significance of the fitted model using the Hosmer-Lemeshow test at 5% level of significance.

Fit a simple linear regression model on the data given in Question 2 for non-smokers only and obtain the followings:

(i) Diagonal of the hat matrix. Also, check the leverage points, if any.

(ii) Cook's Distances. Also, verify the influence points, if any.

A logistics company wants to predict the delivery efficiency score of its drivers based on two primary factors: years of driving experience and average hours of sleep per night. The data for 10 drivers are recorded as follows:

Based on the image provided, here is the data transcribed into a table format:

Evaluate all possible regression models using adjusted R² and AIC. Also, obtain best subset model.

To investigate the effect of Age (in years) and Smoking Status (Group 1: Non-Smokers, Group 2: Smokers) on Systolic Blood Pressure (in mmHg), the following data were collected:

The text from the table in the image is provided below:

(i) Fit a multiple regression model.

(ii) Obtain the individual regression models for Non-Smokers and Smokers separately based on the main model.

(iii) Test the significance of the overall fitted regression model at the 5% level of significance.

State whether the following statements are true or false and also give the reason in support of your answer.

(i) The model Y = BX + & is a linear model.

(ii) If total and residual sum of squares for a dataset are 124 and 15.5, respectively, then the coefficient of determination is 0.875.

(iii) We use Cook's distances to identify the autocorrelation of the error terms.

(iv) If the coefficient of determination for the auxiliary regression model of the explanatory variable X₁ is 0.8, the VIF for X₁ will be 5.

(v) We use baseline category logit models when we have ordered categories of a response variable.

Following data presents a population of 10 clusters of size 3 each. Each cluster represents a bunch of students of standard IV in a school. The marks obtained by students in a competitive test (out of 75 marks) have been shown in the data set. Find the Relative Efficiency (R.E.) of the Cluster Sampling with respect to the Simple Random Sampling without Replacement scheme:

 In a population of size 500, the population mean of the auxiliary variable X was observed to be 834.00. On the basis of a sample of size 40, the following sample values were obtained:

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$y = 740.00; \bar{x} = 865.00; s_y^2 = 9560.00; s_x^2 = 15300.00; s_{yx} = 30540.2.$

Obtain the values of the regression estimate and the ratio estimate of the population mean as obtained on the basis of the sample drawn. $\quad \quad \quad \quad \quad \quad \quad \quad (08)$

 In a population of size 500, the population mean of the auxiliary variable X was observed to be 950.00. On the basis of a sample of size 30, the following sample values were obtained:

Obtain the value of the Ratio estimate of population mean as obtained on the basis of the sample drawn. Also, find the estimated value of the Sample Mean Squared Error of the estimate.

State whether the following statements are true or false and also give the reason in support of your answer: 
a) In Two-Stage Sampling if , it becomes the Cluster Sampling.
b) Among all the members of the General Class of the estimators only Product estimator is an unbiased estimator of the Population mean.
c) With the following parameters , an Incomplete Block Design is found to be a Balanced Incomplete Block Design.
d) a 2³ Factorial design is One-half fractional factorial design of a 2⁶ full factorial design.
e) If M_i and  are correlated, the Cluster estimator  becomes an unbiased estimator of the Population Mean.

Write a Python program using NumPy to
(i) Create following two matrices P and Q with following elements.
$
(ii) Compute the (a) Addition, (b) Multiplication, (c) Determinant and (d) Inverse of these matrices.
(iii) Combine the given matrices row-wise and determine the transpose of the combined matrix.
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Would you like me to write the actual Python code to solve these problems for you?

What are different ways to create a NumPy array? Explain any two with examples.

Describe any two Python libraries used for data visualization.

 Describe the while loop with an example program.

Explain how file handling works in Python for text files. Mention different file modes, and a short description of read(), readline() and write().

 Describe the key features of Spyder.

Write a Python program to accept a list of tuples (product_name, price) for 5 items from the user, then sort the list by price in descending order using a function.

Find and correct the error in the following code.

import numpy as np

arr = np.array[4, 5, 6]

print(arr)

Write the output of the following Python code.

nums = [10, 20, 30, 40, 50]

print(nums[-2])

Consider the following table for the connections between the input neurons and the hidden layer neurons