What are Inrate Ideas? How Locke criticizes the concept of innate ideas?

Contrast Descartes' and Locke's conceptions of substance with Spineca's.

Explain the idea of causality? How does Hume criticize the idea of causation?

How does Descartes prove the existence of the External world?

Explain and analyze Descartes' method of doubt.

Explain the concept of maximum value function.

What is Kant's view on the Nature of Knowledge? Explain and analyze.

Write a brief essay outlining the key ideas of contemporary Western philosophy.

Evaluate 

Singular matrix

Decomposable matrix

Adjugate of a matrix

Find the maximum value for f(x,y) if x and y are constrained to sum to 1 (That is, x+y= 1). Solve the problem in two ways: by substitution and by using the Lagrangian multiplier method.

Solve the following differential equation

given Y(0) = 4

(1) Find the stationary points of z.

(ii) Determine if at these points the function is at a relative maximum, relative minimum, infixion point, or saddle point

An individual consumer consumes two commodities X₁ & X₂. The utility function is

The price of commodity one is P₁= Rs.3.00, the price of commodity two is P₂=Rs.4.00, the individual's income per period is Rs. 108. Determine the utility maximizing level of X₁ & X₂, and derive the demand curves for the two commodities

Consider the following two matrices

(i) Find the rank of 'A' and 'B'

(ii) Show that (AB)=B^-1A^-1

(iii) Show that (A^-1) ^-1=A

(iv) Show that (B^-1)^-1=B

If you are asked to bring a positive change in learning environments of JNVs, what are the changes that you would like to suggest: (a) to practice a schoolwide positive behavioural intervention, (b) to facilitate parents’ involvement? Describe with examples.

यदि आपसे जवाहर नवोदय विद्यालयों के शिक्षण वातावरण में सकारात्मक परिवर्तन लाने के लिए कहा जाए, तो आप क्या परिवर्तन सुझाना चाहेंगे : (क) विद्यालय स्तर पर सकारात्मक व्यवहारिक हस्तक्षेप का अभ्यास करना, (ख) अभिभावकों की सहभागिता को सुगम बनाना? उदाहरणों सहित वर्णन करें।

What are the factors that some of the teachers do not consider to be important but these factors lead to the exclusion of some students from effective learning in the classroom. Discuss.

वे कौन से कारक हैं जिन्हें कुछ शिक्षक महत्वपूर्ण नहीं मानते लेकिन ये कारक कुछ छात्रों को कक्षा में प्रभावी शिक्षण से वंचित कर देते हैं। चर्चा करें।

A house mistress/master can bring several positive changes to residential units of JNVs. Explain the aforesaid statement by listing the challenges in managing students’ hostels and explain the best practices those can be used in overcoming these challenges.

एक हाउस मिस्ट्रेस/मास्टर जेएनवी की आवासीय इकाइयों में कई सकारात्मक बदलाव ला सकता है। छात्रों के छात्रावासों के प्रबंधन में चुनौतियों को सूचीबद्ध करके उपरोक्त कथन की व्याख्या करें और उन सर्वोत्तम प्रथाओं की व्याख्या करें जिनका उपयोग इन चुनौतियों पर काबू पाने में किया जा सकता है।