UPHESC Assistant Professor Agricultural Statistics

UPHESC Assistant Professor Agricultural Statistics Booklet 1A97 (Series A) – Question Paper

100 questions · 200 marks · 120 minutes · +2 for a correct answer, no negative marking. Free PDF with answer key.

Paper pattern

Section	Questions	Marks
General Knowledge	30	60
Agricultural Statistics	70	140

Q1.

The ‘Pravasi Bhartiya Kendra and Foreign Service Institutes’ has been renamed after which former Indian Union Minister ?

‘प्रवासी भारतीय केन्द्र और विदेश सेवा संस्थान’ का नाम बदलकर किस पूर्व भारतीय केन्द्रीय मंत्री के नाम पर रखा गया है ?

Show answer

Concept: In Feb 2020 they were renamed Sushma Swaraj Bhawan and Sushma Swaraj Institute of Foreign Service.

It honoured former External Affairs Minister Sushma Swaraj (died Aug 2019) on her birth anniversary.
Both bodies work under the Ministry of External Affairs, which she headed 2014–19.

Short trick: Foreign service + diaspora → former External Affairs Minister Sushma Swaraj.

अवधारणा: फरवरी 2020 में इनका नाम सुषमा स्वराज भवन तथा सुषमा स्वराज विदेश सेवा संस्थान रखा गया।

यह पूर्व विदेश मंत्री सुषमा स्वराज (निधन अगस्त 2019) की जयंती पर उनके सम्मान में हुआ।
दोनों संस्थाएँ विदेश मंत्रालय के अधीन हैं, जिसकी वे 2014–19 में मंत्री थीं।

याद रखें: विदेश सेवा + प्रवासी → पूर्व विदेश मंत्री सुषमा स्वराज।

UPHESC Assistant Professor Agricultural StatisticsGeneral KnowledgeRenaming of institutions

Q31.

With reference to partial differentiation of

z = x^{2} y^{2}

which of the following statements is/are correct ?
1.

\frac{\partial^{2} z}{\partial x \partial y} = 4

\frac{\partial^{2} z}{\partial x \partial y} = \frac{\partial^{2} z}{\partial y \partial x}

Select the correct answer :

z = x^{2} y^{2}

के आंशिक अवकलन के संदर्भ में निम्न कथनों में कौन सही है/हैं ?
1.

\frac{\partial^{2} z}{\partial x \partial y} = 4

\frac{\partial^{2} z}{\partial x \partial y} = \frac{\partial^{2} z}{\partial y \partial x}

सही उत्तर चुनिये :

Show answer

Concept: For a function with continuous second partials, mixed partial derivatives are equal (Schwarz/Clairaut theorem).

$\frac{\partial z}{\partial y} = 2 x^{2} y$ , then $\frac{\partial^{2} z}{\partial x \partial y} = 4 x y$ — a function of x and y, not the constant 4. Statement 1 is false.
$\frac{\partial z}{\partial x} = 2 x y^{2}$ , then $\frac{\partial^{2} z}{\partial y \partial x} = 4 x y$ — same as above, so statement 2 is true.

Short trick: Polynomials are smooth, so the order of mixed differentiation never matters.

अवधारणा: सतत द्वितीय आंशिक अवकलज वाले फलन में मिश्रित अवकलज बराबर होते हैं (श्वार्ज़/क्लेरो प्रमेय)।

$\frac{\partial z}{\partial y} = 2 x^{2} y$ , अतः $\frac{\partial^{2} z}{\partial x \partial y} = 4 x y$ — यह अचर 4 नहीं है। कथन 1 असत्य।
$\frac{\partial z}{\partial x} = 2 x y^{2}$ , अतः $\frac{\partial^{2} z}{\partial y \partial x} = 4 x y$ — दोनों बराबर, कथन 2 सत्य।

याद रखें: बहुपद फलनों में मिश्रित अवकलन का क्रम बदलने से परिणाम नहीं बदलता।

UPHESC Assistant Professor Agricultural StatisticsAgricultural StatisticsPartial differentiation