This document contains a 30 question mathematics exam with multiple choice questions covering topics like algebra, geometry, trigonometry, and calculus. The questions test concepts such as properties of lines and curves, equivalence relations, matrix operations, differential equations, and integrals. For each question, students must select the single best answer among four options labeled A, B, C or D. The document provides the questions and answer options but no solutions. It directs students to visit an external website to find the solutions.
This is the entrance exam paper for ISI MSQE Entrance Exam for the year 2008. Much more information on the ISI MSQE Entrance Exam and ISI MSQE Entrance preparation help available on http://crackdse.com
This is the entrance exam paper for ISI MSQE Entrance Exam for the year 2004. Much more information on the ISI MSQE Entrance Exam and ISI MSQE Entrance preparation help available on http://crackdse.com
This is the entrance exam paper for ISI MSQE Entrance Exam for the year 2013. Much more information on the ISI MSQE Entrance Exam and ISI MSQE Entrance preparation help available on http://crackdse.com
Model Attribute Check Company Auto PropertyCeline George
In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
The Indian economy is classified into different sectors to simplify the analysis and understanding of economic activities. For Class 10, it's essential to grasp the sectors of the Indian economy, understand their characteristics, and recognize their importance. This guide will provide detailed notes on the Sectors of the Indian Economy Class 10, using specific long-tail keywords to enhance comprehension.
For more information, visit-www.vavaclasses.com
Palestine last event orientationfvgnh .pptxRaedMohamed3
An EFL lesson about the current events in Palestine. It is intended to be for intermediate students who wish to increase their listening skills through a short lesson in power point.
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
This is a presentation by Dada Robert in a Your Skill Boost masterclass organised by the Excellence Foundation for South Sudan (EFSS) on Saturday, the 25th and Sunday, the 26th of May 2024.
He discussed the concept of quality improvement, emphasizing its applicability to various aspects of life, including personal, project, and program improvements. He defined quality as doing the right thing at the right time in the right way to achieve the best possible results and discussed the concept of the "gap" between what we know and what we do, and how this gap represents the areas we need to improve. He explained the scientific approach to quality improvement, which involves systematic performance analysis, testing and learning, and implementing change ideas. He also highlighted the importance of client focus and a team approach to quality improvement.
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
How to Split Bills in the Odoo 17 POS ModuleCeline George
Bills have a main role in point of sale procedure. It will help to track sales, handling payments and giving receipts to customers. Bill splitting also has an important role in POS. For example, If some friends come together for dinner and if they want to divide the bill then it is possible by POS bill splitting. This slide will show how to split bills in odoo 17 POS.
2. SECTION – I Straight Objective Type This section contains multiple choice questions numbered 30 . Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.
3. 01 Problem The lines L1 : y − x = 0 and L2 : 2x + y = 0 intersect the line L3 : y + 2 = 0 at P and Q respectively. The bisector of the acute angle between L1 and L2 intersect L3 at R . Statement – 1 : The ratio PR :RQ equals 2 2: 5 . Statement – 2 : In any triangle, bisector of an angle divides the triangle into two similar triangles. Statement – 1 is true, Statement – 2 is true; Statement – 2 is not a correct explanation for Statement – 1 Statement – 1 is true, Statement– 2 is false. Statement – 1 is false, Statement– 2 is true. Statement – 1 is true, Statement – 2 is true; Statement – 2 is a correct explanation for Statement – 1
4. Problem 02 If A = sin2 x + cos4 x , then for all real Xe a. b. c. d.
5. Problem 03 The coefficient of xE in the expansion of (1−X− X2 + X3 ) 6 is -132 -144 132 144
7. Problem 05 Statement – 1 : The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is empty is 9 C3 Statement – 2 : The number of ways of choosing any 3 places from 9 different places is 9 C3 . Statement – 1 is true, Statement – 2 is true; Statement – 2 is not a correct explanation for Statement – 1 Statement – 1 is true, Statement– 2 is false. Statement – 1 is false, Statement– 2 is true. Statement – 1 is true, Statement – 2 is true; Statement – 2 is a correct explanation for Statement – 1
9. Problem 07 If y 3 0 = + > and y (0) = 2 , then y(ln2) is equal to 5 13 -2 7
10. Problem 08 Let R be the set of real numbers Statement – 1 : A = {(x,y)∈R×R : y − x is an integer} is an equivalence relation on R . Statement – 2 : B = {(x,y)∈R×R : x = αy for some rational number α} is an equivalence relation on Statement – 1 is true, Statement – 2 is true; Statement – 2 is not a correct explanation for Statement – 1 Statement – 1 is true, Statement– 2 is false. Statement – 1 is false, Statement– 2 is true. Statement – 1 is true, Statement – 2 is true; Statement – 2 is a correct explanation for Statement – 1
12. Problem 10 Let α, β be real and z be a complex number. If z2 + αz + β = 0 has two distinct roots on the line Rez = 1, then it is necessary that β∈(−1, 0) |β| = 1 β∈(1, ∞) β∈(0, 1)
13. Problem 11 Consider 5 independent Bernoulli’s trials each with probability of success p. If the probability of at least one failure is greater than or equal to , then p lies in the interval a. b. c. d.
14. Problem 12 A man saves Rs. 200 in each of the first three months of his service. In each of the subsequent months his saving increases by Rs. 40 more than the saving of immediately previous month. His total saving from the start of service will be Rs. 11040 after 19 months 20 months 21 months 18 months
15. Problem 13 The domain of the function f (x) is (0, ∞) (−∞, 0) (−∞, ∞) − {0} (−∞, ∞)
16. Problem 14 If the angle between the line and the planes cos 1then λ equals a. b. ⅖ c. d.⅔
17. Problem 15 If and then the value of a.-3 b.5 c.3 d.-5
18. Problem 16 Equation of the ellipse whose axes are the axes of coordinates and which passes through the point (−3, 1) and has eccentricity is 5x2 + 3y2 − 48 = 0 3x2 + 5y2 −15 = 0 5x2 + 3y2 − 32 = 0 3x2 + 5y2 − 32 = 0
19. Problem 17 Let I be the purchase value of an equipment and V(t) be the value after it has been used for t years. The value V(t) depreciates at a rate given by differential equation , k > 0 is a constant and T is the total life in years of the equipment. Then the scrap value V(T) of the equipment is a. b. c. d.
20. Problem 18 The vector and are not perpendicular and andare two vectors satisfying: and a.d = 0 . Then the vector d is equal to a. b. c. d.
21. Problem 19 The two circles x2 + y2 = ax and x2 + y2 = c2 (c > 0) touch each other if a = c a = 2c a = 2c 2 a = c
22. Problem 20 If C and D are two events such that C ⊂ D and P(D) ≠ 0 , then the correct statement among the following is P(C |D) ≥ P(C) P(C |D) < P(C) P(C |D) = P(C |D) = P(C)
23. Problem 21 The number of values of k for which the linear equations 4x + ky + 2z = 0 ; kx + 4y + z = 0 ; 2x + 2y + z = 0 possess a non-zero solution is 2 1 zero 3
24. Problem 22 Consider the following statements P : Suman is brilliant Q : Suman is rich R : Suman is honest The negation of the statement “Suman is brilliant and dishonest if and only if Suman is rich” can be expressed as ~ (Q ↔ (P∧ ~ R)) ~ Q ↔~ P ∧R ~ (P∧ ~ R) ↔ Q ~ P ∧ (Q ↔~ R)
25. Problem 23 The shortest distance between line y − x = 1 and curve x = y2 is a. b. c. d.
26. Problem 24 If the mean deviation about the median of the numbers a, 2a, …, 50a is 50, then a equals 3 4 5 2
27. Problem 25 Statement – 1 : The point A(1, 0, 7) is the mirror image of the point B(1, 6, 3) in the line Statement – 2 : The line: x y 1 z 2bisects the line segment joining A(1, 0, 7) and B(1, 6, 3) . Statement – 1 is true, Statement–2 is true; Statement–2 is not a correct explanation for Statement – 1 Statement – 1 is true, Statement– 2 is false. Statement – 1 is false, Statement– 2 is true. Statement – 1 is true, Statement – 2 is true; Statement – 2 is a correct explanation for Statement – 1
28. Problem 26 Let A and B be two symmetric matrices of order 3. Statement – 1 : A(BA) and (AB)A are symmetric matrices. Statement – 2 : AB is symmetric matrix if matrix multiplication of A and B is commutative. Statement – 1 is true, Statement – 2 is true; Statement – 2 is not a correct explanation for Statement – 1 Statement – 1 is true, Statement– 2 is false. Statement – 1 is false, Statement– 2 is true. Statement – 1 is true, Statement – 2 is true; Statement – 2 is a correct explanation for Statement – 1
29. Problem 27 If ω(≠ 1) is a cube root of unity, and (1+ ω )7 = A + Bω . Then (A, B) equals (1, 1) (1, 0) (-1, 1) (4) (0, 1)
30. Problem 28 The value of p and q for which the function f is continuous for all x in R, is a. b. c. d.
31. Problem 29 The area of the region enclosed by the curves 1and the positive x-axis is 1 square units square units square units square units
32. Problem 30 For 5 x 0,2 define sintdt . Then f has local minimum at π and 2π local minimum at π and local maximum at 2π local maximum at π and local minimum at 2π local maximum at π and 2π
