1. The document provides an unsolved mathematics test with 35 multiple choice questions covering topics like trigonometry, vectors, complex numbers, functions, and integrals.
2. For each question, 4 possible answers are provided and test takers must select the correct answer.
3. The questions cover a wide range of mathematical concepts to test the test taker's understanding of different areas of mathematics.
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
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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.
Ethnobotany and Ethnopharmacology:
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The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
For more information, visit-www.vavaclasses.com
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
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.
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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.
1. IIT JEE –Past papers MATHEMATICS- UNSOLVED PAPER - 2000
2. SECTION – I Single Correct Answer Type There are 35 items in this question. For each item four alternative answers are provided. Indicate the choice of the alternative that you think to be the correct answer by writing the corresponding letter from (a), (b), (c), (d), whichever is appropriate, in the answer book, strictly according to the order in which these items appear below.
3. 01 Problem Let 0 only when θ 0 0 for all real θ 0 for all real θ 0 only when θ 0
4. Problem 02 If x + y = k is normal to y2 = 12x, then k is 3 9 -9 -3
6. Problem 04 If , are the roots of the equation x2 + bx + c = 0, where c < 0 < b, then a. 0 < α< β b. α< 0 < β<| α| c. α< β < 0 d. α< 0 <α| <
7. Problem 05 Let f : be any function. Define g : by g (x) = |f(x)| for all x. Then g is Onto if f is onto. One-one if f is one-one. Continuous if f is continuous. Differentiable if f is differentiable.
8. Problem 06 The domain of definition of the function y(x) given by the equation 2x + 2y = 2 is a. 0 x 1 - < x 0 d. - < x < 1
10. Problem 08 If a, b, c, d are positive real numbers such that a + b + c + d = 2, then M = (a + b) c + d) satisfies the relation 0 M 1 1 M 2 2 M 3 3 M 4
11. Problem 09 If the system of equations x – ky – z = 0, kx – y – z = 0, x + y –z = 0 has a nonzero solution, then the possible value of k are -1, 2 1, 2 0, 1 -1, 1
12. Problem 10 The triangle PQR is inscribed in the circle x2 + y2 = 25. If Q and R have co-ordinates (3, 4) and (-4, 3) respectively, then is equal π/2 π/3 π/4 π/6
13. Problem 11 In a triangle ABC, 2ac a2 + b2 – c2 c2 + a2 – b2 b2 – c2 – a2 c2 – a2 – b2
15. Problem 13 Consider an infinite geometric series with first term a and common ratio r. If its sum is 4 and the second term is 3/4 then a. b. c. d.
16. Problem 14 Let where f is such that . Then g(2) satisfies the inequality a. b. 0 ≤ g(2)<2 c. 3/2<g(2) < 5/2 d. 2 < g (2) < 4
17. Problem 15 In a triangle ABC, let . If r is the inradius and R is thcircumradius of the triangle, then 2(r + R) is equal to a + b b + c c + a a + b + c
18. Problem 16 How many different nine digit numbers can be formed from the number 223355888 by rearranging the digits so that the odd digits occupy even positions? 16 36 60 180
19. Problem 17 If arg (z) < 0, then arg (-z) –arg(z) = a. π b. - π c. - π/2 d. π/2
20. Problem 18 Let PS be the median of the triangle with vertices P(2, 2), Q(6,-1) and R(7, 3). The equation of the line passing through (1, -1) and parallel to PS is 2x – 9y – 7 = 0 2x – 9y – 11 = 0 2x + 9y – 11 = 0 2x + 9y + 7 = 0
21. Problem 19 A pole stands vertically, inside a triangular park ABC. If the angle of elevation of the top of the pole from each corner of the park is same, then in ABC the foot of the pole is at the Centroid Circumecentre Incentre Orthocentre
23. Problem 21 The incentre of the triangle with vertices (1, ), (0, 0) and (2, 0) is a. b. c. d.
24. Problem 22 Consider the following statements S and R: S: both sin x and cos x are decreasing functions in the interval . R : If a differentiable function decreases in an interval (a, b), then its derivative also decreases in (a, b). Which of the following is true? Both S and R are wrong, Both S and R are correct, but R is not the correct explanation for S is correct and R is the correct explanation for S. S is correct and R is wrong.
25. Problem 23 Let f(x) then f decreases in the interval ( - ∞ , -2) (-2, -1) (1, 2) (2, + ∞ )
26. Problem 24 In the circles x2 + y2 + 2x + 2ky + 6 = 0 and x2 + y2 + 2ky + k = 0 intersect orthogonally, then k is 2 or – 3/2 2 or – 3/2 2 or 3/2 2 or 3/2
27. Problem 25 If the vectors a, b and c form the sides BC, CA and AB respectively, of a triangle ABC, then a . b + b . c + c . a = 0 a x b = b x c = c x a a . b = b . c = c . a a x b + b x c + c x a = 0
28. Problem 26 If the normal to the curve y = f(x) at the point (3, 4) makes an angle 3π/4 with the positive x-axis, then f’(3) = -1 -3/4 4/3 1
29. 27 Problem Let the vectors a, b, c and d be such that (a x b) x (c x d) = 0. Let P1 and P2 be planes determined by the pairs of vectors a, b and c, d respectively. Then the angle between P1 and P2 is 0 π/3 π/2 π/4
30. Problem 28 Let then at x = 0, f has A local maximum No local maximum A local minimum No extremum
31. Problem 29 If a, b and c are nit coplanar vectors, then the scalar triple product [2a – b, 2b – c, 2c - a] = 0 1 - +
32. Problem 30 If b > a, then the equation (x –a) (x -b) – 1 = 0,m has Both roots in [a, b] Both roots in (-∞, a) Both roots in (b, + ∞) One root in (-∞, a) and other in (b, +∞)
33. Problem 31 If z1, z2, z3 are complex number such that | z1| = |z2| = | z3| =1, then | z1, z2, z3| is Equal to 1 Less than 1 Greater than 3 Equal to 3
34. Problem 32 For the equation 3x2 + px + 3 = 0, p > 0, if one of the roots is square of the other, then p is equal to 1/3 1 3 2/3
35. Problem 33 If the line x – 1 = 0 is the directrix of the parabola y2 – kx + 8 = 0, then one of the value of k is 1/8 8 4 1/4
36. Problem 34 For all ex < 1 + x loge (1 + x) < x sin x > x loge x > x