Sr.No | Question Id | Description | Question Body | Options |
---|---|---|---|---|
1 | 13859 | DU_J19_MCA_Q01 | The system of linear equations 2x + 4y + 6z = 4 x + y + 2z = 2 --- Content provided by FirstRanker.com --- x + 2y + ?z = 4has | 25433: Unique solution if ? ? 4 25434: No solution if ?= 4 FirstRanker.com 25435: Infinitely many solutions if ? = 4 --- Content provided by FirstRanker.com --- 25436: Infinitely many solutions if ? ? 4 |
2 | 13860 | DU_J19_MCA_Q02 | Let z=x+iy and z¯=p-iq. If z/z¯ = A = (p²-q²)/pq, then A is equal to | 25437: 2 25438: 4 FirstRanker.com 25439: -4 25440: -2 |
3 | 13861 | DU_J19_MCA_Q03 | Let z = cos(p/7) + i sin(p/7). Then the principal argument of (1+z)/(1-z) is equal to | 25441: 3p/14 --- Content provided by FirstRanker.com --- 25442: 4p/7FirstRanker.com 25443: 11p/14 25444: 5p/7 |
4 | 13862 | DU_J19_MCA_Q04 | The set of all x ? R such that the sequence{an}, where an = v(n² +n+1) -n, n?N, is convergent | 25445: is an empty set 25446: is a singleton --- Content provided by FirstRanker.com --- FirstRanker.com25447: contains exactly two elements 1 and -1 25448: is equal to R |
5 | 13863 | DU_J19_MCA_Q05 | Let T:R²?R³ be a linear transformation defined by T(x) = Mx, where M = [2 1] [-1 -3] [2 3] --- Content provided by FirstRanker.com --- Then which one of the following vectors can NOT be in the range of T? | 25449: [0 0 0] 25450: [2 3 0] FirstRanker.com 25451: [0 5 1] 25452: [4 -2 1] |
6 | 13864 | DU_J19_MCA_Q06 | Let a ? 0, a ? R. Then the matrix M = [a a a] --- Content provided by FirstRanker.com --- [a a a][a a a] | 25453: is not diagonalizable 25454: is an idempotent matrix FirstRanker.com 25455: is nilpotent --- Content provided by FirstRanker.com --- 25456: has different minimal and characteristic polynomials |
7 | 13865 | DU_J19_MCA_Q07 | The complex number 4 + 2i is the root of the quadratic equation with real coefficients described by | 25457: x² - 8x + 20 = 0 25458: x² - 4x + 5 = 0 FirstRanker.com 25459: x² + 4x + 3 = 0 25460: x² + 4x + 5 = 0 |
8 | 13866 | DU_J19_MCA_Q08 | The locus of the point (a, ß) such that the line y = ax + ß becomes a tangent to the hyperbola 9x²-4y²=36, is | 25461: a hyperbola --- Content provided by FirstRanker.com --- 25462: a hyperbolaFirstRanker.com 25463: an ellipse with length 1 25464: an ellipse with length 9 |
9 | 13867 | DU_J19_MCA_Q09 | Using the 2-point Gauss quadrature ?(-1 to 1) cos²xdx is equal to | 25465: 2 25466: 2 cos²(1/v3) --- Content provided by FirstRanker.com --- FirstRanker.com25467: 2 sin²(1/v3) 25468: 2 cos²(v3) |
10 | 13868 | DU_J19_MCA_Q10 | If the non-zero solution y(x) of the differential equation dy/dx = e²x + y², passes through the points (0, 1) and (a, v(2)), then a is equal to | 25469: (1/2)log(2) 25470: 2 FirstRanker.com --- Content provided by FirstRanker.com --- 25471: log(v(2))25472: v(2) |
11 | 13869 | DU_J19_MCA_Q11 | Let ?R, and f:R³ ?R be a function defined by f(x, y, z)=x²y + y²z+zx-(xyz). if the directional derivative of f at the point P(1, 1, 1) in the direction of the unit vector u = (1/v2)i + (?/v2)j + k is -10, then the gradient of f at P is equal to | 25473: 2i + 2j - k 25474: 2i + 2j + k FirstRanker.com 25475: 6i - 4j + k --- Content provided by FirstRanker.com --- 25476: -6i + 8j + k |
12 | 13870 | DU_J19_MCA_Q12 | Let the function f(x,y) possesses continuous first order partial derivatives and Vf (20,-10) = (3,2). If g(x,y)=f(xy², 2x²y), then Vg(5,-2) is equal to | 25477: (-20, -60) 25478: (-200, -100) FirstRanker.com 25479: (-100, 200) 25480: (100, 100) |
13 | 13871 | DU_J19_MCA_Q13 | If f(x) = e^(g(x)) and g(x)= ?(0 to x) t/(1+t²) dt, then the value of the derivative f '(2) is equal to | 25481: e^(log(5)/2) --- Content provided by FirstRanker.com --- 25482: (2/5)e^(log(5)/2)FirstRanker.com 25483: (1/5)e^(log(5)/2) 25484: (1/5)e^(5/2) |
14 | 13872 | DU_J19_MCA_Q14 | If y(x)=xe^(-2x) is a solution of the differential equation d²y/dx² + p dy/dx + (q+1) y=0 then the ordered pair (p, q) is equal to | 25485: (3, 4) 25486: (4, 3) --- Content provided by FirstRanker.com --- FirstRanker.com25487: (2, -1) 25488: (-4, 5) |
15 | 13873 | DU_J19_MCA_Q15 | Let f:R²?R be defined by f(x,y)= x² - xvy / (x²+y), x ? R, y =0, (x,y)?(0,0) 0, otherwise --- Content provided by FirstRanker.com --- Then, which one of the following is NOT correct? | 25489: f is not continuous at (0,0) 25490: f_x (0,0) does not exist FirstRanker.com 25491: f_y (0,0)= 0 25492: f_x (0,0)+f_y (0,0)=0 |
16 | 13874 | DU_J19_MCA_Q16 | Which one of the following is NOT a correct statement? | 25493: A non-cyclic group can be isomorphic to the group of its proper subgroups --- Content provided by FirstRanker.com --- 25494: Every finite cyclic group has an even number of generatorsFirstRanker.com 25495: Infinite cyclic group has exactly two generators 25496: Every non-trivial group has at least two distinct subgroups |
17 | 13875 | DU_J19_MCA_Q17 | Let T:R³?R³ be a linear transformation defined by T(1,1,2)=(1,-1, 1-2, 2-1), rank(T) = p and nullity(T) = r, then the ordered pair (p, r) is equal to | 25497: (0, 3) 25498: (1, 2) --- Content provided by FirstRanker.com --- FirstRanker.com25499: (2, 1) 25500: (3, 0) |
18 | 13876 | DU_J19_MCA_Q18 | If ? sin²x cos³x dx= a sin³x/3 + b sin5x/5 + c sin x, then a + b + c is equal to | 25501: 1/15 25502: 22 FirstRanker.com --- Content provided by FirstRanker.com --- 25503: 2625504: 30 |
19 | 13890 | DU_J19_MCA_Q19 | lim x?0 (e^(x²)-1-x²) cosx / x(sinx-x) is equal to | 25557: 2/3 25558: -3/2 FirstRanker.com 25559: 3/2 --- Content provided by FirstRanker.com --- 25560: -3 |
20 | 13878 | DU_J19_MCA_Q20 | If Taylor's theorem applied on the function f(x) = ?(0 to x) sint/t dt then the value of the derivative f^(21) (0) is equal to | 25509: 1/21 25510: -1/12 FirstRanker.com 25511: 1/(21*21!) 25512: -1/21! |
21 | 13879 | DU_J19_MCA_Q21 | The area (in square units) of the quadrilateral formed by the tangent lines drawn to the ellipse x²/25 + y²/9 =1 at the ends of its two latus rectums is | 25513: 125/2 --- Content provided by FirstRanker.com --- 25514: 125/4FirstRanker.com 25515: 75/2 25516: 75/4 |
22 | 13880 | DU_J19_MCA_Q22 | Let V=M2(R) denotes the vector space of 2×2 matrices with real entries over the real field. Let T:V? V be defined by T(P)=P? for any P?V, where P? is the transpose of P. If E is the matrix representation of T with respect to the standard basis of V then det(E) is equal to | 25517: 1 25518: 2 --- Content provided by FirstRanker.com --- FirstRanker.com25519: -2 25520: -1 |
23 | 13881 | DU_J19_MCA_Q23 | The equation 2x² + y²-2x-4y+16=0 represents | 25521: an ellipse with center at (1,2) 25522: a hyperbola with center at (1,2) FirstRanker.com --- Content provided by FirstRanker.com --- 25523: an ellipse with center at (-1,-2)25524: a hyperbola with center at (-1,-2) |
24 | 13882 | DU_J19_MCA_Q24 | If f(x)=ax³+bx²+x+1 has a local maxima value 3 at the point of local maxima x = -2, then f (2) is equal to | 25525: 19 25526: 20 FirstRanker.com 25527: 24 --- Content provided by FirstRanker.com --- 25528: 25 |
25 | 13883 | DU_J19_MCA_Q25 | If the Newton-Raphson method is applied to find a real root of f(x) = 2x²+x-2=0 with initial approximation x0 =1. Then the second approximation x2 is | 25529: 56/105 25530: 82/105 FirstRanker.com 25531: 84/105 25532: 24/105 |
26 | 13884 | DU_J19_MCA_Q26 | The equation of common tangent to the curve y² = 8x and xy = -1 is | 25533: 3y = 9x+2 --- Content provided by FirstRanker.com --- 25534: y = 2x + 1FirstRanker.com 25535: 2y = x + 8 25536: y = x+2 |
27 | 13885 | DU_J19_MCA_Q27 | The greatest value of the function y = Sin(x) . Sin(2x) on [-p/2,p/2] is | 25537: 3v3/4 25538: 3v3/3 --- Content provided by FirstRanker.com --- FirstRanker.com25539: 2/3v3 25540: 2v3/3 |
28 | 13886 | DU_J19_MCA_Q28 | Let f(x) = sin(x) + Cos(x). The function f increases in the interval | 25541: (p/4, p/2) 25542: (5p/4, 3p/2) FirstRanker.com --- Content provided by FirstRanker.com --- 25543: (0, p/4)25544: (p, 5p/4) |
29 | 13887 | DU_J19_MCA_Q29 | The area of the plane region bounded by the curves x+2y² = 0 and x+3y² = 1 above x-axis is equal to | 25545: 5/3 25546: 1/3 FirstRanker.com 25547: 2/3 --- Content provided by FirstRanker.com --- 25548: 4/3 |
30 | 13888 | DU_J19_MCA_Q30 | The perimeter of the loop of the curve 9 y² =(x-2)(x-5)² is: | 25549: 4v3 25550: 2v3 FirstRanker.com 25551: 3v3 25552: 8v3 |
31 | 13892 | DU_J19_MCA_Q31 | Read the following passage and answer the subsequent questions: I'd been working with plastic bags, which I cut up and sew back together as my primary material for my artwork for the last 20 years. I turn them into two and three-dimensional pieces and sculptures and installations. After about the first eight years, some of my work started to fissure and break down into smaller little bits of plastic. It's a bad thing that plastic breaks down into smaller little bits, because it's always still plastic. And a lot of it is in the marine environment. I learned about the Pacific garbage patch. I wanted to go out there, pick up the plastic, and cold mold it into bricks to be used as building materials in underdeveloped communities. But soon I realized that I needed to look at the bigger picture first: we need to attack the source of this waste that is entering the marine environment every day on a global scale. Rather than the marine plastic pile what I should focus on, is the pile of plastic in the supermarket. I'd go to the supermarket and all of my food is packaged in plastic. I'm concerned about the plastic and the toxins that leach from plastic into us and into our bodies. How did the writer come to be concerned about plastic waste? | 25565: Plastic had been his primary material for his artwork for the last 20 years --- Content provided by FirstRanker.com --- 25566: His work started to fissure and break down into smaller bits of plasticFirstRanker.com 25567: He realized that the bits of plastic his work broke into polluted the marine environment 25568: Plastic breaks down into smaller little bits, but it turns into toxins |
32 | 13893 | DU_J19_MCA_Q32 | Read the following passage and answer the subsequent questions: I'd been working with plastic bags, which I cut up and sew back together as my primary material for my artwork for the last 20 years. I turn them into two and three-dimensional pieces and sculptures and installations. After about the first eight years, some of my work started to fissure and break down into smaller little bits of plastic. It's a bad thing that plastic breaks down into smaller little bits, because it's always still plastic. And a lot of it is in the marine environment. I learned about the Pacific garbage patch. I wanted to go out there, pick up the plastic, and cold mold it into bricks to be used as building materials in underdeveloped communities. But soon I realized that I needed to look at the bigger picture first: we need to attack the source of this waste that is entering the marine environment every day on a global scale. Rather than the marine plastic pile what I should focus on, is the pile of plastic in the supermarket. I'd go to the supermarket and all of my food is packaged in plastic. I'm concerned about the plastic and the toxins that leach from plastic into us and into our bodies. What does he mean by "the bigger picture"? | 25569: Plastic waste that is polluting the marine environment 25570: The massive use of plastic packaging for consumer goods that leach toxins into us and into our bodies --- Content provided by FirstRanker.com --- FirstRanker.com25571: Toxins leaching from plastic 25572: Plastic waste could be cold molded into bricks to be used as building materials |
33 | 13894 | DU_J19_MCA_Q33 | Read the following passage and answer the subsequent questions: I'd been working with plastic bags, which I cut up and sew back together as my primary material for my artwork for the last 20 years. I turn them into two and three-dimensional pieces and sculptures and installations. After about the first eight years, some of my work started to fissure and break down into smaller little bits of plastic. It's a bad thing that plastic breaks down into smaller little bits, because it's always still plastic. And a lot of it is in the marine environment. I learned about the Pacific garbage patch. I wanted to go out there, pick up the plastic, and cold mold it into bricks to be used as building materials in underdeveloped communities. But soon I realized that I needed to look at the bigger picture first: we need to attack the source of this waste that is entering the marine environment every day on a global scale. Rather than the marine plastic pile what I should focus on, is the pile of plastic in the supermarket. I'd go to the supermarket and all of my food is packaged in plastic. I'm concerned about the plastic and the toxins that leach from plastic into us and into our bodies. Why does author want to go to the Pacific? | 25573: To pick up the plastic and cold mold it into bricks. 25574: To see the plastic garbage patch there FirstRanker.com --- Content provided by FirstRanker.com --- 25575: To throw more plastic25576: For sight seeing |
34 | 13895 | DU_J19_MCA_Q34 | Read the following passage and answer the subsequent questions: I'd been working with plastic bags, which I cut up and sew back together as my primary material for my artwork for the last 20 years. I turn them into two and three-dimensional pieces and sculptures and installations. After about the first eight years, some of my work started to fissure and break down into smaller little bits of plastic. It's a bad thing that plastic breaks down into smaller little bits, because it's always still plastic. And a lot of it is in the marine environment. I learned about the Pacific garbage patch. I wanted to go out there, pick up the plastic, and cold mold it into bricks to be used as building materials in underdeveloped communities. But soon I realized that I needed to look at the bigger picture first: we need to attack the source of this waste that is entering the marine environment every day on a global scale. Rather than the marine plastic pile what I should focus on, is the pile of plastic in the supermarket. I'd go to the supermarket and all of my food is packaged in plastic. I'm concerned about the plastic and the toxins that leach from plastic into us and into our bodies. What does the author find in supermarket? | 25577: All the items are packaged in paper 25578: Bricks made of plastic FirstRanker.com 25579: All of his food is packaged in plastic --- Content provided by FirstRanker.com --- 25580: Plastic does not create any problem |
35 | 13897 | DU_J19_MCA_Q35 | Read the following passage and answer the subsequent questions: Recycling - everybody kind of ends their books about being sustainable and greening with the idea of recycling. You put something in a bin and you don't have to think about it again. What is the reality of that? In the United States, less than seven percent of the plastics are recycled, or incinerated, or shipped to China. It is down-cycled and turned into lesser things a plastic bottle can never be a plastic bottle again. We, a group of people concerned about plastic pollution, have added a fourth R onto the front of the "Reduce, Reuse, Recycle," and that is refuse. Whenever possible, refuse single-use and disposable plastics. Alternatives exist; I myself am now collecting these cool Pyrex containers and using those instead of plastic containers to store food in. And I know that I am doing a service to myself and my family. It is a problem that we've created as consumers and we have to solve it -We can solve this by raising awareness of the issue and teaching people to choose alternatives. Why does the author think recycling is not the right solution? | 25585: We simply throw the plastic waste into trash bin 25586: We only write about what we need to recycle FirstRanker.com 25587: Not much of plastic waste is really recycled 25588: Plastic waste is only down-cycled which again turns into waste in the course of time |
36 | 13898 | DU_J19_MCA_Q36 | Read the following passage and answer the subsequent questions: Recycling - everybody kind of ends their books about being sustainable and greening with the idea of recycling. You put something in a bin and you don't have to think about it again. What is the reality of that? In the United States, less than seven percent of the plastics are recycled, or incinerated, or shipped to China. It is down-cycled and turned into lesser things a plastic bottle can never be a plastic bottle again. We, a group of people concerned about plastic pollution, have added a fourth R onto the front of the "Reduce, Reuse, Recycle," and that is refuse. Whenever possible, refuse single-use and disposable plastics. Alternatives exist; I myself am now collecting these cool Pyrex containers and using those instead of plastic containers to store food in. And I know that I am doing a service to myself and my family. It is a problem that we've created as consumers and we have to solve it -We can solve this by raising awareness of the issue and teaching people to choose alternatives.Mark the statement that is NOT true: | 25589: In USA seven percent of plastic waste is recycled --- Content provided by FirstRanker.com --- 25590: Down-cycling only turns the used plastic into another single use plastic productFirstRanker.com 25591: The writer suggests that we refuse to use, as far as possible, single use and disposable plastics 25592: People should prefer using alternatives wherever possible |
37 | 13899 | DU_J19_MCA_Q37 | Read the following passage and answer the subsequent questions: Recycling everybody kind of ends their books about being sustainable and greening with the idea of recycling. You put something in a bin and you don't have to think about it again What is the reality of that? In the United States, less than seven percent of the plastics are recycled, or incinerated, or shipped to China. It is down-cycled and turned into lesser things a plastic bottle can never be a plastic bottle again. We, a group of people concerned about plastic pollution, have added a fourth R onto the front of the "Reduce, Reuse, Recycle," and that is refuse. Whenever possible, refuse single-use and disposable plastics. Alternatives exist; I myself am now collecting these cool Pyrex containers and using those instead of plastic containers to store food in. And I know that I am doing a service to myself and my family. It is a problem that we've created as consumers and we have to solve it -We can solve this by raising awareness of the issue and teaching people to choose alternatives. What service is writer doing to his family? | 25593: Refuse single-use and disposable plastics 25594: Using Pyrex containers to store food --- Content provided by FirstRanker.com --- FirstRanker.com25595: Using only those products which are packaged in Pyrex 25596: None of these |
38 | 13901 | DU_J19_MCA_Q38 | Read the following passage and answer the subsequent questions: Milk contains a type of sugar called lactose. When we are babies, our bodies make a special enzyme called lactase that allows us to digest the lactose in our mother's milk. But after we are weaned in early childhood, for many people this stops. Without lactase, we cannot properly digest the lactose in milk. But then evolution kicked in: some people began to keep their lactase enzymes active into adulthood. This "lactase persistence" allowed them to drink milk without side effects. It is the result of mutations in a section of DNA that controls the activity of the lactase gene. But in many populations, such as those in Africa, in Asia and South America, the trait is uncommon. Even people who are lactase-non-persistent exploit the option of processing milk into butter, yoghurt, cream or cheese all of which have reduced amount of lactose. There is clearly a pattern behind which populations evolved high levels of lactase persistence and which didn't, says a genetics professor Dallas Swallow of University College London. Those with the trait are pastoralists: people who raise livestock. Hunter-gatherers, who do not keep animals, did not acquire the mutations. Neither did "forest gardeners" who cultivated plants. But milk consumption is going down, says a study. Statistics tell a different story. While milk consumption has fallen in the US, in Asia demand is growing, where most people are non-lactase-persistent. Whatever advantages the people there see in milk, they outweigh the potential digestive issues or the need to process the milk. Why is it that some grownups can drink and digest milk while others cannot digest it? | 25601: All babies can drink and digest milk but some grownups cannot digest any milk 25602: An enzyme called lactase allows us to digest mother's milk in infancy, but in case of some people, their bodies stop producing this enzyme FirstRanker.com --- Content provided by FirstRanker.com --- 25603: Some grownups can digest milk as a result of mutations in a section of their DNA that controls the activity of the lactase gene25604: The presence of a sugar called lactose in milk hinders the digestion of milk in some people |
39 | 13902 | DU_J19_MCA_Q39 | Read the following passage and answer the subsequent questions: Milk contains a type of sugar called lactose. When we are babies, our bodies make a special enzyme called lactase that allows us to digest the lactose in our mother's milk. But after we are weaned in early childhood, for many people this stops. Without lactase, we cannot properly digest the lactose in milk. But then evolution kicked in: some people began to keep their lactase enzymes active into adulthood. This "lactase persistence" allowed them to drink milk without side effects. It is the result of mutations in a section of DNA that controls the activity of the lactase gene. But in many populations, such as those in Africa, in Asia and South America, the trait is uncommon. Even people who are lactase-non-persistent exploit the option of processing milk into butter, yoghurt, cream or cheese all of which have reduced amount of lactose. There is clearly a pattern behind which populations evolved high levels of lactase persistence and which didn't, says a genetics professor Dallas Swallow of University College London. Those with the trait are pastoralists: people who raise livestock. Hunter-gatherers, who do not keep animals, did not acquire the mutations. Neither did "forest gardeners" who cultivated plants. But milk consumption is going down, says a study. Statistics tell a different story. While milk consumption has fallen in the US, in Asia demand is growing, where most people are non-lactase-persistent. Whatever advantages the people there see in milk, they outweigh the potential digestive issues or the need to process the milk. How did some populations come to retain lactase- persistence while very many others did not as they grew up? | 25605: Evolution worked in different ways with people in different parts of the world 25606: The need to drink milk to avoid starvation led to evolution of lactase persistence in people eating in this enzyme FirstRanker.com 25607: People whose lives revolved around livestock came to drink more milk --- Content provided by FirstRanker.com --- 25608: It is a genetic change that is uncommon in many populations, such as those in Africa, in Asia and South America this trait is uncommon |
40 | 13903 | DU_J19_MCA_Q40 | Read the following passage and answer the subsequent questions: Milk contains a type of sugar called lactose. When we are babies, our bodies make a special enzyme called lactase that allows us to digest the lactose in our mother's milk. But after we are weaned in early childhood, for many people this stops. Without lactase, we cannot properly digest the lactose in milk. But then evolution kicked in: some people began to keep their lactase enzymes active into adulthood. This "lactase persistence" allowed them to drink milk without side effects. It is the result of mutations in a section of DNA that controls the activity of the lactase gene. But in many populations, such as those in Africa, in Asia and South America, the trait is uncommon. Even people who are lactase-non-persistent exploit the option of processing milk into butter, yoghurt, cream or cheese all of which have reduced amount of lactose. There is clearly a pattern behind which populations evolved high levels of lactase persistence and which didn't, says a genetics professor Dallas Swallow of University College London. Those with the trait are pastoralists: people who raise livestock. Hunter-gatherers, who do not keep animals, did not acquire the mutations. Neither did "forest gardeners" who cultivated plants. But milk consumption is going down, says a study. Statistics tell a different story. While milk consumption has fallen in the US, in Asia demand is growing, where most people are non-lactase-persistent. Whatever advantages the people there see in milk, they outweigh the potential digestive issues or the need to process the milk. Mark the statement that is NOT true: | 25609: The enzyme lactase helps us to digest milk in our infancy 25610: People who are non-lactase persistent can use milk by processing it into butter or cheese as they are lactose reduced FirstRanker.com 25611: Lactase-deficient people everywhere drink milk because of its health benefits 25612: It is interesting that milk consumption is going down in non-lactase persistent populations |
41 | 13905 | DU_J19_MCA_Q41 | Which of the following operands have equal precedence, in C programming language? --- Content provided by FirstRanker.com --- I []II & III <= IV () | 25617: I and II 25618: II and III --- Content provided by FirstRanker.com --- FirstRanker.com25619: I and IV 25620: II and IV |
42 | 13906 | DU_J19_MCA_Q42 | The operator a << b shifts binary representation of integer 'a' by 'b' bit, in C programming language. | 25621: Circularly left 25622: Circularly right FirstRanker.com --- Content provided by FirstRanker.com --- 25623: Left25624: Right |
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