Quiz about Maths in Class 12

Question 1

If the centre of a circle is (3 4) and its size is just sufficient to contain to circle x^(2) + y^(2) =1. Then the radius of the required circle is _____.

Accepted Answer

NA

Question 2

Evaluate the following [[112331][121914][697]]

Accepted Answer

NA

Question 3

(1^(2).2^2)(1!) +(2^(2).3^2)(2!) + (3^(2).4^2)(3!) + .....oo =

Accepted Answer

NA

Question 4

Discuss the continuity of the function f defined byf(x)= (x +3 if x le 1 ) (x -3 if x gt 1)

Accepted Answer

NA

Question 5

If a(b + c) b(c + a) c(a + b) are in A.P. then

Accepted Answer

NA

Question 6

If a set A has m elements and a set B has n elements then the number of relation from a to B is ...........

Accepted Answer

NA

Question 7

If ablt0 a gt b and b gt-b which of the following must be true?

Accepted Answer

NA

Question 8

Let A and B be events with P(A)= 38  P(B)= 12 andP(A cap B) = 14Find P(A^c) and P(B^c)

Accepted Answer

NA

Question 9

Find the equation of the circle passing through the points of intersection of the ellipse (x^(2))(16) + (y^(2))(9) =1 and (x^(2))(9) + (y^(2))(16) =1 ______ .

Accepted Answer

NA

Question 10

If p q and r anre 3 statements then the truth value of ((-p vv q) ^^ r) implies p is

Accepted Answer

NA

Question 11

A If |z+1| -|z-1| =32 then the least value of |z| is 34  R If z_1z_2 are two complex numbers then |z_1-z_2|ge||z_1|-|z_2||

Accepted Answer

NA

Question 12

Given that E and F are events such that P(E) = 0.6P(F)= 0.3 and P(EnnF)=0.2.Find P (FE).

Accepted Answer

NA

Question 13

overset(1)underset(0)int x log(1+2x)dx

Accepted Answer

NA

Question 14

If bara=(1-1-6)barb=(1-34) and barc=(2-53) then compare bara xx(barb xx barc).

Accepted Answer

NA

Question 15

Find the area of the surface out off from a right circular cylinder by a plane passing through the diameter of the base and inclined at an angle of 45^(@) to the base.

Accepted Answer

NA

Question 16

The radius of a circle is increasing at the rate of 0.7 cms. What is the rate of increase of its circumference ?

Accepted Answer

NA

Question 17

Findthe multipleroots ofx^4 - 6x^3 + 13 x^2 - 24 x +36 =0

Accepted Answer

NA

Question 18

(i) Which of the following correspondences can be called a function? (A) f(x)=x^(3)-101to0123  (B)f(x)=+-sqrt(x)014to-2-1012  (C)f(x)=sqrt(x)014to014to-2-1012  (D) f(x)=-sqrt(x)014to-2-1012  (ii) Which of the following pictorial diagrams represent the function

Accepted Answer

NA

Question 19

Find the equation of lines regression from the following data    Correlation of coefficient = (2)(3)

Accepted Answer

NA

Question 20

Hydration energy of A_(g)^(+2) is (in kJmol^(-1))

Accepted Answer

NA

Question 21

Let x_(i) epsilonRi=123……….n are numbers such that sum_(i=1)^(n)isqrt(x_(i)-i^(2))=(sum_(i=1)^(n)x_(i))2 and x_(1)+x_(2)+……….+x_(n)=280 Probability that a randomly selected triangle formed by vertices of a 2n+1 sided regular polygon is isosceles is

Accepted Answer

NA

Question 22

Consider a triangle ABC with vertex A(2-4).The internal bisectors of the angle B and C are x+y=2 and x-3y= 6 respectively Let the two bisector meet at I.  If (x_(1)y_(1)) and (x_(2)y_(2)) are the coordinates of the point B and C respectively the value of (x_(1)x_(2)+y_(1)y_(2)) is equal to

Accepted Answer

NA

Question 23

This passage was adapted from an article titled Quantum Computing Where is it Going? published in a science magazine in 2018. It discusses the background and potential of quantum computing.  Pharmaceutical companies dream of a time when their research and development process shifts from looking for illnesses whose symptoms can be ameliorated by a specific drug to choosing a diseaase and creating a frug to eradicate it.Quantum computing may be the key to that goal. The powerful modeling potential unlocked by quantum computing may also somedey be employed by autonomous vecicles to create a world free of traffic jams. With plausible applications in so many fields it is worthwhile to learn a bit about how quantum computing works.  Any understanding of quantum computing begins with its most bgasic element the qubit In classical computing information is processed by the bit the binary choice of zero or one. Qubits on the other hand allow for infinite superpositions between zero and one and thus can store and process exponentially more complicated values. imagine showing someone where you live on a globe by pointing only to either the North Pole or South Pole While you are likely closer to one pole than the other you need additional information to represent your specific location. If however you could provide your homes lititude and longitude it could be located without any additional information. The power of quantum computing lies in the ability to express precise information in a single qubit Quantum computing may help scientist and engineers overcome another barrie by reducing energy ouptup while increasing computational speed. The positive correlation between energy output and processing speed often causes classical computers to run hot while processing overwhelmine amounts of data. Along with their ability to store multiple value simultaneously qubits are able to process those values in parallel instead of serially. How does processing in parallel conserve energy ? Suppose you want to set the time on five separate alarm clocks spaced ten feet apart. Youd have to walk to each clock to change its time.  However if the clocks were connected such that changing the time on one immediatel7y adjusted the other four you would expend less energy and increase processing speed. Therein lies the benefit of the quantum entanglement of qubits. While quantum computing has moved beyond the realm of the theoretical significant barrieres still stand in he way of its practical application. One barrier is the diffcultly of confirming the results of quantum calculations. If quantum computing is used to solve problems that are impossible to solve with classical compting is there a way to check the results? Scientists hope this paradox may soon be resolved. As a graduate student Urmila Mahadev devoted over a decade to creating a verification process for quantum computing. The result is an interactive protocol based on a type of cryptography called Learning With Errors (LWE) that is similar to blind computing used in cloud-computing to mask data while still performing calculations. Given current limatations Mahadevs protocol remains purely theoretical but rapid progress in quantum comuting combined with further refinement of the protocol will likely result in real world implementation within the next decade or two.  It is unlikely that early pioneers in the field including Stephen Wiesner Richard Feynman and Paul Benioff could have foreseen the rapid progress that has been made to date. In 1960 when Wiesner first developed conjugate coding with the goal of improving cryptography his paper on the subject was rejected for publication because it contained logic far ahead of its time. Feynman proposed a basic quantum computing model at the 1981 First Conference on teh Physics of Computation. At that same conference Benioff spoke on the ability of discreate mechanical processes to rase their own history and their application to Turing machines a natural extension of Wiesners earlier work. A year later Benioff more clearly outlined the theoretical farmework of a quantum computer.  The dawn of the 21st century brought advancements at an even more impressive pace. The first 5-and 7-qubit nuclear magnetic resonance (NMR) computers were demonstrated in Munich Germany and Santa Fe New Mexico respectively. In 2006. researchers at Oxford were able to cage a qubit within a buckyball a buckminsterfullerene molecule and maintain its state for a short time using precies repated microwave pulses. The first company dedicated to quantum computing software 1QB Information Technologies was founded in 2012 and in 2018 Google announced the development of the 72-qubit Bristlecone chip designed to prove quantum supremacy the ability of quantum computers to solve problems beyond the reach of classical computing.  With progress in quantum computing accelerating it seems inevitable that within a fewdecades the general population will be as familiar with quantum computing as they now are with classical computing. At present quantum computing is limited by the struggle to build a computer large enough to prove quantum supremacy and the costs associated with quantum computing are prohibitive to all but the worlds largest corporations and governmental institutions. Still classical computing overcame similar problems so the future of quantum computing looks bright.  The authors attitude toward the potential success of quantum computing can best be described as

Accepted Answer

NA

Question 24

State True or False .There is no function whose derivative is log pi

Accepted Answer

NA

Question 25

This passage was adapted from an article titled Quantum Computing Where is it Going? published in a science magazine in 2018. It discusses the background and potential of quantum computing.  Pharmaceutical companies dream of a time when their research and development process shifts from looking for illnesses whose symptoms can be ameliorated by a specific drug to choosing a diseaase and creating a frug to eradicate it.Quantum computing may be the key to that goal. The powerful modeling potential unlocked by quantum computing may also somedey be employed by autonomous vecicles to create a world free of traffic jams. With plausible applications in so many fields it is worthwhile to learn a bit about how quantum computing works.  Any understanding of quantum computing begins with its most bgasic element the qubit In classical computing information is processed by the bit the binary choice of zero or one. Qubits on the other hand allow for infinite superpositions between zero and one and thus can store and process exponentially more complicated values. imagine showing someone where you live on a globe by pointing only to either the North Pole or South Pole While you are likely closer to one pole than the other you need additional information to represent your specific location. If however you could provide your homes lititude and longitude it could be located without any additional information. The power of quantum computing lies in the ability to express precise information in a single qubit Quantum computing may help scientist and engineers overcome another barrie by reducing energy ouptup while increasing computational speed. The positive correlation between energy output and processing speed often causes classical computers to run hot while processing overwhelmine amounts of data. Along with their ability to store multiple value simultaneously qubits are able to process those values in parallel instead of serially. How does processing in parallel conserve energy ? Suppose you want to set the time on five separate alarm clocks spaced ten feet apart. Youd have to walk to each clock to change its time.  However if the clocks were connected such that changing the time on one immediatel7y adjusted the other four you would expend less energy and increase processing speed. Therein lies the benefit of the quantum entanglement of qubits. While quantum computing has moved beyond the realm of the theoretical significant barrieres still stand in he way of its practical application. One barrier is the diffcultly of confirming the results of quantum calculations. If quantum computing is used to solve problems that are impossible to solve with classical compting is there a way to check the results? Scientists hope this paradox may soon be resolved. As a graduate student Urmila Mahadev devoted over a decade to creating a verification process for quantum computing. The result is an interactive protocol based on a type of cryptography called Learning With Errors (LWE) that is similar to blind computing used in cloud-computing to mask data while still performing calculations. Given current limatations Mahadevs protocol remains purely theoretical but rapid progress in quantum comuting combined with further refinement of the protocol will likely result in real world implementation within the next decade or two.  It is unlikely that early pioneers in the field including Stephen Wiesner Richard Feynman and Paul Benioff could have foreseen the rapid progress that has been made to date. In 1960 when Wiesner first developed conjugate coding with the goal of improving cryptography his paper on the subject was rejected for publication because it contained logic far ahead of its time. Feynman proposed a basic quantum computing model at the 1981 First Conference on teh Physics of Computation. At that same conference Benioff spoke on the ability of discreate mechanical processes to rase their own history and their application to Turing machines a natural extension of Wiesners earlier work. A year later Benioff more clearly outlined the theoretical farmework of a quantum computer.  The dawn of the 21st century brought advancements at an even more impressive pace. The first 5-and 7-qubit nuclear magnetic resonance (NMR) computers were demonstrated in Munich Germany and Santa Fe New Mexico respectively. In 2006. researchers at Oxford were able to cage a qubit within a buckyball a buckminsterfullerene molecule and maintain its state for a short time using precies repated microwave pulses. The first company dedicated to quantum computing software 1QB Information Technologies was founded in 2012 and in 2018 Google announced the development of the 72-qubit Bristlecone chip designed to prove quantum supremacy the ability of quantum computers to solve problems beyond the reach of classical computing.  With progress in quantum computing accelerating it seems inevitable that within a fewdecades the general population will be as familiar with quantum computing as they now are with classical computing. At present quantum computing is limited by the struggle to build a computer large enough to prove quantum supremacy and the costs associated with quantum computing are prohibitive to all but the worlds largest corporations and governmental institutions. Still classical computing overcame similar problems so the future of quantum computing looks bright.  As used in line 123 maintain most nearly means

Accepted Answer

NA

Question 26

This passage was adapted from an article titled Quantum Computing Where is it Going? published in a science magazine in 2018. It discusses the background and potential of quantum computing.  Pharmaceutical companies dream of a time when their research and development process shifts from looking for illnesses whose symptoms can be ameliorated by a specific drug to choosing a diseaase and creating a frug to eradicate it.Quantum computing may be the key to that goal. The powerful modeling potential unlocked by quantum computing may also somedey be employed by autonomous vecicles to create a world free of traffic jams. With plausible applications in so many fields it is worthwhile to learn a bit about how quantum computing works.  Any understanding of quantum computing begins with its most bgasic element the qubit In classical computing information is processed by the bit the binary choice of zero or one. Qubits on the other hand allow for infinite superpositions between zero and one and thus can store and process exponentially more complicated values. imagine showing someone where you live on a globe by pointing only to either the North Pole or South Pole While you are likely closer to one pole than the other you need additional information to represent your specific location. If however you could provide your homes lititude and longitude it could be located without any additional information. The power of quantum computing lies in the ability to express precise information in a single qubit Quantum computing may help scientist and engineers overcome another barrie by reducing energy ouptup while increasing computational speed. The positive correlation between energy output and processing speed often causes classical computers to run hot while processing overwhelmine amounts of data. Along with their ability to store multiple value simultaneously qubits are able to process those values in parallel instead of serially. How does processing in parallel conserve energy ? Suppose you want to set the time on five separate alarm clocks spaced ten feet apart. Youd have to walk to each clock to change its time.  However if the clocks were connected such that changing the time on one immediatel7y adjusted the other four you would expend less energy and increase processing speed. Therein lies the benefit of the quantum entanglement of qubits. While quantum computing has moved beyond the realm of the theoretical significant barrieres still stand in he way of its practical application. One barrier is the diffcultly of confirming the results of quantum calculations. If quantum computing is used to solve problems that are impossible to solve with classical compting is there a way to check the results? Scientists hope this paradox may soon be resolved. As a graduate student Urmila Mahadev devoted over a decade to creating a verification process for quantum computing. The result is an interactive protocol based on a type of cryptography called Learning With Errors (LWE) that is similar to blind computing used in cloud-computing to mask data while still performing calculations. Given current limatations Mahadevs protocol remains purely theoretical but rapid progress in quantum comuting combined with further refinement of the protocol will likely result in real world implementation within the next decade or two.  It is unlikely that early pioneers in the field including Stephen Wiesner Richard Feynman and Paul Benioff could have foreseen the rapid progress that has been made to date. In 1960 when Wiesner first developed conjugate coding with the goal of improving cryptography his paper on the subject was rejected for publication because it contained logic far ahead of its time. Feynman proposed a basic quantum computing model at the 1981 First Conference on teh Physics of Computation. At that same conference Benioff spoke on the ability of discreate mechanical processes to rase their own history and their application to Turing machines a natural extension of Wiesners earlier work. A year later Benioff more clearly outlined the theoretical farmework of a quantum computer.  The dawn of the 21st century brought advancements at an even more impressive pace. The first 5-and 7-qubit nuclear magnetic resonance (NMR) computers were demonstrated in Munich Germany and Santa Fe New Mexico respectively. In 2006. researchers at Oxford were able to cage a qubit within a buckyball a buckminsterfullerene molecule and maintain its state for a short time using precies repated microwave pulses. The first company dedicated to quantum computing software 1QB Information Technologies was founded in 2012 and in 2018 Google announced the development of the 72-qubit Bristlecone chip designed to prove quantum supremacy the ability of quantum computers to solve problems beyond the reach of classical computing.  With progress in quantum computing accelerating it seems inevitable that within a fewdecades the general population will be as familiar with quantum computing as they now are with classical computing. At present quantum computing is limited by the struggle to build a computer large enough to prove quantum supremacy and the costs associated with quantum computing are prohibitive to all but the worlds largest corporations and governmental institutions. Still classical computing overcame similar problems so the future of quantum computing looks bright.  Which choice provides the best evidence for the answer to the previous question ?

Accepted Answer

NA

Question 27

If the distance between the centres of two circles of radio 34 is 25 then the length of the tranverse common tangent is

Accepted Answer

NA

Question 28

Given f A to B and g B to A such that gof (x) = x AA xin B gof = I_(B) and fog = I_(A) then fog(x)=

Accepted Answer

NA

Question 29

Consider the function f(x)=f(x)=(x-1-1lexle0)(x^(2) 0lexle1)  andg(x)=sinx.  If h_(1)(x)=f(|g(x)|)  andh_(2)(x)=|f(g(x))|.  Which of the following is not true about h_(2)(x)?

Accepted Answer

NA

Question 30

Consider the function f(x)=f(x)=(x-1-1lexle0)(x^(2) 0lexle1)  andg(x)=sinx.  If h_(1)(x)=f(|g(x)|)  andh_(2)(x)=|f(g(x))|.  Which of the following is not true about h_(1)(x)?

Accepted Answer

NA

Question 31

P and Q are two points on the parabola ( y-2) ^(2) =(4-3) . The normals and tangents at P and Q form a square then point of intersection of tangents at P Q is

Accepted Answer

NA

Question 32

Match columnI to columan II according to the given condition  In column I the direction ratios of lines are given. In column II angle between them is given.

Accepted Answer

NA

Question 33

From a frequency distribution c = 3 l = 65 . 5 f = 42 m = 23 N = 102 then median is (l = lower limit of the median class m= cumulative frequency of the class preceeding the median class N = total frequency f = frequency of the median class c = width of the median class)

Accepted Answer

NA

Question 34

Let x+y=k be a normal to the parabola y^(2)=12x . If p is the length of the perpendicular from the focus of the parabola onto this normal then 4k-2p^(2) =

Accepted Answer

NA

Question 35

If vec(a)vec(b)vec(c )are three non coplanar vector such that vec(a)+vec(b)+vec(c )=alphavec(d) and vec(b)+vec(c )+vec(d)=betavec(a) then vec(a)+vec(b)+vec(c )+vec(d) is equal to

Accepted Answer

NA

Question 36

Equations of circles which touch both the axes and whose centres are at a distance of 2sqrt(2) units from origin are

Accepted Answer

NA

Question 37

A balanced dice is tossed twice. Find probability on an event that on first trial we get number 4 5 or 6 and in second trial we get number 1 2 3 or 4.

Accepted Answer

NA

Question 38

Two perpendiculars PQ and PR are drawn on the axes of the ellipse (x ^(2))(a^(2)) +(y^(2))(b ^(2))=1 from any arbitrary point P on the ellipse. The find the locus of the point T that divides (internally) QR in the fixed fatio lamda _(1) lamda_(2) (ab) lamda_(1)lamda_(2) in R a lamda_(1)- b lamda_(2)ne0).

Accepted Answer

NA

Question 39

This passage was adapted from an article titled Quantum Computing Where is it Going? published in a science magazine in 2018. It discusses the background and potential of quantum computing.  Pharmaceutical companies dream of a time when their research and development process shifts from looking for illnesses whose symptoms can be ameliorated by a specific drug to choosing a diseaase and creating a frug to eradicate it.Quantum computing may be the key to that goal. The powerful modeling potential unlocked by quantum computing may also somedey be employed by autonomous vecicles to create a world free of traffic jams. With plausible applications in so many fields it is worthwhile to learn a bit about how quantum computing works.  Any understanding of quantum computing begins with its most bgasic element the qubit In classical computing information is processed by the bit the binary choice of zero or one. Qubits on the other hand allow for infinite superpositions between zero and one and thus can store and process exponentially more complicated values. imagine showing someone where you live on a globe by pointing only to either the North Pole or South Pole While you are likely closer to one pole than the other you need additional information to represent your specific location. If however you could provide your homes lititude and longitude it could be located without any additional information. The power of quantum computing lies in the ability to express precise information in a single qubit Quantum computing may help scientist and engineers overcome another barrie by reducing energy ouptup while increasing computational speed. The positive correlation between energy output and processing speed often causes classical computers to run hot while processing overwhelmine amounts of data. Along with their ability to store multiple value simultaneously qubits are able to process those values in parallel instead of serially. How does processing in parallel conserve energy ? Suppose you want to set the time on five separate alarm clocks spaced ten feet apart. Youd have to walk to each clock to change its time.  However if the clocks were connected such that changing the time on one immediatel7y adjusted the other four you would expend less energy and increase processing speed. Therein lies the benefit of the quantum entanglement of qubits. While quantum computing has moved beyond the realm of the theoretical significant barrieres still stand in he way of its practical application. One barrier is the diffcultly of confirming the results of quantum calculations. If quantum computing is used to solve problems that are impossible to solve with classical compting is there a way to check the results? Scientists hope this paradox may soon be resolved. As a graduate student Urmila Mahadev devoted over a decade to creating a verification process for quantum computing. The result is an interactive protocol based on a type of cryptography called Learning With Errors (LWE) that is similar to blind computing used in cloud-computing to mask data while still performing calculations. Given current limatations Mahadevs protocol remains purely theoretical but rapid progress in quantum comuting combined with further refinement of the protocol will likely result in real world implementation within the next decade or two.  It is unlikely that early pioneers in the field including Stephen Wiesner Richard Feynman and Paul Benioff could have foreseen the rapid progress that has been made to date. In 1960 when Wiesner first developed conjugate coding with the goal of improving cryptography his paper on the subject was rejected for publication because it contained logic far ahead of its time. Feynman proposed a basic quantum computing model at the 1981 First Conference on teh Physics of Computation. At that same conference Benioff spoke on the ability of discreate mechanical processes to rase their own history and their application to Turing machines a natural extension of Wiesners earlier work. A year later Benioff more clearly outlined the theoretical farmework of a quantum computer.  The dawn of the 21st century brought advancements at an even more impressive pace. The first 5-and 7-qubit nuclear magnetic resonance (NMR) computers were demonstrated in Munich Germany and Santa Fe New Mexico respectively. In 2006. researchers at Oxford were able to cage a qubit within a buckyball a buckminsterfullerene molecule and maintain its state for a short time using precies repated microwave pulses. The first company dedicated to quantum computing software 1QB Information Technologies was founded in 2012 and in 2018 Google announced the development of the 72-qubit Bristlecone chip designed to prove quantum supremacy the ability of quantum computers to solve problems beyond the reach of classical computing.  With progress in quantum computing accelerating it seems inevitable that within a fewdecades the general population will be as familiar with quantum computing as they now are with classical computing. At present quantum computing is limited by the struggle to build a computer large enough to prove quantum supremacy and the costs associated with quantum computing are prohibitive to all but the worlds largest corporations and governmental institutions. Still classical computing overcame similar problems so the future of quantum computing looks bright.  Which one of the following does the passage imply about the development of quantum computing in the 21st century ?

Accepted Answer

NA

Question 40

Find the equation of the circle which passes through the points (20)(02) and orthogonal to the circle 2x^2+2y^2+5x-6y+4=0 .

Accepted Answer

NA

Question 41

This passage was adapted from an article titled Quantum Computing Where is it Going? published in a science magazine in 2018. It discusses the background and potential of quantum computing.  Pharmaceutical companies dream of a time when their research and development process shifts from looking for illnesses whose symptoms can be ameliorated by a specific drug to choosing a diseaase and creating a frug to eradicate it.Quantum computing may be the key to that goal. The powerful modeling potential unlocked by quantum computing may also somedey be employed by autonomous vecicles to create a world free of traffic jams. With plausible applications in so many fields it is worthwhile to learn a bit about how quantum computing works.  Any understanding of quantum computing begins with its most bgasic element the qubit In classical computing information is processed by the bit the binary choice of zero or one. Qubits on the other hand allow for infinite superpositions between zero and one and thus can store and process exponentially more complicated values. imagine showing someone where you live on a globe by pointing only to either the North Pole or South Pole While you are likely closer to one pole than the other you need additional information to represent your specific location. If however you could provide your homes lititude and longitude it could be located without any additional information. The power of quantum computing lies in the ability to express precise information in a single qubit Quantum computing may help scientist and engineers overcome another barrie by reducing energy ouptup while increasing computational speed. The positive correlation between energy output and processing speed often causes classical computers to run hot while processing overwhelmine amounts of data. Along with their ability to store multiple value simultaneously qubits are able to process those values in parallel instead of serially. How does processing in parallel conserve energy ? Suppose you want to set the time on five separate alarm clocks spaced ten feet apart. Youd have to walk to each clock to change its time.  However if the clocks were connected such that changing the time on one immediatel7y adjusted the other four you would expend less energy and increase processing speed. Therein lies the benefit of the quantum entanglement of qubits. While quantum computing has moved beyond the realm of the theoretical significant barrieres still stand in he way of its practical application. One barrier is the diffcultly of confirming the results of quantum calculations. If quantum computing is used to solve problems that are impossible to solve with classical compting is there a way to check the results? Scientists hope this paradox may soon be resolved. As a graduate student Urmila Mahadev devoted over a decade to creating a verification process for quantum computing. The result is an interactive protocol based on a type of cryptography called Learning With Errors (LWE) that is similar to blind computing used in cloud-computing to mask data while still performing calculations. Given current limatations Mahadevs protocol remains purely theoretical but rapid progress in quantum comuting combined with further refinement of the protocol will likely result in real world implementation within the next decade or two.  It is unlikely that early pioneers in the field including Stephen Wiesner Richard Feynman and Paul Benioff could have foreseen the rapid progress that has been made to date. In 1960 when Wiesner first developed conjugate coding with the goal of improving cryptography his paper on the subject was rejected for publication because it contained logic far ahead of its time. Feynman proposed a basic quantum computing model at the 1981 First Conference on teh Physics of Computation. At that same conference Benioff spoke on the ability of discreate mechanical processes to rase their own history and their application to Turing machines a natural extension of Wiesners earlier work. A year later Benioff more clearly outlined the theoretical farmework of a quantum computer.  The dawn of the 21st century brought advancements at an even more impressive pace. The first 5-and 7-qubit nuclear magnetic resonance (NMR) computers were demonstrated in Munich Germany and Santa Fe New Mexico respectively. In 2006. researchers at Oxford were able to cage a qubit within a buckyball a buckminsterfullerene molecule and maintain its state for a short time using precies repated microwave pulses. The first company dedicated to quantum computing software 1QB Information Technologies was founded in 2012 and in 2018 Google announced the development of the 72-qubit Bristlecone chip designed to prove quantum supremacy the ability of quantum computers to solve problems beyond the reach of classical computing.  With progress in quantum computing accelerating it seems inevitable that within a fewdecades the general population will be as familiar with quantum computing as they now are with classical computing. At present quantum computing is limited by the struggle to build a computer large enough to prove quantum supremacy and the costs associated with quantum computing are prohibitive to all but the worlds largest corporations and governmental institutions. Still classical computing overcame similar problems so the future of quantum computing looks bright.  The passage indicates that which of the following factors slowed early developments in the theory of quantum computing ?

Accepted Answer

NA

Question 42

Evalute the following integrals  int (1)(x^(4)+ x^(2) + 1) dx

Accepted Answer

NA

Question 43

Evalute the following integrals  int (1)(x^(4) - x^(2) + 1) dx

Accepted Answer

NA

Question 44

The order of the differential equation of all circles with centre at (hk) and radius a is …….

Accepted Answer

NA

Question 45

Compute quartile deviation for the following data

Accepted Answer

NA

Question 46

If x is so small that x^(3) and higher power of x may neglected then ((1 + x)^(32) - (1 + 12x)^(3))(1 - x)^(12) may be approximated as

Accepted Answer

NA

Question 47

If P((A)(B)) = 0.75 P((B)(A)) = 0.6 P(A)= 0.4 evaluate P(B).a) 0.26 b) (1)(3) c) (2)(5) d) 0.32

Accepted Answer

NA

Question 48

If z_1 z_2 z_3 are complex numbers such that absz_1 = absz_2 = absz_3 = abs(1z_1 + 1z_2+ 1z_3) =1 then show that abs(z_1 + z_2 + z_3) = 1.

Accepted Answer

NA

Question 49

Integrate the functions  (sin^(-1)sqrtx-cos^(-1)sqrtx)(sin^(-1)sqrtx+cos^(-1)sqrtx).

Accepted Answer

NA

Question 50

If four fair dice are rolled find the probability that exactly three of them show the same number.

Accepted Answer

NA

3351.	If the centre of a circle is (3, 4) and its size is just sufficient to contain to circle x^(2) + y^(2) =1. Then the radius of the required circle is _____.
Answer» ANSWER :6

3352.	Evaluate the following : [[11,23,31],[12,19,14],[6,9,7]]
Answer» SOLUTION :`[[11,23,31],[12,19,14],[6,9,7]]= [[11,23,31],[12,19,14],[6,9,7]]` `(R_2~~R_2-2R_2)` `1[[11,31],[6,7]]` =77-186=-109

3353.	(1^(2).2^2)/(1!) +(2^(2).3^2)/(2!) + (3^(2).4^2)/(3!) + .....oo =
Answer» 27 E 17 e 7e e Answer :A

3354.	Discuss the continuity of the function f defined byf(x)= {:{(x +3, if x le 1 ), (x -3, if x gt 1):}
Answer» Solution :The function f(x) is definedat all points of the real LINE. Case I : LET x = c be any arbitrary real number in the domain of f(x). If c lt 1 , then f(c ) = c +3 , therefore ` underset(x to c) lim f(x) = underset(x to c)lim (x+3) = c +3` Thus, f is CONTINUOUS at all real numbers less than 1. Case II. If c gt 1then f(c) = c -3 , therefore ` underset(x to c) lim f(x) = underset(x to c) lim (x-3) = (c -3) = f(c)` Thus, f(x) is continuous at all points x gt 1 . Case III. If c=1,then the left hand limit of f(c) at x =1 ` underset(x to 1^(-))lim f(x) = underset(x to 1^(+))(x -3) = 1 -3 = -2` Since the left and right hand LIMITS of f(x) at x=1do not coincide, f(x)is , not continuous at x =1 . Hence x =1 is the only pointof DISCONTINUITY of f(x). the graph of the function is as show.

3355.	If a/(b + c), b/(c + a), c/(a + b) are in A.P., then
Answer» `a, B, C` are in A.P. `c, a, b` are in A.P. `a^(2), b^(2), c^(2)` are in A.P. `a, b, c` are in G.P. Answer :C

3356.	If a set A has m elements and a set B has n elements then the number of relation from a to B is ...........
Answer» `2^(m+n)` `2^(MN)` `m+n` `mn` SOLUTION :N/A

3357.	If ablt0, a gt b, and b gt-b, which of the following must be true?
Answer» `a//B GT0` `a+b LT0` `b-(-a) gt0` `a//b=1` ANSWER :C

3358.	Let A and B be events with P(A)= 3/8, P(B)= 1/2 andP(A cap B) = 1/4,Find P(A^c) and P(B^c)
Answer» <P> ANSWER :`P(A)=3/8,P(B)=1/2,P(ACAPB)=1/4` `P(A^c)=1-P(A)=1-3/8=5/8` `P(B^c)=1-P(B)=1-1/2=1/2`

3359.	Find the equation of the circle passing through the points of intersection of the ellipse (x^(2))/(16) + (y^(2))/(9) =1 and (x^(2))/(9) + (y^(2))/(16) =1 ______ .
Answer» SOLUTION :`X^(2) + y^(2) = (288)/(25)`

3360.	If p, q and r anre 3 statements, then the truth value of ((-p vv q) ^^ r) implies p is
Answer» True if truth values of p, q, R are T, F, T RESPECTIVELY FALSE if truth values of p, q, r are T, F, T respectively False if truth values of p, q, r are T, F, F respectively False if truth values of p, q, r are T, T, T respectively Answer :A

3363.	overset(1)underset(0)int x log(1+2x)dx
Answer» ANSWER :`: I=(3)/(8) log_(E)3`

3370.	Hydration energy of A_(g)^(+2) "is" (in kJ//mol^(-1))
Answer» -250 -150 -100 -50 Answer :B

3371.	Let x_(i) epsilonR,i=1,2,3……….n are numbers such that sum_(i=1)^(n)isqrt(x_(i)-i^(2))=(sum_(i=1)^(n)x_(i))/2 and x_(1)+x_(2)+……….+x_(n)=280 Probability that a randomly selected triangle formed by vertices of a 2n+1 sided regular polygon is isosceles is
Answer» `3/13` `5/13` `7/13` `9/13` Solution :`sum_(i=1)^(N-1)(x_(i)-2isqrt(x_(i)-i^(2)))=0` `sum_(i=1)^(n-1)(sqrt(x_(i)-i^(2)))^(2)-2isqrt(x_(i)-i^(2))+i^(2)=0` `sum_(i=1)^(n-1)(sqrt(x_(i)-i^(2))-i)^(2)=0` so, `x_(i)=2i^(2)` Now, `x_(1)^(2)+….+x_(n)^(2)=280` `2[1^(2)+2^(2)+........n^(2)]=280` `n=7` `y_(1)+y_(2)+y_(3)=7` `y_(1)^(1)+y_(2)^(1)+y_(3)^(1)=4` `.^(4+3-1)C_(3)=.^(6)C_(3)=20` Total triangles formed `=.^(15)C_(3)=(15xx14xx13)/6` `N` of isosceles triangles formed `=15xx7` probability `=(15xx7)/(15xx14xx13)xx6` `3/13`

3385.	If vec(a),vec(b),vec(c )are three non coplanar vector such that vec(a)+vec(b)+vec(c )=alphavec(d) and vec(b)+vec(c )+vec(d)=betavec(a), then vec(a)+vec(b)+vec(c )+vec(d) is equal to
Answer» `vec(0)` `alphavec (a)` `betavec(B)` `(alpha-beta)vec(c )` SOLUTION :`because vec(a)+vec(b)+vec(c)=alphavec(d) " and " vec(b)+vec(c)+vec(d)=betavec(a)impliesvec(a)+vec(b)+vec(c)=alphavec(d) " and " vec(d)=betavec(a)-vec(b)-vec(c)` `impliesvec(a)+vec(b)+vec(c)=alpha(betavec(a)-vec(b)-vec(c))IMPLIES(1-alphabeta)vec(a)+(1+alpha)vec(b)+(1+alpha)vec(c)=vec(0)` `impliesalphabeta=1,alpha=-1{because vec(a),vec(b),vec(c)" arenon COPLANAR"}implies alpha=beta=-1` `becausevec(a)+vec(b)+vec(c)=alphavec(d)impliesvec(a)+vec(b)+vec(c)+vec(d)=vec(0)`

3361.	A : If \|z+1\| -\|z-1\| =3/2 then the least value of \|z\| is 3/4 R : If z_1,z_2 are two complex numbers then \|z_1-z_2\|ge\|\|z_1\|-\|z_2\|\|
Answer» A is true , R is true and R CORRECT EXPLANATION of A A is true , R is true and R is not correct explanationof A A is true , R is FALSE A is false, R is true Answer :B

3362.	Given that E and F are events such that P(E) = 0.6,P(F)= 0.3 and P(EnnF)=0.2.Find P (F/E).
Answer» <P> SOLUTION :P(F/E)=(P`(ENNF))/(P(E))`=0.2/0.6=1/3

3364.	If bara=(1,-1,-6),barb=(1,-3,4)" and "barc=(2,-5,3), then compare bara xx(barb xx barc).
Answer» ANSWER :`29bari-67barj+16bark`.

3365.	Find the area of the surface out off from a right circular cylinder by a plane passing through the diameter of the base and inclined at an angle of 45^(@) to the base.
Answer» ANSWER :`2A^(2)`

3366.	The radius of a circle is increasing at the rate of 0.7 cm/s. What is the rate of increase of its circumference ?
Answer» ANSWER :`=1.4 PI cm//sec`.

3367.	Findthe multipleroots ofx^4 - 6x^3 + 13 x^2 - 24 x +36 =0
Answer» ANSWER :`3,3,+- 2I`

3368.	(i) Which of the following correspondences can be called a function? (A) f(x)=x^(3),{-1,0,1}to{0,1,2,3} (B)f(x)=+-sqrt(x),{0,1,4}to{-2,-1,0,1,2} (C)f(x)=sqrt(x),{0,1,4}to{0,1,4}to{-2,-1,0,1,2} (D) f(x)=-sqrt(x),{0,1,4}to{-2,-1,0,1,2} (ii) Which of the following pictorial diagrams represent the function
Answer» Solution :(i) `f(x)` in (C) and (D) are functions as definition of function is satisfied. While in case of (A) the given relation is not a function, as `f(-1)!in` 2nd SET. Hence definition of function is not satisfied. While in case of (B), the given relation is not a function as `f(1)=+-1` and `f(4)=+-2` i.e. element 1 as well as 4 in 1st set is related with TWO ELEMENTS of 2nd set. Hence definition of function is not satisfied. (ii) B and D. In (A) ONE element of domain has no image, while in (C) one element of 1st set has two images in 2nd set

3369.	Find the equation of lines regression from the following data : Correlation of coefficient = (2)/(3)
Answer» ANSWER :REGRESSION equation of yon x : `16 x - 33y + 2229 = 0` Regression equation of x on y : `12- 11Y + 503 = 0`

3372.	Consider a triangle ABC with vertex A(2,-4).The internal bisectors of the angle B and C are x+y=2 and x-3y= 6 respectively, Let the two bisector meet at I. If (x_(1),y_(1)) and (x_(2),y_(2)) are the coordinates of the point B and C respectively, the value of (x_(1)x_(2)+y_(1)y_(2)) is equal to
Answer» 4 5 6 8 Answer :A

3373.	This passage was adapted from an article titled "Quantum Computing, Where is it Going?" published in a science magazine in 2018. It discusses the background and potential of quantum computing. Pharmaceutical companies dream of a time when their research and development process shifts from looking for illnesses whose symptoms can be ameliorated by a specific drug to choosing a diseaase and creating a frug to eradicate it.Quantum computing may be the key to that goal. The powerful modeling potential unlocked by quantum computing may also somedey be employed by autonomous vecicles to create a world free of traffic jams. With plausible applications in so many fields, it is worthwhile to learn a bit about how quantum computing works. Any understanding of quantum computing begins with its most bgasic element, the qubit In classical computing, information is processed by the bit, the binary choice of zero or one. Qubits, on the other hand, allow for infinite superpositions between zero and one and thus can store and process exponentially more complicated values. imagine showing someone where you live on a globe by pointing only to either the North Pole or South Pole While you are likely closer to one pole than the other, you need additional information to represent your specific location. If, however, you could provide your home's lititude and longitude, it could be located without any additional information. The power of quantum computing lies in the ability to express precise information in a single qubit Quantum computing may help scientist and engineers overcome another barrie by reducing energy ouptup while increasing computational speed. The positive correlation between energy output and processing speed often causes classical computers to "run hot" while processing overwhelmine amounts of data. Along with their ability to store m,ultiple value simultaneously, qubits are able to process those values in parallel instead of serially. How does processing in parallel conserve energy ? Suppose you want to set the time on five separate alarm clocks spaced ten feet apart. You'd have to walk to each clock to change its time. However if the clocks were connected such that changing the time on one immediatel7y adjusted the other four, you would expend less energy and increase processing speed. Therein lies the benefit of the quantum entanglement of qubits. While quantum computing has moved beyond the realm of the theoretical, significant barrieres still stand in he way of its practical application. One barrier is the diffcultly of confirming the results of quantum calculations. If quantum computing is used to solve problems that are impossible to solve with classical compting, is there a way to "check" the results? Scientists hope this paradox may soon be resolved. As a graduate student, Urmila Mahadev devoted over a decade to creating a verification process for quantum computing. The result is an interactive protocol, based on a type of cryptography called Learning With Errors (LWE), that is similar to "blind computing" used in cloud-computing to mask data while still performing calculations. Given current limatations, Mahadev's protocol remains purely theoretical, but rapid progress in quantum comuting combined with further refinement of the protocol will likely result in real world implementation within the next decade or two. It is unlikely that early pioneers in the field, including Stephen Wiesner, Richard Feynman, and Paul Benioff, could have foreseen the rapid progress that has been made to date. In 1960, when Wiesner first developed conjugate coding with the goal of improving cryptography, his paper on the subject was rejected for publication because it contained logic far ahead of its time. Feynman proposed a basic quantum computing model at the 1981 First Conference on teh Physics of Computation. At that same conference, Benioff spoke on the ability of discreate mechanical processes to rase their own history and their application to Turing machines, a natural extension of Wiesner's earlier work. A year later, Benioff more clearly outlined the theoretical farmework of a quantum computer. The dawn of the 21st century brought advancements at an even more impressive pace. The first 5-and 7-qubit nuclear magnetic resonance (NMR) computers were demonstrated in Munich, Germany, and Santa Fe, New Mexico, respectively. In 2006. researchers at Oxford were able to cage a qubit within a "buckyball," a buckminsterfullerene molecule, and maintain its state for a short time using precies, repated microwave pulses. The first company dedicated to quantum computing software, 1QB Information Technologies, was founded in 2012, and in 2018, Google announced the development of the 72-qubit Bristlecone chip designed to prove "quantum supremacy," the ability of quantum computers to solve problems beyond the reach of classical computing. With progress in quantum computing accelerating, it seems inevitable that within a fewdecades, the general population will be as familiar with quantum computing as they now are with classical computing. At present, quantum computing is limited by the struggle to build a computer large enough to prove quantum supremacy, and the costs associated with quantum computing are prohibitive to all but the world's largest corporations and governmental institutions. Still classical computing overcame similar problems, so the future of quantum computing looks bright. The author's attitude toward the potential success of quantum computing can best be described as
Answer» skeptical. resigned. incredulous. optimistic. ANSWER :D

Explore topic-wise InterviewSolutions in .

If the centre of a circle is (3, 4) and its size is just sufficient to contain to circle x^(2) + y^(2) =1. Then the radius of the required circle is _____.

Evaluate the following : [[11,23,31],[12,19,14],[6,9,7]]

(1^(2).2^2)/(1!) +(2^(2).3^2)/(2!) + (3^(2).4^2)/(3!) + .....oo =

Discuss the continuity of the function f defined byf(x)= {:{(x +3, if x le 1 ), (x -3, if x gt 1):}

If a/(b + c), b/(c + a), c/(a + b) are in A.P., then

If a set A has m elements and a set B has n elements then the number of relation from a to B is ...........

If ablt0, a gt b, and b gt-b, which of the following must be true?

Let A and B be events with P(A)= 3/8, P(B)= 1/2 andP(A cap B) = 1/4,Find P(A^c) and P(B^c)

Find the equation of the circle passing through the points of intersection of the ellipse (x^(2))/(16) + (y^(2))/(9) =1 and (x^(2))/(9) + (y^(2))/(16) =1 ______ .

If p, q and r anre 3 statements, then the truth value of ((-p vv q) ^^ r) implies p is

A : If |z+1| -|z-1| =3/2 then the least value of |z| is 3/4 R : If z_1,z_2 are two complex numbers then |z_1-z_2|ge||z_1|-|z_2||

Given that E and F are events such that P(E) = 0.6,P(F)= 0.3 and P(EnnF)=0.2.Find P (F/E).

overset(1)underset(0)int x log(1+2x)dx

If bara=(1,-1,-6),barb=(1,-3,4)" and "barc=(2,-5,3), then compare bara xx(barb xx barc).

Find the area of the surface out off from a right circular cylinder by a plane passing through the diameter of the base and inclined at an angle of 45^(@) to the base.

The radius of a circle is increasing at the rate of 0.7 cm/s. What is the rate of increase of its circumference ?

Findthe multipleroots ofx^4 - 6x^3 + 13 x^2 - 24 x +36 =0

Find the equation of lines regression from the following data : Correlation of coefficient = (2)/(3)

Hydration energy of A_(g)^(+2) "is" (in kJ//mol^(-1))

Let x_(i) epsilonR,i=1,2,3……….n are numbers such that sum_(i=1)^(n)isqrt(x_(i)-i^(2))=(sum_(i=1)^(n)x_(i))/2 and x_(1)+x_(2)+……….+x_(n)=280 Probability that a randomly selected triangle formed by vertices of a 2n+1 sided regular polygon is isosceles is

Consider a triangle ABC with vertex A(2,-4).The internal bisectors of the angle B and C are x+y=2 and x-3y= 6 respectively, Let the two bisector meet at I. If (x_(1),y_(1)) and (x_(2),y_(2)) are the coordinates of the point B and C respectively, the value of (x_(1)x_(2)+y_(1)y_(2)) is equal to

State True or False .There is no function whose derivative is log pi

If the distance between the centres of two circles of radio 3,4 is 25 then the length of the tranverse common tangent is

Given f: A to B and g: B to A, such that gof (x) = x , AA xin B , gof = I_(B) and fog = I_(A), then fog(x)=

Consider the function f(x)=f(x)={{:(x-1",",-1lexle0),(x^(2)",", 0lexle1):} and""g(x)=sinx. If h_(1)(x)=f(|g(x)|) " and"h_(2)(x)=|f(g(x))|. Which of the following is not true about h_(2)(x)?

Consider the function f(x)=f(x)={{:(x-1",",-1lexle0),(x^(2)",", 0lexle1):} and""g(x)=sinx. If h_(1)(x)=f(|g(x)|) " and"h_(2)(x)=|f(g(x))|. Which of the following is not true about h_(1)(x)?

P and Q are two points on the parabola ( y-2) ^(2) =(4-3) . The normals and tangents at P and Q form a square then point of intersection of tangents at P, Q is

Match columnI to columan II according to the given condition In column I the direction ratios of lines are given. In column II angle between them is given.

From a frequency distribution, c = 3, l = 65 . 5 f = 42, m = 23, N = 102 then median is (l = lower limit of the median class, m= cumulative frequency of the class preceeding the median class, N = total frequency, f = frequency of the median class, c = width of the median class)

Let x+y=k be a normal to the parabola y^(2)=12x . If p is the length of the perpendicular from the focus of the parabola onto this normal then 4k-2p^(2) =

If vec(a),vec(b),vec(c )are three non coplanar vector such that vec(a)+vec(b)+vec(c )=alphavec(d) and vec(b)+vec(c )+vec(d)=betavec(a), then vec(a)+vec(b)+vec(c )+vec(d) is equal to

Equations of circles which touch both the axes and whose centres are at a distance of 2sqrt(2) units from origin are

A balanced dice is tossed twice. Find probability on an event that on first trial we get number 4, 5 or 6 and in second trial we get number 1, 2, 3 or 4.

Find the equation of the circle which passes through the points (2,0)(0,2) and orthogonal to the circle 2x^2+2y^2+5x-6y+4=0 .

Evalute the following integrals int (1)/(x^(4)+ x^(2) + 1) dx

Evalute the following integrals int (1)/(x^(4) - x^(2) + 1) dx

The order of the differential equation of all circles with centre at (h,k) and radius 'a' is …….

Compute quartile deviation for the following data:

If x is so small that x^(3) and higher power of x may neglected, then ((1 + x)^(3/2) - (1 + 1/2x)^(3))/(1 - x)^(1/2) may be approximated as

If P((A)/(B)) = 0.75, P((B)/(A)) = 0.6, P(A)= 0.4, evaluate P(B).a) 0.26 b) (1)/(3) c) (2)/(5) d) 0.32

If z_1, z_2, z_3 are complex numbers such that absz_1 = absz_2 = absz_3 = abs(1/z_1 + 1/z_2+ 1/z_3) =1 then show that abs(z_1 + z_2 + z_3) = 1.

Integrate the functions (sin^(-1)sqrtx-cos^(-1)sqrtx)/(sin^(-1)sqrtx+cos^(-1)sqrtx).

If four fair dice are rolled, find the probability that exactly three of them show the same number.

3374.	State True or False .There is no function whose derivative is log pi
Answer» ANSWER :F

3375.	This passage was adapted from an article titled "Quantum Computing, Where is it Going?" published in a science magazine in 2018. It discusses the background and potential of quantum computing. Pharmaceutical companies dream of a time when their research and development process shifts from looking for illnesses whose symptoms can be ameliorated by a specific drug to choosing a diseaase and creating a frug to eradicate it.Quantum computing may be the key to that goal. The powerful modeling potential unlocked by quantum computing may also somedey be employed by autonomous vecicles to create a world free of traffic jams. With plausible applications in so many fields, it is worthwhile to learn a bit about how quantum computing works. Any understanding of quantum computing begins with its most bgasic element, the qubit In classical computing, information is processed by the bit, the binary choice of zero or one. Qubits, on the other hand, allow for infinite superpositions between zero and one and thus can store and process exponentially more complicated values. imagine showing someone where you live on a globe by pointing only to either the North Pole or South Pole While you are likely closer to one pole than the other, you need additional information to represent your specific location. If, however, you could provide your home's lititude and longitude, it could be located without any additional information. The power of quantum computing lies in the ability to express precise information in a single qubit Quantum computing may help scientist and engineers overcome another barrie by reducing energy ouptup while increasing computational speed. The positive correlation between energy output and processing speed often causes classical computers to "run hot" while processing overwhelmine amounts of data. Along with their ability to store m,ultiple value simultaneously, qubits are able to process those values in parallel instead of serially. How does processing in parallel conserve energy ? Suppose you want to set the time on five separate alarm clocks spaced ten feet apart. You'd have to walk to each clock to change its time. However if the clocks were connected such that changing the time on one immediatel7y adjusted the other four, you would expend less energy and increase processing speed. Therein lies the benefit of the quantum entanglement of qubits. While quantum computing has moved beyond the realm of the theoretical, significant barrieres still stand in he way of its practical application. One barrier is the diffcultly of confirming the results of quantum calculations. If quantum computing is used to solve problems that are impossible to solve with classical compting, is there a way to "check" the results? Scientists hope this paradox may soon be resolved. As a graduate student, Urmila Mahadev devoted over a decade to creating a verification process for quantum computing. The result is an interactive protocol, based on a type of cryptography called Learning With Errors (LWE), that is similar to "blind computing" used in cloud-computing to mask data while still performing calculations. Given current limatations, Mahadev's protocol remains purely theoretical, but rapid progress in quantum comuting combined with further refinement of the protocol will likely result in real world implementation within the next decade or two. It is unlikely that early pioneers in the field, including Stephen Wiesner, Richard Feynman, and Paul Benioff, could have foreseen the rapid progress that has been made to date. In 1960, when Wiesner first developed conjugate coding with the goal of improving cryptography, his paper on the subject was rejected for publication because it contained logic far ahead of its time. Feynman proposed a basic quantum computing model at the 1981 First Conference on teh Physics of Computation. At that same conference, Benioff spoke on the ability of discreate mechanical processes to rase their own history and their application to Turing machines, a natural extension of Wiesner's earlier work. A year later, Benioff more clearly outlined the theoretical farmework of a quantum computer. The dawn of the 21st century brought advancements at an even more impressive pace. The first 5-and 7-qubit nuclear magnetic resonance (NMR) computers were demonstrated in Munich, Germany, and Santa Fe, New Mexico, respectively. In 2006. researchers at Oxford were able to cage a qubit within a "buckyball," a buckminsterfullerene molecule, and maintain its state for a short time using precies, repated microwave pulses. The first company dedicated to quantum computing software, 1QB Information Technologies, was founded in 2012, and in 2018, Google announced the development of the 72-qubit Bristlecone chip designed to prove "quantum supremacy," the ability of quantum computers to solve problems beyond the reach of classical computing. With progress in quantum computing accelerating, it seems inevitable that within a fewdecades, the general population will be as familiar with quantum computing as they now are with classical computing. At present, quantum computing is limited by the struggle to build a computer large enough to prove quantum supremacy, and the costs associated with quantum computing are prohibitive to all but the world's largest corporations and governmental institutions. Still classical computing overcame similar problems, so the future of quantum computing looks bright. As used in line 123," maintain" most nearly means
Answer» SUSTAIN. repair. resupply. nurture. Answer :A

3376.	This passage was adapted from an article titled "Quantum Computing, Where is it Going?" published in a science magazine in 2018. It discusses the background and potential of quantum computing. Pharmaceutical companies dream of a time when their research and development process shifts from looking for illnesses whose symptoms can be ameliorated by a specific drug to choosing a diseaase and creating a frug to eradicate it.Quantum computing may be the key to that goal. The powerful modeling potential unlocked by quantum computing may also somedey be employed by autonomous vecicles to create a world free of traffic jams. With plausible applications in so many fields, it is worthwhile to learn a bit about how quantum computing works. Any understanding of quantum computing begins with its most bgasic element, the qubit In classical computing, information is processed by the bit, the binary choice of zero or one. Qubits, on the other hand, allow for infinite superpositions between zero and one and thus can store and process exponentially more complicated values. imagine showing someone where you live on a globe by pointing only to either the North Pole or South Pole While you are likely closer to one pole than the other, you need additional information to represent your specific location. If, however, you could provide your home's lititude and longitude, it could be located without any additional information. The power of quantum computing lies in the ability to express precise information in a single qubit Quantum computing may help scientist and engineers overcome another barrie by reducing energy ouptup while increasing computational speed. The positive correlation between energy output and processing speed often causes classical computers to "run hot" while processing overwhelmine amounts of data. Along with their ability to store m,ultiple value simultaneously, qubits are able to process those values in parallel instead of serially. How does processing in parallel conserve energy ? Suppose you want to set the time on five separate alarm clocks spaced ten feet apart. You'd have to walk to each clock to change its time. However if the clocks were connected such that changing the time on one immediatel7y adjusted the other four, you would expend less energy and increase processing speed. Therein lies the benefit of the quantum entanglement of qubits. While quantum computing has moved beyond the realm of the theoretical, significant barrieres still stand in he way of its practical application. One barrier is the diffcultly of confirming the results of quantum calculations. If quantum computing is used to solve problems that are impossible to solve with classical compting, is there a way to "check" the results? Scientists hope this paradox may soon be resolved. As a graduate student, Urmila Mahadev devoted over a decade to creating a verification process for quantum computing. The result is an interactive protocol, based on a type of cryptography called Learning With Errors (LWE), that is similar to "blind computing" used in cloud-computing to mask data while still performing calculations. Given current limatations, Mahadev's protocol remains purely theoretical, but rapid progress in quantum comuting combined with further refinement of the protocol will likely result in real world implementation within the next decade or two. It is unlikely that early pioneers in the field, including Stephen Wiesner, Richard Feynman, and Paul Benioff, could have foreseen the rapid progress that has been made to date. In 1960, when Wiesner first developed conjugate coding with the goal of improving cryptography, his paper on the subject was rejected for publication because it contained logic far ahead of its time. Feynman proposed a basic quantum computing model at the 1981 First Conference on teh Physics of Computation. At that same conference, Benioff spoke on the ability of discreate mechanical processes to rase their own history and their application to Turing machines, a natural extension of Wiesner's earlier work. A year later, Benioff more clearly outlined the theoretical farmework of a quantum computer. The dawn of the 21st century brought advancements at an even more impressive pace. The first 5-and 7-qubit nuclear magnetic resonance (NMR) computers were demonstrated in Munich, Germany, and Santa Fe, New Mexico, respectively. In 2006. researchers at Oxford were able to cage a qubit within a "buckyball," a buckminsterfullerene molecule, and maintain its state for a short time using precies, repated microwave pulses. The first company dedicated to quantum computing software, 1QB Information Technologies, was founded in 2012, and in 2018, Google announced the development of the 72-qubit Bristlecone chip designed to prove "quantum supremacy," the ability of quantum computers to solve problems beyond the reach of classical computing. With progress in quantum computing accelerating, it seems inevitable that within a fewdecades, the general population will be as familiar with quantum computing as they now are with classical computing. At present, quantum computing is limited by the struggle to build a computer large enough to prove quantum supremacy, and the costs associated with quantum computing are prohibitive to all but the world's largest corporations and governmental institutions. Still classical computing overcame similar problems, so the future of quantum computing looks bright. Which choice provides the best evidence for the answer to the previous question ?
Answer» LINES 115-119 ("The FIRST …respectively") Lines 119-124 ("In 2006…pulses") Lines 124-133 ("The first…computing") Lines 139-142 ("At present…supremacy") ANSWER :C

3377.	If the distance between the centres of two circles of radio 3,4 is 25 then the length of the tranverse common tangent is
Answer» 24 12 26 13 Answer :A

3378.	Given f: A to B and g: B to A, such that gof (x) = x , AA xin B , gof = I_(B) and fog = I_(A), then fog(x)=
Answer» a. `x ` B. `-x` C. `x^(2)` d. None of these SOLUTION :N/A

3379.	Consider the function f(x)=f(x)={{:(x-1",",-1lexle0),(x^(2)",", 0lexle1):} and""g(x)=sinx. If h_(1)(x)=f(\|g(x)\|) " and"h_(2)(x)=\|f(g(x))\|. Which of the following is not true about h_(2)(x)?
Answer» The domain is R It is periodic with PERIOD `2PI`The range is [0, 1] ANSWER :B

3380.	Consider the function f(x)=f(x)={{:(x-1",",-1lexle0),(x^(2)",", 0lexle1):} and""g(x)=sinx. If h_(1)(x)=f(\|g(x)\|) " and"h_(2)(x)=\|f(g(x))\|. Which of the following is not true about h_(1)(x)?
Answer» It is a PERIODIC FUNCTION with PERIOD `pi` The range is [0, 1] Domain R None of these Answer :D

3381.	P and Q are two points on the parabola ( y-2) ^(2) =(4-3) . The normals and tangents at P and Q form a square then point of intersection of tangents at P, Q is
Answer» `(-1,0) ` `( -4,2) ` ` ( 2,2) ` `(3,2) ` ANSWER :C

3382.	Match columnI to columan II according to the given condition In column I the direction ratios of lines are given. In column II angle between them is given.
Answer» ANSWER :A::B::C::D

3383.	From a frequency distribution, c = 3, l = 65 . 5 f = 42, m = 23, N = 102 then median is (l = lower limit of the median class, m= cumulative frequency of the class preceeding the median class, N = total frequency, f = frequency of the median class, c = width of the median class)
Answer» `65.5` `67.50` `66.93` `66.43` ANSWER :B