Quiz about Maths in Class 12

Question 1

Evaluate  (ii) int_(0)^(pi2)(1)(3 + 2 cos x ) dx

Accepted Answer

NA

Question 2

Evaluate the following integrals int (sqrtx - 1sqrtx)^2 dx

Accepted Answer

NA

Question 3

Thevaluesof a for whichof aforwhich2x^2-2(2a +1)x+a(a+1) =0mayhaveine root lessthana and otherrootgreaterthana are givenby

Accepted Answer

NA

Question 4

N is a normally distributed set with a mean of 0. If approximately 2% of the observations in N are -10 or smaller what fraction of the observations are between 0 and 5?

Accepted Answer

NA

Question 5

Sand is pouring from a pipe at the rate of 12 cm^(3)s. The falling sand forms a cone on the ground in such a way that the height of the cone is always one - sixth of the radius of the base. How fast is the height of the sand cone increasing when the height is 4 cm ?

Accepted Answer

NA

Question 6

Find the number of 4 digit numbers divisible by 5 that can be formed using the digits 1 2 3 4 5 when repetition of digits is allowed.

Accepted Answer

NA

Question 7

int e^(2x)[cos (3x + 4) + 5x^(2)] dx =

Accepted Answer

NA

Question 8

If P(3 sec theta2 tan theta) and Q(3 sec phi 2 tan phi) where theta+pi=(phi)(2) be two distainct points on the hyperbola then the ordinate of the pointof intersection of the normals at p and Q is

Accepted Answer

NA

Question 9

If the length of the tangent from (hk) to the circle x^(2)+y^2=16 is twice the length of the tangent from the same point to the circle x^(2)+y^(2)+2x+2y=0 then

Accepted Answer

NA

Question 10

Letf(x)=x^(2)+bx+c where b c inRIf f (x) is a factor of both x^(4)+6x^(2)+25and3x^(4)+4x^(2)+28x+5.then the least value of f (x) is

Accepted Answer

NA

Question 11

If =Xcostheta-Ysinthetaq=Xsintheta+Ycosthetaandp^(2)+4pq+q^(2)=AX^(2)+BY^(2)0le0le(pi)(2).What is the value of A ?

Accepted Answer

NA

Question 12

How many real solutions of the equation 6x^(2)-77[x]+147=0 where [x] is the integral part of x?

Accepted Answer

NA

Question 13

I_(m n)= int_(0)^(1) x^(m) (ln x)^(n) dx=

Accepted Answer

NA

Question 14

If each of the lines 5x+8y =13 and 4x -y=3contains a diameter of the circle x^(2) +y^(2) -2 (a^(2) -7a +11) x -2(a^(2) -6a + 6 ) y+b^(3) +1= 0then

Accepted Answer

NA

Question 15

Matchthe following (Given conditionLocus)(I.The sum of the squares ofdistances from P to the coordinate axes is 25(a) x ^ 2+y^ 2 = 25)(II. The distances to the coordinate axes from P arein the ratio2 3 respectively.(b) 4x^2 -9y^2 =0)(III. The square of whosedistancefrom P to the origin is 4 timesof its y- coordinate(c) x^2 +y^2 =4y)(IV.The distance from P to (4 0) is double the distancefrom P to the x -axis(d) x^2 - 3y^2 - 8x +16 = 0)((e) 9x^ 2 -4y^2 = 0)

Accepted Answer

NA

Question 16

Accepted Answer

NA

Question 17

Accepted Answer

NA

Question 18

Accepted Answer

NA

Question 19

If the mean deviation of number 11+d…1+100d from their mean is 255 then a value of d is

Accepted Answer

NA

Question 20

Slope of normal to the curve y=x^(2)-(1)(x^(2)) at (-1 0) is

Accepted Answer

NA

Question 21

If(a+ ib)^(5) = alpha + ibeta then (b+ ia)^(5) =

Accepted Answer

NA

Question 22

Let N be the of natural number and for a in N aN denotes the set axx in N. If bN nn cN=dN where b c d are natural numbers greater than 1 and the greatest common divisor of b and c is 1 then d equals

Accepted Answer

NA

Question 23

Find all pairs of consecutive odd positive integers both of which are smaller than 10 such that their sum is more than 11.

Accepted Answer

NA

Question 24

If x=2(theta-sintheta) and y=2(1+costheta) find (d^(2)y)(dx^(2)) at theta=pi3.

Accepted Answer

NA

Question 25

In a bulb factory machines A Band C manufacture 60% 30% and 10% bulbs respectively. Out of these bulbs 1 % 2% and 3% of the bulbs prodticed respectively by A Band Care found to be defective. A bulb is picked up at random from the total production and found to be defective. Find the probability that this bulb was produced by the machine A.

Accepted Answer

NA

Question 26

There are 5 cards numbered 1 to 5 on it. Two cards are drawn at random without replacement. Let X denotes the sum of the numbers on two cards drawn. Find mean and variance.

Accepted Answer

NA

Question 27

Let [x] be greatest integer function. Then int_(-1)^(1) [ x +2[x+2[x]]]dx=

Accepted Answer

NA

Question 28

sin (pi)(3) - sin^(-1)((-1)(2)) =…….

Accepted Answer

NA

Question 29

Which of the following overlapping is most effective ?

Accepted Answer

NA

Question 30

int (logx)^(2) dx =

Accepted Answer

NA

Question 31

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.  Based on the passage the author would most likely criticize classical computting because it

Accepted Answer

NA

Question 32

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 statement best describes the technique the author uses to advance the main point of the third paragraph (ine 39-62) ?

Accepted Answer

NA

Question 33

The range of sec^(-1)x is

Accepted Answer

NA

Question 34

Let alphabeta and gamma be three distinct real roots of the equation x(3x+2)^(2) + 2 =(a+12 + 9x)x^(2)-bx+c where abc in R. If every solution fo the inequality(x-2)^(2)(4x+b)(x-c) lt 0 is also solution of the inequility 3x^(2) + px +p^(2) + 6p lt 0 then find number of integral values of p

Accepted Answer

NA

Question 35

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.  According to the passage which one of the following is true of Urmila mahadevs graduate work ?

Accepted Answer

NA

Question 36

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.  In the second paragraph the discussion of locating a persons home on a globe (lines 26-36) primarily serves to

Accepted Answer

NA

Question 37

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 38

Findthe values of a and bsucht that thefunction fdefined by  fx = ((x-4)(|x-4|)+a if x lt 4)(a+bif x=4)((x-4)(|x-4|)+b if x gt 4) is a continousfunctionat x = 4 .

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.  The primary purpose of the passage is to

Accepted Answer

NA

Question 40

For the curve 4x^(5)=5y^(4) the ratio of the cube of the suctangent at a point on the curve to the square of the subnormal at the same point is

Accepted Answer

NA

Question 41

int_(0)^(p2) (16x sin x cosx dx)(sin^4 x+cos^4 x)

Accepted Answer

NA

Question 42

Determine the maximum value of z = 3x + 4y if the feasible region (shaded) for a LPP is shown in Figure.

Accepted Answer

NA

Question 43

If L=lim_(nto oo) (n^(3)(e^(1n)+e^(2n)+………+e))((n+1)^(m)(1^(m)+4^(m)+….+n^(2m))) is non zer finite real then

Accepted Answer

NA

Question 44

A company ships notepads in rectangular boxes that each have inside dimensions measuring 9 inches long 9 inches wide and 12 inches tall. Each notepad is in the shape of a cube with an edge length of 3 inches. What is the maximum number of natepads that will fit in 1 closed box?

Accepted Answer

NA

Question 45

If y = (a - x)(a + x) (x != -a) then find (dy)(dx)

Accepted Answer

NA

Question 46

int_(-51)^(51)(dx)(3+f(x))has the value equal to

Accepted Answer

NA

Question 47

Asertion 2 tan^(-1) x = cos^(-1) ((1-x^(2))(1+x^(2))) Reason(1- tan^(2) theta)(1+tan^(2)theta ) = cos 2 thetaand cos^(-1) ( cos theta ) = theta

Accepted Answer

NA

Question 48

STATEMENT-1 If the infinite A.G.P. 1sqrt(3) 2 x ….. has a finite sum then x = 2 and STATEMENT-2 the infinite A.G.P. a ( a + d( r (a + 2d) r^(2) …… has a finite sum only if |r| lt 1 .

Accepted Answer

NA

Question 49

If a b and c are in A.P. then the value of |(x+2 x+3 x+a)(x+4 x+5 x+b)(x+6 x+7 x+c)| is

Accepted Answer

NA

Question 50

Find the second order derivatives of the functions given in Exercises 1 to 10.  e^(x) sin 5x.

Accepted Answer

NA

Explore topic-wise InterviewSolutions in .

Evaluate (ii) int_(0)^(pi/2)(1)/(3 + 2 cos x ) dx

Evaluate the following integrals int (sqrtx - 1/sqrtx)^2 dx

Thevaluesof a for whichof aforwhich2x^2-2(2a +1)x+a(a+1) =0mayhaveine root lessthana and otherrootgreaterthana are givenby

N is a normally distributed set with a mean of 0. If approximately 2% of the observations in N are -10 or smaller, what fraction of the observations are between 0 and 5?

Sand is pouring from a pipe at the rate of 12 cm^(3)//s. The falling sand forms a cone on the ground in such a way that the height of the cone is always one - sixth of the radius of the base. How fast is the height of the sand cone increasing when the height is 4 cm ?

Find the number of 4 digit numbers divisible by 5 that can be formed using the digits 1, 2, 3, 4, 5 when repetition of digits is allowed.

int e^(2x)[cos (3x + 4) + 5x^(2)] dx =

If P(3 sec theta,2 tan theta) and Q(3 sec phi , 2 tan phi) where theta+pi=(phi)/(2) be two distainct points on the hyperbola then the ordinate of the pointof intersection of the normals at p and Q is

If the length of the tangent from (h,k) to the circle x^(2)+y^2=16 is twice the length of the tangent from the same point to the circle x^(2)+y^(2)+2x+2y=0, then

Letf(x)=x^(2)+bx+c, where b, c inRIf f (x) is a factor of both x^(4)+6x^(2)+25and3x^(4)+4x^(2)+28x+5.then the least value of f (x) is

If =Xcostheta-Ysintheta,q=Xsintheta+Ycosthetaandp^(2)+4pq+q^(2)=AX^(2)+BY^(2),0le0le(pi)/(2).What is the value of A ?

How many real solutions of the equation 6x^(2)-77[x]+147=0, where [x] is the integral part of x?

I_(m, n)= int_(0)^(1) x^(m) (ln x)^(n) dx=

If each of the lines 5x+8y =13 and 4x -y=3contains a diameter of the circle x^(2) +y^(2) -2 (a^(2) -7a +11) x -2(a^(2) -6a + 6 ) y+b^(3) +1= 0then

If the mean deviation of number 1,1+d,…1+100d from their mean is 255, then a value of d is

Slope of normal to the curve y=x^(2)-(1)/(x^(2)) at (-1, 0) is

If(a+ ib)^(5) = alpha + ibeta then (b+ ia)^(5) =

Let N be the of natural number and for a in N, aN denotes the set {ax:x in N}. If bN nn cN=dN, where b, c, d are natural numbers greater than 1 and the greatest common divisor of b and c is 1 then d equals

Find all pairs of consecutive odd positive integers both of which are smaller than 10 such that their sum is more than 11.

If x=2(theta-sintheta) and y=2(1+costheta), " find "(d^(2)y)/(dx^(2))" at "theta=pi/3.

There are 5 cards numbered 1 to 5 on it. Two cards are drawn at random without replacement. Let X denotes the sum of the numbers on two cards drawn. Find mean and variance.

Let [x] be greatest integer function. Then, int_(-1)^(1) [ x +2[x+2[x]]]dx=

sin {(pi)/(3) - sin^(-1)((-1)/(2)) }=…….

Which of the following overlapping is most effective ?

int ("logx")^(2) dx =

The range of sec^(-1)x is

Let alpha,beta , and gamma be three distinct real roots of the equation x(3x+2)^(2) + 2 =(a+12 + 9x)x^(2)-bx+c where, a,b,c in R. If every solution fo the inequality(x-2)^(2)(4x+b)(x-c) lt 0 is also solution of the inequility 3x^(2) + px +p^(2) + 6p lt 0 , then find number of integral values of 'p'

Findthe values of a and bsucht that thefunction fdefined by fx = {{:((x-4)/(|x-4|)+a, if x lt 4),(a+b,if x=4),((x-4)/(|x-4|)+b, if x gt 4):} is a continousfunctionat x = 4 .

For the curve 4x^(5)=5y^(4), the ratio of the cube of the suctangent at a point on the curve to the square of the subnormal at the same point is

int_(0)^(p//2) (16x sin x cosx dx)/(sin^4 x+cos^4 x)

Determine the maximum value of z = 3x + 4y if the feasible region (shaded) for a LPP is shown in Figure.

If L=lim_(nto oo) (n^(3)(e^(1//n)+e^(2//n)+………+e))/((n+1)^(m)(1^(m)+4^(m)+….+n^(2m))) is non zer finite real, then

A company ships notepads in rectangular boxes that each have inside dimensions measuring 9 inches long, 9 inches wide, and 12 inches tall. Each notepad is in the shape of a cube with an edge length of 3 inches. What is the maximum number of natepads that will fit in 1 closed box?

If y = (a - x)/(a + x), (x != -a) then find (dy)/(dx)

int_(-51)^(51)(dx)/(3+f(x))has the value equal to

Asertion :2 tan^(-1) x = cos^(-1) ((1-x^(2))/(1+x^(2))) Reason(1- tan^(2) theta)/(1+tan^(2)theta ) = cos 2 thetaand cos^(-1) ( cos theta ) = theta

STATEMENT-1 : If the infinite A.G.P. 1,sqrt(3) , 2 , x ….. has a finite sum , then x = 2 and STATEMENT-2 :the infinite A.G.P. a ,( a + d( r, (a + 2d) r^(2) …… has a finite sum only if |r| lt 1 .

If a, b and c are in A.P., then the value of |(x+2, x+3, x+a),(x+4, x+5, x+b),(x+6, x+7, x+c)| is

Find the second order derivatives of the functions given in Exercises 1 to 10. e^(x) sin 5x.

4151.	Evaluate (ii) int_(0)^(pi/2)(1)/(3 + 2 cos x ) dx
Answer» ANSWER :`(2)/(SQRT(5)) tan^-1 (1/sqrt(5))`

4152.	Evaluate the following integrals int (sqrtx - 1/sqrtx)^2 dx
Answer» SOLUTION :`int (sqrtx-1/sqrtx)^2 DX = int(x-2+1/x)dx = x^2/2 -2X +log \|x\| +c`

4153.	Thevaluesof a for whichof aforwhich2x^2-2(2a +1)x+a(a+1) =0mayhaveine root lessthana and otherrootgreaterthana are givenby
Answer» `1 GT a gt 0` ` -1lta LT0` `a gt 0` ` a GT0 ora LT -1` Answer :D

4154.	N is a normally distributed set with a mean of 0. If approximately 2% of the observations in N are -10 or smaller, what fraction of the observations are between 0 and 5?
Answer» ANSWER :`(1)/(3)`

4155.	Sand is pouring from a pipe at the rate of 12 cm^(3)//s. The falling sand forms a cone on the ground in such a way that the height of the cone is always one - sixth of the radius of the base. How fast is the height of the sand cone increasing when the height is 4 cm ?
Answer» ANSWER :`(1)/(48 PI)` cm/sec.

4156.	Find the number of 4 digit numbers divisible by 5 that can be formed using the digits 1, 2, 3, 4, 5 when repetition of digits is allowed.
Answer» ANSWER :2160

4157.	int e^(2x)[cos (3x + 4) + 5x^(2)] dx =
Answer» `e^(2X)[(2)/(13) cos(3X + 4) + (3)/(13) sin(3x + 4) + (5x^(2))/(2) - (5x)/(2) + (5)/(4)]` `e^(2x)[(2)/(13) cos(3x + 4) - (3)/(13) sin(3x + 4) + (5x^(2))/(2) - (5x)/(2) + (5)/(4)]` `e^(2x)[(2)/(13) cos(3x + 4) - (3)/(13) sin(3x + 4) - (5x^(2))/(2) - (5x)/(2) - (5)/(4)]` `e^(2x)[(2)/(13) cos(3x + 4) - (3)/(13) sin(3x + 4) + (5x^(2))/(2) - (5x)/(2) + (5)/(4)]` Answer :A

4158.	If P(3 sec theta,2 tan theta) and Q(3 sec phi , 2 tan phi) where theta+pi=(phi)/(2) be two distainct points on the hyperbola then the ordinate of the pointof intersection of the normals at p and Q is
Answer» `11/3` `11/3` `13/2` `-13/2` ANSWER :d

4159.	If the length of the tangent from (h,k) to the circle x^(2)+y^2=16 is twice the length of the tangent from the same point to the circle x^(2)+y^(2)+2x+2y=0, then
Answer» `h^(2)+K^(2)_4h+4k+16=0` `h^(2)+k^(2)+3H+3K=0` `3h^(2)+3k^(2)+8y+8k+16=0` `3h^(2)+3k^(2)+4h+4k+16=0` ANSWER :C

4160.	Letf(x)=x^(2)+bx+c, where b, c inRIf f (x) is a factor of both x^(4)+6x^(2)+25and3x^(4)+4x^(2)+28x+5.then the least value of f (x) is
Answer» SOLUTION :`f(X)` will also be a factor of `3(x^(4)+6X^(2)+25)-(3x^(4)+4x^(2)+28+5)`. Which EQUALS `14(x^(2)-2x+5)`. So, `f(x)=x^(2)-2x+5 le 4`

4161.	If =Xcostheta-Ysintheta,q=Xsintheta+Ycosthetaandp^(2)+4pq+q^(2)=AX^(2)+BY^(2),0le0le(pi)/(2).What is the value of A ?
Answer» 4 3 2 1 Solution :`p=xcostheta-ysintheta` `Q=xsintheta+ycostheta` Given, `p^(2)+4pq+q^(2)=Ax^(2)+By^(2)` Letus take`theta=(pi)/(4)`. `p=X"COS"(pi)/(4)-y" cos"(pi)/(4)=(x+y)/(sqrt(2))` `q=x" SIN"(pi)/(4)+y" cos"(pi)/(4)=(x+y)/(sqrt(2))` `pq=(x^(2)-y^(2))/(2)rArr2pq=x^(2)-y^(2)rArr4pq=2x^(2)-2y^(2)` . . . (1) Now, `p^(2)+q^(2)=x^(2)cos^(2)theta+y^(2)sin^(2)theta-2xycosthetasintheta+x^(2)sin^(2)theta+y^(2)cos^(2)theta+2xysinthetacostheta=x^(2)+y^(2)`. . . (2) From(1) , (2) , `p^(2)+q^(2)+4pq=x^(2)+y^(2)+2x^(2)-2y^(2)=3x^(2)-y^(2)` Comparingthis with the given from , we get `theta=(pi)/(4),A=3,B=-1`

4162.	How many real solutions of the equation 6x^(2)-77[x]+147=0, where [x] is the integral part of x?
Answer» Solution :We have `6x^(2)-77[x]+147=0` `implies(6x^(2)+147)/77=[x]` `(0.078)x^(2)=[x]-1.9` `:'(0.078)x^(2)gt0=x^(2)gt0` `:.[x]-1.9gt0` or `[x]gt1.9` `:.[x]=2,3,4,5`………… If `[x]=2` i.e. `2lexlt3` Then `x^(2)=(2-1.9)/0.078=1.28` `:.x=1.13` [fail] If `[x]=3,` i.e. `3lexlt4` Then `x^(2)=(3-1.9)/0.078=14.1` `:.x=3.75` [true] If `[x]=4`, i.e. `4lexlt5` Then `x^(2)=(4-1.9)/(0.078)=26.9` `:.x=5.18` ..[fail] If `[x]=5,` i.e. `5lexlt6` Then `x^(2)=(5-1.9)/0.078=39.7` `:.x=6.3` [fail] If `[x]=6,` i.e. `6lexlt7` Then `x^(2)=(6-=1+N3269)/0.078=4.1/0.078=52.56` `:.x==.25`[fail] If `[x]=7`, i.e. /7lexlt8` Then `x^(2)=(7-1.9)/0.078=5.1/0.078=65.38` `:.x=8.08` [fail] If `[x]=8` i.e. `8lexlt9` Then `x^(2)=(8-1.9)/0.078=6.1/0.078=78.2` `:.x=8.8` [true] If `[x]=9,` i.e. `9lexlt10` Then `x^(2)=(9-1.9)/0.078=7.1/0.078=91.03` `:.x=9.5` [true] If `[x]=10`, i.e `10lexlt11` Then `x^(2)=(10-1.9)/0.078=8.1/0.078=103.8` `:.x=10.2` If `[x]=11`, i.e. `11lexlt12` Then `x^(2)=(11-1.9)/(0.078` `=9.1/0.078=116.7` `:.x=10.8` [fail] Other values of fail. hence number of SOLUTIONS is four.

4166.	If a,b,c are there given non-coplanar vectors and any arbitrary vector r is in space. Where, Delta_(1) =\|{:(r.a,b.a,c.a),(r.b,b.b,a.b),(r.a,b.c,c.c):}\|, Delta_(2)=\|{:(a.a,r.a,c.a),(a.b,r.b,c.b),(a.c,r.c,c.c):}\|, Delta_(3) =\|{:(a.a,b.a,r.a),(a.b,b.b,r.b),(a.c,b.c,r.c):}\|, Delta=\|{:(a.a,b.a,c.a),(a.b,b.b,c.b),(a.c,c.c,c.c):}\| The vector r is expressible in the form:
Answer» `R=Delta_(1)/(2Delta)a + (Delta_(2))/(2Delta)b +(Delta_(3))/(2Delta)c` `r=(2Delta_(1))/Deltaa+ (2Delta_(2))/Delta b + (2Delta_(3))/(Delta)c` `r=Delta/Delta_(1) a + Delta/Delta_(2)b+Delta/Delta_(3)c` `r= Delta_(1)/Delta a + (Delta_(2))/DELTAB+ Delta_(3)/DELTAC` ANSWER :D

4167.	If a,b,c are there given non-coplanar vectors and any arbitrary vector r is in space. Where, Delta_(1) =\|{:(r.a,b.a,c.a),(r.b,b.b,a.b),(r.a,b.c,c.c):}\|, Delta_(2)=\|{:(a.a,r.a,c.a),(a.b,r.b,c.b),(a.c,r.c,c.c):}\|, Delta_(3) =\|{:(a.a,b.a,r.a),(a.b,b.b,r.b),(a.c,b.c,r.c):}\|, Delta=\|{:(a.a,b.a,c.a),(a.b,b.b,c.b),(a.c,c.c,c.c):}\| The vector r is expressible as:
Answer» `r=(r b C)/(2[ABC]) a + [rcb]/(2[abc]) b+ [cab]/(2[abc])`c `r=(2[abc])/[abc]a + (2[rcb])/(abc) b + (2[rab])/[abc]c` `r=1/[abc][(abc)a+(rca)b +(rab)c]` None of these Answer :C

4163.	I_(m, n)= int_(0)^(1) x^(m) (ln x)^(n) dx=
Answer» 0 `(N)/(m+1)` `-(n)/(m+1) I_(m-1, n)` `- (n)/(m+1) I_(m, n-1)` ANSWER :D

4164.	If each of the lines 5x+8y =13 and 4x -y=3contains a diameter of the circle x^(2) +y^(2) -2 (a^(2) -7a +11) x -2(a^(2) -6a + 6 ) y+b^(3) +1= 0then
Answer» ` a= 5 and B in(-1,1) ` ` a= 1 and b in (-1,1) ` ` a=2 and b in (-INFTY ,1) ` ` a= 5 and b in (- infty ,1 )` ANSWER :D

4165.	Matchthe following {:(,"Given condition",,,"Locus"),(I.,"The sum of the squares ofdistances from P to the coordinate axes is 25",,(a), x ^ 2+y^ 2 = 25),(II., "The distances to the coordinate axes from P arein the ratio2 : 3 respectively.",,(b), 4x^2 -9y^2 =0),(III., "The square of whosedistancefrom P to the origin is 4 timesof its y- coordinate",,(c), x^2 +y^2 =4y),(IV.,"The distance from P to (4, 0) is double the distancefrom P to the x -axis",,(d), x^2 - 3y^2 - 8x +16 = 0),(,,,(e), 9x^ 2 -4y^2 = 0):}
Answer» `a, B, C, d ` `a, E, c, d ` `a, b, d, c` `b, a, c, e ` ANSWER :A

4168.	If a,b,c are there given non-coplanar vectors and any arbitrary vector r is in space. Where, Delta_(1) =\|{:(r.a,b.a,c.a),(r.b,b.b,a.b),(r.a,b.c,c.c):}\|, Delta_(2)=\|{:(a.a,r.a,c.a),(a.b,r.b,c.b),(a.c,r.c,c.c):}\|, Delta_(3) =\|{:(a.a,b.a,r.a),(a.b,b.b,r.b),(a.c,b.c,r.c):}\|, Delta=\|{:(a.a,b.a,c.a),(a.b,b.b,c.b),(a.c,c.c,c.c):}\| If vector is expressible as r=xa + yb + gc, then:
Answer» `a=1/(ABC)[(a.a)(B XX c)+(b.b)(c xx a)+(c.c)(a xx b)]` `1/[abc][(a.a)[b xx c]+(b.a)(c xx a) +(a.a)(a xx b)]` `a=(a.a)(b xx c)+(a.b)(c xx a)+(a.a)(a xx b)` None of these ANSWER :D

4169.	If the mean deviation of number 1,1+d,…1+100d from their mean is 255, then a value of d is
Answer» 10.1 5.05 20.2 10 Answer :A

4170.	Slope of normal to the curve y=x^(2)-(1)/(x^(2)) at (-1, 0) is
Answer» `-4` 4 `-(1)/(4)` `(1)/(4)` ANSWER :D

4171.	If(a+ ib)^(5) = alpha + ibeta then (b+ ia)^(5) =
Answer» `BETA + IALPHA` `beta - ialpha` `ALPHA + IBETA` `alpha-ibeta` ANSWER :A

4172.	Let N be the of natural number and for a in N, aN denotes the set {ax:x in N}. If bN nn cN=dN, where b, c, d are natural numbers greater than 1 and the greatest common divisor of b and c is 1 then d equals
Answer» MAX {b, c} min {b, c} BC `b+c` ANSWER :C

4173.	Find all pairs of consecutive odd positive integers both of which are smaller than 10 such that their sum is more than 11.
Answer» Answer :x can have VALUES 5,6,7. (But 6 is not an ODD NUMBER )

4174.	If x=2(theta-sintheta) and y=2(1+costheta), " find "(d^(2)y)/(dx^(2))" at "theta=pi/3.
Answer» ANSWER :B

4175.	In a bulb factory, machines A, Band C manufacture 60%, 30% and 10% bulbs respectively. Out of these bulbs 1 %, 2% and 3% of the bulbs prodticed respectively by A, Band Care found to be defective. A bulb is picked up at random from the total production and found to be defective. Find the probability that this bulb was produced by the machine A.
Answer» ANSWER :`2/5`

4176.	There are 5 cards numbered 1 to 5 on it. Two cards are drawn at random without replacement. Let X denotes the sum of the numbers on two cards drawn. Find mean and variance.
Answer» ANSWER :6, 3

4177.	Let [x] be greatest integer function. Then, int_(-1)^(1) [ x +2[x+2[x]]]dx=
Answer» 0 -5 -7 10 Answer :C

4178.	sin {(pi)/(3) - sin^(-1)((-1)/(2)) }=…….
Answer» `1/2` `1/3` `1/4` `1` ANSWER :D

4179.	Which of the following overlapping is most effective ?
Answer» `2p_pi-3p_pi` `3p_pi-3p_pi` `3p_pi-3d_pi` `2p_pi-3d_pi`

4180.	int ("logx")^(2) dx =
Answer» `x [ (LOG x)^(2) -"log x - 2"] + C ` `x [ (log x)^(2) -2"log x + 2"] + c ` `x [ (log x)^(2) -3"log x - 3"] + c ` `x [ (log x)^(2) +"log x - 2"] + c ` Answer :B

4181.	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. Based on the passage, the author would most likely criticize classical computting because it
Answer» has devolped more slowly than quantum computing in recent years. LACKS any APPLICATION for autonomous vehicles. employs SERIAL processing. cannot verify quantum computing calculations. Answer :C

4182.	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 statement best describes the technique the author uses to advance the main point of the third paragraph (ine 39-62) ?
Answer» She describes research done by leading scientists and engineers. She PROPOSE a LABORATORY experiment that would prove a HYPOTHESIS. She offers a hypotetical example to illustrate a COMPLEX comparison. She cites data demonstrating the superior efficiency of one TECHNIQUE. Answer :C

4183.	The range of sec^(-1)x is
Answer» `[(-PI)/(2),(pi)/(2)]` `((-pi)/(2),(pi)/(2))` `[0,pi]` `[0,pi]-{(pi)/(2)}` ANSWER :A

4184.	Let alpha,beta , and gamma be three distinct real roots of the equation x(3x+2)^(2) + 2 =(a+12 + 9x)x^(2)-bx+c where, a,b,c in R. If every solution fo the inequality(x-2)^(2)(4x+b)(x-c) lt 0 is also solution of the inequility 3x^(2) + px +p^(2) + 6p lt 0 , then find number of integral values of 'p'
Answer» ANSWER :`0005`