Quiz about Maths in Class 12

Question 1

If abc are in H.P. then which of the following is true.

Accepted Answer

NA

Question 2

Verify that the function y = a cos x + b sin x where ab in R is a solution of the differential equation (d^(2)y)(dx^(2)) + y = 0

Accepted Answer

NA

Question 3

Obtain the parametric equation of each  of the following circles.  (x-3)^(2) + (y-4)^(2) = 8^(2)

Accepted Answer

NA

Question 4

All the letters of the word AGAIN be arranged and the words thus formed are known as Simple Words. Further two new types of words are defined as follows  (i) Smart word all the letters of the word AGAIN are being used but vowels can be repeated as many times as we need.  (ii) Dull word All the letters of the word AGAIN are being used but consonants can be repeated as many times as we need.  Q. Number of 7 letter dull words inw hich no two vowels are together is

Accepted Answer

NA

Question 5

A medical company has factories at two places A and B. From these places supply is madeto each of its three agencies situated at P Q and R. The monthly requirements of the agen cies are respectively 4040 and 50 packets of the medicines while the production capacity of the factories A and B are 60 and 70 packets respectively. The transportation costs per packet from the factories to the agencies are given below

Accepted Answer

NA

Question 6

There are ten boxes numbered from 1 to 10 and 10 balls numbered from 1 to 10. If the number of ways of putting all balls in given boxes such that no box remains empty oddnumbered balls go to odd numbered box and no ball goes to the box having same number which is written on the ball is K^(2) then find K

Accepted Answer

NA

Question 7

The orthocentre of the triangle with vertices A(00) B(0 (3)(2)) C(-5 0) is

Accepted Answer

NA

Question 8

If AA h in R - 0 two distinct tangents can be drawn from the points (2+h3h-1) to the curve y=x^(3)-6x^(2) - a+ bx then (a)(b) is equal to _____

Accepted Answer

NA

Question 9

If n in Nthen11^(n+2)+12^(2n +1)is divisibleby

Accepted Answer

NA

Question 10

Find the acute angle or angle or intersection of the following circles.  a. x^(2)+y^(2)-12x-6y+41=0 x^(2)+y^(2)+4x+6y-59=0

Accepted Answer

NA

Question 11

A number n is chosen at random from the natural numbers 2 to 1001. The probability that n is a number that leaves remainder 1 when divided by 7 is

Accepted Answer

NA

Question 12

The minimum value of sec x x in [(2pi)(3)pi] is ……….

Accepted Answer

NA

Question 13

Define f(x) as the product of two real functions f_(1)(x)=x x epsilon IR and f_(2)(x)=(sin1x if x!=0)(0 if x=0) as follows f(x)=(f_(1)(x).f_(2)(x) if x!=0)(0 if x=0)

Accepted Answer

NA

Question 14

If xy inR then the determinant  Delta=|(cosx-sinx1)(sinxcosx1)(cos(x+y)-sin(x+y)0)|lies in the interval .

Accepted Answer

NA

Question 15

The marginal cost of a product is given by MC =(14000)(sqrt(7x+ 4)) and the fixed cost is 18000.  Find the total cost and the average cost of producing 3 units of output.

Accepted Answer

NA

Question 16

Four persons entered the lift cabin on the ground floor of a 5-floor house (Assume ground floor as also one floor). Assume that each of them independently and with equal probability can leave the cabin at any floor beginning from the first. Find the probability for all the four persons to leave the cabin at different floors

Accepted Answer

NA

Question 17

If Delta = abs(x+y+z^(2) x^(2) + y+ z x+y^(2) + z)(z^2 x^2 y^2)(x+yy+zx+z) (where ( x ne y ne z) x y z in R- 0 ) then Delta= ........

Accepted Answer

NA

Question 18

Find the value of y if the matrix A = ((02yz)(xy-z)(x-yz)) obeys the law A^(T).A = I.

Accepted Answer

NA

Question 19

Find two positive numbers x and y such that their sum is 35 and the product x^(2) y^(5 )is a maximum.

Accepted Answer

NA

Question 20

From points on the circlex^(2) +y^(2) =a ^(2) tangents are drawn to the hyperbolax^(2) - y^(2) =a^(2)The locus of the midpoints of chords of contact is

Accepted Answer

NA

Question 21

Integrate the following functions sin^2(2x+5)

Accepted Answer

NA

Question 22

f(24)rarr(13)f(x) = x - [(x)2] where [.] is a greatest integer function then f^(-1)(x) = ......

Accepted Answer

NA

Question 23

int_(0)^(a+b)(f(x-a))(f(x-a)+f(b-x))dxis equal to

Accepted Answer

NA

Question 24

If x in (0 1) then intcos2cot^(-1) sqrt((1+x)(1-x))dx=

Accepted Answer

NA

Question 25

Solve as directed x2 - x3 + x5 le 113 for non-negative real numbers.

Accepted Answer

NA

Question 26

Evaluate the integerals.int e ^(x) log (e ^(2x) +5e^(x) +6)dx on R.

Accepted Answer

NA

Question 27

If |x| lt 1 then the coefficient of x^(n) in (1 + 2x + 3x^(2) + 4x^(3) + ......)^(12) is

Accepted Answer

NA

Question 28

The sum of the first n terms of the series 1(sqrt(2) + sqrt(5)) + 1(sqrt(5) + sqrt(8)) + 1(sqrt(8) + sqrt(11)) +... is

Accepted Answer

NA

Question 29

Find the angle between the line (x+1)2=y3=(z-3)6 and the plane 10x + 2y - 11z = 3.

Accepted Answer

NA

Question 30

Two friends A and B have equal number of sons. There are 3 cinema tickets which are to be distributed among the sons of A and B. The probability that all the tickets go to the sons of B is 120. The no. of sons each of them having is

Accepted Answer

NA

Question 31

A diet is to contain at leat 80 units of vitamin A and 100 units of minerals. Two foods F_(1) and F_(2) are available. Food F_(1) cost Rs. 4 per unit and F_(2)costs Rs. 6 per unit. One unit of food F_(1) contains 3 uinits of vitamin A and 4 units of minerals. One unit of food F_(2) contains 6 units of minerals. One unit of food F_(2) contains 6 units of vitamin A and 3 units of minerals. Formulate this as a linear programming problem. Find the minimum cost for diet that consists of mixture of these two foods and also meets the minimal nutritional requirements.

Accepted Answer

NA

Question 32

A tangent is drawn at any point (l m) l mne0 on the parabola y^(2)=4ax and the tangents are drawn from any point on this tangent to the circle x^(2)+y^(2)=0 (where agt0) such that all chords of contact pass through a fixed point (alphabeta) then

Accepted Answer

NA

Question 33

Evaluate intx^(3) e^(2x) dx

Accepted Answer

NA

Question 34

Prove that the angle of rotation of the axes to eliminate xy term from the equation ax^2+2hxy+by^2=0 is Tan^(-1)((2h)(a-b)) where a neb and (pi)(4) ifa=b.

Accepted Answer

NA

Question 35

If a_(r)=a+(r-1)d is rth term of an A.P. then a_(n)^(2)-2a_(n-1)^(2)+a_(n-2)^(2) is independent of

Accepted Answer

NA

Question 36

Evaluate the following integrals int_0^1 dx(1+x^2)

Accepted Answer

NA

Question 37

This passage is adapted from a 2018 article summarizing two different proposals for solving problems with maintaining New York Citys mass transit system.  The history of the New York City subsaw system quickly told the first stations opened in 1904 and over the next century it expended to 472 stations more than any other subway system in the world with 850 miles of track. Operating 24 hours a day seven days a week with an average weekday ridership of approximately 5.7 million it is the plants 7th-busiest rapid transit system. While the system is on many levels an amazing chievement it is also beset by a problem that harms both quality of life and economic activity. Such a large system must inevitably suffer from service interruptions and delays normal wear and tear combined with the sheer age of the system necessitates regular maintanance. However there is no consensus as to the best way to accomplish the required repairs. The current maintanance scheme is designed to minimize service interruptions. A subway line in need of repair will be taken out of sevice during a comaratively less busy time such as nights or weekends while another line is re-routed to cover as many as possible of the missing lines stops. The main advantage to this approach is that trains are not taken out of service during rush hour when most subway trips occur subway service generally remains predictable and commuters are for the most part able to use the system to get to their desinations on time.  But critics are quick to point out the disadvantages to this approach. Perhaps most obvious is the confusion caused by trains swithing lines. The labyrinthine system is hard enough to navigate at the best of times. especially for tourists A subway rider on the A terain naturally expects the train to make stops on teh A line. If instead it is diverted temporatily to the F line the rader may find herself miles from her intended destination.  While annoying the confusion arising from route switching is hardly the most serious problem with the current approach to repairs. Because the system runs 24 hours a day routine maintenance can generally be done only during the temporary closures on nights and weekends. This means that more serious repair and crucial preventative maintenance is often neglected. Problems that could have been fixed or prevented reasonably expeditiously given a slightly longer closure wind up leading to major breakdowns and service interruptions later on.  On rare occasions such breakdowns have resulted in entire subway lines being shut down for months or even a year. Beginning in 2019 for example the I. Train connecting lower Manhattan to parts of Brooklyn was scheduled to close for as much as 15 months for long overdue service and upgrades. In a city fewar than half of whose households own a car this can have serious economic impacts Residents of the affected area may face a much longer commute via an alternate subway line if one is available or if there is no alternate subway service they may need to take other potentially more exppensive modes of transportation such as taxis or ferries. Morover studies indicate that increased stress from the commute to work can lead to lower productivity and that businesses near the impacted lines may see decreased revenue as potential customers have a harder time getting to them.  One controversial proposal for reducing breakdowns and the resulting transit interruptions is to end the subways 24-hour service and to shut down for several hours each night. Proponents of this plan argue that this would allow time on a regular rather than sporadic basis for more preventative maintanacnce. This they claim would ultimately lead to more consistent service rrather than shutting down entire lines for long periods of a time there would merely be shorter service outages overnight when fewer people use the subway system. While this may seem a preferable outcome to the economic consequence of a total shutdown resulting from a breakdown it has its liabilities as well. While most subway trips may occur during rush hour not everyone works during the daytime. New yourk is famously known as the the city that never sleeps. Doctors nurses bartenders police officers and firefighters are just a few examples of occupations whose workers need transportion at all hours of the day and night. Rather than be subjected to a relatively short period of inconvenience these workers would find their commutes irrevocably altered. One thing at least is clear the city must carefully condider many economic and social factors in designing a subway maintenance plan.  In the third paragraph the siscussion of two specific subway lines (lines 44-49) primarily serves to

Accepted Answer

NA

Question 38

The variance of the data 23511131719 is nearly

Accepted Answer

NA

Question 39

Find the value of the (1)(root(3)(999) ) correct to 4 decimal places

Accepted Answer

NA

Question 40

This passage is adapted from a 2018 article summarizing two different proposals for solving problems with maintaining New York Citys mass transit system.  The history of the New York City subsaw system quickly told the first stations opened in 1904 and over the next century it expended to 472 stations more than any other subway system in the world with 850 miles of track. Operating 24 hours a day seven days a week with an average weekday ridership of approximately 5.7 million it is the plants 7th-busiest rapid transit system. While the system is on many levels an amazing chievement it is also beset by a problem that harms both quality of life and economic activity. Such a large system must inevitably suffer from service interruptions and delays normal wear and tear combined with the sheer age of the system necessitates regular maintanance. However there is no consensus as to the best way to accomplish the required repairs. The current maintanance scheme is designed to minimize service interruptions. A subway line in need of repair will be taken out of sevice during a comaratively less busy time such as nights or weekends while another line is re-routed to cover as many as possible of the missing lines stops. The main advantage to this approach is that trains are not taken out of service during rush hour when most subway trips occur subway service generally remains predictable and commuters are for the most part able to use the system to get to their desinations on time.  But critics are quick to point out the disadvantages to this approach. Perhaps most obvious is the confusion caused by trains swithing lines. The labyrinthine system is hard enough to navigate at the best of times. especially for tourists A subway rider on the A terain naturally expects the train to make stops on teh A line. If instead it is diverted temporatily to the F line the rader may find herself miles from her intended destination.  While annoying the confusion arising from route switching is hardly the most serious problem with the current approach to repairs. Because the system runs 24 hours a day routine maintenance can generally be done only during the temporary closures on nights and weekends. This means that more serious repair and crucial preventative maintenance is often neglected. Problems that could have been fixed or prevented reasonably expeditiously given a slightly longer closure wind up leading to major breakdowns and service interruptions later on.  On rare occasions such breakdowns have resulted in entire subway lines being shut down for months or even a year. Beginning in 2019 for example the I. Train connecting lower Manhattan to parts of Brooklyn was scheduled to close for as much as 15 months for long overdue service and upgrades. In a city fewar than half of whose households own a car this can have serious economic impacts Residents of the affected area may face a much longer commute via an alternate subway line if one is available or if there is no alternate subway service they may need to take other potentially more exppensive modes of transportation such as taxis or ferries. Morover studies indicate that increased stress from the commute to work can lead to lower productivity and that businesses near the impacted lines may see decreased revenue as potential customers have a harder time getting to them.  One controversial proposal for reducing breakdowns and the resulting transit interruptions is to end the subways 24-hour service and to shut down for several hours each night. Proponents of this plan argue that this would allow time on a regular rather than sporadic basis for more preventative maintanacnce. This they claim would ultimately lead to more consistent service rrather than shutting down entire lines for long periods of a time there would merely be shorter service outages overnight when fewer people use the subway system. While this may seem a preferable outcome to the economic consequence of a total shutdown resulting from a breakdown it has its liabilities as well. While most subway trips may occur during rush hour not everyone works during the daytime. New yourk is famously known as the the city that never sleeps. Doctors nurses bartenders police officers and firefighters are just a few examples of occupations whose workers need transportion at all hours of the day and night. Rather than be subjected to a relatively short period of inconvenience these workers would find their commutes irrevocably altered. One thing at least is clear the city must carefully condider many economic and social factors in designing a subway maintenance plan.  The passage indicates that non-rush hour commuters

Accepted Answer

NA

Question 41

This passage is adapted from a 2018 article summarizing two different proposals for solving problems with maintaining New York Citys mass transit system.  The history of the New York City subsaw system quickly told the first stations opened in 1904 and over the next century it expended to 472 stations more than any other subway system in the world with 850 miles of track. Operating 24 hours a day seven days a week with an average weekday ridership of approximately 5.7 million it is the plants 7th-busiest rapid transit system. While the system is on many levels an amazing chievement it is also beset by a problem that harms both quality of life and economic activity. Such a large system must inevitably suffer from service interruptions and delays normal wear and tear combined with the sheer age of the system necessitates regular maintanance. However there is no consensus as to the best way to accomplish the required repairs. The current maintanance scheme is designed to minimize service interruptions. A subway line in need of repair will be taken out of sevice during a comaratively less busy time such as nights or weekends while another line is re-routed to cover as many as possible of the missing lines stops. The main advantage to this approach is that trains are not taken out of service during rush hour when most subway trips occur subway service generally remains predictable and commuters are for the most part able to use the system to get to their desinations on time.  But critics are quick to point out the disadvantages to this approach. Perhaps most obvious is the confusion caused by trains swithing lines. The labyrinthine system is hard enough to navigate at the best of times. especially for tourists A subway rider on the A terain naturally expects the train to make stops on teh A line. If instead it is diverted temporatily to the F line the rader may find herself miles from her intended destination.  While annoying the confusion arising from route switching is hardly the most serious problem with the current approach to repairs. Because the system runs 24 hours a day routine maintenance can generally be done only during the temporary closures on nights and weekends. This means that more serious repair and crucial preventative maintenance is often neglected. Problems that could have been fixed or prevented reasonably expeditiously given a slightly longer closure wind up leading to major breakdowns and service interruptions later on.  On rare occasions such breakdowns have resulted in entire subway lines being shut down for months or even a year. Beginning in 2019 for example the I. Train connecting lower Manhattan to parts of Brooklyn was scheduled to close for as much as 15 months for long overdue service and upgrades. In a city fewar than half of whose households own a car this can have serious economic impacts Residents of the affected area may face a much longer commute via an alternate subway line if one is available or if there is no alternate subway service they may need to take other potentially more exppensive modes of transportation such as taxis or ferries. Morover studies indicate that increased stress from the commute to work can lead to lower productivity and that businesses near the impacted lines may see decreased revenue as potential customers have a harder time getting to them.  One controversial proposal for reducing breakdowns and the resulting transit interruptions is to end the subways 24-hour service and to shut down for several hours each night. Proponents of this plan argue that this would allow time on a regular rather than sporadic basis for more preventative maintanacnce. This they claim would ultimately lead to more consistent service rrather than shutting down entire lines for long periods of a time there would merely be shorter service outages overnight when fewer people use the subway system. While this may seem a preferable outcome to the economic consequence of a total shutdown resulting from a breakdown it has its liabilities as well. While most subway trips may occur during rush hour not everyone works during the daytime. New yourk is famously known as the the city that never sleeps. Doctors nurses bartenders police officers and firefighters are just a few examples of occupations whose workers need transportion at all hours of the day and night. Rather than be subjected to a relatively short period of inconvenience these workers would find their commutes irrevocably altered. One thing at least is clear the city must carefully condider many economic and social factors in designing a subway maintenance plan.  The fifth paragraph (lines 66-90) serves mainly to

Accepted Answer

NA

Question 42

This passage is adapted from a 2018 article summarizing two different proposals for solving problems with maintaining New York Citys mass transit system.  The history of the New York City subsaw system quickly told the first stations opened in 1904 and over the next century it expended to 472 stations more than any other subway system in the world with 850 miles of track. Operating 24 hours a day seven days a week with an average weekday ridership of approximately 5.7 million it is the plants 7th-busiest rapid transit system. While the system is on many levels an amazing chievement it is also beset by a problem that harms both quality of life and economic activity. Such a large system must inevitably suffer from service interruptions and delays normal wear and tear combined with the sheer age of the system necessitates regular maintanance. However there is no consensus as to the best way to accomplish the required repairs. The current maintanance scheme is designed to minimize service interruptions. A subway line in need of repair will be taken out of sevice during a comaratively less busy time such as nights or weekends while another line is re-routed to cover as many as possible of the missing lines stops. The main advantage to this approach is that trains are not taken out of service during rush hour when most subway trips occur subway service generally remains predictable and commuters are for the most part able to use the system to get to their desinations on time.  But critics are quick to point out the disadvantages to this approach. Perhaps most obvious is the confusion caused by trains swithing lines. The labyrinthine system is hard enough to navigate at the best of times. especially for tourists A subway rider on the A terain naturally expects the train to make stops on teh A line. If instead it is diverted temporatily to the F line the rader may find herself miles from her intended destination.  While annoying the confusion arising from route switching is hardly the most serious problem with the current approach to repairs. Because the system runs 24 hours a day routine maintenance can generally be done only during the temporary closures on nights and weekends. This means that more serious repair and crucial preventative maintenance is often neglected. Problems that could have been fixed or prevented reasonably expeditiously given a slightly longer closure wind up leading to major breakdowns and service interruptions later on.  On rare occasions such breakdowns have resulted in entire subway lines being shut down for months or even a year. Beginning in 2019 for example the I. Train connecting lower Manhattan to parts of Brooklyn was scheduled to close for as much as 15 months for long overdue service and upgrades. In a city fewar than half of whose households own a car this can have serious economic impacts Residents of the affected area may face a much longer commute via an alternate subway line if one is available or if there is no alternate subway service they may need to take other potentially more exppensive modes of transportation such as taxis or ferries. Morover studies indicate that increased stress from the commute to work can lead to lower productivity and that businesses near the impacted lines may see decreased revenue as potential customers have a harder time getting to them.  One controversial proposal for reducing breakdowns and the resulting transit interruptions is to end the subways 24-hour service and to shut down for several hours each night. Proponents of this plan argue that this would allow time on a regular rather than sporadic basis for more preventative maintanacnce. This they claim would ultimately lead to more consistent service rrather than shutting down entire lines for long periods of a time there would merely be shorter service outages overnight when fewer people use the subway system. While this may seem a preferable outcome to the economic consequence of a total shutdown resulting from a breakdown it has its liabilities as well. While most subway trips may occur during rush hour not everyone works during the daytime. New yourk is famously known as the the city that never sleeps. Doctors nurses bartenders police officers and firefighters are just a few examples of occupations whose workers need transportion at all hours of the day and night. Rather than be subjected to a relatively short period of inconvenience these workers would find their commutes irrevocably altered. One thing at least is clear the city must carefully condider many economic and social factors in designing a subway maintenance plan.  With which of the following statements would the authou of the passage be most likely to agree ?

Accepted Answer

NA

Question 43

The volume of spherical balloon being inflated changes at a constant rate.If initially its radius is 3 units and after 3 seconds it is 6units. Find the radius ofballoon after t seconds.

Accepted Answer

NA

Question 44

Measure of angle bewtwen lines (3+2sqrt(3))x^(2)-2xy-y^(2)=0 is

Accepted Answer

NA

Question 45

5 boys and 5 girls sit in a row at random. The probability that the boys and girls sit alternatively is

Accepted Answer

NA

Question 46

Find the derivative of the following functions with respect to x  (2 + 3 sinx) (3-2 cos x)

Accepted Answer

NA

Question 47

Integrate the function  (2x+4)(sqrt(x^(2)+4x+10))

Accepted Answer

NA

Question 48

Integrate int sqrt(x^2-8x+7) dx

Accepted Answer

NA

Question 49

This passage is adapted from a 2018 article summarizing two different proposals for solving problems with maintaining New York Citys mass transit system.  The history of the New York City subsaw system quickly told the first stations opened in 1904 and over the next century it expended to 472 stations more than any other subway system in the world with 850 miles of track. Operating 24 hours a day seven days a week with an average weekday ridership of approximately 5.7 million it is the plants 7th-busiest rapid transit system. While the system is on many levels an amazing chievement it is also beset by a problem that harms both quality of life and economic activity. Such a large system must inevitably suffer from service interruptions and delays normal wear and tear combined with the sheer age of the system necessitates regular maintanance. However there is no consensus as to the best way to accomplish the required repairs. The current maintanance scheme is designed to minimize service interruptions. A subway line in need of repair will be taken out of sevice during a comaratively less busy time such as nights or weekends while another line is re-routed to cover as many as possible of the missing lines stops. The main advantage to this approach is that trains are not taken out of service during rush hour when most subway trips occur subway service generally remains predictable and commuters are for the most part able to use the system to get to their desinations on time.  But critics are quick to point out the disadvantages to this approach. Perhaps most obvious is the confusion caused by trains swithing lines. The labyrinthine system is hard enough to navigate at the best of times. especially for tourists A subway rider on the A terain naturally expects the train to make stops on teh A line. If instead it is diverted temporatily to the F line the rader may find herself miles from her intended destination.  While annoying the confusion arising from route switching is hardly the most serious problem with the current approach to repairs. Because the system runs 24 hours a day routine maintenance can generally be done only during the temporary closures on nights and weekends. This means that more serious repair and crucial preventative maintenance is often neglected. Problems that could have been fixed or prevented reasonably expeditiously given a slightly longer closure wind up leading to major breakdowns and service interruptions later on.  On rare occasions such breakdowns have resulted in entire subway lines being shut down for months or even a year. Beginning in 2019 for example the I. Train connecting lower Manhattan to parts of Brooklyn was scheduled to close for as much as 15 months for long overdue service and upgrades. In a city fewar than half of whose households own a car this can have serious economic impacts Residents of the affected area may face a much longer commute via an alternate subway line if one is available or if there is no alternate subway service they may need to take other potentially more exppensive modes of transportation such as taxis or ferries. Morover studies indicate that increased stress from the commute to work can lead to lower productivity and that businesses near the impacted lines may see decreased revenue as potential customers have a harder time getting to them.  One controversial proposal for reducing breakdowns and the resulting transit interruptions is to end the subways 24-hour service and to shut down for several hours each night. Proponents of this plan argue that this would allow time on a regular rather than sporadic basis for more preventative maintanacnce. This they claim would ultimately lead to more consistent service rrather than shutting down entire lines for long periods of a time there would merely be shorter service outages overnight when fewer people use the subway system. While this may seem a preferable outcome to the economic consequence of a total shutdown resulting from a breakdown it has its liabilities as well. While most subway trips may occur during rush hour not everyone works during the daytime. New yourk is famously known as the the city that never sleeps. Doctors nurses bartenders police officers and firefighters are just a few examples of occupations whose workers need transportion at all hours of the day and night. Rather than be subjected to a relatively short period of inconvenience these workers would find their commutes irrevocably altered. One thing at least is clear the city must carefully condider many economic and social factors in designing a subway maintenance plan.  Which of the following best expresses the primary purpose of the passage ?

Accepted Answer

NA

Question 50

A circle of radius 4 cm is inscribed in DeltaABC which touches side BC at D. If BD = 6 cm DC = 8 cm then

Accepted Answer

NA

1.	If a,b,c are in H.P. then which of the following is true.
Answer» `(a)/(1-2a),(b)/(1-2b),( C)/(1-2c)` are in H.P. `LN(a-(b)/(2)),ln(b)/(2),ln(c-(b)/(2))` are in H.P. `c-(b)/(2),(b)/(2),a-(b)/(2)` are in G.P. `e^(2//a),e^(1//b),e^(1//c)` are in G.P. Answer :A::C::D

2.	Verify that the function y = a cos x + b sin x, where a,b in R is a solution of the differential equation (d^(2)y)/(dx^(2)) + y = 0
Answer» ANSWER :L.H.S = (- a COS X - b sin x ) + (a cos x + b sin x) = 0 = R.H.S

3.	Obtain the parametric equation of each of the following circles. (x-3)^(2) + (y-4)^(2) = 8^(2)
Answer» Answer :` x= 3 +8 COS THETA, y=4 + 8 SIN theta `

4.	All the letters of the word 'AGAIN' be arranged and the words thus formed are known as 'Simple Words'. Further two new types of words are defined as follows: (i) Smart word: all the letters of the word 'AGAIN' are being used, but vowels can be repeated as many times as we need. (ii) Dull word: All the letters of the word 'AGAIN' are being used, but consonants can be repeated as many times as we need. Q. Number of 7 letter dull words inw hich no two vowels are together, is
Answer» 402 420 840 42 Solution :Now, 3 vowels A,I,A are to be placed in the FIVE AVAILABLE places. `{{:("XNXGXNXNX"),("OR"),("XNXGXGXGX"),("OR"),("XNXGXGXNX):}` Hence, required number of ways `=.^(5)C_(3)xx(3!)/(2!)xx{(4!)/(3!)+(4!)/(3!)+(4!)/(2!2!)}` `=30(4+4+6)=420`

5.	A medical company has factories at two places A and B. From these places supply is madeto each of its three agencies situated at P, Q and R. The monthly requirements of the agen cies are respectively 40,40 and 50 packets of the medicines, while the production capacity of the factories A and B are 60 and 70 packets respectively. The transportation costs per packet from the factories to the agencies are given below:
Answer» Answer :To MINIME the TRANSPORTATION cost, following table illustrates the order schedule. `(##VVA_ISC_MAT_XII_MTP_16_E01_054_A01##)` Minimum transport cost = rs. 400

6.	There are ten boxes numbered from 1 to 10 and 10 balls numbered from 1 to 10. If the number of ways of putting all balls in given boxes such that no box remains empty, oddnumbered balls go to odd numbered box and no ball goes to the box having same number which is written on the ball is K^(2), then find K
Answer» ANSWER :44

7.	The orthocentre of the triangle with vertices A(0,0), B(0, (3)/(2)), C(-5, 0) is
Answer» `((5)/(2),(3)/(4))` `((-5)/(2),(3)/(4))` `(-5, (3)/(2))` `(0,0)` ANSWER :D

8.	If AA h in R - {0}, two distinct tangents can be drawn from the points (2+h,3h-1) to the curve y=x^(3)-6x^(2) - a+ bx then (a)/(b) is equal to "_____"
Answer» <P> SOLUTION :`y''=0impliesx=2` Let `P` be the POINT of inflection So `P-=(2,2b-a-16)` Equation of tangent line passing through inflection Point: `y=(b-12)x-a+8`…….(1) Let `Q-=(2+h,3h-1)` Locus of `Q:3x-y=7`…….(2) From equation (1) and (2) we GET ! So, `a=15` adn `b=15`

9.	If n in N,then11^(n+2)+12^(2n +1)is divisibleby
Answer» 113 123 133 Noneof these Answer :C

10.	Find the acute angle or angle or intersection of the following circles. a. x^(2)+y^(2)-12x-6y+41=0, x^(2)+y^(2)+4x+6y-59=0
Answer» ANSWER :`THETA=(PI)/4`

13.	Define f(x) as the product of two real functions f_(1)(x)=x, x epsilon IR and f_(2)(x)={("sin"1/x, "if", x!=0),(0 , "if", x=0):} as follows f(x)={(f_(1)(x).f_(2)(x), "if", x!=0),(0, "if", x=0):}
Answer» Statement-1 is True, Statement -2 is True, Statement -2 is True and Statement -2 is a CORRECT explanation for statement -1. Statement -1 is True, Statement -2 is True and Statement -2 is Not is a correct explanation for Statement -1. Statement -1 is True, Statement -2 is FALSE. Statement -1 is False, Statement -2 is True. Answer :D

14.	If, x,y inR , then the determinant: Delta=\|(cosx,-sinx,1),(sinx,cosx,1),(cos(x+y),-sin(x+y),0)\|lies in the interval .
Answer» `[-SQRT2,sqrt2]` `[-1,1]` `[-sqrt2,sqrt2]` `[-1,-sqrt2]` ANSWER :A

17.	If Delta = abs{:(x+y+z^(2) , x^(2) + y+ z, x+y^(2) + z),(z^2, x^2, y^2),(x+y,y+z,x+z):}, (where ( x ne y ne z) x, y, z in R- {0} ) then Delta= ........
Answer» `0` `1` `x+y+z` `x^2 + y^2 + z^2` ANSWER :A

21.	Integrate the following functions: sin^2(2x+5)
Answer» Solution :`sin^2(2x+5) = (1-cos2(2x+5))/2` =1/2[1-cos(4x+10)] therefore` INT sin^2(2x+5) DX` =`1/2[x-sin(4x+10)/4]+C`

11.	A number n is chosen at random from the natural numbers 2 to 1001. The probability that n is a number that leaves remainder 1 when divided by 7, is
Answer» `(73)/(500)` `(71)/(1000)` `(143)/(1000)` `(71)/(500)` Answer :D

12.	The minimum value of sec x, x in [(2pi)/(3),pi] is ……….
Answer» 1 `-2` 2 `PI` ANSWER :B

15.	The marginal cost of a product is given by MC =(14000)/(sqrt(7x+ 4)) and the fixed cost is 18000. Find the total cost and the average cost of producing 3 units of output.
Answer» ANSWER :RUPES 30,000 , rupes 10,000

16.	Four persons entered the lift cabin on the ground floor of a 5-floor house (Assume ground floor as also one floor). Assume that each of them independently and with equal probability can leave the cabin at any floor beginning from the first. Find the probability for all the four persons to leave the cabin at different floors :
Answer» `3//32` `1//256` `1//1024` `5//1024` ANSWER :A

18.	Find the value of y, if the matrix A = ((0,2y,z),(x,y,-z),(x,-y,z)) obeys the law A^(T).A = I.
Answer» ANSWER :`(16)/(21) ~~ 0.76`

19.	Find two positive numbers x and y such that their sum is 35 and the product x^(2) y^(5 )is a maximum.
Answer» ANSWER :25,10

20.	From points on the circlex^(2) +y^(2) =a ^(2) ,tangents are drawn to the hyperbolax^(2) - y^(2) =a^(2)The locus of the midpoints of chords of contact is
Answer» `(X^(2) +y^(2)) ^(2) =a^(2) (x^(2) - y^(2)) ` `(x^(2) -y^(2)) ^(2) =a^(2) (x^(2) + y^(2)) ` `a^(2) (x^(2) +y^(2)) ^(2) = (x^(2) - y^(2)) ` `a^(2) (x^(2) - y^(2)) ^(2) = (x^(2) + y^(2)) ` ANSWER :B

22.	f:(2,4)rarr(1,3),f(x) = x - [(x)/2] , where [.] is a greatest integer function then f^(-1)(x) = ......
Answer» 2X `X+[x/2]` `x+1` does not EXIST SOLUTION :N/A

23.	int_(0)^(a+b)(f(x-a))/(f(x-a)+f(b-x))dx,is equal to
Answer» a b 0 `(a+b)//2`. ANSWER :D

24.	If x in (0, 1) then intcos{2cot^(-1) sqrt((1+x)/(1-x))}dx=
Answer» `COT^(-1)X+c` `-cot^(-1)x+c` `(x^(2))/(2)+c` `(-x^(2))/(2)+c` Answer :4

Explore topic-wise InterviewSolutions in Current Affairs.

If a,b,c are in H.P. then which of the following is true.

Verify that the function y = a cos x + b sin x, where a,b in R is a solution of the differential equation (d^(2)y)/(dx^(2)) + y = 0

Obtain the parametric equation of each of the following circles. (x-3)^(2) + (y-4)^(2) = 8^(2)

The orthocentre of the triangle with vertices A(0,0), B(0, (3)/(2)), C(-5, 0) is

If AA h in R - {0}, two distinct tangents can be drawn from the points (2+h,3h-1) to the curve y=x^(3)-6x^(2) - a+ bx then (a)/(b) is equal to "_____"

If n in N,then11^(n+2)+12^(2n +1)is divisibleby

Find the acute angle or angle or intersection of the following circles. a. x^(2)+y^(2)-12x-6y+41=0, x^(2)+y^(2)+4x+6y-59=0

A number n is chosen at random from the natural numbers 2 to 1001. The probability that n is a number that leaves remainder 1 when divided by 7, is

The minimum value of sec x, x in [(2pi)/(3),pi] is ……….

Define f(x) as the product of two real functions f_(1)(x)=x, x epsilon IR and f_(2)(x)={("sin"1/x, "if", x!=0),(0 , "if", x=0):} as follows f(x)={(f_(1)(x).f_(2)(x), "if", x!=0),(0, "if", x=0):}

If, x,y inR , then the determinant: Delta=|(cosx,-sinx,1),(sinx,cosx,1),(cos(x+y),-sin(x+y),0)|lies in the interval .

The marginal cost of a product is given by MC =(14000)/(sqrt(7x+ 4)) and the fixed cost is 18000. Find the total cost and the average cost of producing 3 units of output.

If Delta = abs{:(x+y+z^(2) , x^(2) + y+ z, x+y^(2) + z),(z^2, x^2, y^2),(x+y,y+z,x+z):}, (where ( x ne y ne z) x, y, z in R- {0} ) then Delta= ........

Find the value of y, if the matrix A = ((0,2y,z),(x,y,-z),(x,-y,z)) obeys the law A^(T).A = I.

Find two positive numbers x and y such that their sum is 35 and the product x^(2) y^(5 )is a maximum.

From points on the circlex^(2) +y^(2) =a ^(2) ,tangents are drawn to the hyperbolax^(2) - y^(2) =a^(2)The locus of the midpoints of chords of contact is

Integrate the following functions: sin^2(2x+5)

f:(2,4)rarr(1,3),f(x) = x - [(x)/2] , where [.] is a greatest integer function then f^(-1)(x) = ......

int_(0)^(a+b)(f(x-a))/(f(x-a)+f(b-x))dx,is equal to

If x in (0, 1) then intcos{2cot^(-1) sqrt((1+x)/(1-x))}dx=

Solve as directed : x/2 - x/3 + x/5 le 11/3 for non-negative real numbers.

Evaluate the integerals.int e ^(x) log (e ^(2x) +5e^(x) +6)dx on R.

If |x| lt 1, then the coefficient of x^(n) in (1 + 2x + 3x^(2) + 4x^(3) + ......)^(1//2), is

The sum of the first n terms of the series 1/(sqrt(2) + sqrt(5)) + 1/(sqrt(5) + sqrt(8)) + 1/(sqrt(8) + sqrt(11)) +... is

Find the angle between the line (x+1)/2=y/3=(z-3)/6 and the plane 10x + 2y - 11z = 3.

Two friends A and B have equal number of sons. There are 3 cinema tickets which are to be distributed among the sons of A and B. The probability that all the tickets go to the sons of B is 1//20. The no. of sons each of them having is

A tangent is drawn at any point (l, m), l, mne0 on the parabola y^(2)=4ax and the tangents are drawn from any point on this tangent to the circle x^(2)+y^(2)=0 (where agt0) such that all chords of contact pass through a fixed point (alpha,beta), then

Evaluate intx^(3) e^(2x) dx

Prove that the angle of rotation of the axes to eliminate xy term from the equation ax^2+2hxy+by^2=0" is " Tan^(-1)((2h)/(a-b)) where a neb and (pi)/(4) ifa=b.

If a_(r)=a+(r-1)d is rth term of an A.P., then a_(n)^(2)-2a_(n-1)^(2)+a_(n-2)^(2) is independent of

Evaluate the following integrals: int_0^1 dx/(1+x^2)

The variance of the data 2,3,5,11,13,17,19 is nearly

Find the value of the (1)/(root(3)(999) ) correct to 4 decimal places

The volume of spherical balloon being inflated changes at a constant rate.If initially its radius is 3 units and after 3 seconds it is 6units. Find the radius ofballoon after t seconds.

Measure of angle bewtwen lines (3+2sqrt(3))x^(2)-2xy-y^(2)=0 is

5 boys and 5 girls sit in a row at random. The probability that the boys and girls sit alternatively is

Find the derivative of the following functions with respect to x (2 + 3 sinx) (3-2 cos x)

Integrate the function (2x+4)/(sqrt(x^(2)+4x+10))

Integrate int sqrt(x^2-8x+7) dx

A circle of radius 4 cm is inscribed in DeltaABC, which touches side BC at D. If BD = 6 cm, DC = 8 cm then

25.	Solve as directed : x/2 - x/3 + x/5 le 11/3 for non-negative real numbers.
Answer» Solution : x/2 - x/3 + x/5 `LE` 11/3 `rArr (15x-10x-6x)/30 le 11/3` `rArr 11x le (11/3) XX 30` `rArr 11x le 110 `rArr x le 10 If x is a non NEGATIVE real number then the solution set is S = {x:x `in` R and `0 le x le 10`} = {0, 10 }

26.	Evaluate the integerals.int e ^(x) log (e ^(2x) +5e^(x) +6)dx on R.
Answer» ANSWER :`e^(x)log(e^(2X)+5e^(x)+6)+2log(e^(x)+2)+3LOG(e^(x)+3)-2E^(x)+c`

27.	If \|x\| lt 1, then the coefficient of x^(n) in (1 + 2x + 3x^(2) + 4x^(3) + ......)^(1//2), is
Answer» N `n + 1` `-n` `1` ANSWER :D

28.	The sum of the first n terms of the series 1/(sqrt(2) + sqrt(5)) + 1/(sqrt(5) + sqrt(8)) + 1/(sqrt(8) + sqrt(11)) +... is
Answer» `1/3(SQRT(3N + 2) - sqrt(2))` `sqrt(3n + 2) - sqrt(2)` `sqrt(3n + 2) + sqrt(2)` `1/3(sqrt(2) -sqrt(3n + 2))` ANSWER :A

29.	Find the angle between the line (x+1)/2=y/3=(z-3)/6 and the plane 10x + 2y - 11z = 3.
Answer» ANSWER :`SIN^(-1)(8/21)`

30.	Two friends A and B have equal number of sons. There are 3 cinema tickets which are to be distributed among the sons of A and B. The probability that all the tickets go to the sons of B is 1//20. The no. of sons each of them having is
Answer» `2` `4` `5` `3` ANSWER :D

31.	A diet is to contain at leat 80 units of vitamin A and 100 units of minerals. Two foods F_(1) and F_(2) are available. Food F_(1) cost Rs. 4 per unit and F_(2)costs Rs. 6 per unit. One unit of food F_(1) contains 3 uinits of vitamin A and 4 units of minerals. One unit of food F_(2) contains 6 units of minerals. One unit of food F_(2) contains 6 units of vitamin A and 3 units of minerals. Formulate this as a linear programming problem. Find the minimum cost for diet that consists of mixture of these two foods and also meets the minimal nutritional requirements.
Answer» Solution :Let `x` units of `F_(1)` and `y` units of `F_(2)` be in the food. Then, Maximise `Z=4x+6y`…………….1 Constraints `3x+6yge80` ………………….2 `4x+3yge100`……………….3 `xge0,yge0`…………………..4 First, draw the graph of the line `3x+6y=80`,. Put `(0,0)` in the inequation `3x+6yge80`, `3xx0+6xx0ge80implies0ge80` (FALSE) Thus, the half plane does not contain the ORIGIN. Since `x,yge0` so the feasible solution is in the first QUADRANT. Now, draw the graph of the line `4x+3y=100` Put `(0,0)` in the inequation `4x+3yge100`, `4xx0+3xx0ge100` `implies0ge100` (False) Thus, the half plane does not contain the origin. From equations `3x+6y=80` and `4x+3y=100`. The POINT of intersection is `B(24, 4/3)` CLEARLY, the feasible region is unbounded. The vertices the feasible region are `A(80/3,0), B(24,4/3)` and `C(0,100/3)`. We find the value of `Z` at these vertices. Since the feasible region is unbounded, so the minimum value of `z` may or may not be 104. For this we draw the graph of inequations `4x+6t lt 104` or `2x+3ylt52`. There is no common point here, so the minimum cost of mixture is Rs. 104.

32.	A tangent is drawn at any point (l, m), l, mne0 on the parabola y^(2)=4ax and the tangents are drawn from any point on this tangent to the circle x^(2)+y^(2)=0 (where agt0) such that all chords of contact pass through a fixed point (alpha,beta), then
Answer» `alphalgt0,betamgt0` `alphallt0,betamgt0` `2(1/alpha)^(2)+(m/beta)^(2)=8` `4(1/alpha)+(m/beta)^(2)=0` Answer :B::D

33.	Evaluate intx^(3) e^(2x) dx
Answer» ANSWER :`(E^(2x))/(16)(2x)^(3)-3(2x)^(2)+6(2x)-6]+C`

34.	Prove that the angle of rotation of the axes to eliminate xy term from the equation ax^2+2hxy+by^2=0" is " Tan^(-1)((2h)/(a-b)) where a neb and (pi)/(4) ifa=b.
Answer» ANSWER :If a=b, then `THETA=(1)/(2)((pi)/(2))=(pi)/(4)`.