Quiz about Maths in Class 12

Question 1

If D(210) E (200) and F(010) are mid - points ofthe sidesBCCA and AB of triangleABC respectively Then the centroid of DeltaABC is

Accepted Answer

NA

Question 2

Choose the correct answers  The value of int_(0)^(1)tan^(-1)((2x-1)(1+x-x^(2)))dx is

Accepted Answer

NA

Question 3

The mean marks got by 300 students in the subject of statistics was 45. The mean of the top 100 of them was found to be 70 and the mean of the last 100 was known to be 20 then the mean of the remaining 100 students is

Accepted Answer

NA

Question 4

Mr. A randomly picks 3 distinct numbers from the set 1 2 3 4 5 6 7 8 9 and arrangesthem in descending order to form a three digit number. Mr. B randomly picks 3 distinct numbers from the set 1 2 3 4 5 6 7 8 and also arrangesthem in descending order to form a 3 digit number. Q. The probabilitythat Mr. As numberis larger than Mr. Bs number is

Accepted Answer

NA

Question 5

This passage was adapted from an aritcle entitled John Snow knew Something published in a popular history magazine in 2018.  Few would deny that doctors use critical thinking to solve problems but most imagine a difference between the partice of medicine and say the methods a police detective might use to solve a case. In fact medical researchers have long used forensic methods of detection and analysis. The case of John Snow a 19th-century anesthesiologist is often said to have ushered in the modern era of epidemiology the branch of medicine that tracks the incidence and distribution of diseases and proposes solutions for their control and prevention.  It would not be until 1861 that Louis Pasteur would 1861 Louis Pasteur would propose the link between microorganisms and disease now know as the germ theory. Before Pasteurs breakthrough the predominant explanation for the cause of most illnesses was the so-called miasma theory which held that noxious fumes and pollution-quite literally as the theorys name implies bed air-were responsible for making people sick. Consequently during the 1854 outbreak of cholera in Westminster London doctors and government officials alike blamed miasmatic particles released into the air by decaying organic matter in the soil of the River Thames.  Despite the widespread acceptance of the miasma theory there were those Snow included who were skeptical of this view. Snow sould not have known as doctors do today that cholera is caused by a cbacterial infection Vibrio cholerae. Nevertheless he was convinced that the spread of the disease was caused by some form of matter passed between individuals likely through contaaminated water. To demonstrate this Snow targeted a particularly deadly outbreak in the Soho district of Westminster in London. From August 31 to September 31854 127 people in the area died of cholera. Within a week that number had risen to over 500. Snow took to the streets. Speaking to residents of the area he found a commonality among them most of the victims had used a single public water pump located on Broad Street. Though he was unable to find conclusive proof that the pump was the source of the outbreak his demonstration of a pattern in the cholera cases prompted authorities to disable the pump by removing its handle. The epidemic quickly subsided. Soon after the Borad Steet pump was shut down Snows continued investigation provided additional evidence that contaminated water was the source of the outbreak. Snow created a dot map of the case of cholera in Lndon and demonstrated that they occured in areas were water was supplied by two companies that obtained their water from wells near the Thames. investigation of these wells showed that they had been dug three feet from a cespit that was leaking sewage into the surrounding soil. Snow also discovered that there were no cases of cholera among workers in a berwery close to the Broad Street pump. These workers were provided a daily allowance fo beer which they drank instead of water and althought the beer was brewed using the contaminated water it was boiled during the brewing process. This revelation provided a partical solution for the prevention of future outbreaks.  Snow is now hailed as the father of modern epidemiology and the radical nature of his approach-formulating a new theory substantiating it with verifiable avidence and proposing preventative action-is fully appreciated. At the time however not all were convinced at least publicly of Snows fiagged government officials replaced the handle on the Broad Street pump and publicly denounced Snows conclusions. It seems they felt that the citys residents would be upset and disgusted to have the unsettling nature of the wells contamination confirmed. It wasnt until 1866 more than a decade after Snows original investigation and theory-when another cholera outbreak killed more than 5500 residents of Londons East End-that officials working in public health began to accept the link between contaminated water and certain kinds of illness and to take appropriate actions to quell such outbreaks.  It can be reasonably inferred from the passage that scientists in 1855 would have found which of the following solutions to be most practical in dealing with future outbreaks of cholera ?

Accepted Answer

NA

Question 6

Mr. A randomly picks 3 distinct numbers from the set 1 2 3 4 5 6 7 8 9 and arrangesthem in descending order to form a three digit number. Mr. B randomly picks 3 distinct numbers from the set 1 2 3 4 5 6 7 8 and also arrangesthem in descending order to form a 3 digit number. Q. The probabilitythat Mr. As 3 digit number is alwaysgreater than Mr. Bs 3 digit number is

Accepted Answer

NA

Question 7

Each element of the second order determinant is 1 and - 1 then ....... is the probability that value of determinant is not zero.

Accepted Answer

NA

Question 8

Evaluate the followinglim_(xtoinfty)(3x^2+x-1)(2x^2-7x+5)

Accepted Answer

NA

Question 9

This passage was adapted from an aritcle entitled John Snow knew Something published in a popular history magazine in 2018.  Few would deny that doctors use critical thinking to solve problems but most imagine a difference between the partice of medicine and say the methods a police detective might use to solve a case. In fact medical researchers have long used forensic methods of detection and analysis. The case of John Snow a 19th-century anesthesiologist is often said to have ushered in the modern era of epidemiology the branch of medicine that tracks the incidence and distribution of diseases and proposes solutions for their control and prevention.  It would not be until 1861 that Louis Pasteur would 1861 Louis Pasteur would propose the link between microorganisms and disease now know as the germ theory. Before Pasteurs breakthrough the predominant explanation for the cause of most illnesses was the so-called miasma theory which held that noxious fumes and pollution-quite literally as the theorys name implies bed air-were responsible for making people sick. Consequently during the 1854 outbreak of cholera in Westminster London doctors and government officials alike blamed miasmatic particles released into the air by decaying organic matter in the soil of the River Thames.  Despite the widespread acceptance of the miasma theory there were those Snow included who were skeptical of this view. Snow sould not have known as doctors do today that cholera is caused by a cbacterial infection Vibrio cholerae. Nevertheless he was convinced that the spread of the disease was caused by some form of matter passed between individuals likely through contaaminated water. To demonstrate this Snow targeted a particularly deadly outbreak in the Soho district of Westminster in London. From August 31 to September 31854 127 people in the area died of cholera. Within a week that number had risen to over 500. Snow took to the streets. Speaking to residents of the area he found a commonality among them most of the victims had used a single public water pump located on Broad Street. Though he was unable to find conclusive proof that the pump was the source of the outbreak his demonstration of a pattern in the cholera cases prompted authorities to disable the pump by removing its handle. The epidemic quickly subsided. Soon after the Borad Steet pump was shut down Snows continued investigation provided additional evidence that contaminated water was the source of the outbreak. Snow created a dot map of the case of cholera in Lndon and demonstrated that they occured in areas were water was supplied by two companies that obtained their water from wells near the Thames. investigation of these wells showed that they had been dug three feet from a cespit that was leaking sewage into the surrounding soil. Snow also discovered that there were no cases of cholera among workers in a berwery close to the Broad Street pump. These workers were provided a daily allowance fo beer which they drank instead of water and althought the beer was brewed using the contaminated water it was boiled during the brewing process. This revelation provided a partical solution for the prevention of future outbreaks.  Snow is now hailed as the father of modern epidemiology and the radical nature of his approach-formulating a new theory substantiating it with verifiable avidence and proposing preventative action-is fully appreciated. At the time however not all were convinced at least publicly of Snows fiagged government officials replaced the handle on the Broad Street pump and publicly denounced Snows conclusions. It seems they felt that the citys residents would be upset and disgusted to have the unsettling nature of the wells contamination confirmed. It wasnt until 1866 more than a decade after Snows original investigation and theory-when another cholera outbreak killed more than 5500 residents of Londons East End-that officials working in public health began to accept the link between contaminated water and certain kinds of illness and to take appropriate actions to quell such outbreaks.  Which of the following is cited as the primary reason Snow suspected the Broad Steet pump as the source of the epidemic ?

Accepted Answer

NA

Question 10

Definecollinervectors.

Accepted Answer

NA

Question 11

A mapping is selected at random from the set of all the mappings of the set of A= 1234 into itself. The probability that the mapping selected is a bijection is

Accepted Answer

NA

Question 12

Minimise Z=3x+2y  Subject to the constraints  x+yge8  3x+5y le 15  x ge0 y ge0

Accepted Answer

NA

Question 13

One value of (1+isqrt3)^(34)+(1-isqrt3)^(34) is equal to

Accepted Answer

NA

Question 14

A tangent drawn to the curve x=e^(t)cos t y=e^(t) sin t at t=(pi)(4) makes an angle ………… with positive side of X - axis.

Accepted Answer

NA

Question 15

Solve the following linear programming problems graphically  Minimise Z = 3x + 2y subject to the constraints x+y le 8 3x+5y ge 15 x ge 0 y ge 0

Accepted Answer

NA

Question 16

If f((t+1)(2t+1))=t+1 then int f (x)dx=

Accepted Answer

NA

Question 17

The set A=xx in Rx^(2)=16 and 2x=6 equals

Accepted Answer

NA

Question 18

The number of waysof selecting 6 clerksfrom8 male&7 femaleapplicantsif theselectionis toconsistof eitherall malesor allfemales is

Accepted Answer

NA

Question 19

Transform eanc of the following equations into ones in which of the coefficients of the second highest power of x is zero and also find their transformed equations x^4+4x^3+2x^2-4x-2=0

Accepted Answer

NA

Question 20

Ifalpha beta gammaare therootsofx^3 +px^2 +qx +r=0then find sum alpha^3

Accepted Answer

NA

Question 21

if roots of the equation log_2^2x-100 log_2 x+3=0 and x_1 and x_2 then number of digits in x_1x_2 is (log_10 2 =0.3010 log_10 3 =0.4771) -

Accepted Answer

NA

Question 22

In a bank principal increases continuously at the rateof 5% per year. An amount of Rs 1000 is deposited with this bank how much will it worth after 10 years (e^((1)(2)) = 1.648)

Accepted Answer

NA

Question 23

If the equation x^(2)+px+q=0 has integral solutions for prime number p and q then p+q=

Accepted Answer

NA

Question 24

In triangleABCthevalue of( cotA2cot B2 -1)( cotA2 cotB2) is

Accepted Answer

NA

Question 25

Find (dy)(dx) in the following  y= sin^(-1) ((1-x^(2))(1+ x^(2))) 0 lt x lt 1

Accepted Answer

NA

Question 26

Find the following integrals  (i) int(x^(3)-1)(x^(2))dx (ii) int(x^(23)+1)dx (iii) int(x^(32)+2e^(x)-1x)dx

Accepted Answer

NA

Question 27

Prove that int_(0)^(1)(dx)(1+x^(n))gt1-(1)(n)for ninN

Accepted Answer

NA

Question 28

Find the number of ways of selecting 6 members out of 12 members always including a specified member.

Accepted Answer

NA

Question 29

If the straight lines 2x + 3y - 1 = 0 x + 2y - 1 = 0 and ax + by - 1 = 0 form a triangle with orthocentre at the origin then (a b) =

Accepted Answer

NA

Question 30

Find the area of the region (xy) y^(2)le 4x 4x^(2) + 4y^(2) le 9.

Accepted Answer

NA

Question 31

Find the centre and radius of the circle  3x^(2)+(a+1)y^(2)+6x-9y+a+4=0.

Accepted Answer

NA

Question 32

This passage was adapted from an aritcle entitled John Snow knew Something published in a popular history magazine in 2018.  Few would deny that doctors use critical thinking to solve problems but most imagine a difference between the partice of medicine and say the methods a police detective might use to solve a case. In fact medical researchers have long used forensic methods of detection and analysis. The case of John Snow a 19th-century anesthesiologist is often said to have ushered in the modern era of epidemiology the branch of medicine that tracks the incidence and distribution of diseases and proposes solutions for their control and prevention.  It would not be until 1861 that Louis Pasteur would 1861 Louis Pasteur would propose the link between microorganisms and disease now know as the germ theory. Before Pasteurs breakthrough the predominant explanation for the cause of most illnesses was the so-called miasma theory which held that noxious fumes and pollution-quite literally as the theorys name implies bed air-were responsible for making people sick. Consequently during the 1854 outbreak of cholera in Westminster London doctors and government officials alike blamed miasmatic particles released into the air by decaying organic matter in the soil of the River Thames.  Despite the widespread acceptance of the miasma theory there were those Snow included who were skeptical of this view. Snow sould not have known as doctors do today that cholera is caused by a cbacterial infection Vibrio cholerae. Nevertheless he was convinced that the spread of the disease was caused by some form of matter passed between individuals likely through contaaminated water. To demonstrate this Snow targeted a particularly deadly outbreak in the Soho district of Westminster in London. From August 31 to September 31854 127 people in the area died of cholera. Within a week that number had risen to over 500. Snow took to the streets. Speaking to residents of the area he found a commonality among them most of the victims had used a single public water pump located on Broad Street. Though he was unable to find conclusive proof that the pump was the source of the outbreak his demonstration of a pattern in the cholera cases prompted authorities to disable the pump by removing its handle. The epidemic quickly subsided. Soon after the Borad Steet pump was shut down Snows continued investigation provided additional evidence that contaminated water was the source of the outbreak. Snow created a dot map of the case of cholera in Lndon and demonstrated that they occured in areas were water was supplied by two companies that obtained their water from wells near the Thames. investigation of these wells showed that they had been dug three feet from a cespit that was leaking sewage into the surrounding soil. Snow also discovered that there were no cases of cholera among workers in a berwery close to the Broad Street pump. These workers were provided a daily allowance fo beer which they drank instead of water and althought the beer was brewed using the contaminated water it was boiled during the brewing process. This revelation provided a partical solution for the prevention of future outbreaks.  Snow is now hailed as the father of modern epidemiology and the radical nature of his approach-formulating a new theory substantiating it with verifiable avidence and proposing preventative action-is fully appreciated. At the time however not all were convinced at least publicly of Snows fiagged government officials replaced the handle on the Broad Street pump and publicly denounced Snows conclusions. It seems they felt that the citys residents would be upset and disgusted to have the unsettling nature of the wells contamination confirmed. It wasnt until 1866 more than a decade after Snows original investigation and theory-when another cholera outbreak killed more than 5500 residents of Londons East End-that officials working in public health began to accept the link between contaminated water and certain kinds of illness and to take appropriate actions to quell such outbreaks.  The passage indicates that the main reason government officials rejected Snows hypothesis was

Accepted Answer

NA

Question 33

If f(x)=1-(4)(x^(2)) and f(1)=6 then find f(x) and f(2).

Accepted Answer

NA

Question 34

Let a pair of dice be thrown and the random variable X be the sum of the﻿ numbers that appear on the two dice. Find the mean or expectation of X.﻿

Accepted Answer

NA

Question 35

This passage was adapted from an aritcle entitled John Snow knew Something published in a popular history magazine in 2018.  Few would deny that doctors use critical thinking to solve problems but most imagine a difference between the partice of medicine and say the methods a police detective might use to solve a case. In fact medical researchers have long used forensic methods of detection and analysis. The case of John Snow a 19th-century anesthesiologist is often said to have ushered in the modern era of epidemiology the branch of medicine that tracks the incidence and distribution of diseases and proposes solutions for their control and prevention.  It would not be until 1861 that Louis Pasteur would 1861 Louis Pasteur would propose the link between microorganisms and disease now know as the germ theory. Before Pasteurs breakthrough the predominant explanation for the cause of most illnesses was the so-called miasma theory which held that noxious fumes and pollution-quite literally as the theorys name implies bed air-were responsible for making people sick. Consequently during the 1854 outbreak of cholera in Westminster London doctors and government officials alike blamed miasmatic particles released into the air by decaying organic matter in the soil of the River Thames.  Despite the widespread acceptance of the miasma theory there were those Snow included who were skeptical of this view. Snow sould not have known as doctors do today that cholera is caused by a cbacterial infection Vibrio cholerae. Nevertheless he was convinced that the spread of the disease was caused by some form of matter passed between individuals likely through contaaminated water. To demonstrate this Snow targeted a particularly deadly outbreak in the Soho district of Westminster in London. From August 31 to September 31854 127 people in the area died of cholera. Within a week that number had risen to over 500. Snow took to the streets. Speaking to residents of the area he found a commonality among them most of the victims had used a single public water pump located on Broad Street. Though he was unable to find conclusive proof that the pump was the source of the outbreak his demonstration of a pattern in the cholera cases prompted authorities to disable the pump by removing its handle. The epidemic quickly subsided. Soon after the Borad Steet pump was shut down Snows continued investigation provided additional evidence that contaminated water was the source of the outbreak. Snow created a dot map of the case of cholera in Lndon and demonstrated that they occured in areas were water was supplied by two companies that obtained their water from wells near the Thames. investigation of these wells showed that they had been dug three feet from a cespit that was leaking sewage into the surrounding soil. Snow also discovered that there were no cases of cholera among workers in a berwery close to the Broad Street pump. These workers were provided a daily allowance fo beer which they drank instead of water and althought the beer was brewed using the contaminated water it was boiled during the brewing process. This revelation provided a partical solution for the prevention of future outbreaks.  Snow is now hailed as the father of modern epidemiology and the radical nature of his approach-formulating a new theory substantiating it with verifiable avidence and proposing preventative action-is fully appreciated. At the time however not all were convinced at least publicly of Snows fiagged government officials replaced the handle on the Broad Street pump and publicly denounced Snows conclusions. It seems they felt that the citys residents would be upset and disgusted to have the unsettling nature of the wells contamination confirmed. It wasnt until 1866 more than a decade after Snows original investigation and theory-when another cholera outbreak killed more than 5500 residents of Londons East End-that officials working in public health began to accept the link between contaminated water and certain kinds of illness and to take appropriate actions to quell such outbreaks.  Which choice provides the best evidence for the answer to the previous question ?

Accepted Answer

NA

Question 36

A square piece of tin of side 18 cm is to be made into a box without top by cutting a square from each corner and folding up the flaps to form the box. What should be the side of the square to be cut off so that the volume of the box is the maximum possible.

Accepted Answer

NA

Question 37

This passage was adapted from an aritcle entitled John Snow knew Something published in a popular history magazine in 2018.  Few would deny that doctors use critical thinking to solve problems but most imagine a difference between the partice of medicine and say the methods a police detective might use to solve a case. In fact medical researchers have long used forensic methods of detection and analysis. The case of John Snow a 19th-century anesthesiologist is often said to have ushered in the modern era of epidemiology the branch of medicine that tracks the incidence and distribution of diseases and proposes solutions for their control and prevention.  It would not be until 1861 that Louis Pasteur would 1861 Louis Pasteur would propose the link between microorganisms and disease now know as the germ theory. Before Pasteurs breakthrough the predominant explanation for the cause of most illnesses was the so-called miasma theory which held that noxious fumes and pollution-quite literally as the theorys name implies bed air-were responsible for making people sick. Consequently during the 1854 outbreak of cholera in Westminster London doctors and government officials alike blamed miasmatic particles released into the air by decaying organic matter in the soil of the River Thames.  Despite the widespread acceptance of the miasma theory there were those Snow included who were skeptical of this view. Snow sould not have known as doctors do today that cholera is caused by a cbacterial infection Vibrio cholerae. Nevertheless he was convinced that the spread of the disease was caused by some form of matter passed between individuals likely through contaaminated water. To demonstrate this Snow targeted a particularly deadly outbreak in the Soho district of Westminster in London. From August 31 to September 31854 127 people in the area died of cholera. Within a week that number had risen to over 500. Snow took to the streets. Speaking to residents of the area he found a commonality among them most of the victims had used a single public water pump located on Broad Street. Though he was unable to find conclusive proof that the pump was the source of the outbreak his demonstration of a pattern in the cholera cases prompted authorities to disable the pump by removing its handle. The epidemic quickly subsided. Soon after the Borad Steet pump was shut down Snows continued investigation provided additional evidence that contaminated water was the source of the outbreak. Snow created a dot map of the case of cholera in Lndon and demonstrated that they occured in areas were water was supplied by two companies that obtained their water from wells near the Thames. investigation of these wells showed that they had been dug three feet from a cespit that was leaking sewage into the surrounding soil. Snow also discovered that there were no cases of cholera among workers in a berwery close to the Broad Street pump. These workers were provided a daily allowance fo beer which they drank instead of water and althought the beer was brewed using the contaminated water it was boiled during the brewing process. This revelation provided a partical solution for the prevention of future outbreaks.  Snow is now hailed as the father of modern epidemiology and the radical nature of his approach-formulating a new theory substantiating it with verifiable avidence and proposing preventative action-is fully appreciated. At the time however not all were convinced at least publicly of Snows fiagged government officials replaced the handle on the Broad Street pump and publicly denounced Snows conclusions. It seems they felt that the citys residents would be upset and disgusted to have the unsettling nature of the wells contamination confirmed. It wasnt until 1866 more than a decade after Snows original investigation and theory-when another cholera outbreak killed more than 5500 residents of Londons East End-that officials working in public health began to accept the link between contaminated water and certain kinds of illness and to take appropriate actions to quell such outbreaks.  Which of the following is most analogous to John Snows theory that contaminated water caused teh cholera outbreak?

Accepted Answer

NA

Question 38

5 different toys are distributed among 6 children at random. Find the probability that atleast one child receives more than one toy.

Accepted Answer

NA

Question 39

Show that the middle term in the expansion of (1 + x)^(2n) is (1.3.5.........(2n - 1))(n!)2^(n)x^(n) where n is a positive integer.

Accepted Answer

NA

Question 40

This passage was adapted from an aritcle entitled John Snow knew Something published in a popular history magazine in 2018.  Few would deny that doctors use critical thinking to solve problems but most imagine a difference between the partice of medicine and say the methods a police detective might use to solve a case. In fact medical researchers have long used forensic methods of detection and analysis. The case of John Snow a 19th-century anesthesiologist is often said to have ushered in the modern era of epidemiology the branch of medicine that tracks the incidence and distribution of diseases and proposes solutions for their control and prevention.  It would not be until 1861 that Louis Pasteur would 1861 Louis Pasteur would propose the link between microorganisms and disease now know as the germ theory. Before Pasteurs breakthrough the predominant explanation for the cause of most illnesses was the so-called miasma theory which held that noxious fumes and pollution-quite literally as the theorys name implies bed air-were responsible for making people sick. Consequently during the 1854 outbreak of cholera in Westminster London doctors and government officials alike blamed miasmatic particles released into the air by decaying organic matter in the soil of the River Thames.  Despite the widespread acceptance of the miasma theory there were those Snow included who were skeptical of this view. Snow sould not have known as doctors do today that cholera is caused by a cbacterial infection Vibrio cholerae. Nevertheless he was convinced that the spread of the disease was caused by some form of matter passed between individuals likely through contaaminated water. To demonstrate this Snow targeted a particularly deadly outbreak in the Soho district of Westminster in London. From August 31 to September 31854 127 people in the area died of cholera. Within a week that number had risen to over 500. Snow took to the streets. Speaking to residents of the area he found a commonality among them most of the victims had used a single public water pump located on Broad Street. Though he was unable to find conclusive proof that the pump was the source of the outbreak his demonstration of a pattern in the cholera cases prompted authorities to disable the pump by removing its handle. The epidemic quickly subsided. Soon after the Borad Steet pump was shut down Snows continued investigation provided additional evidence that contaminated water was the source of the outbreak. Snow created a dot map of the case of cholera in Lndon and demonstrated that they occured in areas were water was supplied by two companies that obtained their water from wells near the Thames. investigation of these wells showed that they had been dug three feet from a cespit that was leaking sewage into the surrounding soil. Snow also discovered that there were no cases of cholera among workers in a berwery close to the Broad Street pump. These workers were provided a daily allowance fo beer which they drank instead of water and althought the beer was brewed using the contaminated water it was boiled during the brewing process. This revelation provided a partical solution for the prevention of future outbreaks.  Snow is now hailed as the father of modern epidemiology and the radical nature of his approach-formulating a new theory substantiating it with verifiable avidence and proposing preventative action-is fully appreciated. At the time however not all were convinced at least publicly of Snows fiagged government officials replaced the handle on the Broad Street pump and publicly denounced Snows conclusions. It seems they felt that the citys residents would be upset and disgusted to have the unsettling nature of the wells contamination confirmed. It wasnt until 1866 more than a decade after Snows original investigation and theory-when another cholera outbreak killed more than 5500 residents of Londons East End-that officials working in public health began to accept the link between contaminated water and certain kinds of illness and to take appropriate actions to quell such outbreaks.  The second paragraph serves mainly to

Accepted Answer

NA

Question 41

If n=3m then the coefficient of x^(n) in the expansion of log(1+x+x^(2)) is

Accepted Answer

NA

Question 42

This passage was adapted from an aritcle entitled John Snow knew Something published in a popular history magazine in 2018.  Few would deny that doctors use critical thinking to solve problems but most imagine a difference between the partice of medicine and say the methods a police detective might use to solve a case. In fact medical researchers have long used forensic methods of detection and analysis. The case of John Snow a 19th-century anesthesiologist is often said to have ushered in the modern era of epidemiology the branch of medicine that tracks the incidence and distribution of diseases and proposes solutions for their control and prevention.  It would not be until 1861 that Louis Pasteur would 1861 Louis Pasteur would propose the link between microorganisms and disease now know as the germ theory. Before Pasteurs breakthrough the predominant explanation for the cause of most illnesses was the so-called miasma theory which held that noxious fumes and pollution-quite literally as the theorys name implies bed air-were responsible for making people sick. Consequently during the 1854 outbreak of cholera in Westminster London doctors and government officials alike blamed miasmatic particles released into the air by decaying organic matter in the soil of the River Thames.  Despite the widespread acceptance of the miasma theory there were those Snow included who were skeptical of this view. Snow sould not have known as doctors do today that cholera is caused by a cbacterial infection Vibrio cholerae. Nevertheless he was convinced that the spread of the disease was caused by some form of matter passed between individuals likely through contaaminated water. To demonstrate this Snow targeted a particularly deadly outbreak in the Soho district of Westminster in London. From August 31 to September 31854 127 people in the area died of cholera. Within a week that number had risen to over 500. Snow took to the streets. Speaking to residents of the area he found a commonality among them most of the victims had used a single public water pump located on Broad Street. Though he was unable to find conclusive proof that the pump was the source of the outbreak his demonstration of a pattern in the cholera cases prompted authorities to disable the pump by removing its handle. The epidemic quickly subsided. Soon after the Borad Steet pump was shut down Snows continued investigation provided additional evidence that contaminated water was the source of the outbreak. Snow created a dot map of the case of cholera in Lndon and demonstrated that they occured in areas were water was supplied by two companies that obtained their water from wells near the Thames. investigation of these wells showed that they had been dug three feet from a cespit that was leaking sewage into the surrounding soil. Snow also discovered that there were no cases of cholera among workers in a berwery close to the Broad Street pump. These workers were provided a daily allowance fo beer which they drank instead of water and althought the beer was brewed using the contaminated water it was boiled during the brewing process. This revelation provided a partical solution for the prevention of future outbreaks.  Snow is now hailed as the father of modern epidemiology and the radical nature of his approach-formulating a new theory substantiating it with verifiable avidence and proposing preventative action-is fully appreciated. At the time however not all were convinced at least publicly of Snows fiagged government officials replaced the handle on the Broad Street pump and publicly denounced Snows conclusions. It seems they felt that the citys residents would be upset and disgusted to have the unsettling nature of the wells contamination confirmed. It wasnt until 1866 more than a decade after Snows original investigation and theory-when another cholera outbreak killed more than 5500 residents of Londons East End-that officials working in public health began to accept the link between contaminated water and certain kinds of illness and to take appropriate actions to quell such outbreaks.  The author of this passage writes from the perspective of

Accepted Answer

NA

Question 43

Find the area of the region bounded by  y= |cos x| y=0 x= - pi and x= pi

Accepted Answer

NA

Question 44

Which of the following sentences are propositions and which are not ? Write with reason It is possible that there is life in Mars.

Accepted Answer

NA

Question 45

Net force acting on a particle is always perpendicular to its velocity then -

Accepted Answer

NA

Question 46

If |(m-2)(52m)|=|(5-4)(53)| then find m

Accepted Answer

NA

Question 47

This passage was adapted from an aritcle entitled John Snow knew Something published in a popular history magazine in 2018.  Few would deny that doctors use critical thinking to solve problems but most imagine a difference between the partice of medicine and say the methods a police detective might use to solve a case. In fact medical researchers have long used forensic methods of detection and analysis. The case of John Snow a 19th-century anesthesiologist is often said to have ushered in the modern era of epidemiology the branch of medicine that tracks the incidence and distribution of diseases and proposes solutions for their control and prevention.  It would not be until 1861 that Louis Pasteur would 1861 Louis Pasteur would propose the link between microorganisms and disease now know as the germ theory. Before Pasteurs breakthrough the predominant explanation for the cause of most illnesses was the so-called miasma theory which held that noxious fumes and pollution-quite literally as the theorys name implies bed air-were responsible for making people sick. Consequently during the 1854 outbreak of cholera in Westminster London doctors and government officials alike blamed miasmatic particles released into the air by decaying organic matter in the soil of the River Thames.  Despite the widespread acceptance of the miasma theory there were those Snow included who were skeptical of this view. Snow sould not have known as doctors do today that cholera is caused by a cbacterial infection Vibrio cholerae. Nevertheless he was convinced that the spread of the disease was caused by some form of matter passed between individuals likely through contaaminated water. To demonstrate this Snow targeted a particularly deadly outbreak in the Soho district of Westminster in London. From August 31 to September 31854 127 people in the area died of cholera. Within a week that number had risen to over 500. Snow took to the streets. Speaking to residents of the area he found a commonality among them most of the victims had used a single public water pump located on Broad Street. Though he was unable to find conclusive proof that the pump was the source of the outbreak his demonstration of a pattern in the cholera cases prompted authorities to disable the pump by removing its handle. The epidemic quickly subsided. Soon after the Borad Steet pump was shut down Snows continued investigation provided additional evidence that contaminated water was the source of the outbreak. Snow created a dot map of the case of cholera in Lndon and demonstrated that they occured in areas were water was supplied by two companies that obtained their water from wells near the Thames. investigation of these wells showed that they had been dug three feet from a cespit that was leaking sewage into the surrounding soil. Snow also discovered that there were no cases of cholera among workers in a berwery close to the Broad Street pump. These workers were provided a daily allowance fo beer which they drank instead of water and althought the beer was brewed using the contaminated water it was boiled during the brewing process. This revelation provided a partical solution for the prevention of future outbreaks.  Snow is now hailed as the father of modern epidemiology and the radical nature of his approach-formulating a new theory substantiating it with verifiable avidence and proposing preventative action-is fully appreciated. At the time however not all were convinced at least publicly of Snows fiagged government officials replaced the handle on the Broad Street pump and publicly denounced Snows conclusions. It seems they felt that the citys residents would be upset and disgusted to have the unsettling nature of the wells contamination confirmed. It wasnt until 1866 more than a decade after Snows original investigation and theory-when another cholera outbreak killed more than 5500 residents of Londons East End-that officials working in public health began to accept the link between contaminated water and certain kinds of illness and to take appropriate actions to quell such outbreaks.  The passage primarilly serves to

Accepted Answer

NA

Question 48

If a makes an acute angle with br cdota = 0 and r xx b = c xx b then r =

Accepted Answer

NA

Question 49

If arg((z-1)(z+1))=(pi)(3) then the of z is

Accepted Answer

NA

Question 50

A 50 L tank initailly contains 10 L of fresh water At t=0 a brine solution containing 1 lb of salt per gallon is poured into the tank at the rate of 4 Lmin while the well-stirred mixture leaves the tank at the rate of 2 Lmin. Then the amount of time required for overflow to occur in

Accepted Answer

NA

27401.	If D(2,1,0) , E (2,0,0) and F(0,1,0) are mid - points ofthe sidesBC,CA and AB of triangleABC , respectively , Then , the centroid of DeltaABC is
Answer» `(1/3,1/3,1/3)` `(4/3,2/3,0)` `(-1/3,1/3,1/3)` `(2/3,1/3,1/3)` ANSWER :B

27402.	Choose the correct answers The value of int_(0)^(1)tan^(-1)((2x-1)/(1+x-x^(2)))dx is
Answer» 1 0 `-1` `pi/4` ANSWER :B

27403.	The mean marks got by 300 students in the subject of statistics was 45. The mean of the top 100 of them was found to be 70 and the mean of the last 100 was known to be 20, then the mean of the remaining 100 students is
Answer» 45 58 68 88 Answer :A

27404.	Mr. A randomly picks 3 distinct numbers from the set {1, 2, 3, 4, 5, 6, 7, 8, 9} and arrangesthem in descending order to form a three digit number. Mr. B randomly picks 3 distinct numbers from the set {1, 2, 3, 4, 5, 6, 7, 8} and also arrangesthem in descending order to form a 3 digit number. Q. The probabilitythat Mr. A's numberis larger than Mr. B's number, is :
Answer» `(37)/(56)` `(39)/(56)` `(31)/(56)` none of these ANSWER :A

27405.	This passage was adapted from an aritcle entitled "John Snow knew Something" published in a popular history magazine in 2018. Few would deny that doctors use critical thinking to solve problems, but most imagine a difference between the partice of medicine and, say, the methods a police detective might use to solve a case. In fact, medical researchers have long used forensic methods of detection and analysis. The case of John Snow, a 19th-century anesthesiologist, is often said to have ushered in the modern era of epidemiology, the branch of medicine that tracks the incidence and distribution of diseases and proposes solutions for their control and prevention. It would not be until 1861 that Louis Pasteur would 1861 Louis Pasteur would propose the link between microorganisms and disease, now know as the germ theory. Before Pasteur's breakthrough, the predominant explanation for the cause of most illnesses was the so-called miasma theory, which held that noxious fumes and pollution-quite literally, as the theory's name implies, "bed air"-were responsible for making people sick. Consequently, during the 1854 outbreak of cholera in Westminster, London, doctors and government officials alike blamed "miasmatic particles" released into the air by decaying organic matter in the soil of the River Thames. Despite the widespread acceptance of the miasma theory, there were those, Snow included, who were skeptical of this view. Snow sould not have known, as doctors do today, that cholera is caused by a cbacterial infection, Vibrio cholerae. Nevertheless, he was convinced that the spread of the disease was caused by some form of matter passed between individuals, likely through contaaminated water. To demonstrate this, Snow targeted a particularly deadly outbreak in the Soho district of Westminster in London. From August 31 to September 3,1854, 127 people in the area died of cholera. Within a week that number had risen to over 500. Snow took to the streets. Speaking to residents of the area, he found a commonality among them: most of the victims had used a single public water pump located on Broad Street. Though he was unable to find conclusive proof that the pump was the source of the outbreak, his demonstration of a pattern in the cholera cases prompted authorities to disable the pump by removing its handle. The epidemic quickly subsided. Soon after the Borad Steet pump was shut down Snow's continued investigation provided additional evidence that contaminated water was the source of the outbreak. Snow created a dot map of the case of cholera in Lndon and demonstrated that they occured in areas were water was supplied by two companies that obtained their water from wells near the Thames. investigation of these wells showed that they had been dug three feet from a cespit that was leaking sewage into the surrounding soil. Snow also discovered that there were no cases of cholera among workers in a berwery close to the Broad Street pump. These workers were provided a daily allowance fo beer, which they drank instead of water, and althought the beer was brewed using the contaminated water, it was boiled during the brewing process. This revelation provided a partical solution for the prevention of future outbreaks. Snow is now hailed as the "father of modern epidemiology," and the radical nature of his approach-formulating a new theory, substantiating it with verifiable avidence, and proposing preventative action-is fully appreciated. At the time, however, not all were convinced, at least publicly, of Snow's fiagged, government officials replaced the handle on the Broad Street pump and publicly denounced Snow's conclusions. It seems they felt that the city's residents would be upset and disgusted to have the unsettling nature of the well's contamination confirmed. It wasn't until 1866, more than a decade after Snow's original investigation and theory-when another cholera outbreak killed more than 5,500 residents of London's East End-that officials working in public health began to accept the link between contaminated water and certain kinds of illness and to take appropriate actions to quell such outbreaks. It can be reasonably inferred from the passage that scientists in 1855 would have found which of the following solutions to be most practical in dealing with future outbreaks of cholera ?
Answer» USING alcoholic beverages in place of WATER for all applications Removing the handles from all water pumps in the AFFECTED area Vaccinating the public against the disease using inactive V. cholerae bacteria ADVISING the public to boil all water from municipal SOURCES before use Answer :D

27406.	Mr. A randomly picks 3 distinct numbers from the set {1, 2, 3, 4, 5, 6, 7, 8, 9} and arrangesthem in descending order to form a three digit number. Mr. B randomly picks 3 distinct numbers from the set {1, 2, 3, 4, 5, 6, 7, 8} and also arrangesthem in descending order to form a 3 digit number. Q. The probabilitythat Mr. A's 3 digit number is alwaysgreater than Mr. B's 3 digit number is :
Answer» `(37)/(56)` `(1)/(3)` `( 2)/(3)` `(1)/(4)` ANSWER :A

27407.	Each element of the second order determinant is 1 and - 1 then ....... is the probability that value of determinant is not zero.
Answer» `(1)/(2)` `(3)/(8)` `(5)/(8)` `(1)/(3)` ANSWER :A

27408.	Evaluate the following:lim_(xtoinfty)(3x^2+x-1)/(2x^2-7x+5)
Answer» SOLUTION :`lim_(xtoinfty)(3x^2+x-1)/(2x^2-7x+5)` `(3+1/x-1/x^2)/(2-7/x+5/x^2)=3/2`

27409.	This passage was adapted from an aritcle entitled "John Snow knew Something" published in a popular history magazine in 2018. Few would deny that doctors use critical thinking to solve problems, but most imagine a difference between the partice of medicine and, say, the methods a police detective might use to solve a case. In fact, medical researchers have long used forensic methods of detection and analysis. The case of John Snow, a 19th-century anesthesiologist, is often said to have ushered in the modern era of epidemiology, the branch of medicine that tracks the incidence and distribution of diseases and proposes solutions for their control and prevention. It would not be until 1861 that Louis Pasteur would 1861 Louis Pasteur would propose the link between microorganisms and disease, now know as the germ theory. Before Pasteur's breakthrough, the predominant explanation for the cause of most illnesses was the so-called miasma theory, which held that noxious fumes and pollution-quite literally, as the theory's name implies, "bed air"-were responsible for making people sick. Consequently, during the 1854 outbreak of cholera in Westminster, London, doctors and government officials alike blamed "miasmatic particles" released into the air by decaying organic matter in the soil of the River Thames. Despite the widespread acceptance of the miasma theory, there were those, Snow included, who were skeptical of this view. Snow sould not have known, as doctors do today, that cholera is caused by a cbacterial infection, Vibrio cholerae. Nevertheless, he was convinced that the spread of the disease was caused by some form of matter passed between individuals, likely through contaaminated water. To demonstrate this, Snow targeted a particularly deadly outbreak in the Soho district of Westminster in London. From August 31 to September 3,1854, 127 people in the area died of cholera. Within a week that number had risen to over 500. Snow took to the streets. Speaking to residents of the area, he found a commonality among them: most of the victims had used a single public water pump located on Broad Street. Though he was unable to find conclusive proof that the pump was the source of the outbreak, his demonstration of a pattern in the cholera cases prompted authorities to disable the pump by removing its handle. The epidemic quickly subsided. Soon after the Borad Steet pump was shut down Snow's continued investigation provided additional evidence that contaminated water was the source of the outbreak. Snow created a dot map of the case of cholera in Lndon and demonstrated that they occured in areas were water was supplied by two companies that obtained their water from wells near the Thames. investigation of these wells showed that they had been dug three feet from a cespit that was leaking sewage into the surrounding soil. Snow also discovered that there were no cases of cholera among workers in a berwery close to the Broad Street pump. These workers were provided a daily allowance fo beer, which they drank instead of water, and althought the beer was brewed using the contaminated water, it was boiled during the brewing process. This revelation provided a partical solution for the prevention of future outbreaks. Snow is now hailed as the "father of modern epidemiology," and the radical nature of his approach-formulating a new theory, substantiating it with verifiable avidence, and proposing preventative action-is fully appreciated. At the time, however, not all were convinced, at least publicly, of Snow's fiagged, government officials replaced the handle on the Broad Street pump and publicly denounced Snow's conclusions. It seems they felt that the city's residents would be upset and disgusted to have the unsettling nature of the well's contamination confirmed. It wasn't until 1866, more than a decade after Snow's original investigation and theory-when another cholera outbreak killed more than 5,500 residents of London's East End-that officials working in public health began to accept the link between contaminated water and certain kinds of illness and to take appropriate actions to quell such outbreaks. Which of the following is cited as the primary reason Snow suspected the Broad Steet pump as the source of the epidemic ?
Answer» The discovery of decaying organic matter in SOIL near the THAMES releasing gases into the air The decline of CASES of the disease following the removal of the pump HANDLE A PATTERN in the geographical location of cases of the disease A lack of cases of the disease among those working in a brewary near the pump Answer :C

27410.	Definecollinervectors.
Answer» ANSWER :CollinearvectorsTwoor morenon - zerovectorsare SAIDTO becollinear, iftheyare paralleltothesameline.Twovectorsaandbarecollinearif`a=lamdab`forsomescalar`LAMDA `.

27413.	One value of (1+isqrt3)^(3//4)+(1-isqrt3)^(3//4) is equal to
Answer» `(16)^(1//4)` `(64)^(1//4)` `(32)^(1//4)` `(48)^(1//4)` Answer :C

27416.	If f((t+1)/(2t+1))=t+1, then int f (x)dx=
Answer» `(X^(2))/(2)+c` `"log"_(E)(2x=-1)+(1)/(2)"log"_(e)\|(x+1)\|+c` `(1)/(2) log_(e)\|((x+1)/(2x+1))\|+c` `(x)/(2)+(1)/(4) log_(e)\|2x-1\|+c` ANSWER :D

27417.	The set A={x:x in R,x^(2)=16," and "2x=6} equals
Answer» `PHI` {14, 3, 4} {3} {4} ANSWER :A

27424.	In triangleABCthevalue of( cotA/2cot ""B/2 -1)/( cot""A/2 cot""B/2) is
Answer» `(a)/( a+b+C)` `(c )/(a+b+c)` `(2A)/(a+b+c)` `(2C )/(a+b+c)` ANSWER :D

27411.	A mapping is selected at random from the set of all the mappings of the set of A= {1,2,3,4} into itself. The probability that the mapping selected is a bijection is
Answer» `(1)/(4^(4))` `(1)/(4!)` `(3!)/(4^(3))` `(1)/(4)` ANSWER :C

27412.	Minimise Z=3x+2y Subject to the constraints x+yge8 3x+5y le 15 x ge0, y ge0
Answer» ANSWER :no FEASIBLE SOLUTION.

27414.	A tangent drawn to the curve x=e^(t)cos t, y=e^(t) sin t at t=(pi)/(4) makes an angle ………… with positive side of X - axis.
Answer» 0 `(PI)/(4)` `(pi)/(3)` `(pi)/(2)` Answer :D

27415.	Solve the following linear programming problems graphically : Minimise : Z = 3x + 2y subject to the constraints x+y le 8, 3x+5y ge 15, x ge 0, y ge 0
Answer» Answer :Minimum Z = 6, at (0, 3).

27418.	The number of waysof selecting 6 clerksfrom8 male&7 femaleapplicantsif theselectionis toconsistof eitherall malesor allfemales is
Answer» 25 30 35 40 Answer :C

27419.	Transform eanc of the following equations into ones in which of the coefficients of the second highest power of x is zero and also find their transformed equations x^4+4x^3+2x^2-4x-2=0
Answer» ANSWER :`x^4 -4x^2 +1=0`

27420.	Ifalpha, beta, gammaare therootsofx^3 +px^2 +qx +r=0then find sum alpha^3
Answer» ANSWER :`-p^3 +3PQ =3R`

27421.	if roots of the equation log_2^2x-100 log_2 x+3=0 and x_1 and x_2 then number of digits in x_1x_2 is (log_10 2 =0.3010, log_10 3 =0.4771) :-
Answer» 30 47 31 48

27422.	In a bank, principal increases continuously at the rateof 5% per year. An amount of Rs 1000 is deposited with this bank, how much will it worth after 10 years (e^((1)/(2)) = 1.648)
Answer» 1648 164.8 16480 32296 Answer :A

27423.	If the equation x^(2)+px+q=0 has integral solutions for prime number p and q, then p+q=
Answer» 3 5 4 10 Solution :`ALPHA,BETA` be the ROOTS `alpha+beta=-p` and `alphabeta=qimplies" "beta=-1 ,alpha=-2` only POSSIBLITY

Explore topic-wise InterviewSolutions in .

If D(2,1,0) , E (2,0,0) and F(0,1,0) are mid - points ofthe sidesBC,CA and AB of triangleABC , respectively , Then , the centroid of DeltaABC is

Choose the correct answers The value of int_(0)^(1)tan^(-1)((2x-1)/(1+x-x^(2)))dx is

The mean marks got by 300 students in the subject of statistics was 45. The mean of the top 100 of them was found to be 70 and the mean of the last 100 was known to be 20, then the mean of the remaining 100 students is

Each element of the second order determinant is 1 and - 1 then ....... is the probability that value of determinant is not zero.

Evaluate the following:lim_(xtoinfty)(3x^2+x-1)/(2x^2-7x+5)

Definecollinervectors.

A mapping is selected at random from the set of all the mappings of the set of A= {1,2,3,4} into itself. The probability that the mapping selected is a bijection is

Minimise Z=3x+2y Subject to the constraints x+yge8 3x+5y le 15 x ge0, y ge0

One value of (1+isqrt3)^(3//4)+(1-isqrt3)^(3//4) is equal to

A tangent drawn to the curve x=e^(t)cos t, y=e^(t) sin t at t=(pi)/(4) makes an angle ………… with positive side of X - axis.

Solve the following linear programming problems graphically : Minimise : Z = 3x + 2y subject to the constraints x+y le 8, 3x+5y ge 15, x ge 0, y ge 0

If f((t+1)/(2t+1))=t+1, then int f (x)dx=

The set A={x:x in R,x^(2)=16," and "2x=6} equals

The number of waysof selecting 6 clerksfrom8 male&7 femaleapplicantsif theselectionis toconsistof eitherall malesor allfemales is

Transform eanc of the following equations into ones in which of the coefficients of the second highest power of x is zero and also find their transformed equations x^4+4x^3+2x^2-4x-2=0

Ifalpha, beta, gammaare therootsofx^3 +px^2 +qx +r=0then find sum alpha^3

if roots of the equation log_2^2x-100 log_2 x+3=0 and x_1 and x_2 then number of digits in x_1x_2 is (log_10 2 =0.3010, log_10 3 =0.4771) :-

In a bank, principal increases continuously at the rateof 5% per year. An amount of Rs 1000 is deposited with this bank, how much will it worth after 10 years (e^((1)/(2)) = 1.648)

If the equation x^(2)+px+q=0 has integral solutions for prime number p and q, then p+q=

In triangleABCthevalue of( cotA/2cot ""B/2 -1)/( cot""A/2 cot""B/2) is

Find (dy)/(dx) in the following y= sin^(-1) ((1-x^(2))/(1+ x^(2))), 0 lt x lt 1

Find the following integrals: (i) int(x^(3)-1)/(x^(2))dx (ii) int(x^(2/3)+1)dx (iii) int(x^(3/2)+2e^(x)-1/x)dx

Prove that int_(0)^(1)(dx)/(1+x^(n))gt1-(1)/(n)"for n"inN

Find the number of ways of selecting 6 members out of 12 members always including a specified member.

If the straight lines 2x + 3y - 1 = 0, x + 2y - 1 = 0 and ax + by - 1 = 0 form a triangle with orthocentre at the origin, then (a, b) =

Find the area of the region {(x,y): y^(2)le 4x, 4x^(2) + 4y^(2) le 9}.

Find the centre and radius of the circle 3x^(2)+(a+1)y^(2)+6x-9y+a+4=0.

If f'(x)=1-(4)/(x^(2)) and f(1)=6 then find f(x) and f(2).

Let a pair of dice be thrown and the random variable X be the sum of the﻿ numbers that appear on the two dice. Find the mean or expectation of X.﻿

A square piece of tin of side 18 cm is to be made into a box without top, by cutting a square from each corner and folding up the flaps to form the box. What should be the side of the square to be cut off so that the volume of the box is the maximum possible.

5 different toys are distributed among 6 children at random. Find the probability that atleast one child receives more than one toy.

Show that the middle term in the expansion of (1 + x)^(2n) is (1.3.5.........(2n - 1))/(n!)2^(n)x^(n), where n is a positive integer.

If n=3m then the coefficient of x^(n) in the expansion of log(1+x+x^(2)) is

Find the area of the region bounded by y= |cos x|, y=0, x= - pi and x= pi

Which of the following sentences are propositions and which are not ? Write with reason :It is possible that there is life in Mars.

Net force acting on a particle is always perpendicular to its velocity then : -

If |{:(m,-2),(5,2m):}|=|{:(5,-4),(5,3):}| then find m

If a makes an acute angle with b,r cdota = 0 and r xx b = c xx b, then r =

If arg((z-1)/(z+1))=(pi)/(3) then the of z is

A 50 L tank initailly contains 10 L of fresh water, At t=0, a brine solution containing 1 lb of salt per gallon is poured into the tank at the rate of 4 L/min, while the well-stirred mixture leaves the tank at the rate of 2 L/min. Then the amount of time required for overflow to occur in

Let a pair of dice be thrown and the random variable X be the sum of the numbers that appear on the two dice. Find the mean or expectation of X.

27425.	Find (dy)/(dx) in the following y= sin^(-1) ((1-x^(2))/(1+ x^(2))), 0 lt x lt 1
Answer» ANSWER :`(-2)/(1+ X^(2))`

27426.	Find the following integrals: (i) int(x^(3)-1)/(x^(2))dx (ii) int(x^(2/3)+1)dx (iii) int(x^(3/2)+2e^(x)-1/x)dx
Answer» ANSWER :`(X^(2))/(2)+(1)/(x)+C`

27427.	Prove that int_(0)^(1)(dx)/(1+x^(n))gt1-(1)/(n)"for n"inN
Answer» Solution :`X^(n-1)-x^(n)+x^(2n-1)` `""=x^(n-1)(1-x)+x^(2n-1) GT 0 " for "x in (0,1)` `rArr""int_(0)^(1)(x^(n-1)-x^(n)+x^(2n-1))/(1+x^n)dxgt 0` `rArr""int_(0)^(1){(1)/(1+x^(n))-(1-x^(n-1))}dxgt0` `rArr""int_(0)^(1)(dx)/(1+x^(n))gt int_(0)^(1)(1-x^(n-1))dx` `rArr""int_(0)^(1)(dx)/(1+x^(n))gt1-(1)/(n),AA n in N`

27428.	Find the number of ways of selecting 6 members out of 12 members always including a specified member.
Answer» ANSWER :`""^(11)C_5`

27429.	If the straight lines 2x + 3y - 1 = 0, x + 2y - 1 = 0 and ax + by - 1 = 0 form a triangle with orthocentre at the origin, then (a, b) =
Answer» (-8, 8) (0, 7) (6, 4) (-3, 3) ANSWER :A

27430.	Find the area of the region {(x,y): y^(2)le 4x, 4x^(2) + 4y^(2) le 9}.
Answer» ANSWER :`(23)/(6)`

27431.	Find the centre and radius of the circle 3x^(2)+(a+1)y^(2)+6x-9y+a+4=0.
Answer» ANSWER :`SQRT(65)`

27432.	This passage was adapted from an aritcle entitled "John Snow knew Something" published in a popular history magazine in 2018. Few would deny that doctors use critical thinking to solve problems, but most imagine a difference between the partice of medicine and, say, the methods a police detective might use to solve a case. In fact, medical researchers have long used forensic methods of detection and analysis. The case of John Snow, a 19th-century anesthesiologist, is often said to have ushered in the modern era of epidemiology, the branch of medicine that tracks the incidence and distribution of diseases and proposes solutions for their control and prevention. It would not be until 1861 that Louis Pasteur would 1861 Louis Pasteur would propose the link between microorganisms and disease, now know as the germ theory. Before Pasteur's breakthrough, the predominant explanation for the cause of most illnesses was the so-called miasma theory, which held that noxious fumes and pollution-quite literally, as the theory's name implies, "bed air"-were responsible for making people sick. Consequently, during the 1854 outbreak of cholera in Westminster, London, doctors and government officials alike blamed "miasmatic particles" released into the air by decaying organic matter in the soil of the River Thames. Despite the widespread acceptance of the miasma theory, there were those, Snow included, who were skeptical of this view. Snow sould not have known, as doctors do today, that cholera is caused by a cbacterial infection, Vibrio cholerae. Nevertheless, he was convinced that the spread of the disease was caused by some form of matter passed between individuals, likely through contaaminated water. To demonstrate this, Snow targeted a particularly deadly outbreak in the Soho district of Westminster in London. From August 31 to September 3,1854, 127 people in the area died of cholera. Within a week that number had risen to over 500. Snow took to the streets. Speaking to residents of the area, he found a commonality among them: most of the victims had used a single public water pump located on Broad Street. Though he was unable to find conclusive proof that the pump was the source of the outbreak, his demonstration of a pattern in the cholera cases prompted authorities to disable the pump by removing its handle. The epidemic quickly subsided. Soon after the Borad Steet pump was shut down Snow's continued investigation provided additional evidence that contaminated water was the source of the outbreak. Snow created a dot map of the case of cholera in Lndon and demonstrated that they occured in areas were water was supplied by two companies that obtained their water from wells near the Thames. investigation of these wells showed that they had been dug three feet from a cespit that was leaking sewage into the surrounding soil. Snow also discovered that there were no cases of cholera among workers in a berwery close to the Broad Street pump. These workers were provided a daily allowance fo beer, which they drank instead of water, and althought the beer was brewed using the contaminated water, it was boiled during the brewing process. This revelation provided a partical solution for the prevention of future outbreaks. Snow is now hailed as the "father of modern epidemiology," and the radical nature of his approach-formulating a new theory, substantiating it with verifiable avidence, and proposing preventative action-is fully appreciated. At the time, however, not all were convinced, at least publicly, of Snow's fiagged, government officials replaced the handle on the Broad Street pump and publicly denounced Snow's conclusions. It seems they felt that the city's residents would be upset and disgusted to have the unsettling nature of the well's contamination confirmed. It wasn't until 1866, more than a decade after Snow's original investigation and theory-when another cholera outbreak killed more than 5,500 residents of London's East End-that officials working in public health began to accept the link between contaminated water and certain kinds of illness and to take appropriate actions to quell such outbreaks. The passage indicates that the main reason government officials rejected Snow's hypothesis was
Answer» a LACK of CONCRETE SCIENTIFIC proof. a fear of public backlash. MISTRUST of Snow's methods. financial ties to the city's water suippliers. Answer :B

27433.	If f'(x)=1-(4)/(x^(2)) and f(1)=6 then find f(x) and f(2).
Answer» Answer :`x+(4)/(x)+1,F(2)=5`

27434.	Let a pair of dice be thrown and the random variable X be the sum of the numbers that appear on the two dice. Find the mean or expectation of X.
Answer» ANSWER :7