Explore topic-wise InterviewSolutions in .

This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.

7651.

The equation of the line perpendicular to the line 2x+3y-5=0 and passing through (3, -4) is

Answer»

only I is TRUE
only II is true
both I and II are true
NEITHER I nor II are true

ANSWER :B
7652.

If k int_(0)^(1) x f (3 x) dx= int_(0)^(3) t f(t) dt then k=

Answer»

9
3
`1/9`
`1/3`

ANSWER :A
7653.

If P (A) =6/11,P(B)=5/11and P(AuuB)=7/11,find P(A/B)

Answer»

<P>

SOLUTION :P(A/B)=`(P(ANNB))/(P(B))`=4/11/5/11=4/5
7654.

If p is a point lying on the line passingthroiugh the point A(hat i-hatj +2hatk) and parallel tothe vector 2hat i+hatj =2hat k such that |AP|=18 then a position vectorof p is

Answer»

`-13hat(j )-5hat(j)+ 9hat(K )`
`11hat(i) + 7j - 15 hat(k)`
`13hat(i)- 5hat(j) + 9hat(k )`
`13 hat(I ) + hat(j ) - 9hat(k )`

ANSWER :D
7655.

Among the following, the function (s) on which LMVT theorem is applicable in the indecatd intervals is/are

Answer»

`f(X)=x^((1)/(3))"in"[-1,1]`
`f(x)=x+1/x"in"[(1)/(2),3]`
`f(x)=(x-1)|(x-1)(x-2)|"in"[-1,1]`
`f(x)=e^(|(x-1)(x-3)|)"in"[1,3]`

ANSWER :B::C::D
7656.

Show that abs((a,b,c),(a+2x,b+2y,c+2z),(x,y,z)) =0

Answer»


ANSWER :`DELTA =Delta _1`
7657.

If f(x) = sin |x| -|x| , find f'(0^+)

Answer»

SOLUTION :`f(x) - SIN |x| -|x| f(0+)=underset(hto0)LIM(f(0+h)-f(0))/h=underset(hto0)lim(sin|h|-|h|)/h=underset(hto0)lim(sinh)/h-h/h=1-1=0`
7658.

Mario faces a door with a huge lock in front of him, requiring him to fill various alpha- bets in the different-looking lock as shown below. Just above the lock was written - ‘EACH CIRCLE IS UNIQUE’. He finds six plates buried below that door- five of them read ‘FROZEN’, ‘DENTIST’, LISTED’ , ‘TORS’and ‘FASTEN’. But the sixth one was damaged. Mario saw that joint lines as given in the figure meant trails of the words on the plates. For eg-1, the trail of‘SWORDS’ will be a set of continuous lines joining S-W-O-R-D-- S.(W may not be Immediate next to S but they have to be in the same line) Eg-2 : In the problem figure T,Z can be consequitive letters of word in plates as they are in same line, but N,Z are not in same line, so they cannot be consecutive . He has to fill all the letters correctly in order to open the lock to the castle. From the word MONSTER, how many letters are there in horizontal line containing ‘Z’ ?

Answer»

1
2
3
4

Solution :The Key to get the letters is :Only ADJACENT letters can be connected by a line SEGMENT directly.e.g. look at T & Z in FASTEN and FROZEN there is only 1 place for E to make ZEN and TEN.Look at the neighbours of T in DEN​ T­I​ST & LI​ S­T​ED implies I & S have to be in line with T.similarly, 
F­A​STEN & ​ F­R​OZEN implies E1 & R should be in line with F. 
LIST​ E­D​implies D has to be in a line with E. 
FR​ O­Z​EN implies O has to be in line with Z.

Now, see that a,r must be only in the upper two CIRCLES. ...(sudoku logic same 2 numbers in 2boxes)similarly, i,s,o will be in middle line.implies d has to be in the lower circle &o will be in line of r (FROZEN), 
which leaves it in 2 circles on middle left.
Now, F​ A­S​TEN implies s shall be in line with a, so it can only in middle left. hence I is fixed onthe middle right.
Solving similarly will give the following ANSWER
7659.

((y-1)-(1)/(2)(y-1)^(2)+(1)/(3)(y-1)^(3)-....oo)/((a-1)-(1)/(2)(a-1)^(2)+(1)/(3)(a-1)^(3)-....oo)=

Answer»

`log_(y)a`
`log_(a)y`
`log_(a)(y//a)`
`log_(E )(a//y)`

ANSWER :B
7660.

Mario faces a door with a huge lock in front of him, requiring him to fill various alpha- bets in the different-looking lock as shown below. Just above the lock was written - ‘EACH CIRCLE IS UNIQUE’. He finds six plates buried below that door- five of them read ‘FROZEN’, ‘DENTIST’, LISTED’ , ‘TORS’and ‘FASTEN’. But the sixth one was damaged. Mario saw that joint lines as given in the figure meant trails of the words on the plates. For eg-1, the trail of‘SWORDS’ will be a set of continuous lines joining S-W-O-R-D-- S.(W may not be Immediate next to S but they have to be in the same line) Eg-2 : In the problem figure T,Z can be consequitive letters of word in plates as they are in same line, but N,Z are not in same line, so they cannot be consecutive . He has to fill all the letters correctly in order to open the lock to the castle. Which of the following words could be written on the plate ?

Answer»

TOASTED
FRIEND
AROSE
TARZAN

Solution :The Key to get the letters is :Only adjacent letters can be connected by a line SEGMENT directly.e.g. look at T & Z in FASTEN and FROZEN there is only 1 place for E to MAKE ZEN and TEN.Look at the neighbours of T in DEN​ T­I​ST & LI​ S­T​ED implies I & S have to be in line with T.similarly, 
F­A​STEN & ​ F­R​OZEN implies E1 & R should be in line with F. 
LIST​ E­D​implies D has to be in a line with E. 
FR​ O­Z​EN implies O has to be in line with Z.

Now, see that a,r must be only in the upper two circles. ...(sudoku logic same 2 NUMBERS in 2boxes)similarly, i,s,o will be in middle line.implies d has to be in the lower circle &o will be in line of r (FROZEN), 
which leaves it in 2 circles on middle left.
Now, F​ A­S​TEN implies s shall be in line with a, so it can only in middle left. hence I is fixed onthe middle right.
Solving similarly will give the following answer
7661.

Two fixed straight lines X - axis and y = mx are cut by a variable line in the points A(a,0) and B(b,mb) respectively .P and Q are the feet of the perpendiculars drawn from A and B upon the lines y = mx and X - axis ,Show that ,if AB passes through a fixed point (h,k) then PQ will also pass through a fixed point .Find the fixed point

Answer»


ANSWER :`((h+mk)/(1+m^(2)),(mh-k)/(1+m^(2)))((h+mk)/(1+m^(2)),(mh-k)/(1+m^(2)))`
7662.

{:(" " Lt),(n rarroo):} 1/n sum_(r=1)^(n)sqrt(r/n)=

Answer»

`2/3`
`3/4`
`3/2`
`4/3`

ANSWER :A
7663.

If the distance between the foci of an ellipse is 6 and the length of the minor axis is 8, then the ecentricity is

Answer»

`1/sqrt5`
`1/2`
`3/5`
`4/5`

ANSWER :C
7664.

Passage 1 is adapted from an 1823 speech by president james Monre, in which he discusses European colonialism in the Americas. The position expressed in this speech would eventually become known as the Monroe Doctrine. Passage 2 is adapted from a 1095 speech by President Theodore Roosevelt. His position wouldbecome known as the Roosevelt Corollary to the Monroe Doctrine. Passage 1 The American continents, by the free and independent cnditin which they have assumed and maintain, are hence forth not to be considered as subjects for future colonization by any European powers. The citizens of the United States cherish friendaly sentiments in favor of teh liberty and happiness of their fellow men on the European side of the Atlantic. in the wars of the European powers in matters relating to themselves we have never taken any part, nor does it comport with out policy to do so. It is only when our rights are invarded or seriously menaced that we resent injuries or make preparatin for our defense. With the movements in our own hemisphere we are more immediately connected, by causes which must be obvious to all enlightened and impartial observers. We owe it, therefore, to candor and to the amicable relations existing between the United States and European nations to declear that we should consider any attempt on their part to extend their system of government to any protion of this hemisphere as dangerous to our peace and safety. With the existing colonies or dependncies of any Wuropean powe we have not interfered and shall not interfere. however, we could not view any middling with those former European colonies who have declared their independence and maintained it, and whose independence we have, on great consideration and on just rinciples, acknowledged, in any other light than as the manifestation of an unfriendly desposition toward the united States. Passage 2 It isw not true that the united States feels any land hunger or entertains any projects regarding the other nations of the Western Hemisphere except for their welfare. All that this country desires is to see our neighboring countries stable, orderly, and prosperous. Any country whose people conduct themselves well can count upon our hearty friendship. If a nation shows that it knows how to act with reasonalbe efficiency and decency in social and plitical matters, if it keeps order and pays its obligations, it need not fear interference from the United States. However, chronic wrongdoing, or an impotence which results in a general loosening of the ties of civilized society, may in America, as elsewhere, ultimately require intervention.... In thw Western Hempisphere, the adherence of the United States to the Monroe Doctrine may force the United States, however reluctantly, in flagrant cases of such wrongdoing or impotence, to the exercise of an inernational police power. If every country washed by the Caribbean Sea would show the progress in stable and just civilization which Cuba has shown since our troops left the island, and which so many of the republics in both Americas are constantly and brilliantly showing, all question of interference by this Nation with their affairs wouldbe at an end. Our intersets and those of our southern neighbors are in reality identical. They have great natural riches, and if within their borders the reign of law and justice obtains, prosperity is sure to come to them. While they thus obey the primary laws of civilized society, they may rest assured that they will be treated by us in a spirit of cordial and helpful sympthy. We would interfere with them only in the last resort, and then only if it became evident that their inability or unwillingness to do justic at home and abroad had violated the rights of the United States or had invited foreign aggression to the determent of the entire body of American nations. Every nation, whether in America or anywhere else, which desires to maintain its freedom and independence must ultimately realize that the right of such independence can not be separated from the respondibility of making good use of it. When discussing his veews on foreign policy in Passage 1, Monroe indicates that the United States does not inteend to

Answer»

prevent further Euuropean colonization in the AMERICAS.
INTERVENE in conficts that exist solely between EUROPEAN powers.
maintain a friendly RELATIONSHIP with European powers.
allow European powers to keep their existing colonies in the Americas.

Answer :B
7665.

Passage 1 is adapted from an 1823 speech by president james Monre, in which he discusses European colonialism in the Americas. The position expressed in this speech would eventually become known as the Monroe Doctrine. Passage 2 is adapted from a 1095 speech by President Theodore Roosevelt. His position wouldbecome known as the Roosevelt Corollary to the Monroe Doctrine. Passage 1 The American continents, by the free and independent cnditin which they have assumed and maintain, are hence forth not to be considered as subjects for future colonization by any European powers. The citizens of the United States cherish friendaly sentiments in favor of teh liberty and happiness of their fellow men on the European side of the Atlantic. in the wars of the European powers in matters relating to themselves we have never taken any part, nor does it comport with out policy to do so. It is only when our rights are invarded or seriously menaced that we resent injuries or make preparatin for our defense. With the movements in our own hemisphere we are more immediately connected, by causes which must be obvious to all enlightened and impartial observers. We owe it, therefore, to candor and to the amicable relations existing between the United States and European nations to declear that we should consider any attempt on their part to extend their system of government to any protion of this hemisphere as dangerous to our peace and safety. With the existing colonies or dependncies of any Wuropean powe we have not interfered and shall not interfere. however, we could not view any middling with those former European colonies who have declared their independence and maintained it, and whose independence we have, on great consideration and on just rinciples, acknowledged, in any other light than as the manifestation of an unfriendly desposition toward the united States. Passage 2 It isw not true that the united States feels any land hunger or entertains any projects regarding the other nations of the Western Hemisphere except for their welfare. All that this country desires is to see our neighboring countries stable, orderly, and prosperous. Any country whose people conduct themselves well can count upon our hearty friendship. If a nation shows that it knows how to act with reasonalbe efficiency and decency in social and plitical matters, if it keeps order and pays its obligations, it need not fear interference from the United States. However, chronic wrongdoing, or an impotence which results in a general loosening of the ties of civilized society, may in America, as elsewhere, ultimately require intervention.... In thw Western Hempisphere, the adherence of the United States to the Monroe Doctrine may force the United States, however reluctantly, in flagrant cases of such wrongdoing or impotence, to the exercise of an inernational police power. If every country washed by the Caribbean Sea would show the progress in stable and just civilization which Cuba has shown since our troops left the island, and which so many of the republics in both Americas are constantly and brilliantly showing, all question of interference by this Nation with their affairs wouldbe at an end. Our intersets and those of our southern neighbors are in reality identical. They have great natural riches, and if within their borders the reign of law and justice obtains, prosperity is sure to come to them. While they thus obey the primary laws of civilized society, they may rest assured that they will be treated by us in a spirit of cordial and helpful sympthy. We would interfere with them only in the last resort, and then only if it became evident that their inability or unwillingness to do justic at home and abroad had violated the rights of the United States or had invited foreign aggression to the determent of the entire body of American nations. Every nation, whether in America or anywhere else, which desires to maintain its freedom and independence must ultimately realize that the right of such independence can not be separated from the respondibility of making good use of it. According to Roosevelt in Passage 2, what circumstance must exist before the United SDtates may justifiably interfere with the affairs of another nation in the Western Hemisphere ?

Answer»

The other nation must have been invaded by a
The other nation must have invaded of foregin power.
The ORDER nation must have harmed the UNITED States.
The order nation must have committed HUMAN RIGHTS abuses.

Answer :C
7666.

Passage 1 is adapted from an 1823 speech by president james Monre, in which he discusses European colonialism in the Americas. The position expressed in this speech would eventually become known as the Monroe Doctrine. Passage 2 is adapted from a 1095 speech by President Theodore Roosevelt. His position wouldbecome known as the Roosevelt Corollary to the Monroe Doctrine. Passage 1 The American continents, by the free and independent cnditin which they have assumed and maintain, are hence forth not to be considered as subjects for future colonization by any European powers. The citizens of the United States cherish friendaly sentiments in favor of teh liberty and happiness of their fellow men on the European side of the Atlantic. in the wars of the European powers in matters relating to themselves we have never taken any part, nor does it comport with out policy to do so. It is only when our rights are invarded or seriously menaced that we resent injuries or make preparatin for our defense. With the movements in our own hemisphere we are more immediately connected, by causes which must be obvious to all enlightened and impartial observers. We owe it, therefore, to candor and to the amicable relations existing between the United States and European nations to declear that we should consider any attempt on their part to extend their system of government to any protion of this hemisphere as dangerous to our peace and safety. With the existing colonies or dependncies of any Wuropean powe we have not interfered and shall not interfere. however, we could not view any middling with those former European colonies who have declared their independence and maintained it, and whose independence we have, on great consideration and on just rinciples, acknowledged, in any other light than as the manifestation of an unfriendly desposition toward the united States. Passage 2 It isw not true that the united States feels any land hunger or entertains any projects regarding the other nations of the Western Hemisphere except for their welfare. All that this country desires is to see our neighboring countries stable, orderly, and prosperous. Any country whose people conduct themselves well can count upon our hearty friendship. If a nation shows that it knows how to act with reasonalbe efficiency and decency in social and plitical matters, if it keeps order and pays its obligations, it need not fear interference from the United States. However, chronic wrongdoing, or an impotence which results in a general loosening of the ties of civilized society, may in America, as elsewhere, ultimately require intervention.... In thw Western Hempisphere, the adherence of the United States to the Monroe Doctrine may force the United States, however reluctantly, in flagrant cases of such wrongdoing or impotence, to the exercise of an inernational police power. If every country washed by the Caribbean Sea would show the progress in stable and just civilization which Cuba has shown since our troops left the island, and which so many of the republics in both Americas are constantly and brilliantly showing, all question of interference by this Nation with their affairs wouldbe at an end. Our intersets and those of our southern neighbors are in reality identical. They have great natural riches, and if within their borders the reign of law and justice obtains, prosperity is sure to come to them. While they thus obey the primary laws of civilized society, they may rest assured that they will be treated by us in a spirit of cordial and helpful sympthy. We would interfere with them only in the last resort, and then only if it became evident that their inability or unwillingness to do justic at home and abroad had violated the rights of the United States or had invited foreign aggression to the determent of the entire body of American nations. Every nation, whether in America or anywhere else, which desires to maintain its freedom and independence must ultimately realize that the right of such independence can not be separated from the respondibility of making good use of it. Which choice privides the best evidence for the answer to the previous question ?

Answer»

LINES 9-12 ("In the …do so")
Lines 15-19 ("With the …observes ")
Lines 20-26 ("We owe…safety")
Lines 29-36 ("HOWEVER …States")

ANSWER :A
7667.

If 4 different biscuits are distributed among 3 children then the probability of receiving atleast one biscut by the 1^(st) child is

Answer»


ANSWER :`1-(2^(4))/3^(4)`
7668.

If thereare 5perids in eachworkingdayof a school, thenthe numberof waysthatyou canarrage4 subjects duringthe workingday is

Answer»

125
180
220
240

Answer :D
7669.

Passage 1 is adapted from an 1823 speech by president james Monre, in which he discusses European colonialism in the Americas. The position expressed in this speech would eventually become known as the Monroe Doctrine. Passage 2 is adapted from a 1095 speech by President Theodore Roosevelt. His position wouldbecome known as the Roosevelt Corollary to the Monroe Doctrine. Passage 1 The American continents, by the free and independent cnditin which they have assumed and maintain, are hence forth not to be considered as subjects for future colonization by any European powers. The citizens of the United States cherish friendaly sentiments in favor of teh liberty and happiness of their fellow men on the European side of the Atlantic. in the wars of the European powers in matters relating to themselves we have never taken any part, nor does it comport with out policy to do so. It is only when our rights are invarded or seriously menaced that we resent injuries or make preparatin for our defense. With the movements in our own hemisphere we are more immediately connected, by causes which must be obvious to all enlightened and impartial observers. We owe it, therefore, to candor and to the amicable relations existing between the United States and European nations to declear that we should consider any attempt on their part to extend their system of government to any protion of this hemisphere as dangerous to our peace and safety. With the existing colonies or dependncies of any Wuropean powe we have not interfered and shall not interfere. however, we could not view any middling with those former European colonies who have declared their independence and maintained it, and whose independence we have, on great consideration and on just rinciples, acknowledged, in any other light than as the manifestation of an unfriendly desposition toward the united States. Passage 2 It isw not true that the united States feels any land hunger or entertains any projects regarding the other nations of the Western Hemisphere except for their welfare. All that this country desires is to see our neighboring countries stable, orderly, and prosperous. Any country whose people conduct themselves well can count upon our hearty friendship. If a nation shows that it knows how to act with reasonalbe efficiency and decency in social and plitical matters, if it keeps order and pays its obligations, it need not fear interference from the United States. However, chronic wrongdoing, or an impotence which results in a general loosening of the ties of civilized society, may in America, as elsewhere, ultimately require intervention.... In thw Western Hempisphere, the adherence of the United States to the Monroe Doctrine may force the United States, however reluctantly, in flagrant cases of such wrongdoing or impotence, to the exercise of an inernational police power. If every country washed by the Caribbean Sea would show the progress in stable and just civilization which Cuba has shown since our troops left the island, and which so many of the republics in both Americas are constantly and brilliantly showing, all question of interference by this Nation with their affairs wouldbe at an end. Our intersets and those of our southern neighbors are in reality identical. They have great natural riches, and if within their borders the reign of law and justice obtains, prosperity is sure to come to them. While they thus obey the primary laws of civilized society, they may rest assured that they will be treated by us in a spirit of cordial and helpful sympthy. We would interfere with them only in the last resort, and then only if it became evident that their inability or unwillingness to do justic at home and abroad had violated the rights of the United States or had invited foreign aggression to the determent of the entire body of American nations. Every nation, whether in America or anywhere else, which desires to maintain its freedom and independence must ultimately realize that the right of such independence can not be separated from the respondibility of making good use of it. The primary purpose of the statement in lines 6-9 ("The citizens ...of the Atlantic") is to

Answer»

respondto critics of the United States.
mislead the audience regarding Monroe's INTENT.
recommend that people ADOPT a certain ATTITUDE.
BALANCE the OVERALL tone of the massage.

Answer :D
7670.

If A and B are two events of a random experiment such that P(A)=0.6, P(B)=0.3 and P(A//B)=0.5then P(barB//barA)=

Answer»

`0.75`
`0.625`
`0.525`
`0.4`

ANSWER :B
7671.

Passage 1 is adapted from an 1823 speech by president james Monre, in which he discusses European colonialism in the Americas. The position expressed in this speech would eventually become known as the Monroe Doctrine. Passage 2 is adapted from a 1095 speech by President Theodore Roosevelt. His position wouldbecome known as the Roosevelt Corollary to the Monroe Doctrine. Passage 1 The American continents, by the free and independent cnditin which they have assumed and maintain, are hence forth not to be considered as subjects for future colonization by any European powers. The citizens of the United States cherish friendaly sentiments in favor of teh liberty and happiness of their fellow men on the European side of the Atlantic. in the wars of the European powers in matters relating to themselves we have never taken any part, nor does it comport with out policy to do so. It is only when our rights are invarded or seriously menaced that we resent injuries or make preparatin for our defense. With the movements in our own hemisphere we are more immediately connected, by causes which must be obvious to all enlightened and impartial observers. We owe it, therefore, to candor and to the amicable relations existing between the United States and European nations to declear that we should consider any attempt on their part to extend their system of government to any protion of this hemisphere as dangerous to our peace and safety. With the existing colonies or dependncies of any Wuropean powe we have not interfered and shall not interfere. however, we could not view any middling with those former European colonies who have declared their independence and maintained it, and whose independence we have, on great consideration and on just rinciples, acknowledged, in any other light than as the manifestation of an unfriendly desposition toward the united States. Passage 2 It isw not true that the united States feels any land hunger or entertains any projects regarding the other nations of the Western Hemisphere except for their welfare. All that this country desires is to see our neighboring countries stable, orderly, and prosperous. Any country whose people conduct themselves well can count upon our hearty friendship. If a nation shows that it knows how to act with reasonalbe efficiency and decency in social and plitical matters, if it keeps order and pays its obligations, it need not fear interference from the United States. However, chronic wrongdoing, or an impotence which results in a general loosening of the ties of civilized society, may in America, as elsewhere, ultimately require intervention.... In thw Western Hempisphere, the adherence of the United States to the Monroe Doctrine may force the United States, however reluctantly, in flagrant cases of such wrongdoing or impotence, to the exercise of an inernational police power. If every country washed by the Caribbean Sea would show the progress in stable and just civilization which Cuba has shown since our troops left the island, and which so many of the republics in both Americas are constantly and brilliantly showing, all question of interference by this Nation with their affairs wouldbe at an end. Our intersets and those of our southern neighbors are in reality identical. They have great natural riches, and if within their borders the reign of law and justice obtains, prosperity is sure to come to them. While they thus obey the primary laws of civilized society, they may rest assured that they will be treated by us in a spirit of cordial and helpful sympthy. We would interfere with them only in the last resort, and then only if it became evident that their inability or unwillingness to do justic at home and abroad had violated the rights of the United States or had invited foreign aggression to the determent of the entire body of American nations. Every nation, whether in America or anywhere else, which desires to maintain its freedom and independence must ultimately realize that the right of such independence can not be separated from the respondibility of making good use of it. Which of the following statements can be supported by Passage 2 but not by Passage 1 ?

Answer»

The United STATES intends to maintain friendly relationships with other NATIONS.
European POWERS should refrain from intervening in matters affecting only North and SOUTH America.
At least one NATION in the Americas other than the United States has achieved political stability.
The United States should adopt a position of neutrality regarding all conflicts between foreign powers.

Answer :C
7672.

Passage 1 is adapted from an 1823 speech by president james Monre, in which he discusses European colonialism in the Americas. The position expressed in this speech would eventually become known as the Monroe Doctrine. Passage 2 is adapted from a 1095 speech by President Theodore Roosevelt. His position wouldbecome known as the Roosevelt Corollary to the Monroe Doctrine. Passage 1 The American continents, by the free and independent cnditin which they have assumed and maintain, are hence forth not to be considered as subjects for future colonization by any European powers. The citizens of the United States cherish friendaly sentiments in favor of teh liberty and happiness of their fellow men on the European side of the Atlantic. in the wars of the European powers in matters relating to themselves we have never taken any part, nor does it comport with out policy to do so. It is only when our rights are invarded or seriously menaced that we resent injuries or make preparatin for our defense. With the movements in our own hemisphere we are more immediately connected, by causes which must be obvious to all enlightened and impartial observers. We owe it, therefore, to candor and to the amicable relations existing between the United States and European nations to declear that we should consider any attempt on their part to extend their system of government to any protion of this hemisphere as dangerous to our peace and safety. With the existing colonies or dependncies of any Wuropean powe we have not interfered and shall not interfere. however, we could not view any middling with those former European colonies who have declared their independence and maintained it, and whose independence we have, on great consideration and on just rinciples, acknowledged, in any other light than as the manifestation of an unfriendly desposition toward the united States. Passage 2 It isw not true that the united States feels any land hunger or entertains any projects regarding the other nations of the Western Hemisphere except for their welfare. All that this country desires is to see our neighboring countries stable, orderly, and prosperous. Any country whose people conduct themselves well can count upon our hearty friendship. If a nation shows that it knows how to act with reasonalbe efficiency and decency in social and plitical matters, if it keeps order and pays its obligations, it need not fear interference from the United States. However, chronic wrongdoing, or an impotence which results in a general loosening of the ties of civilized society, may in America, as elsewhere, ultimately require intervention.... In thw Western Hempisphere, the adherence of the United States to the Monroe Doctrine may force the United States, however reluctantly, in flagrant cases of such wrongdoing or impotence, to the exercise of an inernational police power. If every country washed by the Caribbean Sea would show the progress in stable and just civilization which Cuba has shown since our troops left the island, and which so many of the republics in both Americas are constantly and brilliantly showing, all question of interference by this Nation with their affairs wouldbe at an end. Our intersets and those of our southern neighbors are in reality identical. They have great natural riches, and if within their borders the reign of law and justice obtains, prosperity is sure to come to them. While they thus obey the primary laws of civilized society, they may rest assured that they will be treated by us in a spirit of cordial and helpful sympthy. We would interfere with them only in the last resort, and then only if it became evident that their inability or unwillingness to do justic at home and abroad had violated the rights of the United States or had invited foreign aggression to the determent of the entire body of American nations. Every nation, whether in America or anywhere else, which desires to maintain its freedom and independence must ultimately realize that the right of such independence can not be separated from the respondibility of making good use of it. Based on the ideas expassed in Passage 1, Monroe would most likely characterize Roosevelt's claim in line 67-68 ("Our intersets...identical") as

Answer»

an appropariate understanding of the relationship between countries in the Americas.
an unfair characterization of an opinion expressed in the Monroe Doctrine.
an UNWARRANTED EXAGGERATION of the actual state of AFFAIRS in the Western Hemisphere.
AN EXAMPLE OF A PHENOMENON MENTIONED IN THE Monroe Doctrine.

Answer :A
7673.

Solve the following linear programming problems graphically : Minimise : Z = 20x + 10y subject to the constraints x+2y le 40, 3x+y ge 30, 4x+3y ge 60, x, y ge 0.

Answer»


Answer :MINIMUM Z = 240 at (6, 12)
7674.

Passage 1 is adapted from an 1823 speech by president james Monre, in which he discusses European colonialism in the Americas. The position expressed in this speech would eventually become known as the Monroe Doctrine. Passage 2 is adapted from a 1095 speech by President Theodore Roosevelt. His position wouldbecome known as the Roosevelt Corollary to the Monroe Doctrine. Passage 1 The American continents, by the free and independent cnditin which they have assumed and maintain, are hence forth not to be considered as subjects for future colonization by any European powers. The citizens of the United States cherish friendaly sentiments in favor of teh liberty and happiness of their fellow men on the European side of the Atlantic. in the wars of the European powers in matters relating to themselves we have never taken any part, nor does it comport with out policy to do so. It is only when our rights are invarded or seriously menaced that we resent injuries or make preparatin for our defense. With the movements in our own hemisphere we are more immediately connected, by causes which must be obvious to all enlightened and impartial observers. We owe it, therefore, to candor and to the amicable relations existing between the United States and European nations to declear that we should consider any attempt on their part to extend their system of government to any protion of this hemisphere as dangerous to our peace and safety. With the existing colonies or dependncies of any Wuropean powe we have not interfered and shall not interfere. however, we could not view any middling with those former European colonies who have declared their independence and maintained it, and whose independence we have, on great consideration and on just rinciples, acknowledged, in any other light than as the manifestation of an unfriendly desposition toward the united States. Passage 2 It isw not true that the united States feels any land hunger or entertains any projects regarding the other nations of the Western Hemisphere except for their welfare. All that this country desires is to see our neighboring countries stable, orderly, and prosperous. Any country whose people conduct themselves well can count upon our hearty friendship. If a nation shows that it knows how to act with reasonalbe efficiency and decency in social and plitical matters, if it keeps order and pays its obligations, it need not fear interference from the United States. However, chronic wrongdoing, or an impotence which results in a general loosening of the ties of civilized society, may in America, as elsewhere, ultimately require intervention.... In thw Western Hempisphere, the adherence of the United States to the Monroe Doctrine may force the United States, however reluctantly, in flagrant cases of such wrongdoing or impotence, to the exercise of an inernational police power. If every country washed by the Caribbean Sea would show the progress in stable and just civilization which Cuba has shown since our troops left the island, and which so many of the republics in both Americas are constantly and brilliantly showing, all question of interference by this Nation with their affairs wouldbe at an end. Our intersets and those of our southern neighbors are in reality identical. They have great natural riches, and if within their borders the reign of law and justice obtains, prosperity is sure to come to them. While they thus obey the primary laws of civilized society, they may rest assured that they will be treated by us in a spirit of cordial and helpful sympthy. We would interfere with them only in the last resort, and then only if it became evident that their inability or unwillingness to do justic at home and abroad had violated the rights of the United States or had invited foreign aggression to the determent of the entire body of American nations. Every nation, whether in America or anywhere else, which desires to maintain its freedom and independence must ultimately realize that the right of such independence can not be separated from the respondibility of making good use of it. Based on the informatin contained in the passages, it is likely that Monore and Roosevelt were each motivated at least in part by

Answer»

a lack of plitical stability in the Western Hemisphere.
threatened or POTENTIAL aggression by FOREIGN powers.
ongoing criticism from their policical opponents.
a storng COMMITMENT of pacifism.

ANSWER :B
7675.

Passage 1 is adapted from an 1823 speech by president james Monre, in which he discusses European colonialism in the Americas. The position expressed in this speech would eventually become known as the Monroe Doctrine. Passage 2 is adapted from a 1095 speech by President Theodore Roosevelt. His position wouldbecome known as the Roosevelt Corollary to the Monroe Doctrine. Passage 1 The American continents, by the free and independent cnditin which they have assumed and maintain, are hence forth not to be considered as subjects for future colonization by any European powers. The citizens of the United States cherish friendaly sentiments in favor of teh liberty and happiness of their fellow men on the European side of the Atlantic. in the wars of the European powers in matters relating to themselves we have never taken any part, nor does it comport with out policy to do so. It is only when our rights are invarded or seriously menaced that we resent injuries or make preparatin for our defense. With the movements in our own hemisphere we are more immediately connected, by causes which must be obvious to all enlightened and impartial observers. We owe it, therefore, to candor and to the amicable relations existing between the United States and European nations to declear that we should consider any attempt on their part to extend their system of government to any protion of this hemisphere as dangerous to our peace and safety. With the existing colonies or dependncies of any Wuropean powe we have not interfered and shall not interfere. however, we could not view any middling with those former European colonies who have declared their independence and maintained it, and whose independence we have, on great consideration and on just rinciples, acknowledged, in any other light than as the manifestation of an unfriendly desposition toward the united States. Passage 2 It isw not true that the united States feels any land hunger or entertains any projects regarding the other nations of the Western Hemisphere except for their welfare. All that this country desires is to see our neighboring countries stable, orderly, and prosperous. Any country whose people conduct themselves well can count upon our hearty friendship. If a nation shows that it knows how to act with reasonalbe efficiency and decency in social and plitical matters, if it keeps order and pays its obligations, it need not fear interference from the United States. However, chronic wrongdoing, or an impotence which results in a general loosening of the ties of civilized society, may in America, as elsewhere, ultimately require intervention.... In thw Western Hempisphere, the adherence of the United States to the Monroe Doctrine may force the United States, however reluctantly, in flagrant cases of such wrongdoing or impotence, to the exercise of an inernational police power. If every country washed by the Caribbean Sea would show the progress in stable and just civilization which Cuba has shown since our troops left the island, and which so many of the republics in both Americas are constantly and brilliantly showing, all question of interference by this Nation with their affairs wouldbe at an end. Our intersets and those of our southern neighbors are in reality identical. They have great natural riches, and if within their borders the reign of law and justice obtains, prosperity is sure to come to them. While they thus obey the primary laws of civilized society, they may rest assured that they will be treated by us in a spirit of cordial and helpful sympthy. We would interfere with them only in the last resort, and then only if it became evident that their inability or unwillingness to do justic at home and abroad had violated the rights of the United States or had invited foreign aggression to the determent of the entire body of American nations. Every nation, whether in America or anywhere else, which desires to maintain its freedom and independence must ultimately realize that the right of such independence can not be separated from the respondibility of making good use of it. As used in line 70, "obtains most nearly means

Answer»

GATHERS.
SEIZES.
COLLECTS.
PREVAILS.

ANSWER :D
7676.

Passage 1 is adapted from an 1823 speech by president james Monre, in which he discusses European colonialism in the Americas. The position expressed in this speech would eventually become known as the Monroe Doctrine. Passage 2 is adapted from a 1095 speech by President Theodore Roosevelt. His position wouldbecome known as the Roosevelt Corollary to the Monroe Doctrine. Passage 1 The American continents, by the free and independent cnditin which they have assumed and maintain, are hence forth not to be considered as subjects for future colonization by any European powers. The citizens of the United States cherish friendaly sentiments in favor of teh liberty and happiness of their fellow men on the European side of the Atlantic. in the wars of the European powers in matters relating to themselves we have never taken any part, nor does it comport with out policy to do so. It is only when our rights are invarded or seriously menaced that we resent injuries or make preparatin for our defense. With the movements in our own hemisphere we are more immediately connected, by causes which must be obvious to all enlightened and impartial observers. We owe it, therefore, to candor and to the amicable relations existing between the United States and European nations to declear that we should consider any attempt on their part to extend their system of government to any protion of this hemisphere as dangerous to our peace and safety. With the existing colonies or dependncies of any Wuropean powe we have not interfered and shall not interfere. however, we could not view any middling with those former European colonies who have declared their independence and maintained it, and whose independence we have, on great consideration and on just rinciples, acknowledged, in any other light than as the manifestation of an unfriendly desposition toward the united States. Passage 2 It isw not true that the united States feels any land hunger or entertains any projects regarding the other nations of the Western Hemisphere except for their welfare. All that this country desires is to see our neighboring countries stable, orderly, and prosperous. Any country whose people conduct themselves well can count upon our hearty friendship. If a nation shows that it knows how to act with reasonalbe efficiency and decency in social and plitical matters, if it keeps order and pays its obligations, it need not fear interference from the United States. However, chronic wrongdoing, or an impotence which results in a general loosening of the ties of civilized society, may in America, as elsewhere, ultimately require intervention.... In thw Western Hempisphere, the adherence of the United States to the Monroe Doctrine may force the United States, however reluctantly, in flagrant cases of such wrongdoing or impotence, to the exercise of an inernational police power. If every country washed by the Caribbean Sea would show the progress in stable and just civilization which Cuba has shown since our troops left the island, and which so many of the republics in both Americas are constantly and brilliantly showing, all question of interference by this Nation with their affairs wouldbe at an end. Our intersets and those of our southern neighbors are in reality identical. They have great natural riches, and if within their borders the reign of law and justice obtains, prosperity is sure to come to them. While they thus obey the primary laws of civilized society, they may rest assured that they will be treated by us in a spirit of cordial and helpful sympthy. We would interfere with them only in the last resort, and then only if it became evident that their inability or unwillingness to do justic at home and abroad had violated the rights of the United States or had invited foreign aggression to the determent of the entire body of American nations. Every nation, whether in America or anywhere else, which desires to maintain its freedom and independence must ultimately realize that the right of such independence can not be separated from the respondibility of making good use of it. Which of the following best describes the relationship between the passage ?

Answer»

Passage 2 expands in IDEA that was mentioned briefly in Passage 1.
Passage 2 DISPUTES the primary argument advanced in Passage 1.
Passage 2 provides EXAMPLES to support a central claim made in Passage 1.
Passage 2 OFFERS a justification for the MAIN opinion asserted in Passage 1.

Answer :A
7677.

Passage 1 is adapted from an 1823 speech by president james Monre, in which he discusses European colonialism in the Americas. The position expressed in this speech would eventually become known as the Monroe Doctrine. Passage 2 is adapted from a 1095 speech by President Theodore Roosevelt. His position wouldbecome known as the Roosevelt Corollary to the Monroe Doctrine. Passage 1 The American continents, by the free and independent cnditin which they have assumed and maintain, are hence forth not to be considered as subjects for future colonization by any European powers. The citizens of the United States cherish friendaly sentiments in favor of teh liberty and happiness of their fellow men on the European side of the Atlantic. in the wars of the European powers in matters relating to themselves we have never taken any part, nor does it comport with out policy to do so. It is only when our rights are invarded or seriously menaced that we resent injuries or make preparatin for our defense. With the movements in our own hemisphere we are more immediately connected, by causes which must be obvious to all enlightened and impartial observers. We owe it, therefore, to candor and to the amicable relations existing between the United States and European nations to declear that we should consider any attempt on their part to extend their system of government to any protion of this hemisphere as dangerous to our peace and safety. With the existing colonies or dependncies of any Wuropean powe we have not interfered and shall not interfere. however, we could not view any middling with those former European colonies who have declared their independence and maintained it, and whose independence we have, on great consideration and on just rinciples, acknowledged, in any other light than as the manifestation of an unfriendly desposition toward the united States. Passage 2 It isw not true that the united States feels any land hunger or entertains any projects regarding the other nations of the Western Hemisphere except for their welfare. All that this country desires is to see our neighboring countries stable, orderly, and prosperous. Any country whose people conduct themselves well can count upon our hearty friendship. If a nation shows that it knows how to act with reasonalbe efficiency and decency in social and plitical matters, if it keeps order and pays its obligations, it need not fear interference from the United States. However, chronic wrongdoing, or an impotence which results in a general loosening of the ties of civilized society, may in America, as elsewhere, ultimately require intervention.... In thw Western Hempisphere, the adherence of the United States to the Monroe Doctrine may force the United States, however reluctantly, in flagrant cases of such wrongdoing or impotence, to the exercise of an inernational police power. If every country washed by the Caribbean Sea would show the progress in stable and just civilization which Cuba has shown since our troops left the island, and which so many of the republics in both Americas are constantly and brilliantly showing, all question of interference by this Nation with their affairs wouldbe at an end. Our intersets and those of our southern neighbors are in reality identical. They have great natural riches, and if within their borders the reign of law and justice obtains, prosperity is sure to come to them. While they thus obey the primary laws of civilized society, they may rest assured that they will be treated by us in a spirit of cordial and helpful sympthy. We would interfere with them only in the last resort, and then only if it became evident that their inability or unwillingness to do justic at home and abroad had violated the rights of the United States or had invited foreign aggression to the determent of the entire body of American nations. Every nation, whether in America or anywhere else, which desires to maintain its freedom and independence must ultimately realize that the right of such independence can not be separated from the respondibility of making good use of it. As used in line 59, "washed" most nearly means

Answer»

cleaned.
OVERWHELMED.
TOUCHED.
BATHED.

ANSWER :C
7678.

Passage 1 is adapted from an 1823 speech by president james Monre, in which he discusses European colonialism in the Americas. The position expressed in this speech would eventually become known as the Monroe Doctrine. Passage 2 is adapted from a 1095 speech by President Theodore Roosevelt. His position wouldbecome known as the Roosevelt Corollary to the Monroe Doctrine. Passage 1 The American continents, by the free and independent cnditin which they have assumed and maintain, are hence forth not to be considered as subjects for future colonization by any European powers. The citizens of the United States cherish friendaly sentiments in favor of teh liberty and happiness of their fellow men on the European side of the Atlantic. in the wars of the European powers in matters relating to themselves we have never taken any part, nor does it comport with out policy to do so. It is only when our rights are invarded or seriously menaced that we resent injuries or make preparatin for our defense. With the movements in our own hemisphere we are more immediately connected, by causes which must be obvious to all enlightened and impartial observers. We owe it, therefore, to candor and to the amicable relations existing between the United States and European nations to declear that we should consider any attempt on their part to extend their system of government to any protion of this hemisphere as dangerous to our peace and safety. With the existing colonies or dependncies of any Wuropean powe we have not interfered and shall not interfere. however, we could not view any middling with those former European colonies who have declared their independence and maintained it, and whose independence we have, on great consideration and on just rinciples, acknowledged, in any other light than as the manifestation of an unfriendly desposition toward the united States. Passage 2 It isw not true that the united States feels any land hunger or entertains any projects regarding the other nations of the Western Hemisphere except for their welfare. All that this country desires is to see our neighboring countries stable, orderly, and prosperous. Any country whose people conduct themselves well can count upon our hearty friendship. If a nation shows that it knows how to act with reasonalbe efficiency and decency in social and plitical matters, if it keeps order and pays its obligations, it need not fear interference from the United States. However, chronic wrongdoing, or an impotence which results in a general loosening of the ties of civilized society, may in America, as elsewhere, ultimately require intervention.... In thw Western Hempisphere, the adherence of the United States to the Monroe Doctrine may force the United States, however reluctantly, in flagrant cases of such wrongdoing or impotence, to the exercise of an inernational police power. If every country washed by the Caribbean Sea would show the progress in stable and just civilization which Cuba has shown since our troops left the island, and which so many of the republics in both Americas are constantly and brilliantly showing, all question of interference by this Nation with their affairs wouldbe at an end. Our intersets and those of our southern neighbors are in reality identical. They have great natural riches, and if within their borders the reign of law and justice obtains, prosperity is sure to come to them. While they thus obey the primary laws of civilized society, they may rest assured that they will be treated by us in a spirit of cordial and helpful sympthy. We would interfere with them only in the last resort, and then only if it became evident that their inability or unwillingness to do justic at home and abroad had violated the rights of the United States or had invited foreign aggression to the determent of the entire body of American nations. Every nation, whether in America or anywhere else, which desires to maintain its freedom and independence must ultimately realize that the right of such independence can not be separated from the respondibility of making good use of it. Which choice provides the best evidence for the answer to the previous question

Answer»

LINES 42-44 ("Any counry…friendship")
Lines 59-67 ("If EVERY …end")
Lines 68-71 ("They have…them")
Lines 75-81 ("We WOULD …nations")

ANSWER :D
7679.

int(x^(5)dx)/(sqrt((1+x^(3))))=...

Answer»

`(2)/(3) SQRT((1+X^(3)))(x^(3)+2)`
`(2)/(9) sqrt((1+x^(3)))(x^(3)-4)`
`(2)/(9) sqrt((1+x^(3)))(x^(3)+4)`
`(2)/(9) sqrt((1+x^(3)))(x^(3)-2)`

ANSWER :D
7680.

Sum of the first p, q and r terms of an A.P. are a, b and c, respectively. Prove that a/p(q-r)+b/q (r-p) +c/r (p-q)=0

Answer»


ANSWER :` = 0`
7681.

Value of f(5)=

Answer»

1
-3
5
13

Answer :d
7682.

If the cartesian equation of the line (2-x)/(4)=(y-3)/(-2),z+4=0 then its vector equation is ….....

Answer»

`BARR=(4,-2,0)+K(2,3,-4),k EPSILON R`
`barr=(2,3,-4)+k(4,2,0),k epsilon R`
`barr=(-2,3,-4)+k(4,-2,0),k epsilon R`
`barr=(2,3,-4)+k(-4,-2,1),k epsilon R`

ANSWER :B
7683.

overset((pi)/(4)) underset(-(pi)/(4)) int (1)/(1+cos(2x))dx=.....

Answer»

1
2
3
4

Answer :A
7684.

The perpendicular distance between the planes 2x-y+ 2z = 1 and 4x - 2y + 4z =1 is...............

Answer»

`1/3`
`3`
`1/6`
`6`

ANSWER :C
7685.

If the equation ax^(2)+2hxy+by^(2)=0 has one line as the bisector of angle between the co-ordinate axes then

Answer»

`(a-b)^(2)=H^(2)`
`(a+b)^(2)=h^(2)`
`(a-b)^(2)=4H^(2)`
`(a+b)^(2)=4h^(2)`

SOLUTION :NA
7686.

(i) int(sec x* cosec x)/(log cot x) dx(ii) int tan^(4) x\ dx

Answer»


Answer :`(i) -log |log COT x|+c""(ii)(1)/(3) TAN^(3) x-tan x+x+c`
7687.

Find the number of solution of the equation underset(l=1)overset(501)Sigma x_(l)=1501, where x_(l)'s are odd natural numbers:

Answer»


ANSWER :`""^(1000)C_(500)`
7688.

If(1 +x + x^(2) + …+ x^(9))^(4) (x + x^(2) + x^(3) + … + x^(9))= sum_(r=1)^(45) a_(r) x^(r)and the value ofa_(2) + a_(6) + a_(10) + … + a_(42) " is " lambda the sum of all digits oflambdais .

Answer»


ANSWER :9
7689.

Solution(s) of the equation abs(z)^(2)+7barz=0 is/are

Answer»

z=0
z=3
z=7
z=-7

Answer :A::D
7690.

the valueof sec ""(2pi)/(3) + cosec "" ( 5 pi)/(6)isequal to

Answer»

2
`-2`
`4`
0

Answer :D
7691.

If alpha, beta, gamma are roots of x^(3) + px^(2) + qx + r = 0then (beta^(2) + gamma^(2))/(beta gamma) + (gamma^(2) + alpha^(2))/(gamma alpha) + (alpha^(2) + beta^(2))/( alpha beta)=

Answer»

`(q^(2) - 2pr)//R^(2)`
`q^(3) - 3pqr + 3r^(2)`
`(p^(2) - 2q)//r^(2)`
`pq//r - 3`

Answer :4
7692.

If (dy)/(dx)+2xtan(x-y)=1, then sin(x-y) is equal to

Answer»

`AE^(-x^(2))`
`Ae^(2X)`
`Ae^(x^(2))`
`Ae^(-2x)`

Answer :C
7693.

If I_(n) = int (sin nx)/(cos x) dx " then " I_(n)

Answer»

`(-2)/(N - 1) COS (n - 1) x - l_(n_(-2))`
`(2)/(n - 1) cos (n - 1) x + l_(n _( -2))`
`(-2)/(n +1) SIN (n +1) x - l_(n_(-2))`
`(-2)/(n +1)cos (n-1) x - l_(n_(-2))`

Answer :A
7694.

If the expression sqrt(log^2x)+sqrt(4 cos^2 y-4 cos y+1) takes its least value , then value of x+y is greater than, (where x,y gt 0)

Answer»

2
3
4
5

7695.

int(xdx)/((x^(2)-3x+2)sqrt(x^(2)-4x+3)).

Answer»


Answer :`-SQRT(x^(2)_4x+3)/(x-1)-2arc SIN""(1)/(x-2)+C.`
7696.

Select the correct answer :Principal value of tan^- √3 =

Answer»

`π/6`
`π/4`
`π/3`
`π/2`

ANSWER :C
7697.

If f(x)=2x+1 and f(a)=2, what is the value of a?

Answer»

`(1)/(2)`
`(1)/(2)`
`2`
`5`

ANSWER :B
7698.

Lt_(x to oo) ((int_(0)^(x) e^(t) dt)^(2))/(int_(0)^(x)e^(2t^(2))dt)

Answer»

1
-1
0
`1//2`

ANSWER :3
7699.

If the eccentric angle of point on the hyperbola where the common tangent meets it is (3pi)/4 then the value of 2 alpha^(2) is

Answer»

`1/2`
`3/2`
1
none of these

SOLUTION :N/A
7700.

A variable plane passes through a fixed point (1,-2,3) and meets the coordinate axes at points A, B, C then the point of intersection of the planes through A, B, C parallel to the coordinate planes lies on:

Answer»

`XY-(1//2)YZ+(1//3)zx=6`
`yz-2zx+3xy=xyz`
`xy-2yz+3zx=3xyz`
`xy+(1//2)yz-(1//3)zx=6`

ANSWER :B