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This section includes 7 InterviewSolutions, each offering curated multiple-choice questions to sharpen your Current Affairs knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
Passage 1 is adapted from a speech given by Senator Robert Y. hayne in 1830. Passage 2 is adapted from a speech given in response by Sanator Daniel Webster on the following day. Passage 1. If I could, by a mere act of my will put at the disposal of the Federal Government any amount of treasur which I might think proper to name, I should limit the amount to the means necessary for the legitimate purpose of Government. Sir, an immense national treasuring would be a fund for corruption. It would enable Congress and the Executive to exercise a control over States, as well as over great intersts in teh country, nay even over corporations and individuals-utterly destructive of the purity, and fatal to the duration of our institutions. It would be equally fatal to the sovereignty and independence of the States. Sir, I am one of those who believe that the very life of our system is the independence of teh States, and there is no evil more to be deprecated than the consolidation of this Government. It is only by a strict adherence to the limitations imp[osed by the constitution on the Federal Government, that this system works well, and can answer the great ends for which it was instituted. i am opposed, therefore, in any shape, to all unnecessary extension of the powers, or the influence of the Legislature of Exective of influence of the Legislature of Executive of the Union over the States, or the people of the States, and, most of all, I am opposed to those partial distibutions of favors, whether by legislation or appropriation, which has a direct and powerful tendency to spread corruption through the land, to create and abject spirit of dependence, to sow the seeds of dissolution, to produce jealousy among the different portions of teh Union, and finally to sap the very foundations of the Government itself. Passage 2 As a reason for sishing to get rid of the public lands as soon as we could, and as we might, the honorable gentlmeman said, he wanted no permanent sources of income. He wished to see the time when the Government should not possess a shilling of permanent revenue. If he could speak a magical word, and by that word convert the whole capital into gold, the work should not be spoken. The administration of a fixed revenue, [he said] only consolidates the Government, and corrupts the people! Sir, I confess I heard these sentiments uttered on this floor with deep regret and pain. I am aware that these, and similar opinions, are espoused by certain persons out of the capinions, are espoused by certain persons out of the capitol, and out of this Government, but I did non expect so soon to find them here. Consolidation!-that perpetual cry, both of terror and delusion- consolidation! Sir, when gentelmen speak of the effects of a common fund, belonging to all the States, as having a tendency to consolidation, what do they mesn? Do they mean, ior can they mean, anything more than that the Union of the States will be strenghened, by whatever continues or furnishes inducements to the people of the States to hold together? If they mean merely this, then, no doubt, the public lands as well as everyhing else in which we have a common interest, tends to consolidation, and to this idea of consolidation every true American ought to be attached, it is neiher more nor less than strengthening the Union itself. This is the sense in which the framers of teh constitution use the would consolidation, and in which sense I adopt and cherish i.... This,sir, is General Washington's consolidation. This is the ture constitutional consolidation. I wish to see no new powers drawn to the General Government, but I confess I rejoice in whatever tends to strengthen the bond that unites us, and encourages the hope that our Union may be perpetual. And, therefore, I cannot but feel regret at teh expression of such opinions as teh gentleman has ovowed, because I think their obvious tendency is to weaken the bond of our connection. Which choice provides the best evidence for the answer to the previous question ? |
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Answer» LINES 1-6 ("If I could…of GOVERNMENT") |
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| 2. |
A : In triangle ABC if a,A and R are fixed then Deltaa *sec A+Deltab*secB+Deltac*secC=0 R : In any triangle , A+B+C = pi and soDelta A+DeltaB+DeltaC=0 |
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Answer» A,R are TRUE and R is CORRECT EXPLANATION of A |
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| 3. |
Passage 1 is adapted from a speech given by Senator Robert Y. hayne in 1830. Passage 2 is adapted from a speech given in response by Sanator Daniel Webster on the following day. Passage 1. If I could, by a mere act of my will put at the disposal of the Federal Government any amount of treasur which I might think proper to name, I should limit the amount to the means necessary for the legitimate purpose of Government. Sir, an immense national treasuring would be a fund for corruption. It would enable Congress and the Executive to exercise a control over States, as well as over great intersts in teh country, nay even over corporations and individuals-utterly destructive of the purity, and fatal to the duration of our institutions. It would be equally fatal to the sovereignty and independence of the States. Sir, I am one of those who believe that the very life of our system is the independence of teh States, and there is no evil more to be deprecated than the consolidation of this Government. It is only by a strict adherence to the limitations imp[osed by the constitution on the Federal Government, that this system works well, and can answer the great ends for which it was instituted. i am opposed, therefore, in any shape, to all unnecessary extension of the powers, or the influence of the Legislature of Exective of influence of the Legislature of Executive of the Union over the States, or the people of the States, and, most of all, I am opposed to those partial distibutions of favors, whether by legislation or appropriation, which has a direct and powerful tendency to spread corruption through the land, to create and abject spirit of dependence, to sow the seeds of dissolution, to produce jealousy among the different portions of teh Union, and finally to sap the very foundations of the Government itself. Passage 2 As a reason for sishing to get rid of the public lands as soon as we could, and as we might, the honorable gentlmeman said, he wanted no permanent sources of income. He wished to see the time when the Government should not possess a shilling of permanent revenue. If he could speak a magical word, and by that word convert the whole capital into gold, the work should not be spoken. The administration of a fixed revenue, [he said] only consolidates the Government, and corrupts the people! Sir, I confess I heard these sentiments uttered on this floor with deep regret and pain. I am aware that these, and similar opinions, are espoused by certain persons out of the capinions, are espoused by certain persons out of the capitol, and out of this Government, but I did non expect so soon to find them here. Consolidation!-that perpetual cry, both of terror and delusion- consolidation! Sir, when gentelmen speak of the effects of a common fund, belonging to all the States, as having a tendency to consolidation, what do they mesn? Do they mean, ior can they mean, anything more than that the Union of the States will be strenghened, by whatever continues or furnishes inducements to the people of the States to hold together? If they mean merely this, then, no doubt, the public lands as well as everyhing else in which we have a common interest, tends to consolidation, and to this idea of consolidation every true American ought to be attached, it is neiher more nor less than strengthening the Union itself. This is the sense in which the framers of teh constitution use the would consolidation, and in which sense I adopt and cherish i.... This,sir, is General Washington's consolidation. This is the ture constitutional consolidation. I wish to see no new powers drawn to the General Government, but I confess I rejoice in whatever tends to strengthen the bond that unites us, and encourages the hope that our Union may be perpetual. And, therefore, I cannot but feel regret at teh expression of such opinions as teh gentleman has ovowed, because I think their obvious tendency is to weaken the bond of our connection. On which of the following points do thte writers of the passages express agreement ? |
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Answer» The Federal GOVERNMENT should not acquire new powers. |
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| 5. |
Passage 1 is adapted from a speech given by Senator Robert Y. hayne in 1830. Passage 2 is adapted from a speech given in response by Sanator Daniel Webster on the following day. Passage 1. If I could, by a mere act of my will put at the disposal of the Federal Government any amount of treasur which I might think proper to name, I should limit the amount to the means necessary for the legitimate purpose of Government. Sir, an immense national treasuring would be a fund for corruption. It would enable Congress and the Executive to exercise a control over States, as well as over great intersts in teh country, nay even over corporations and individuals-utterly destructive of the purity, and fatal to the duration of our institutions. It would be equally fatal to the sovereignty and independence of the States. Sir, I am one of those who believe that the very life of our system is the independence of teh States, and there is no evil more to be deprecated than the consolidation of this Government. It is only by a strict adherence to the limitations imp[osed by the constitution on the Federal Government, that this system works well, and can answer the great ends for which it was instituted. i am opposed, therefore, in any shape, to all unnecessary extension of the powers, or the influence of the Legislature of Exective of influence of the Legislature of Executive of the Union over the States, or the people of the States, and, most of all, I am opposed to those partial distibutions of favors, whether by legislation or appropriation, which has a direct and powerful tendency to spread corruption through the land, to create and abject spirit of dependence, to sow the seeds of dissolution, to produce jealousy among the different portions of teh Union, and finally to sap the very foundations of the Government itself. Passage 2 As a reason for sishing to get rid of the public lands as soon as we could, and as we might, the honorable gentlmeman said, he wanted no permanent sources of income. He wished to see the time when the Government should not possess a shilling of permanent revenue. If he could speak a magical word, and by that word convert the whole capital into gold, the work should not be spoken. The administration of a fixed revenue, [he said] only consolidates the Government, and corrupts the people! Sir, I confess I heard these sentiments uttered on this floor with deep regret and pain. I am aware that these, and similar opinions, are espoused by certain persons out of the capinions, are espoused by certain persons out of the capitol, and out of this Government, but I did non expect so soon to find them here. Consolidation!-that perpetual cry, both of terror and delusion- consolidation! Sir, when gentelmen speak of the effects of a common fund, belonging to all the States, as having a tendency to consolidation, what do they mesn? Do they mean, ior can they mean, anything more than that the Union of the States will be strenghened, by whatever continues or furnishes inducements to the people of the States to hold together? If they mean merely this, then, no doubt, the public lands as well as everyhing else in which we have a common interest, tends to consolidation, and to this idea of consolidation every true American ought to be attached, it is neiher more nor less than strengthening the Union itself. This is the sense in which the framers of teh constitution use the would consolidation, and in which sense I adopt and cherish i.... This,sir, is General Washington's consolidation. This is the ture constitutional consolidation. I wish to see no new powers drawn to the General Government, but I confess I rejoice in whatever tends to strengthen the bond that unites us, and encourages the hope that our Union may be perpetual. And, therefore, I cannot but feel regret at teh expression of such opinions as teh gentleman has ovowed, because I think their obvious tendency is to weaken the bond of our connection. Based on the ideas expressed in Passage 1, hayne would most likely rebut Webster's claim in lines 61-67 ("If they mean....strenghtening the Union itself") by stating that |
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Answer» he(Hayne) does not wish the Union the have more money. |
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| 6. |
Find the range of the expression (x^(2) + 34x - 71)/(x^(2) + 2x -7), if x is a real. |
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Answer» |
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| 7. |
Find the eccentricity, foci, vertices, length of latus rectum and equations of directrices of hyperbola. (i) x^(2)-4y^(2)=4 (ii) 4x^(2)-9y^(2)=27 |
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Answer» (II) `SQRT(13)/3, (pm sqrt(39)/2,0), (pm (3sqrt3)/(2),0), 4/sqrt3` `2sqrt(13x)=pm 9sqrt3` |
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| 8. |
Passage 1 is adapted from a speech given by Senator Robert Y. hayne in 1830. Passage 2 is adapted from a speech given in response by Sanator Daniel Webster on the following day. Passage 1. If I could, by a mere act of my will put at the disposal of the Federal Government any amount of treasur which I might think proper to name, I should limit the amount to the means necessary for the legitimate purpose of Government. Sir, an immense national treasuring would be a fund for corruption. It would enable Congress and the Executive to exercise a control over States, as well as over great intersts in teh country, nay even over corporations and individuals-utterly destructive of the purity, and fatal to the duration of our institutions. It would be equally fatal to the sovereignty and independence of the States. Sir, I am one of those who believe that the very life of our system is the independence of teh States, and there is no evil more to be deprecated than the consolidation of this Government. It is only by a strict adherence to the limitations imp[osed by the constitution on the Federal Government, that this system works well, and can answer the great ends for which it was instituted. i am opposed, therefore, in any shape, to all unnecessary extension of the powers, or the influence of the Legislature of Exective of influence of the Legislature of Executive of the Union over the States, or the people of the States, and, most of all, I am opposed to those partial distibutions of favors, whether by legislation or appropriation, which has a direct and powerful tendency to spread corruption through the land, to create and abject spirit of dependence, to sow the seeds of dissolution, to produce jealousy among the different portions of teh Union, and finally to sap the very foundations of the Government itself. Passage 2 As a reason for sishing to get rid of the public lands as soon as we could, and as we might, the honorable gentlmeman said, he wanted no permanent sources of income. He wished to see the time when the Government should not possess a shilling of permanent revenue. If he could speak a magical word, and by that word convert the whole capital into gold, the work should not be spoken. The administration of a fixed revenue, [he said] only consolidates the Government, and corrupts the people! Sir, I confess I heard these sentiments uttered on this floor with deep regret and pain. I am aware that these, and similar opinions, are espoused by certain persons out of the capinions, are espoused by certain persons out of the capitol, and out of this Government, but I did non expect so soon to find them here. Consolidation!-that perpetual cry, both of terror and delusion- consolidation! Sir, when gentelmen speak of the effects of a common fund, belonging to all the States, as having a tendency to consolidation, what do they mesn? Do they mean, ior can they mean, anything more than that the Union of the States will be strenghened, by whatever continues or furnishes inducements to the people of the States to hold together? If they mean merely this, then, no doubt, the public lands as well as everyhing else in which we have a common interest, tends to consolidation, and to this idea of consolidation every true American ought to be attached, it is neiher more nor less than strengthening the Union itself. This is the sense in which the framers of teh constitution use the would consolidation, and in which sense I adopt and cherish i.... This,sir, is General Washington's consolidation. This is the ture constitutional consolidation. I wish to see no new powers drawn to the General Government, but I confess I rejoice in whatever tends to strengthen the bond that unites us, and encourages the hope that our Union may be perpetual. And, therefore, I cannot but feel regret at teh expression of such opinions as teh gentleman has ovowed, because I think their obvious tendency is to weaken the bond of our connection. Which choice best characterizes how Webster responds to Hayne ? |
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Answer» He challenges Hayne's understanding of economics. |
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| 9. |
If Xand Y are 2xx2 matrices , then solve the following matrix equations for X and Y 2X+3Y=[{:(2,3),(4,0):}],3X+2Y=[{:(-2,2),(1,-5):}] |
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Answer» |
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| 10. |
sin^(-1){sin(2x^(2)+4)/(x^(2)+1)=ltpi-3 if |
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Answer» `x in [-1,0]` `(2x^(2)+4)/(x^(2)+1)=(2(x^(2)+1)+2)/(x^(2)+1)=2+(2)/(x^(2)+1)` `THEREFORE 2LT(2x^(2)+4)/(x^(2)+1)le 4 forall x in R` `rarr PI-4ltpi-(2x^(2)+45)/(x^(2)+1)ltpi-2 forall x in R` `rarr -(pi)/(2)ltpi-(2x^(2)+4)/(x^(2)+1 lt(pi)/(2) forall x in R` `=pi-(2x^(2)+4)/(x^(2)+1)` Hence `sin^(-1){sin(2x^(2)+4)/(x^(2)+1)}ltpi-3` `rarr pi-(2x^(2)+4)/(x^(2)+1)ltpi-3` `rarr (2x^(2)+4)/(x^(2)+1)gt3` `rarr 2+(2)/(x^(2)+1)rarr2gt3gtx^(2)+1rarrx^(2)1lt0rarrx in (-1,1)` |
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| 11. |
State which of the following matrices is symmetric,slew symmetric, both or not either: [[0,0,1],[0,0,-2],[-1,2,0]] |
| Answer» SOLUTION :SKEW SYMMETRIC | |
| 12. |
Evaluation of definite integrals by subsitiution and properties of its : If f(y)=e^(y) and g(y),ygt0 and F(t)=int_(0)^(t)f(t-y)g(y)dy then F(t)= …….. |
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Answer» `1-E^(-t)(1+t)` |
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| 14. |
If the segment of the line between the lines x-y+2=0 and x+y+4=0 is bisected at the origin, equation of the line is |
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Answer» `y+3x=0` |
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| 15. |
Let A={1,2,3,4,5} and functions f:A to and g: A to A to defined by f(1)=3,f(2)=5,f(3)=3,f(4)=1,f(5)=2,g(1)=4 |
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Answer» fog= {(1,1), (2,3), (3, 2), (4,5)} |
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| 16. |
If |bar(a).bar(b)|=3 and |bar(a)xx bar(b)|=4 then the angle between bar(a) and bar(b) is ……………… |
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Answer» `cos^(-1)""(3)/(4)` |
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| 17. |
Find the asymptotes of the curve f(x)=(2x^(2)-8)/(x^(2)-16) |
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Answer» |
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| 18. |
Prove that y=(4sin theta)/((2+cos theta))-theta is an increasing function of theta in [0, (pi)/(2)]. |
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Answer» |
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| 19. |
IF therootsofax^3 +bx^2 +cx+d =0are inG.Pthen therootsof ay^3 +bky^2 +ck^2 y+ dk^3=0arein |
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Answer» A.P |
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| 20. |
If y = y (x) is the solution of the differential equation ((2 + sin x)/(y + 1)) (dy)/(dx) + cos x = 0 with y(0) = 1 then y ((pi)/(2))= |
| Answer» ANSWER :A | |
| 21. |
On a multiple choice examination with three possible answers for each of the five questions, what is the probability that a candidate would get four or more correct answers just by guessing? |
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Answer» |
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| 23. |
Using elementary transformations, find the inverseof the matrices [(2,-6),(1,-2)] |
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Answer» |
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| 24. |
Number of X is randomly selected from the set of odd numbers and Y is randomly selected from the set of even numbers of the set {1,2,3,4,5,6,7}. Let Z = X + Y, then What is P(Z=10) equal to? |
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Answer» <P>0 |
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| 25. |
Evaluation of definite integrals by subsitiution and properties of its : f:RtoR is a differentiable function. If f(1)=4 then lim_(xto1)int_(4)^(f(x))(2t)/(x-1)dt=.............. |
| Answer» ANSWER :A | |
| 26. |
The range of values of m for which the line y = mx and the curve y=(x)/(x^(2)+1) enclose a region, is |
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Answer» `(-1, 1)` |
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| 27. |
If the equation of the circle having the coordinates of the ends of its diameter as (3,5) and (5,1) is (x-a)^(2)+(y-b)^(2)=r^(2) , whatis the value of (a+b+r) tothe nearest tenth? |
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Answer» |
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| 28. |
Integrate the following functions sqrt(sin2x) cos2x |
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Answer» Solution :LET sin2x = t Then `dt = COS2X XX 2 dx` `GT cos2x dx = 1/2 dt` therefore` int SQRT(sin2x) cos2x dx = int sqrtt 1/2 dt` `1/2 xx t^(1/2+1)/(1/2+1) +c` `1/3t^(3/2) +c = 1/3 (sin2x)^(3/2) +c` |
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| 29. |
If 4 fair coins are tossed simultaneously, then find the probability that 2 heads and 2 tails appear. |
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Answer» |
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| 31. |
If O,G , are respectively the orthocentre centroid and circumcentre of a orthocentre whose vertices are A(2,3) , B (2,4), then AO^(2)+9BG^(2)+4CS^(2) |
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Answer» `(77)/(36)` |
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| 32. |
Use complex numbers to prove that the sum , sum_(r-0)^(n-1)cos^2(alpha+(alphapi)/(n))=n/2" where " n inN, n ge2. |
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Answer» |
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| 33. |
if vec = 2hati+hatj-hatk, vecb = -hati+2hatj-4hatk, vecc = hati+hatj+hatk, find (vecaxxvecb).(vecaxxvecc). |
Answer» SOLUTION :  =`2hati-3hatj+hatk(VECAXXVECB).(vecaxxvecc)` `(2hati-9hatj+5hatk).(2hati-3hatj+hatk)` =-4-27+5 = -26. |
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| 34. |
A man draws a card from a pack one after another with replacementuntil he gets red card. The probabilitythathe gets red card in 4^(th) draw is |
| Answer» Answer :A | |
| 35. |
If I_(1)=int_(e)^(e^(2))(dx)/(logx)andI_(2)=int_(1)^(2)(e^(x))/(x)dx, then |
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Answer» `I_(1)=I_(2)` |
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| 36. |
If the three planes rcdotn_1=p_1, rcdotn_2=p_2 and rcdotn_3=p_3 have a common line of intersection, then p_1(n_2timesn_3)+p_2(n_3timesn_1)+p_3(n_1timesn_2) is equal to |
| Answer» ANSWER :(B) | |
| 37. |
Find the centre and radius of each of the circles whose equations are given below. 2x^(2) + 2y^(2) - 4x + 6y - 3 =0 |
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Answer» |
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| 38. |
Prove that (3!)/(2(n+3)) =sum_(r=0)^(n) (-1)^(r ) ((""^(n)C_(r ))/(""^(r+3)C_(r ))) |
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Answer» Solution :`underset(R=0)overset(N)sum(-1)^(r ) ((.^(n)C_(r))/(.^(r+3)C_(3)))` `= underset(r=0)overset(n)sum(-1)^(r)(n!)/((n-r)!r!)(3!r!)/((r+3)!)` `= 3!underset(r=0)overset(n)sum(-1)^(r) (n!)/((n-r)!(r+3!))` `=(3!)/((n+1)(n+2)(n+3))underset(r=0)overset(n)sum(-1)^(r).^(n+3)C_(r+3)` ` = - (3!)/((n+1)(n+2)(n+3))underset(r=0)overset(n)sum(-1)^(r+3).^(n+3)C_(r+3)` `= - (3!)/((n+1)(n+2)(n+3))[-.^(n+3)C_(3) +.^(n+3)C_(4)-"....."+(-1)^(n+3).^(n+3)C_(n+3)]` `= - (3!)/((n+1)(n+2)(n+3))[(.^(n+3)C_(0)-.^(n+3)C_(1)+.^(n+3)C_(2)-.^(n+3)C_(3)+"...."+(-1)^(n+3).^(n+3)C_(n+3))-(.^(n+3)C_(0)-.^(n+3)C_(1)+.^(n+3)C_(2))]` `- (3!)/((n+1)(n+2)(n+3))[(1-1)^(n+3)-(1-(n+3))-((n+3)(n+2))/(2)]` `= (3!)/((n+1)(n+2)(n+3))[1-n-3+((n+3)(n+2))/(2)]` `= (3!)/((n+1)(n+2)(n+3)) ((n^(2)+3n+2))/(2)` `= (3!)/(2(n+3))` |
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| 39. |
Evaluate the following integrals: int_1^2 (4x^3-5x^2+6x+9) dx |
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Answer» Solution :`int_1^2 (4x^3-5x^2+6x+9)DX` =`[4 x^4/4-5 x^3/3 +6 x^2/2 +9x]_1^2` =`[x^4 - (5x^3)/3 +3x^2 +9x]_1^2` =(16-(40)/3 +12 +18)-(1-5/3 +3 +9) =(40-(40)/3)-(13-5/3) = (98)/3 - (34)/3 = (64)/3 |
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| 40. |
Find an equation of normal line the curve y = x^(3)+ 2x +6 which is parallel to the linex+ 14y + 4=0 |
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Answer» |
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| 41. |
Find the value of a if,lim_(xto0)(e^(ax)-e^x)/x=2 |
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Answer» SOLUTION :`lim_(xto0)(e^(ax)-e^x)/x=2` `implieslim_(xto0){(e^(ax)-1)/x-(e^x-1)/x}=2` `implieslim_(xto0){a(e^(ax)-1)/(ax)-(e^x-1)/x}=2` `impliesalim_(xto0)(e^(ax)-1)/(ax)-lim_(xto0)(e^x-1)/x=2` `a-1=2impliesa=3` |
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| 42. |
If the direction cosines of two lines are such that l+m+n=0,l^(2)+m^(2)-n^(2)=0, then the angle between them is |
| Answer» Answer :C | |
| 43. |
Maximum value of Z=3x+y for the constraints x+yle4, xge0, yge0 is : |
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Answer» 12 |
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| 44. |
The vertices of a triangle are (3,2,5),(3,2,-1) and (7,2,5). The circumcentre is |
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Answer» a. `(4,3,1)` |
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| 45. |
y= x + (1)/(x + (1)/(x + (1)/(x + ...oo))) then find (dy)/(dx) |
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Answer» |
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| 47. |
A :A ( 0 ,2 ) ,B(0,- 2 )and PA + PB = 3the locusof Pisanellipse R :Locus ofa point, thesum ofwhosedistances from twofixedpointsalwaysconstant( whichis less than distancebetweenthe points ) is anellipse |
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Answer» A TRUE, R TRUEAND R iscorrectexplanationof A |
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| 48. |
Formthe polynomialwithrationalcoefficientswhoserootsare 4sqrt(3) ,5+2i |
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Answer» |
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| 49. |
4 + 5 ( - (1)/(2) + (isqrt3)/(2))^(334) + 3 ( - (1)/(2) + (isqrt3)/(2))^(365) = |
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Answer» `1 - isqrt3` |
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