Saved Bookmarks
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. |
If sqrt(3)(sin theta +cos theta)=2 + sin thetathen theta equal to |
|
Answer» `PM(pi)/(2)` |
|
| 2. |
sum (1)/(alpha^2 beta^2) |
|
Answer» `(q^2 -2pr)/(r^2)` |
|
| 3. |
The unit vector perpendicular to (3,-4) in R^(2) is ……………… |
|
Answer» `((3)/(5),-(4)/(5))` |
|
| 4. |
A line L passes through the poins hati+ 2 hatj + hatk and - 2 hati + 3 hatk. A plane P passes through the origin and the points 4 hatk, 2 hati + hatj. The point where the line L meets the plane P is |
|
Answer» `-hati -HATJ + 3hatk` |
|
| 5. |
As you reach Iraq, you see 49 people fighting among themselves to split their prize money. Many don't want to divide it into 49 equal parts as they worked harder than the others. To resolve the issue, the Owl suggests a way: "If 50% or more people in the group agree on splitting equal- ly, then they will split equally. If not, the person with the least contribution loses his claim, and is out of the group. The voting continues till a solution is reached".(ex : Suppose there are 10 people left. If 5 or more agree to divide the prize money equally, each would get an equal share. If not, the 10th ranked person is out of the group, and voting continues with the 9 people left). Next, just to make your life even more difficult, he says that while you are checking out of the hotel, you should pay him any amount(in integer value of dinars) exactly that he asks (the maximum that he can ask is 302 dinars). So, you decide to divide 302 dinars into ‘N’ different pouches such that you can pay him any amount from 1 to 302 dinars by giving certain number of pouches. What is the minimumvalue of‘N’? [Note: The above 4 questions are 2-digit integer type i.e., the answer can be any integer from 00 to 99]. |
|
Answer» Solution :9 302 dinars can be DIVIDED into 9 pouches in the following way 1, 2, 4, 8, 16, 32, 64, 128, 47 You can also find other combination but the minimum number of pouches required will be 9. |
|
| 6. |
Evaluate int_(0)^(int) (tan^(-1)(ax))/(xsqrt(1-x^(2)))dx, 'a'being parameter. |
|
Answer» Solution :Let `I(a) = underset(0)overset(1)int(tan^(-1)(AX))/(xsqrt(1-x^(2)))dx rArr (dI(a))/(DA) = underset(0)overset(1)(int)(x)/((1+a^(2)x^(2)))(1)/(xsqrt(1 x^(2)))dx=underset(0)overset(1)int(dx)/((1+a^(2)x^(2))sqrt(1-x^(2)))` Put `x = SINT rArr dx = cos t dt` L.L : `x = 0 rArr t = 0` U.L. `x = 1 rArr t = (PI)/(2)` `(dI(a))/(da) = underset(0)overset(pi/2)(int)(sec^(2)tdt)/(1+(1+a^(2))tan^(2)t)= (1)/(sqrt(1+a^(2))) tan^(-1)(sqrt(1+a^(2))TANT)]_(0)^(pi/2) = (1)/(sqrt(1+a^(2))).pi/2` `rArr I(a) = pi/2ln (a+sqrt(1+a^(2)))+c` But `I(0)= 0 rArr c = 0 rArr I(a) = (pi)/(2) ln (a+sqrt(1+a^(2)))` |
|
| 8. |
Given |z| = 14 and amp z = (7pi)/(6) , then z is = |
|
Answer» `-SQRT3 + i` |
|
| 9. |
As you reach Iraq, you see 49 people fighting among themselves to split their prize money. Many don't want to divide it into 49 equal parts as they worked harder than the others. To resolve the issue, the Owl suggests a way: "If 50% or more people in the group agree on splitting equal- ly, then they will split equally. If not, the person with the least contribution loses his claim, and is out of the group. The voting continues till a solution is reached".(ex : Suppose there are 10 people left. If 5 or more agree to divide the prize money equally, each would get an equal share. If not, the 10th ranked person is out of the group, and voting continues with the 9 people left). After resolving the issue, you stop at the hotel to take rest for the night. Unfortunately, the hotel is owned by Poseidon. Poseidon is Athena's greatest enemy. Poseidon, on knowing that you are coming from Parthenon(Temple of Athena),decides to make life awful for all of you. There are 32 rooms in the hotel and there are 32 identical looking keys. He gives them all and says that the second heaviest key is the one which opens your room. He also says that there is a balance (it compares two keys at a time) which can be used only N times ,where N is the minimum number of comparisons required to find the second heaviest key. What is the value of N? |
|
Answer» Solution :35 We will have a knockout tournament such that 16 pairs of keys are taken and heavier in each case is retained for next round. Next round will have 8 pairs hence 8 weighings. Next round 4, then 2 and finally 1 more. THUS in 31 weighings, we will get the heaviest key. Now the second heaviest key is the one which has lost only to the heaviest key. But since it could have lost in any of the 5 rounds, the second heaviest key is the heaviest among the 5 keys which were defeated by the heaviest key. This will further need 4 weighings and hence 35 weighings in total are needed. (Many are expected to get ‘61’ as answer as the common thinking might be that find the heaviestkey in 31 steps, remove it and find the heaviest out of remaining in 30 more steps ) |
|
| 10. |
If y= log_(10) sin x then (dy)/(dx) = …….. |
|
Answer» cot X |
|
| 11. |
Prove that the product of the perpendicular from any point on the hyperbola x^(2)/a^(2)-y^(2)/b^(2)=1 to its asymptodes is constant. |
|
Answer» |
|
| 12. |
As you reach Iraq, you see 49 people fighting among themselves to split their prize money. Many don't want to divide it into 49 equal parts as they worked harder than the others. To resolve the issue, the Owl suggests a way: "If 50% or more people in the group agree on splitting equal- ly, then they will split equally. If not, the person with the least contribution loses his claim, and is out of the group. The voting continues till a solution is reached".(ex : Suppose there are 10 people left. If 5 or more agree to divide the prize money equally, each would get an equal share. If not, the 10th ranked person is out of the group, and voting continues with the 9 people left). In short, among how many people should the prize money be divided equally if every person is self-cen- tred and every time he/she votes, tries to get maximum benefit? After your suggestion, the people of Iraq pay you a little as a reward for your help. Later, on your way to a hotel you find some people debating on an issue. Help them resolve it and earn some more money in return for your favour. |
|
Answer» Solution :32 1ST RANKED PERSON will DISAGREE on dividing in every case 2nd ranked will only say agree on dividing when 2 pirates are remaining 3rd will only say to divide when 4 pirates are remaining because if 4th get killed, 3rd will also get killed as 1st and 2nd will not be willing to divide 4th will only say to divide when 4 pirates are remaining. Similarly 5th, 6th, 7th, 8th will say to divide only when 8 are remaining 9th to 16th ranked pirates will say to divide only when 16 are remaining and it continues So, finally 32 pirates will divide the TREASURE. |
|
| 13. |
Evaluate the following definite integrals : int_(0)^(pi/4)sin^(3)2tcos2tdt |
|
Answer» |
|
| 14. |
As you reach Iraq, you see 49 people fighting among themselves to split their prize money. Many don't want to divide it into 49 equal parts as they worked harder than the others. To resolve the issue, the Owl suggests a way: "If 50% or more people in the group agree on splitting equal- ly, then they will split equally. If not, the person with the least contribution loses his claim, and is out of the group. The voting continues till a solution is reached".(ex : Suppose there are 10 people left. If 5 or more agree to divide the prize money equally, each would get an equal share. If not, the 10th ranked person is out of the group, and voting continues with the 9 people left). The issue is: The government of Iraq wants to issue ‘d’ denominations of coins (in whole numbers of dinars(Iraqi curren- cy)) so that by using no more than 3 coins, citizens can pay any amount from 1 dinar to 36 dinar. Find the value of‘d’ and all the ‘d’ denominations and give the sum of all these ‘d’ denominations? (Ex: if d=3 and 3 denominations are {4,5,3},answer= 4+5+3= 12.) |
|
Answer» Solution :40 ‘d’ =5 is the most OPTIMIZED solution and the following is the only possible combination for d=5 1+4+6+14+15. |
|
| 15. |
Value of F(4)= |
|
Answer» 1 |
|
| 16. |
If the parabola y^(2)=ax passes through (1, 2) then the equation of the directrix is |
|
Answer» `x+ 2Y =0 ` |
|
| 17. |
If a flagstaff subtends the same angle at the points A, B, C and D on the horizontal plane through its foot, then ABCD is a |
|
Answer» square |
|
| 18. |
Let R be a relation defined on the set Z xx Z as follows: (a,b),(c,d) in Z xx Z (a,b) R(c,d) if ony if a-d = b-c Then R is |
|
Answer» REFLEXIVE and SYMMETRIC only |
|
| 20. |
Find the value of sin105^@ |
| Answer» | |
| 21. |
When they are walking, one of the men, Sharktooth, in the troop is planning something against Tintin, and walks up to him saying that he does not believe Tintin is smart enough to lead them, so he throws up a challenge for him. He places 2 boxes, one having 15 apples and the other having 12 apples, he tells Tintin that either he can eat equal number of apples from both boxes or any number of apples from any of the boxes. He says that whoever eats the last apple will be their leader, and tells Tintin to make his choice first. How many apples will Tintin eat in his first move to win? |
| Answer» Solution : If you have the first move to make, what will be your stretagy? One THING is for sure that you can not always win. For example in a configuration (1,2) it is impossible for you to win no matter what move you make. In a sense (1,2) is a losing state. Your job is to find out WHETHER given configuration is a winning state or not and if it is a winning state, what will be the sequence of moves that will lead you to victory. There cannot be any losing state which has a difference of 1 SINCE they can be brought to (1,2) which is a losing state and there is no other losing state with one of the 2 numbers i.e 1,2 since they can be brought to losing state. Next (3,5) is a losing state and then (4,7) (5,9) (6,11) (8,14) (10,17) (11,19) (12,21) (3,23) (15,26) From (12,15), the only loosing state you can bring to is (4,7) which requires TINTIN to eat16 apples( 8 from each) | |
| 22. |
The value of sum_(n= 1)^(13)(i^(n) + i^(n + 1)) , where i=sqrt(-1) is |
|
Answer» `i` |
|
| 23. |
The region of the argand plane defined by |z-i| +|z+i|le4 is |
|
Answer» INTERIOR of an ellipse |
|
| 24. |
The total number of ordered pairs (x, y) satisfying|x| + |y| = 2and"sin"((pix^(2))/(3)) = 1is : |
|
Answer» 2 |
|
| 25. |
Semivertical angle of a cone is 45^@ and height is 30*05 cm I : Error in volume is 45pi cubic cm . Approximately II : Percentage error in volume is 1/2 |
|
Answer» only I is TRUE |
|
| 26. |
Evaluate int(cos 2x - cos 2 alpha)/(cos x - cos alpha) |
|
Answer» |
|
| 27. |
Let A = {-1,0,1,2},B= {-4,-2,0,2}and f , g , A to B be functions defined by f (x) =x ^(2) - x, x in A and g (x) =2 |x - (1)/(2) |-1, x in A Are f and g equal ? Justify your answer. |
|
Answer» |
|
| 28. |
Let S=overset(oo)underset(n=1)Sigma(5^(n)7^(n))/((7^(n)-5^(n))(7^(n+1)-5^(n+1))) then S= |
|
Answer» |
|
| 29. |
Differentiate (log x)^(logx) w.r.t x. |
|
Answer» |
|
| 30. |
40 boys of a class are divided into two equal group. Find the probability that the 2 tallest boys are in two different groups. |
|
Answer» |
|
| 31. |
Evaluate (i) int_(0)^(pi/2) (sin^(2)x)/(sin x + cos x ) dx |
|
Answer» |
|
| 32. |
int_(a+c)^(b+c) f(x) dx is equal to: |
|
Answer» `int_a^b F(X-c) DX` |
|
| 33. |
Differential equation of the family of circles with fixed radius 5 units, and centre on the line y=2, is |
|
Answer» `(x-2)^(2)(y')^(2)=25-(y-2)^(2)` |
|
| 34. |
Solve the following differential equations. x(dy)/(dx)+y=(1+x)e^(x) |
|
Answer» |
|
| 35. |
Let A be a squarre matrix of order of order 3 satisfies the matrix equationA^(3)-6 A ^(2) + 7 A - 8 I = O and B = A- 2 I .Also, det A = 8.If adj((B/2)^(-1))= (p/q)B, where p,q in N , the least valuse of(p+q) is equal to |
|
Answer» <P>7 `therefore A^(-1) B = I - 2A^(-1)`...(i) `adj[(B/2)^(-1)]= (B/2)/abs(B/2) = (B/2)/(1/8abs(B)) = (4B)/abs(B) = 4/10 B[becauseabs(B) = 10 ]` `= 2/5 B = p/q B`[GIVEN] `THEREFOREP= 2 and q = 5 ` Hence,p + q =7 |
|
| 36. |
A six faced die is so baised that it is twice as likely to show an odd number as an even number when rolled. The probability that the sum of the numbers on the upturned faces is even when the die is throwntwice is |
|
Answer» `(5)/(9)` |
|
| 38. |
Consider the equation (xy)/(x+y)=2^(3)3^(4)5^(6) then the number of positive integral solutions of equation are |
|
Answer» 140 |
|
| 39. |
Integrate the functions 1/(sqrt(sin^(3)xsin(x+alpha)) |
|
Answer» |
|
| 40. |
Evaluate :int(I+tan^2)/(I+cot^2x)dx |
|
Answer» `tan X - 1 + c` |
|
| 41. |
If z_(1) , z_(2) are two complex numbers satisfying |(z_(1) - 3z_(2))/(3 - z_(1) barz_(2))| = 1 , |z_(1)|ne 3 then |z_(2)|= |
|
Answer» 1 |
|
| 42. |
int (dx)/(x[ 10 + 7 log x + (log x)^(2)]) = |
|
Answer» `(1)/(3) log |(2 + log x )/(5 + log x )| + C` |
|
| 43. |
Find the slope of the lines whose inclinations are given.60^@. |
| Answer» SOLUTION :SLOPE = `TAN60^@` = `SQRT3` . | |
| 44. |
In the List-I some arrangement with ideal string & frictionless & light pulley are shown. In string CD tension may be written as T=etamg.Then match the List-II and List-I. |
|
Answer» P`to`1.5, Q`to`2,4 , R`to`5, S`to`3,5 |
|
| 45. |
2 mole of an ideal gas is expanded from (2 bar, 1L) to 1 bar isothermally. Calculate magnitude of minimum possible work in the change ( in Joules). (1 bar =100 J) [Given: 1 bar L=100 J] |
|
Answer» <P> SOLUTION :[0100]`W-P(V_(2)-V_(1))=P_(2)xxnRT((1)/(P_(2))-(1)/(P_(1)))` ` or , W=-1xxP_(1)V_(1)((1)/(1)-(1)/(2))=-2xx1((1)/(2))=-1 "BAR L"=-100J` |
|
| 46. |
If two cards are drawn from pack 52 cards at random, then find the probability of getting both club cards. |
|
Answer» |
|
| 47. |
LetD = { x in R : f(x) = sqrt((x - |x|)/(x - |x|)) "is difined"}and C be the range of the real functiong(x) = (2x)/(4 + x^(2)). "then"D cap C = |
|
Answer» `[-(1)/(2),(1)/(2)]` |
|
| 48. |
If x^(logx ) = y^(x) and (dy)/(dx) = (2y log x+ k log y)/(x^(2)), then k= |
| Answer» Answer :D | |
| 49. |
The value of tan^(2) (sec^(-1)2)+ cot^(2) ("cosec"^(-1)3) is |
|
Answer» 11 |
|
| 50. |
The value of "^(1000)C_(50)+^(999)C_(49)+^(998)C_(48)+......+^(950)C_(0) is |
|
Answer» `"^(1001)C_(50)` `="coefficient of" x^(950) "in" {(1+x)^(950)+(1+x)^(951)+…+(1+x)^(1000)}` `="coefficient of" x^(950) "in" (1+x)^(950){1+(1+x)+(1+x)^(2)+….+(1+x)^(50)}` `="coefficient of" x^(950) "in" (1+x)^(950) ({(1+x)^(51)-1})/(1+x-1)` `="coefficient of" x^(950) "in" ((1+x)^(1001)-(1+x)^(950))/(x)` `=^(1000)C_(951)=^(1001)C_(50)=^(1002)C_(951)-^(1001)C_(51)=^(1002)C_(51)-^(1001)C_(950)`, Since `'^(n)C_(R )+^(n)C_(r-1)=^((n+1))C_(r )` |
|