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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. |
Equation of a plane passing through (1,1,1) and containg X-axis is |
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Answer» x-y=0 |
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| 2. |
find the number of terms in the expansion of (a+b+c)^6 where ninN |
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| 3. |
From the differential equation by eliminating the arbitrary constant from the equations y = a (x - a)^(2) |
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Answer» `((dy)/(dx))^(3) - 4xy (dy)/(dx) + 8Y^(2) = 0` |
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| 4. |
Let a sequence whose n ^(th) term is {a _(n)} be defined as a _(1) = 1/2 and ( n -1) a _(n-1) = (n +1) a _(n) for n ge 2then find Lim _(nb to oo) S _(n) |
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| 5. |
lim_(xto2)(x-2)/(|x-2|) |
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Answer» SOLUTION :L.H.L.`=lim_(hto0)(2-h-2)/(|2-h-2)|` `=lim_(hto0)(-h)/(|-h|)=lim_(hto0)(-h)/h=-1` R.H.L.`=lim_(hto0)(2+h-2)/(2+h-2)=lim_(hto0)(h)/(|h|)=1` As `L.H.LneR.H.L.` the LIMIT does not EXIST. |
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| 6. |
Integrate thefunction in Exercise. e^(2x)+3 |
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| 7. |
Locus of point of intersection of the perpendicular lines one belonging to (x + y-2) + lamda(2x+3y-5)=0 and other to (2x+y -11) + lamda(x+2y-13)=0 is a |
| Answer» Answer :A | |
| 8. |
The sets S_(1) and S_(2) are given by |
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Answer» EVEN function |
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| 10. |
He then enters a mushroom market. In the market, whenever two people greet each other, they have to swap their mushrooms. There are 64 people present in the Market.In order to save time, each pair of people is only allowed to greet each other atmost once. After a lot of greetings, Mario notices that it is no longer possible to return all mushrooms to their respective owners through more greetings. To sensibly resolve this maddening confusion, he decides to bring in even more people (with more mushrooms), to allow for even more greetings and mushroom swappings. How many extra people are needed to return all mushrooms (including the extra ones) to their rightful owners?Assume a person has exactly one mushroom. |
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Answer» Solution :Two extra people are needed to return correct mushrooms using the followingmethodLet the extra people have names E1 and E2. Step 1: Arrange the 64 people into lines such that In each LINE, every person is having themushroom of the person directly BEHIND. Except the last person whose mushroom is withthe first person in that line. NOTE : If two people have each others’ mushrooms, they will make a separate line of onlytwo people. Step 2:: For a single line, first E1 SWAPS mushrooms with the last person. Then E2 swapsmushrooms with each person in middle one at a time from front to back. Finally E1 willswap mushrooms with the first person.Then E1 & E2 swap each others’ mushrooms. Thisway everyone in this line ALONG with E1 & E2 will have their own mushrooms. Step 3: Repeat Step 2 for each line. |
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| 11. |
A and B are two variable points on x and y axes such that OA +OB= 1//2. Then the locus of the foot of the perpendicular from the origin on the line AB is |
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Answer» `2 (X^2 + y^2) (x + y) - XY =0` |
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| 12. |
Number of unpaired electron present in Gadolinium is _____ |
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| 13. |
f(x) = (e^(x)-e^(-x))/(e^(x)+e^(-x))+2 . The inverse of f(x) is ........ |
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Answer» `log_(E)((X-2)/(x-1))^(1/2)` |
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| 14. |
If A gt 0 and C gt 0," then e" (AX+B, CY+D)= |
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Answer» `E(X,y)` |
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| 15. |
In the given circuit diagram, the currents, I_1=-0.3A,I_4=0.8A and I_5=0.4A, are flowing as shown. The currents I_2,I_3 and I_6 respectively, are : |
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Answer» `1.1A,-0.4A,0.4A` |
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| 16. |
Express the following as trigonometric ratios of some acute angles. cos 500^@ |
| Answer» SOLUTION :`cos 500^@ = cos (5 (pi)/2 + 50^@) = (-1)^(5+1)/2) sin 50^@ = -sin 50^@` | |
| 17. |
Find the ratio in which (ii) the Y-axis divide the line segment AB joining the points A (2, -3) and B(3, -6). |
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| 18. |
If A=[(i,0),(0,-i)],B=[(0,-1),(1,0)],C=[(0,i),(i,0)] then |
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Answer» `AB=-BA=-I` |
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| 20. |
The remainder when 5^(4n) is divided by 13, is |
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Answer» 1 |
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| 21. |
Find the area of triangle if position vector of vertices w.r.t. O is -hat(i)+2hat(j)+3hat(k),2hat(i)-hat(j)-hat(k),hat(i)+hat(j)-hat(k). |
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Answer» `(SQRT(89))/(2)sq.units` |
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| 22. |
xy^(2)(dy)/(dx) + x(dy)/(dx)=1-x^(2)-x |
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Answer» `X^(2)-y^(2)+LOG[x^(2)(y^(2)-1)]=c` |
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| 23. |
Find the 13^(th) term in the expansion of (8x-(1)/(2sqrt(x)))^(18),xgt0 |
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Answer» Solution :`13^(th)` term in the EXPANSION of `(9x-(1)/(2sqrt(x)))^(18)` is given by `T_(13)=.^(18)C_(12)(9x)^(18-12)(-(1)/(2sqrt(x)))^(12)` `=(18xx17xx16xx15xx14xx13)/(6xx5xx4xx3xx2xx1).9^(6)x^(6)*(1)/(2^(12))*(1)/(x^(6))` `=(2466417681)/(1024)=2408611(17)/(1024)` |
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| 24. |
How many seven letters words can be formed by using the letters of theword SUCCESS so that |
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Answer» <P> SOLUTION :A(r),B(Q),C(s),D(p) |
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| 25. |
If arg z = pi/4 ,then |
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Answer» `Re(Z^(2))=9lm(z ^(2))` |
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| 26. |
Check the validity of q :125is a multiple if 5 and 7. |
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Answer» SOLUTION :Here the connective is .and. Step -1: 125 is a multiple of 5 (True) Step -2: 125 is a multiple of 7 (false) `:.`The STATEMENT .q. is (false), i.e. the statement .q. is not a valid statement |
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| 28. |
inte^x(cotx+Insinx)dx |
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Answer» Solution :`inte^x(COTX+Insinx)DX` [Integrating by parts TAKING `e^x` as FIRST function and cotx as SECOND function.] =`e^x.Insinx-inte^x.Insinxdx+inte^xInsinxdx+C` =`e^xInsinx+C` |
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| 29. |
Find derivatives of the following functions.sin((1-x^2)/(1 + x^2)). |
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Answer» Solution :`y = SIN((1 - x^2)/(1 + x^2) dy/dx = cos((1 - x^2)/(1 + x^2)). d/dx((1 - x^2)/(1 +x^2)) = cos((1 - x^2)/(1 +x^2)).(-2X(1+x^2)-(1-x^2).2x)/{(1 + x^2)^2 cos((1-x^2)/(1 + x^2)). {-2x(1+x^2)-(1-x^2).2x}/{(1+x^2)^2}` |
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| 30. |
A triangle park is enclosed on two sides by a fence and, on the third side, by a straight river bank. If the two fenced side have same length x, then the maximum area of the park is |
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Answer» `3/2 X^(2)` |
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| 31. |
The solution of the differential equation x(dy)/(dx)-y=3 represents a family of |
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Answer» STRAIGHT lines |
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| 32. |
Let x^(2)+y^(2)-4x-2y-11=0 be a fixex circle.A pair of tangents to the circle from the point (4,5) with a pair of its radii form quadrilaterla. Find the area of the quadrilaterla. |
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| 33. |
ABC is right -angled triangle of given area S. Find the sides of the triangle for which the area of the circumscribed circle is least. |
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| 34. |
IFtheslopeof thetangentof thecircleS =-x^2+ y^2 -13=0at(2,3)is m, thenthepoint( m , (-1)/(m)) is |
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Answer» anexternalpointwithrespectto thecircleS=0 |
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| 35. |
Let X and Y be sets containing m and n elements respectively.What is the total number of functions from X toY. |
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Answer» SOLUTION :If|x|=m and |y|=n then NUMBER of fumctions `=n^m` |
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| 36. |
Conditions that should be imposed on a and b such that S_(2) is nmon empty |
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Answer» `375/32 PI^(3)` |
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| 37. |
The values of (1+i)^(2//3) are |
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Answer» `2^(1//3)CIS[(6k+1)pi/6],k=0,1,2` |
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| 38. |
Obtain the integral values of p for which the following system of equations possesses real solutions:cos ^(-1) x + ( sin^(-1) y) ^(2) = (p pi^(2))/4 " and " ( cos^(-1) x ) ( sin ^(-1) x) ( sin^(-1) y) ^(2) =pi^(4)/( 16)Also ,findthese solutions. |
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| 39. |
int (x + sin x)/(1 + cosx )dx = |
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Answer» `X tan""(x)/(2) + c` |
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| 40. |
Determinewhether or not eachof thedefinition of given below gives a binary operation. In theevent that isnot a binary operation, given justificantion for this. (i) On Z^(+), define * by a * b = a- b (ii)On Z^(+), define * by a * b = ab (iii) On R,define * by a * b - ab^(2) (iv) On Z^(+), define * by a *b = |a - b| (v)On Z^(+), define * by a* b = a |
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Answer» Solution :In `Z^(+), a ** B =a - b` `2**3 = 2-3 = -1 in Z^(+)` `THEREFORE` Given operation is notbinary. (ii) In `Z^(+), a ** b = ab` The product of every TWO positive intergers is a positiveinterger. `therefore` Given operations is binary. (iii) In R,`a ** b= ab^(2)` The square of every real NUMBERIS always a real number. (iv)In `Z^(+) , ""a**b = a` The modulus of the difference ofevery two positiveinteger. `therefore` Givenoperation in binary. (v)`In Z^(+), "" a**b=a` For each `a,b in Z^(+)` `""a * b = a in Z^(+)` `therefore` Given operation is binary. |
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| 41. |
A = { setof allmultiplesof 3 less than20} B = {set of the multiplesof 2 less than18} n((Axx B) nn (B xx A)) is |
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Answer» 9 |
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| 42. |
In 324throwsof 4 dice ,the expectednumberoftimes three sixes occur is: |
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Answer» 81 |
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| 43. |
I=int(dx)/((1+e^(x))(1+e^(-x)))=... |
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Answer» `(-1)/(1+E^(X))` |
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| 44. |
If x_n=cos(pi/2^n)+isin(pi/2^n), then x1 x2 x3......infinity |
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Answer» -1 |
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| 45. |
The plane containing the line (x-1)/(1)=(y-2)/(2)=(z-3)/(3) and parallel to the line (x)/(1)=(y)/(1)=(z)/(4) passes through the point: |
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Answer» `(1,-2,5)` |
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| 47. |
I. The function f(x)=sqrtx" is continuous at x=0" II. The function f(x)=|x| is continuous at x=0. |
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Answer» only I is true |
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| 48. |
A manufacturer maks two types A and B of tea cups. Three machines are needed for the manufacture and the time in minutes required for each cup on the machines is given below. Each machine is available for a maximum of 6 hours per day. If the profit on each cup A is 75 paise and that on each cup B is 50 paise. How many both type of tea cups should be manufactured in a day to get the maximum profit ? |
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| 49. |
Solution of the differential equation cos x dy = y (sin x-y) dx, 0 lt x lt pi//2 is |
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Answer» `SEC X =y("TAN"x+c)` |
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| 50. |
Let n be a positive integer. If R is a relation defined on Z as xRy iff x-y is divisible by n then R is |
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Answer» REFLEXIVE |
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