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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. |
Solve system of linear equations , using matrix method if exists x-y+z=4 2x+y-3z=0 x+y+z=2 |
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| 3. |
For the following probability distribution : E(X) is equal to ....... |
| Answer» ANSWER :D | |
| 4. |
A storage facility is currently offering a special rate to customers who sign contracts for 6 months or more. According to this special rate, the first month's rent is $1, and for each month after the first month, customers pay the regular monthly rental rate. The table below shows the storage unit sizes avialble, the floor dimensions, and the regular monthly rental rate. All the units have the same heigher. Size 5 units can be subdivided to form other sizes of units. What is the greatest number of Size 1 units that can be formed from a single size 5 unit? |
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Answer» 2 |
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| 5. |
Find all points of discontinuityof f, where f is defined by f(x)={{:(x+1," if "x ge1),(x^(2)+1," if "x lt 1):} |
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| 6. |
A storage facility is currently offering a special rate to customers who sign contracts for 6 months or more. According to this special rate, the first month's rent is $1, and for each month after the first month, customers pay the regular monthly rental rate. The table below shows the storage unit sizes avialble, the floor dimensions, and the regular monthly rental rate. All the units have the same heigher. Daria will sign a contract to rent a Size 3 unit for 12 months at the current special rate. The amount Daria will pay for 12 months at the current special rate represents what decrase from the regular rental rate for 12 months? |
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Answer» 0.0825 |
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| 7. |
Let a function , f:(-1,3) to R be defined as f(x) =min {x[x], |x[x]-2|+2} , where [x] denotes the greatest integer le x. Then f is : |
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Answer» neither CONTINUOUS nor differentiable at EXACTLY 3 points. |
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| 8. |
Let f be a function with domain [0, 7] and g(x)=|2x+1|. Then the domain of (fog)(x) is |
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Answer» `[0,7)` |
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| 9. |
A committee of 12 members is to be formed from 9 women and 8 men. The number of ways of forming the committee with women in majority is |
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Answer» 1008 |
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| 10. |
Solve the inequality 2-3x ge2(x+6) , when x is a real number. |
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| 11. |
Find the odd one out :If sqrtp+sqrtq is a root of a polynomial equation with rational coefficient then |
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Answer» `sqrtp-sqrtq` |
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| 12. |
A storage facility is currently offering a special rate to customers who sign contracts for 6 months or more. According to this special rate, the first month's rent is $1, and for each month after the first month, customers pay the regular monthly rental rate. The table below shows the storage unit sizes avialble, the floor dimensions, and the regular monthly rental rate. All the units have the same heigher. Janelle, the owner of the storage facility, is considering building new units that have floor dimensions larger than size 5 units. She will use the floor area to determine the heating requirements of these larger units. For this calculation, Janelle will use the same relationship between the unit size number and the respective floor area for sizes 1 through 5, which of the following expressions gives the floor area, in square meters, of a Size x storage unit? |
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Answer» `2^(3) CDOT x` |
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| 13. |
The point dividing the join of (3,-2,1)and (-2,3,11) in the ratio 2:3 is |
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Answer» `(1,1,4)` |
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| 14. |
int dx/(secx+cosx) |
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| 15. |
Prove thatpi/2 letan^(-1) x + 2 cot^(-1) x le(3pi)/2 |
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| 16. |
As you travel from Iraq towards IIT Guwahati, after a long time you find yourselves on a mountain trail in Tehran, Iran. The mountain trail is difficult and slippery. You suddenly get caught in a landslide and fall into a deep hole. Then the stones of 2 kg weight start falling onto you from above. The hole is a 4x4 grid i.e., it is divided into 16 squares. Each square can accommodate only one stone (of any weight). To survive, you need at least one empty square. Owl notices your trouble and gives you the magical power to meld together stones, but only those of the same mass can be mould together. Since the stones are falling very fast, you are only able to push the stones in straight lines (horizontally/vertical- ly). For example, when the arrangement of one of the rows in figure 1 when pushed horizontally to left trans- forms as shown: What is the largest stone that you can make if every second, either 2kg stone or 4 kg stones fall? |
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Answer» 2^17 The LARGEST stone that can be made if both 2 and 4kg STONES fall would be when the below situation OCCURS: THEREFORE, the largest stone that can be made is of weight =`2^(17) kg` 
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| 17. |
As you travel from Iraq towards IIT Guwahati, after a long time you find yourselves on a mountain trail in Tehran, Iran. The mountain trail is difficult and slippery. You suddenly get caught in a landslide and fall into a deep hole. Then the stones of 2 kg weight start falling onto you from above. The hole is a 4x4 grid i.e., it is divided into 16 squares. Each square can accommodate only one stone (of any weight). To survive, you need at least one empty square. Owl notices your trouble and gives you the magical power to meld together stones, but only those of the same mass can be mould together. Since the stones are falling very fast, you are only able to push the stones in straight lines (horizontally/vertical- ly). For example, when the arrangement of one of the rows in figure 1 when pushed horizontally to left trans- forms as shown: If one stone falls every second, what is the maximum time for which you can survive i.e., when no square is empty and all stones become immovable? |
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Answer» (2^16)-1 The maximum time for which you can survive is till the below SITUATION occurs: The time REQUIRED for the above situation to OCCURE is `(2+2^(2)+2^(3)+.....+2^(16))//2=2^(16)-1` 
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| 18. |
The value of |(a-b,b+c,a),(b-a,c+a,b),(c-a,a+b,c)| is |
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Answer» A) `a^(3)+B^(3)+C^(3)` |
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| 19. |
Let 4x^2 - 4(alpha - 2)x + alpha - 2 = 0 (alpha in R) be a quadratic equation. Find the values of 'a' for which (i) Both roots are real and distinct. (ii) Both roots are equal. (iii) Both roots are imaginary (iv) Both roots are opposite in sign. (v) Both roots are equal in magnitude but opposite in sign |
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| 20. |
f:[0,5]rarrR,y=f(x) such that f''(x)=f''(5-x)AAx in [0,5] f'(0)=1 and f'(5)=7, then the value of int_(1)^(4)f'(x)dx is |
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Answer» 4 Now `I=int_(1)^(4)xf''(x)dx=int_(1)^(4)(5-x)f''(5-x)dx` `=5int_(1)^(4)f''(x)dx=-I` `therefore""I=(5)/(2)[f'(4)-f'(1)]` `therefore""int_(1)^(4)f'(x)dx=(3)/(2)[f'(4)+f'(1)]` Now, `f''(x)=f''(5-x)` `rArr""f'(x)=-f'(5-x)+C` `rArr""f'(0)+f'(5)=c rArr c=8` `"so"f'(x)+f'(5-x)=8 rArr f'(4)+f'(1)=8` |
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| 21. |
Differentiate the following functions with respect to x: x^(2) + y^(2) - 4x- 6y - 25= 0 |
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| 22. |
The mean derviation about the mean for the following data, is |
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Answer» 6.3 |
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| 23. |
If f(x) = |cos x|, then f'((pi)/(4)) is equal to …… 0 lt x lt (pi)/(2) |
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Answer» f is EVERYWHERE DIFFERENTIABLE |
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| 24. |
Let a vector bar(r) make angle 60^(@), 30^(@) with x and y-axes respectively. What are the direction cosines of bar(r) ? |
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Answer» `(:1/2,(SQRT(3))/(2),0:)` Direction cosines of `vec(r)= lt (1)/(2) , (sqrt(3))/(2) , 0 lt` |
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| 25. |
Let ABCbe atrianglewithb = 5 , c = 11if themediumADis perpendicularto AC , thena = |
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Answer» 12 |
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| 26. |
Evalute the following integrals int (1)/(x^(3) + 1) dx |
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| 27. |
If z=((sqrt3)/2+i/2)^(5)+((sqrt3)/2-i/2)^(5), then |
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Answer» Re (Z) = 0 |
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| 28. |
The orthocentre of a triangle formed by the lines x - 2y = 1, x = 0 and 2x + y - 2 = 0 is |
| Answer» ANSWER :B | |
| 29. |
Equation of plane which contains the line (x-1)/(1)=(y-2)/(3)=(z-3)/(2) and which is perpendicular to the plane 2x+7y+5z=2, is |
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Answer» `x+y+z=6` |
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| 30. |
Rewriite problem by either distributings or factoring and then solve. Question 3, 4, and 5 have no numbers in them, therefore, they can't be solved with a calculator. Q.a(b+c-d)=___ |
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| 31. |
If alpha, beta , gammaare the roots of the equation x^3 + 2x^2 + 3x + 1 =0, then form an equation whose roots are: 1/beta^(2) + 1/gamma^(2) -1/alpha^(3), 1/alpha^(3) + 1/gamma^(2) - 1/beta^(2) , 1/alpha^(3) + 1/beta^(3) -1/gamma^(3) |
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| 32. |
If ""^(n)P_(r)=5040 and ""^(n)C_(r)=210, find n and r. |
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| 33. |
If the sum of the first 40 terms of the series, 3+4+8+9+13+14+18+19+ . . . is (102)m, then m is equal to : |
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Answer» 10 |
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| 34. |
If the regression coefficients be given b_(yx)=1.6 and b_(xy)=0.4 then find the sum of the slopes of the two regression lines. |
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| 35. |
Let p and q be two statements, then (p ^^ q) vv ~ p is |
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Answer» TAUTOLOGY  It is clear that, `(p VV Q) ^^ ~ p` is a tautology. |
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| 36. |
Find the length of the latus rectum of the ellipsex^(2) + 2y^(2) = 2. |
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| 37. |
Construct truth tables for the following and indicate which of these are tautologiesprarr(~q) |
Answer» SOLUTION :
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| 38. |
If A=[(1,2,-3),(5,0,2),(1,-1,1)],B=[(3,-1,2),(4,2,5),(2,0,3)]andC=[(4,1,2),(0,3,2),(1,-2,3)] then compute (A + B) and (B - C). Also verify that A + (B - C) = (A + B) - C. |
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| 39. |
If hati xx [ (veca-hatj) xxhati]+ hatj xx [(veca - hatk)xx hatj] +hatk xx [(veca-hati) xx hatk]=0 and veca=xhati+y hatj+z hatk, then : |
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Answer» `x+y=1` |
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| 40. |
If bar(mu)=hati xx(bar(a)xx hati)+hatj xx(bar(a)xx hatj))+hatk xx(bar(a)xx hatk) then bar(mu) = …………. |
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Answer» 0 |
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| 41. |
The product of two number x and y is twice the sum of the numbers. What is the sum of the reciprocals of x and y? |
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Answer» `1//8` |
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| 42. |
Solve system of linear equations, using matrix method in examples 7 to 14 x-y+2z=7 3x+4y-5z=-5 2x-y+3z=12 |
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| 43. |
Find the maximum value of 2x^(3) - 24x + 107 in the interval [1,3]. Find the maximum value of the same function in [-3, -1]. |
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| 44. |
Find the area of the triangle with vertices at(1,0),(6,0),(4,3) using determinants. |
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Answer» SOLUTION :`Delta=1/2|[1,0,1],[6,0,1],[4,3,1]|=1/2[-3|[1,1],[6,1]|]` (on EXPANDING ALONG `C_2`) `=-3/2(1-6)=15/2 sq.units` |
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| 45. |
One kind of cake requires 200 gm of flour and 25 g of fat and another kind of cake requires 100 gm of flour and 50 gm of fat. Find the maximum number of cakes which can be made from 5kg of flour and 1kg of fat assuming that there is no shortage of the other ingredients used in making the cakes. |
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| 46. |
An open box with a square base is to be made out of a given iron sheet of area 27 sq. m. Show that the maximum volume of the box is 13.5 cu.cm. |
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| 48. |
If Y=SX, Z=tX all the variables being differentiable functions of x and lower suffices denote the derivative with respect to x and |{:(X,Y,X),(X_(1),Y_(1),Z_(1)),(X_(2),Y_(2),Z_(2)):}|+|{:(S_(1),t_(1)),(S_(2),t_(2)):}|=X^(n), then n= |
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Answer» Solution :`(c )` `Delta=|{:(X,SX,tX),(X_(1),SX_(1)+S_(1)X,tX_(1)+t_(1)X),(X_(2),SX_(2)+2S_(1)X_(1)+S_(2)X,tX_(2)+2t_(1)X_(1)+t_(2)X):}|` `({:(C_(2)toC_(2)-SC_(1)),(C_(3)toC_(3)-tC_(1)):})` `=|{:(X,0,0),(X_(1),S_(1)X,t_(1)X),(X_(2),2S_(1)X_(1)+S_(2)X,2t_(1)X_(1)+t_(2)X):}|` `=X^(2)|{:(S_(1),t_(1)),(2S_(1)X_(1)+S_(2)X,2t_(1)X_(1)+t_(2)X):}|` `=X^(3)|{:(S_(1),t_(1)),(S_(2),t_(2)):}|(R_(2)toR_(2)-2X_(1)R_(1))` `:.n=3` |
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| 49. |
Ifthecoefficient of(2r + 1 )thterm and(r + 2 )thterm inthe expansionof(1 + x ) ^(43 )areequal, then r is equalto |
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Answer» 12 Co -efficientof` T _ (2r + 1 ) `=co- efficient of` T _ (r + 2 ) ` ` RARR ""^(43)C_(2r)=""^(43)C_( r +1 ) ` `rArr2r=r + 1or2r+r+ 1=43 [because""^nC_r =""^nC_( N -r ) ] ` ` rArrr= 1or 3R+ 1=43 ` ` 3r=42` `r =14 ` `thereforer= 1orr=14` |
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