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InterviewSolution
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.
| 9001. |
Find thearea ofthe region by the curvey=|x+3 |,Xaxisand thelines x=-6 and x=0. |
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| 9002. |
Find the equation of the circle with centre C and radius r where C = ((5)/(2) , (-4)/(3)) , r= 6 |
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| 9003. |
Let veca=hati-2hatj+3hatk, vecb=2hati+3hatj-hatk and vecc=lambda hati+hatj+(2lambda-1) hatk." If "vecc is parallel to the plane containing veca, vecb" then "lambda is equal to |
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Answer» 0 |
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| 9004. |
If a fair coin is tossed 10 times, find the probability of Exactly six heads |
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| 9005. |
The sum of the non real root of (P^(2)+P-3)(P^(3)+P-2)-12=0 is |
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Answer» 1 |
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| 9006. |
Determine order and degree (if defined) of differential equations y" + 2y' + sin y = 0 |
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| 9007. |
Differentiate sqrtx(sqrtx+1) |
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Answer» SOLUTION :`y=sqrtx(sqrtx+1)=x+x^(1/2)` `dy/dx=1+1/2x^(-1/2)` |
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| 9008. |
If n(A) = 4, then number of relations on A that are not reflexive is |
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Answer» `2^(16)` |
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| 9009. |
Locus of a point, w hose chord of contact with respect to the circlex^(2)+y^(2)=4is a tangentto the hyperbolaxy=1 is a/an : |
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Answer» ellipse |
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| 9010. |
Find values of k if area of trianlge is 13 and vertices are (8,2), (k,4) and (6,4) |
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| 9011. |
If the distances between two parallel tangents drawn to the hyperbola(x^(2))/(9) -(y^(2))/( 49)= 1is 2 , then their slope is equal to |
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Answer» ` +- ( 5)/(2) ` |
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| 9012. |
If int (1)/(sqrt(x^(2) + x+ 1))dx = a sinh^(-1) (bx + c ) + dthen descending order of a, b,c is |
| Answer» Answer :C | |
| 9013. |
Evaluate the following inegrals int(x^(2)+1)/(x^(4)+1)dx |
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| 9014. |
A fair coin is tossed 100 times . The probability of getting tails an odd number of times is |
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Answer» `1/2` |
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| 9015. |
Six faces of a balanced die are numbered from integers 1 to 6. This die is tossed 60 times and the frequency distriction of the integers obtained is given below. Then the mean of the grouped data is {:("Integer",1,2,3,4,5,6),("Frequency",8,9,10,16,9,8):} |
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Answer» 3.25 |
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| 9016. |
If [x] denotes the greatest integer less than or equal to x then int_(1)^(oo) [(1)/(1+x^(2))]dx= |
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Answer» 1 |
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| 9017. |
If cos(2theta)=0" then "|{:(0,costheta,sintheta),(costheta,sintheta,0),(sintheta,0,costheta):}|^2="............" |
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| 9018. |
If the angle between the pair of lines x^(2)+2sqrt(2)xy+ky^(2)=0, k gt 0 is 45^(@), then the area ( in square units) of the triangle formed by the pair of bisectors of angles between the given lines and the line x+2y+1=0 is |
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Answer» `1/3` |
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| 9019. |
Find (dy)/(dx) in the following xy + y^(2)= tan x + y |
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| 9020. |
If (cosx-cosalpha)/(cosx-cosbeta)=(sin^(2)alphacosbeta)/(sin^(2)betacosalpha), then |
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Answer» `cosx=(cosalpha+cosbeta)/(1+cosalphacosbeta)` |
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| 9021. |
If area of triangle is 35 sq. units with vertices (2,-6), (5,4) and (k,4). Then k is_____ |
| Answer» ANSWER :D | |
| 9022. |
If sqrt(2x - 4) le 2 - x, then the range of x is |
| Answer» ANSWER :D | |
| 9023. |
Compute the indicated products : (1)[{:(3,-1,4),(2,3,1):}][{:(1,3,4),(2,1,0),(-3,2,3):}] (2)[{:(1,3),(2,1):}][{:(4),(-1):}] (3)[{:(1,4,2),(5,-2,3):}][{:(2,-4),(1,-3),(4,0):}] (4)[1" "2," "3][{:(2),(4),(6):}] (5)[{:(2),(4),(6):}][1" "2," "3] |
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Answer» (2) `[{:(1),(7):}]` `[{:(14,-16),(20,-14):}]` `[28]` (5)`[{:(2,4,6),(4,8,12),(6,12,18):}]` |
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| 9024. |
If p,q, r arepositiveintegers,find themaximum possiblevalue of(p+q+ r)ifpx - (x + r) = 23x- 15 . |
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| 9025. |
There are two values of a which makes determinant Delta=|{:(1,-2,5),(2,a,-1),(0,4,2a):}|=86, then sum of these number is "........." |
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Answer» 4 |
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| 9026. |
Two cards are drawn from pack of cards at random and given that those two cards belong to different suits. Find the probability of getting one king and one queen. |
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| 9027. |
What was M. Hamel going to question Franz about? |
| Answer» Answer :A | |
| 9029. |
Find the member of 4-digit numbers that can be formed using the digits 2,3,5,6,8 (without repetition). How many of them are divisible by 3 |
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| 9030. |
Find the member of 4-digit numbers that can be formed using the digits 2,3,5,6,8 (without repetition). How many of them are divisible by 4 |
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| 9031. |
Find the member of 4-digit numbers that can be formed using the digits 2,3,5,6,8 (without repetition). How many of them are divisible by 2 |
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| 9032. |
Column I : Parabola y^(2)=16x is given. In column I, 4 points (P) is given on directrix. A ray from the these points (P) parallel to axis is reflected through given parabola at M and after reflection goes through point (N). Column II : Angle Bisector of PM and MN Column III : Foot of perpendicular of focus on angle bisector (R). Which of the following options is the only CORRECT combination? |
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Answer» (I) (i) (Q) |
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| 9033. |
Find the member of 4-digit numbers that can be formed using the digits 2,3,5,6,8 (without repetition). How many of them are divisible by 5 |
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| 9034. |
Find the member of 4-digit numbers that can be formed using the digits 2,3,5,6,8 (without repetition). How many of them are divisible by 25 |
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| 9035. |
Column I : Parabola y^(2)=16x is given. In column I, 4 points (P) is given on directrix. A ray from the these points (P) parallel to axis is reflected through given parabola at M and after reflection goes through point (N). Column II : Angle Bisector of PM and MN Column III : Foot of perpendicular of focus on angle bisector (R). Which of the following options is the only CORRECT combination? |
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Answer» (II) (i) (S) |
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| 9036. |
Column I : Parabola y^(2)=16x is given. In column I, 4 points (P) is given on directrix. A ray from the these points (P) parallel to axis is reflected through given parabola at M and after reflection goes through point (N). Column II : Angle Bisector of PM and MN Column III : Foot of perpendicular of focus on angle bisector (R). Which of the following options is the only CORRECT combination? |
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Answer» <P>(III) (II) (S) |
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| 9037. |
The plane contains the vectors 2 hat i + 3 hat j - hat k and hat i + hat j+2hat k. The acute angle made by this plane with the vector 2 hat i + 3 hat j - hat kis .......... |
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Answer» `cos^(-1) ""((1)/(SQRT(3)))` |
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| 9038. |
It’s time for one of the most awaited events of the Tri-Wizard Tournament, The Yule Ball. Viktor Krum decides to ask out Hermione as his date for the ball. Knowing how smart she is, he decides to impress Hermione by scoring the highest ever score in one the most played games at Hogwarts The game is described as follows: This is a game played with a sequence of tiles, each labelled with two numbers. You start at the first tile in the sequence and choose one number from each tile that you stop at, according to the following rules: •At tile i, if you pick up the smaller number, you move on to the next tile, i+1, in the sequence. •At tile i, if you pick up the larger number, you skip the next tile and move to tile i+2 inthe sequence. The game ends when your next move takes you beyond the end of the sequence. Your score is the sum of all the numbers you have picked up. The goal is to maximize the final score. For example, suppose you have a sequence of four tiles as follows: Then, the maximum score you can achieve is 3, by choosing the numbers that are circled. In each of the cases (a) and (b) below, compute the maximum store that Viktor can achieve by picking up numbers according to the rules given above. |
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Answer» Solution :C) 14, 15 (a) 2, -1, 1 (B) 1,4,1,3,3,4, -1 |
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| 9039. |
Show that A(3,-1) lies on the circle x^(2) +_ y^(2) - 2x + 4y = 0. Also find the other end of the diameter through A. |
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| 9040. |
Evaluate the following determinants.[[1,x,y],[0,sinx,siny],[0,cosx,cosy]] |
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Answer» Solution :`[[0,x,y],[0,sinx,SINY],[0,COSX,COSY]]=1[[sinx,siny],[cosx,cosy]]` =sinxcosy-cosxsiny=sin(x-y). |
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| 9041. |
If a,b,c are three positive real numbers then the minimum value of (a+3c)/(a+2b+c)+(4b)/(a+b+3c)-(8c)/(a+b+3c) is alpha+betasqrt(2) (where a,b in Z), then |alpha+beta| is equal to_____ |
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Answer» `a=-x+5y-3z,b=z+x-2, c-z-y` APPLY A.M. `ge` G.M. `(a+3c)/(a+2b+c)+(4b)/(a+b+2c)-(8C)/(a+b+3c) ge -17 + 12 sqrt(2)` |
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| 9042. |
1+(2^(3))/(1!)x+(3^(3))/(2!)x^(2)+....= |
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Answer» `(X^(3)-6x^(2)+7x-1)e^(x)` |
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| 9043. |
Evaluate:int_(0)^(pi//3)(secxtanx)/(1+sec^(2) x)dx |
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| 9045. |
If C_(r)=""^(25)C_(r) and C_(0)+5*C_(1)+9*C_(2)+ . . .+(101)*C_(25)=225*k, then k is equal to _______. |
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| 9046. |
Solve the following differential equations (i) (1+y^(2))dx = (tan^(-1)y - x)dy (ii) (x+2y^(3))(dy)/(dx) = y (x-(1)/(y))(dy)/(dx) + y^(2) = 0 (iv) (dy)/(dx)(x^(2)y^(3)+xy) = 1 |
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Answer» (II) `x = y(y^(2) + c)` (III) `xy = 1+ y + CY e^((1)/(y))` (IV) `1+x(y^(2) - 2+ce^(-y^(2)//2)) = 0` |
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| 9047. |
Find the are enclosed between y=sqrt(5-x^(2)) and the lines y=|x-1|. |
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| 9048. |
A card is drawn from a well shuffled pack of 52 cards and it is found to be red. Find the probability that it is a king. |
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| 9049. |
According to Newton's law, rate of coolingis proportional to the difference between the temperature of the body and the temperature of the air. If the temperature of the air is 20^(@)C and body cools for 20 min from 100^(@)C to 60^(@)C then the time it will take for it temperature to drop to 30^(@) is |
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Answer» 30 min |
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| 9050. |
If (1+x+x^(2))^(20) = a_(0) + a_(1)x^(2) "……" + a_(40)x^(40), then following questions. The valueof a_(0)^(2) - a_(1)^(2) + a_(2)^(2)- "……" - a_(19)^(2) is |
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Answer» Replacing x by `1//x`, we get `(1+x1/x+1/(x^(2)))^(20) = underset(r=0)overset(40)suma_(r)(1/x)^(r )` or `(1+x+x^(2))^(20) = underset(r=0)overset(40)suma_(r)x^(40-r) ""(2)` Since (1) and (2) are same series, coefficient of `x^(r )` is (1) `=` coefficient of `x^(r)` in (2). `rArr a_(r) = a_(40-r)` In (1) Putting `x = 1`, we get `3^(20) = a_(0)+a_(1)+a_(2)+"...."+a_(40)` `= (a_(0)+a_(1)+a_(2)+"...."+a_(19))+a_(20)+(a_(21)+a_(n+2)+"..."+a_(40))` `= 2(a_(0)+a_(1)+a_(2)+"...."+a_(19))+a_(20)""( :' a_(r) = a_(40-r))` or `a_(0) + a_(1) + a_(2) + "......."+ a_(19) = 1/2 (3^(20)-a_(20)) = 1/2(9^(10) - a_(20))` Also, `a_(0)+3a_(1)+5a_(2)+81a_(40)` `= (a_(0)+81a_(40))+(3a_(1)+79a_(39))+"...."+(39a_(19)+43a_(21))+41a_(20)` `= 82(a_(0) + a_(1) + a_(2) + "......" + a_(19)) + 41a_(20)` `= 41 xx 3^(20)` `a_(0)^(2) - a_(1)^(2) + a_(2)^(2) - a_(3)^(2) + "....."` suggests that we have to multiply the two expansions. Replacing x by `-1//x` in (1), we get `(1-1/x+1/(x^(2)))^(20) = a_(0) - (a_(1))/(x)+(a_(2))/(x^(2))-"...."+(a_(40))/(a_(40))` `rArr (1-x+x^(2))^(20) = a_(0)x^(40) - a_(1)x^(39) + a_(2)x^(38) - "....."a_(40)""(3)` Clearly, `a_(0)^(3) - a_(1)^(2) + a_(2)^(2) + "....."+ a_(0)^(2)` is the coefficeint of `x^(40)` in `(1+x+x^(2)) (1-x+x^(2))^(20)` = Coefficient of `x^(40)` in `(1+x^(2)+x^(4))^(20)` In `(1+x^(2)+x^(4))^(20)` REPLACE `x^(2)`, by y, then the coefficientof `y^(20)` in `(1+y+y^(2))^(20)` is `a_(20)`. Hence `a_(0)^(2) - a_(1)^(2) -"......"+a_(40)^(2) = a_(20)` or `(a_(0)^(2) - a_(1)^(2) + a_(2)^(2) - "....." - a_(19)^(2)) + a_(20)^(2) + (-a_(21)^(2) + "....." + a_(40)^(2)) = a_(20)` or `2(a_(0)^(2) - a_(1)^(2) + a_(2)^(2) - "....." - a_(19)^(2)) + a_(20)^(2) = a_(20)` or `a_(0)^(2) - a_(1)^(2) -"......" - a_(19)^(2) = (a_(20))/(2)[1-a_(20)]` |
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