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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.
| 27001. |
Let f:R to R,g:R to R be differentiable functions such that (fog)(x) = x. If f(x)=2x+cosx+sin^(2)x, then the value of underset(n=1)overset(99)sumg(1+(2n-1)pi) is |
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Answer» `1250pi` |
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| 27002. |
Let A = {1,2,3}. Then number of relations containing (1,2) and (1,3) which are reflexive and symmetric but not transitive is |
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Answer» 1 |
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| 27003. |
If the variance of 4,7,8,9,10,11 is sigma^(2) then the variance of 12 14, 16,18,20,22 is |
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Answer» `2sigma^(2)` |
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| 27004. |
An aerplane at an altitude of 400 metres, flying horizontally with a speed of 250 m//sec, passes directly the observer, it is approaching him at the rate of |
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Answer» `100 m//SEC`. |
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| 27005. |
A coin tossed twice. Find the probability of getting at least one head |
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Answer» <P> `therefore S={HH,HT,TH,T T}, |S|=4` Let B be the event of GETTING at LEAST one HEAD. `thereforeB={HT,TH, HH}implies|B|=3` `P(B)=|B|/|S|=3/4` |
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| 27006. |
If A is a matrix of order 3xx3, then number of minors in determinant of A are "............" |
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| 27007. |
A tosses 2 fair coins & B tosses 3 fair cons after game is won by the person who throws greater number of heads. In case of a tie, the game is continued under identical rules until someone finally wins the game. The probability that A finally wins the game is K//11, then K is |
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Answer» `B_(i)=` no of heads obtained by `B` when tosses `3` coins `P(E)=P{(A_(1)nnB_(0))uu(A_(2)nnB_(2))uu(A_(2)nnB_(1))}` `=2C_(1)(1/2)(1/2)(1/2)^(3)+(1/2)^(2)+(1/2)^(2)3C_(1)(1/2)(1/2)^(2)` `=2/32+1/32+3/32=3/36` `F={A` & `B` tie a PARTICULAR game `}`then`P(F)=P{(A_(0)nnB_(0))uu(A_(1)nnB_(1))uu(A_(2)nnB_(2))}=5/16` `P` (`A` finally wins the game ) `=P(E` or `FE` or `FFE` or ........) `=3/11` |
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| 27008. |
Find the angle between pair of lines given by: vecr = 3hati + 2hatj - 4hatk + lambda(hati + 2hatj + 2hatk)and r=3ˆi+2ˆj−4ˆk+λ(ˆi+2ˆj+2ˆk) |
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| 27009. |
lim_(n rarr oo)n[(1)/((3n^2+8n+4))+(1)/(3n^2+16n+16)+.....+1/(15n^2)]= |
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Answer» `1/2log""9/5` |
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| 27010. |
int_(0)^(1//2) (x sin^(-1)x)/(sqrt(1-x^(2)))dx=? |
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Answer» `(pi SQRT(3))/(12)+(1)/(2)` |
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| 27011. |
Prove that cos20^(@)cos40^(@)cos60^(@)cos80^(@)=1/16 |
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| 27012. |
y= f(x) is a polynomial function passing through point (0, 1) and which increases in the intervals (1, 2) and (3, oo) and decreases in the intervals (oo,1) and (2, 3). If f(1) = -8, then the value of f(2) is |
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Answer» -3 Hence, `f'(x)=a(x-1)(x-2)(x-3), a gt 0` `implies f(x)=int a(x^(3)-6x^(2)+11x-6)dx` `=a((x^(4))/(4)-2x^(3)+(11x^(2))/(2)-6x)+C` Also, `f(0)=1 implies c=1` ` :. f(x)=a((x^(4))/(4)-2x^(3)+(11x^(2))/(2)-6x)+1 "(1)" ` So, graph is symmetrical about line `x=2` and range is `[f(1), OO) or [f(3),oo).` `f(1)=8` `implies a(-(9)/(4))+1=-8` `impliesa=4` `:. f(2)= -7` |
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| 27013. |
y= f(x) is a polynomial function passing through point (0, 1) and which increases in the intervals (1, 2) and (3, oo) and decreases in the intervals (oo,1) and (2, 3). If f(x)=0 has four real roots, then the range of values of leading coefficient of polynomial is |
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Answer» [4/9, 1/2] HENCE, `f'(x)=a(x-1)(x-2)(x-3), a gt 0` `implies f(x)=INT a(x^(3)-6x^(2)+11x-6)dx` `=a((x^(4))/(4)-2x^(3)+(11x^(2))/(2)-6x)+C` Also, `f(0)=1 implies c=1` ` :. f(x)=a((x^(4))/(4)-2x^(3)+(11x^(2))/(2)-6x)+1 "(1)" ` So, graph is symmetrical about line `x=2` and range is `[f(1), oo) or [f(3),oo).` For `f(x)=0, " we have " (x^(4))/(4)-2x^(3)+(11x^(2))/(2)-6x= -(1)/(a)` For `x=1, -(9)/(4) = -(1)/(a) " or " a=(4)/(9)` For `x=2, -2= -(1)/(a) " or " a=(1)/(2)` So, `f(x)=0` has FOUR roots if `a in [(4)/(9),(1)/(2)]`. |
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| 27014. |
The solution of (12x + 5y -9) dx + (dx + 2y-4) dy = 0 is |
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Answer» `6x^(2) + 5xy + y^(2) + 9X + 4Y = c` |
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| 27015. |
Let f(x) be a continuous function and I = int_(1)^(9) sqrt(x)f(x) dx, then |
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Answer» There exists some `c in (1,9 )` such that `I = 8sqrt(c)F(c)` |
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| 27016. |
What will be the pH of 4xx10^(-5)M A_(2)B solution which is assumed to be dissociated 75% in water. [Given : K_(b)(AHO)=5xx10^(-9),H_(2)B is strng acid.] |
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Answer» `{:(A^(+)+""H_(2)O""hArr""AOH+H^(+)),((6xx10^(-5)-x)""x ""x):}` or `(10^(-5))/(5)=(x^(2))/((6xx10^(-5)-x))` or `5x^(2)=6xx10^(-10)-x xx10^(-5)` `5x^(2)+10^(-5)x+6xx10^(-10)=0` or `x=(-10^(-5)+SQRT(10^(-10)+120xx10^(-10)))/(10)` `x=(-10^(-5)+10^(-5)xxsqrt(121))/(10)` `x=(10^(-5)(11-1))/(10)=10^(-5)` `pH=5` |
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| 27017. |
If the line bar r= (5,5,2) +k (3,6,9) k in R and bar = (0,3,-1) + k (1,2,b),k in Rare parallel then b = ...... . |
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Answer» 3 |
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| 27019. |
If veca is a unit vector such that (vecx-veca).(vecx+veca)=8, find |x|. |
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| 27020. |
Find the number of positive integral solutions of x_1x_2x_3x_4=2310 such that each x_i ne 1 for i=1,2,3,4 |
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| 27021. |
Let X be a set of 5 elements. The number d of ordered pairs (A,B) of subsets of X such that Anephi,Bnephi,AnnB=phi satisfies |
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Answer» `50le dle100` `10(2)+10(6)+5(8+6)+(10+20)` =20+60+70+30=180 |
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| 27022. |
If [axxb bxxc c xxa]=lambda[abc]^(2), then lambda is euqual to |
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Answer» Solution :Given,` [ a xx b "" b xx C "" c xx a] = lambda [ "a b c"]^(2)` `LHS = (a xx b ) * [ (b xx c) xx (c xx a ) ]` ` = (a xx b)*[{b*(cxxa)}c-{c*(cxxa)}b]` `=(a xx b) *{["b c a"] c - 0} "" [ because c *(c xx a) = 0] ` `={(a xx b) *c} [ "b c a"]=["a b c"]["b c a"] ` `=[ "a b c"]["a b c"] "" [ because ["b c a"]=["a b c"]]` `=["a b c"]^(2)=RHS` `THEREFORE lambda = 1` |
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| 27023. |
Integrate the following intsec(2x-3)^2dx |
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Answer» SOLUTION :`intsec(2X-3)^2dx` `intsec^2(2x)dx-6intsec2xdx+9intdx` `(1/2)tan2x-3Inabs(sec2x+tan2x+9x+C` |
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| 27024. |
An urn contains four balls bearing numbers 1,2,3 and 123 respectively . A ball is drawn at random from the urn. Let E_(p) i = 1,2,3 donote the eventthat digit i appearson the ball drawnstatement 1 : P(E_(1)capE_(2)) = P(E_(1) cap E_(3)) = P(E_(2) cap E_(3)) = (1)/(4)Statement 2 : P_(E_(1)) = P(E_(2)) = P(E_(3)) = (1)/(2) |
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Answer» Statement 1 and statement 2 are both false |
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| 27025. |
If (1+x)^(n)=1+C_(1)x+C_(2)x^(2)+ . . .+C_(n)x^(n), then: C_(1)^(2)-2C_(2)^(2)+3C_(3)^(2)- . .. -2nC_(2n)^(2) is: |
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Answer» `N^(2)` |
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| 27026. |
A kite is moving horizontally at a height of 151.5 meters. If the speed of kite is 10 m/s, how fast is the string being let out , when the kite is 250 m away from the boy who is flying the kite ? The height of boy is 1.5 m. |
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| 27027. |
Let f'(x) ={(|x|)/(1) underset(x=0)(0le|x|le2). Examine the behaviour of f(x) at x=0. |
Answer» SOLUTION :F(X) has localmaxima at x=0 (SEE FIGURE). 
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| 27028. |
Differentiate x^(sin x), x gt 0 w.r.t. x. |
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| 27029. |
Which of the following set are finite and which are infinite ?The set of integers less than 10. |
| Answer» Solution :"The SET of INTEGERS LESS than 10" is an INFINITE set. | |
| 27030. |
Let f(x) = minimum (tan x, cot x, 1//sqrt(3)) AA xx in [0, pi//2]. Then area of bounded by y = f(x) and the x-axis is in ((4)/(3)) + (pi)/(ksqrt(3)), then the value of k is ______ |
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| 27031. |
Let A and b be events with P(A) = 1/3, P(A cup B)= 3/4andP(A cap B)= 1/4, Find P(B) |
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Answer» <P> ` (A CAP B)=1/4` `P(A)=1/3` |
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| 27032. |
Differentiate w.r.t.x the function in Exercises 1 to 11. x^(x)+x^(a)+a^(x)+a^(a), for some fixed a gt 0" and "x gt 0. |
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| 27033. |
If a rectangular hyperbola circum scribes a triangle, then it also passes through the |
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Answer» incentre of the triangle |
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| 27034. |
Let f(x)=x, x in Q , f(x)=1-x , x in R ~ Q then f is continuous only at x= |
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Answer» `1//2` |
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| 27035. |
Statement - 1: If two whole numbers are multipled then probability of the last digit being zero is (1)/(10). because Statement - 2: If one number is drawn from the set S={10,11,12,…,19}, then the probability of the last digit being zero is (1)/(10). |
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Answer» Statement - 1 is True, Statement - 2 is True, Statement-2 is CORRECT explanation for Statement - 1 |
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| 27036. |
Let f:{1,\ 3,4\ }->{1,\ 2,\ 5}and g:{1,\ 2,\ 5}->{1,\ 3}be given by f={(1,\ 2),\ (3,\ 5),\ (4,\ 1)}and g={(1,\ 3),\ (2,\ 3),\ (5,\ 1)}. Write down gofdot |
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Answer» {(1, 3), (3, 1), (4, 3)} |
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| 27037. |
If cosalpha+cosbeta+cosgamma=0=sinalpha+sinbeta+singamma then sin3alpha+sin3beta+sin3gamma= |
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Answer» `3SIN(alpha+beta+gamma)` |
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| 27038. |
Integrate the following intx^2cosx^3dx |
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Answer» SOLUTION :`intx^2cosx^3dx` PUT `x^3=z`then`3x^2dx=DZ` or `x^2dx=(1/3)dz` intcoszcdot(1/3)dz `1/3sinz+C=(1/3)sinx^3+C` |
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| 27039. |
Evaluate the limit . underset(n to 00)("lim") [(1+(1)/(n^(2)))(1+(2^(2))/(n^(2)))………(1+(n^(2))/(n^(2)))]^(1/n) |
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| 27040. |
Differentiate the following w.r.t. x : e^(sin^(-1)x) |
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| 27041. |
The radius of the circle passing through the foci of the ellipse (x^2)/(16)+(y^2)/(9)=1 and having its centre at (0,3) is |
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Answer» 6 |
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| 27042. |
The solution set of the constraints x+2y le 2000, x+y le 1500, y le 600" and "x ge 0 does not include the point ………. |
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Answer» (1000, 0) |
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| 27043. |
Two equal parabolas have the same vertex and their axes are at right angles. Then the angle between the tangents to them at their point of intersection (other than vertex) is- |
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Answer» `(PI)/(4)` |
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| 27044. |
Define f(x)=(1)/(2)[|sinx|+sinx], 0 lt x le 2pi. Then , f is |
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Answer» INCREASING in `((pi)/(2),(3pi)/(2))` |
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| 27045. |
IFin Rand theequation -3(x-[x]) +a^2 =0( where[x]denotesthegreatest inetegerlex) hasnointegralsolution, thenall possiblevaluesof aliein theinterval |
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Answer» `(-2,1)` |
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| 27047. |
If""^(n)P_(r)=""^(n)P_((r+1))and""^(n)C_(r) = ""^(n)C_(r-1), then(n,r) = |
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Answer» (8,9) |
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| 27048. |
Let z_1,z_2 be the roots of the equation z^2+pz+q=0,p,q are complex numbers. Suppose A and B represent z_1 and z_2 in the complex plane . If angleAOB = alpha(ne0) and OA=OB (where O is the origin ) then p^2= |
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Answer» `4qcos(alpha/2)` |
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| 27049. |
Thetangent at an extremityof latus rectum of the hyperbolameets x axis and y axis A and B respectively then (OA)^(2)-(OB)^(2) where O is the origin is equal to |
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Answer» `-20/9` |
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| 27050. |
If |(a+a_(1)x,1+b_(1)x,1+c_(1)x),(1+a_(2)x,1+b_(2)x,1+c_(2)x),(1+a_(3)x,1+b_(3)x,1+c_(3)x)|=A_(0)+A_(1)x+A_(2)x^(2)+A_(3)x^(3), then the value of A_(1) is - |
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Answer» `a_(1)a_(2)a_(3)+b_(1)b_(2)b_(3)+c_(1)c_(2)c_(3)` |
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