28278 + Interview Questions in Maths in Class 12 Page 560 InterviewSolution

27951.	The normal ata point P on the parabola y^(2)=4axcuts the curve again at Q . If M is the midpoint of PQ then the product of the ordinates of P and M is
Answer» <html><body><p>`a^(<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a>)` <br/>`<a href="https://interviewquestions.tuteehub.com/tag/2a-300249" style="font-weight:bold;" target="_blank" title="Click to know more about 2A">2A</a>^(2)` <br/>`<a href="https://interviewquestions.tuteehub.com/tag/4a-318696" style="font-weight:bold;" target="_blank" title="Click to know more about 4A">4A</a>^(2)`<br/>`-4a^(2)`</p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :D</body></html>

Discussion

27952.	Let f be a continuous function satisfying f(x+y)=f(x)+f(y) for all x,y in R and f(1)=5 then lim_(x to 4) f(x) is equal to
Answer» <html><body><p>4<br/>80<br/>0<br/>none of these </p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :D</body></html>

Discussion

27953.	Prove that following i) 2.C_(0)+5.C_(1)+8.C_(2)+…..+(3n+2)C_(n)=(3n+4).2^(n-1)
Answer» <html><body><p>`(<a href="https://interviewquestions.tuteehub.com/tag/4-311707" style="font-weight:bold;" target="_blank" title="Click to know more about 4">4</a> -<a href="https://interviewquestions.tuteehub.com/tag/3n-310768" style="font-weight:bold;" target="_blank" title="Click to know more about 3N">3N</a>).<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a>^(2n-1)` <br/>`(4 - 3n).2^(n+1)` <br/>`(4 + 3n).2^(n-1)` <br/>`(2-3n).2^(n+1)` </p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :<a href="https://interviewquestions.tuteehub.com/tag/c-7168" style="font-weight:bold;" target="_blank" title="Click to know more about C">C</a></body></html>

Discussion

27954.	Pick out a function which is one - one but not onto
Answer» <html><body><p>Let `A={a,<a href="https://interviewquestions.tuteehub.com/tag/b-387190" style="font-weight:bold;" target="_blank" title="Click to know more about B">B</a>,<a href="https://interviewquestions.tuteehub.com/tag/c-7168" style="font-weight:bold;" target="_blank" title="Click to know more about C">C</a>},B={2,<a href="https://interviewquestions.tuteehub.com/tag/4-311707" style="font-weight:bold;" target="_blank" title="Click to know more about 4">4</a>}`. Define <br/> `f:<a href="https://interviewquestions.tuteehub.com/tag/atob-1987470" style="font-weight:bold;" target="_blank" title="Click to know more about ATOB">ATOB</a>" as "f(a)=4,f(b)=2,f(c)=2`. <br/>Let `A={a,b,c},B={2,4,6,8}`. Define <br/> `f:AtoB" as "f(a)=8,f(b)=2,f(c)=4`. <br/>Let `A={a,b,c},B=(2,4,6}`. Define <br/> `f:AtoB" as "f(a)=2,f(b)=4,f(c)=6` <br/>Let `A={a,b,c},B={2,4,6,8}`. Define `f:AtoB" as "f(a)=2,f(b)=2,f(c)=2`. </p>Answer :B</body></html>

Discussion

27955.	Let R = {(a,a^3) \| ais a prime number less than 10}.Find dom R^(-1).
Answer» <html><body><p></p>Solution :R = {(a,a^3)\| a is a prime number <a href="https://interviewquestions.tuteehub.com/tag/less-1071906" style="font-weight:bold;" target="_blank" title="Click to know more about LESS">LESS</a> than <a href="https://interviewquestions.tuteehub.com/tag/10-261113" style="font-weight:bold;" target="_blank" title="Click to know more about 10">10</a>. <a href="https://interviewquestions.tuteehub.com/tag/dom-11474" style="font-weight:bold;" target="_blank" title="Click to know more about DOM">DOM</a> R^(-<a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a>) = {8,27,125,343) <a href="https://interviewquestions.tuteehub.com/tag/rng-2240734" style="font-weight:bold;" target="_blank" title="Click to know more about RNG">RNG</a> R</body></html>

Discussion

27956.	Find the point at which the tangent to the curve y=sqrt(4x-3)-1 has its slope (2)/(3).
Answer» <html><body><p><br/></p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :(<a href="https://interviewquestions.tuteehub.com/tag/3-301577" style="font-weight:bold;" target="_blank" title="Click to know more about 3">3</a>, <a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a>)</body></html>

Discussion

27957.	At present, a firm is manufacturing 2000 items. It is estimated that the rate of change of production P w.r.t additional number of workers x is given by (dP)/(dx) = 100 - 12 sqrtx. If the firm employs 25 more workers, then the new level of production of items is
Answer» <html><body><p>3500<br/>4500<br/>2500<br/>300</p>Answer :A</body></html>

Discussion

27958.	Let p,q, r denote respectively the statements :" you are honest ", "you are laborious ","you will receive a promotion" Translate p^^q^^rstatements into English language.
Answer» <html><body><p></p><a href="https://interviewquestions.tuteehub.com/tag/solution-25781" style="font-weight:bold;" target="_blank" title="Click to know more about SOLUTION">SOLUTION</a> :You are <a href="https://interviewquestions.tuteehub.com/tag/honest-480284" style="font-weight:bold;" target="_blank" title="Click to know more about HONEST">HONEST</a> and <a href="https://interviewquestions.tuteehub.com/tag/laborious-2153283" style="font-weight:bold;" target="_blank" title="Click to know more about LABORIOUS">LABORIOUS</a> and you will <a href="https://interviewquestions.tuteehub.com/tag/receive-1179283" style="font-weight:bold;" target="_blank" title="Click to know more about RECEIVE">RECEIVE</a> a <a href="https://interviewquestions.tuteehub.com/tag/promotion-1169623" style="font-weight:bold;" target="_blank" title="Click to know more about PROMOTION">PROMOTION</a>.</body></html>

Discussion

27959.	I:(1)/(1!)+(1+2)/(2!)+(1+2+2^(2))/(3!)+....=e^(2)-e II:(2)/(2!)+(2+4)/(3!)+(2+4+6)/(4!)+....=e
Answer» <html><body><p>only I is <a href="https://interviewquestions.tuteehub.com/tag/true-713260" style="font-weight:bold;" target="_blank" title="Click to know more about TRUE">TRUE</a> <br/>only <a href="https://interviewquestions.tuteehub.com/tag/ii-1036832" style="font-weight:bold;" target="_blank" title="Click to know more about II">II</a> is true<br/>both I and II are true <br/><a href="https://interviewquestions.tuteehub.com/tag/neither-1113494" style="font-weight:bold;" target="_blank" title="Click to know more about NEITHER">NEITHER</a> I nor II true </p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :<a href="https://interviewquestions.tuteehub.com/tag/c-7168" style="font-weight:bold;" target="_blank" title="Click to know more about C">C</a></body></html>

Discussion

27960.	A die is thrown three times. Events A and B are defined as below: A : 4 on the third throw B : 6 on the first and 5 on the second throw Find the probability of A given that B has already occurred.
Answer» <html><body><p><br/></p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :`(<a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a>)/(<a href="https://interviewquestions.tuteehub.com/tag/6-327005" style="font-weight:bold;" target="_blank" title="Click to know more about 6">6</a>)`</body></html>

Discussion

27961.	consider the function f(x) =1+(1)/(x)^(x) The range of the function f(x) is
Answer» <html><body><p>`(0,poo)`<br/>`(-oo,<a href="https://interviewquestions.tuteehub.com/tag/e-444102" style="font-weight:bold;" target="_blank" title="Click to know more about E">E</a>)`<br/>`1,oo)`<br/>`(1,e)cup(e,oo)`</p>Solution :`f(x)=(1+(1)/(X))^(X)` <br/> f(x) is defined if`1+1/xgt0 or (x+1)/(x)gt0` <br/> or `(-oo,-1)cup(0,oo)` <br/> Now f(X)=`(1+(1)/(x))^(x)ln (1+(1)/(x))+(x)/(1+(1)/(x))(-1)/(x^(2))` <br/> `=(1+(1)/(x))^(x)ln(1+(1)/(x))-(1)/(x+1)` <br/> Now `(1+(1)/(x))^(x)` is always positive Hence the sign of f(X) <br/> Depends on the sign of ln `(1+(1)/(x))-(1)/(1+x)`<br/> Let `g(x)=In (1+(1)/(x))-(1)/(x+1)` <br/> `g(x)=(1)/(1+(1))(x)(-1)/(x^(2))+(1)/(x+1)^(2)=(-1)/(x(x+1)^(2)` <br/> (i)for `x in (0,oo)g(x)lt0` <br/> Thus g(X) is monotonically decreasing for x in `(0,oo)` <br/> or `g(X) gt underset(xrarroo)limg(x)` <br/> or `g(X)gt0, so f(X) gt0`<br/> (ii)for `x in (-oo,-1),g(x)gt0` <br/> Thus g(X) is monotonically <a href="https://interviewquestions.tuteehub.com/tag/increasing-1040633" style="font-weight:bold;" target="_blank" title="Click to know more about INCREASING">INCREASING</a> for `x in (-oo,-1)` <br/> or `g(X) gt underset(xrarroo)limg(X)gt0` <br/> `<a href="https://interviewquestions.tuteehub.com/tag/therefore-706901" style="font-weight:bold;" target="_blank" title="Click to know more about THEREFORE">THEREFORE</a> f(x)gt0` <br/> Hence <a href="https://interviewquestions.tuteehub.com/tag/form-996208" style="font-weight:bold;" target="_blank" title="Click to know more about FORM">FORM</a> (i) nd (ii) we get <br/> `f(X) gt0 <a href="https://interviewquestions.tuteehub.com/tag/forall-995230" style="font-weight:bold;" target="_blank" title="Click to know more about FORALL">FORALL</a> x in (-oo,-1)cup(0,oo)` <br/> Thus f(x) is montonically increasing in its domain Also <br/> `underset(xrarroo)lim(1+(1)/(x))^(x)`=e <br/> `underset(xrarr0)lim(1+(1)/(x))^(x)=1 and underset(xrarr-1)lim(1+(1)/(x))^(x)=oo` <br/> The graph of f(X) is shown in figure <br/> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/CEN_CAL_C06_E10_030_S01.png" width="80%"/> <br/> Range is `y in (1,oo)-{e}`</body></html>

Discussion

27962.	Differentiate the following with respect to x: cos^(-1) (e^(x))
Answer» <html><body><p><br/></p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :`(-<a href="https://interviewquestions.tuteehub.com/tag/e-444102" style="font-weight:bold;" target="_blank" title="Click to know more about E">E</a>^(<a href="https://interviewquestions.tuteehub.com/tag/x-746616" style="font-weight:bold;" target="_blank" title="Click to know more about X">X</a>))/(<a href="https://interviewquestions.tuteehub.com/tag/sqrt-1223129" style="font-weight:bold;" target="_blank" title="Click to know more about SQRT">SQRT</a>(1-e^(<a href="https://interviewquestions.tuteehub.com/tag/2x-301182" style="font-weight:bold;" target="_blank" title="Click to know more about 2X">2X</a>)))`</body></html>

Discussion

27963.	int_0^(pi//2)(sqrttanx+sqrtcotx)dx
Answer» <html><body><p></p><a href="https://interviewquestions.tuteehub.com/tag/solution-25781" style="font-weight:bold;" target="_blank" title="Click to know more about SOLUTION">SOLUTION</a> :`int_0^(pi/2)(sqrttanx+sqrtcotx)<a href="https://interviewquestions.tuteehub.com/tag/dx-960990" style="font-weight:bold;" target="_blank" title="Click to know more about DX">DX</a>` <br/> =`int_0^(pi/2)(sinx+cosx)/sqrt(sinxcosx)dx` <br/> =`sqrt2int_0^(pi/2)(sinx+cosx)/sqrt(1-(sinx-cosx)^2)dx` <br/> =`<a href="https://interviewquestions.tuteehub.com/tag/sqrt2-3056932" style="font-weight:bold;" target="_blank" title="Click to know more about SQRT2">SQRT2</a>[sin^-1(sinx-cosx)]_0^(pi/2)` <br/> =`sqrt2(sin^-1 1-sin^-1(-1))` <br/> =`sqrt2(pi/2+pi/2)=sqrt2pi`</body></html>

Discussion

27964.	Which of the following is not a requirement of binomial distribution?
Answer» <html><body><p>There are <a href="https://interviewquestions.tuteehub.com/tag/two-714195" style="font-weight:bold;" target="_blank" title="Click to know more about TWO">TWO</a> outcomes for each trial<br/>There are <a href="https://interviewquestions.tuteehub.com/tag/fixed-457597" style="font-weight:bold;" target="_blank" title="Click to know more about FIXED">FIXED</a> <a href="https://interviewquestions.tuteehub.com/tag/number-582134" style="font-weight:bold;" target="_blank" title="Click to know more about NUMBER">NUMBER</a> of trials<br/>The outcomes must be dependent on each other<br/>The <a href="https://interviewquestions.tuteehub.com/tag/probability-13327" style="font-weight:bold;" target="_blank" title="Click to know more about PROBABILITY">PROBABILITY</a> of success must be same for all trials</p>Answer :C</body></html>

Discussion

27965.	If int(2e^(5x)+e^(4x)-4e^(3x)+2e^(x))/((e^(2x)+4)(e^(2x)-1)^(2))dx=tan^(-1)(e^(x//2))-(K)/((e^(2x-1)))+C then K is equalto
Answer» <html><body><p><br/></p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :0.5</body></html>

Discussion

27966.	int_(-1)^(1) (17x^(5)-x^(4)+29 x^(3) -31 x +1)/(x^(2)+1)dx=
Answer» <html><body><p>`4/5`<br/>`5/4`<br/>`4/3`<br/>`3/4`</p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :<a href="https://interviewquestions.tuteehub.com/tag/c-7168" style="font-weight:bold;" target="_blank" title="Click to know more about C">C</a></body></html>

Discussion

27967.	If a_1,a_2,a_3….a_r are in G.P then show that \|{:(a_(r+1),a_(r+5),a_(r+9)),(a_(r+7),a_(r+11),a_(r+15)),(a_(r+11),a_(r+7),a_(r+21)):}\| is independent of r
Answer» <html><body><p><br/></p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :<a href="https://interviewquestions.tuteehub.com/tag/r-611811" style="font-weight:bold;" target="_blank" title="Click to know more about R">R</a></body></html>

Discussion

27968.	Probability distribution of random variable X is as follows: WhereC gt 0 Find (i) C (ii) P(X lt 2) (iii) P(1 lt X le 2).
Answer» <html><body><p><br/></p>Answer :`(i) (1)/(<a href="https://interviewquestions.tuteehub.com/tag/3-301577" style="font-weight:bold;" target="_blank" title="Click to know more about 3">3</a>) (<a href="https://interviewquestions.tuteehub.com/tag/ii-1036832" style="font-weight:bold;" target="_blank" title="Click to know more about II">II</a>)(1)/(3) (<a href="https://interviewquestions.tuteehub.com/tag/iii-497983" style="font-weight:bold;" target="_blank" title="Click to know more about III">III</a>)(<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a>)/(3)`</body></html>

Discussion

27969.
Answer» <html><body><p><br/></p><a href="https://interviewquestions.tuteehub.com/tag/solution-25781" style="font-weight:bold;" target="_blank" title="Click to know more about SOLUTION">SOLUTION</a> :N//A</body></html>

Discussion

27970.	Draw the graph of y = tan^(2) x.
Answer» <html><body><p></p>Solution :We have `y = f(x) = tan^(2) x` <br/> Period of the function is `pi`. <br/> Function is <a href="https://interviewquestions.tuteehub.com/tag/even-976335" style="font-weight:bold;" target="_blank" title="Click to know more about EVEN">EVEN</a>, so the graph is symmetrical above the x - axis. <br/> Let us <a href="https://interviewquestions.tuteehub.com/tag/draw-959456" style="font-weight:bold;" target="_blank" title="Click to know more about DRAW">DRAW</a> the graph for `0 lt x lt pi//2`. <br/> For `0 lt x lt pi//4, 0 lt tan x lt 1` <br/> `therefore` `tan^(2) x lt tan x` <br/> For `x gt pi//4` <br/> `tan x gt 1` <br/> `therefore` `tan^(2) x gt tan x` <br/> Hence the graph of `y = tan^(2) x` lies below and above the graph of y = tan x for `x in (0, pi//4)` and `x in (pi//4, pi//2)`. <br/> So the graph of the function for `x in (-pi//2, pi//2)` is as <a href="https://interviewquestions.tuteehub.com/tag/shown-1206565" style="font-weight:bold;" target="_blank" title="Click to know more about SHOWN">SHOWN</a> in the <a href="https://interviewquestions.tuteehub.com/tag/following-463335" style="font-weight:bold;" target="_blank" title="Click to know more about FOLLOWING">FOLLOWING</a> figure. <br/> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/CEN_GRA_C03_E01_005_S01.png" width="80%"/> <br/> Since the function has period `pi` , the graph of the function is as shown in the following figure. <br/> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/CEN_GRA_C03_E01_005_S02.png" width="80%"/></body></html>

Discussion

27971.	int (x^2)/((2 + 3x^3)^(3))dx
Answer» <html><body><p><br/></p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :`-1/(18(2+3x^(<a href="https://interviewquestions.tuteehub.com/tag/3-301577" style="font-weight:bold;" target="_blank" title="Click to know more about 3">3</a>))^(2))+<a href="https://interviewquestions.tuteehub.com/tag/c-7168" style="font-weight:bold;" target="_blank" title="Click to know more about C">C</a>`</body></html>

Discussion

27972.	If a variable takes the values 0, 1, 2,…,n with frequencies proporiotnal to binomial coefficient n_(C_(0)), n_(C_(1)), n_(C_(2)),….n_(C_(n)), then mean of distribution is
Answer» <html><body><p>`(<a href="https://interviewquestions.tuteehub.com/tag/n-568463" style="font-weight:bold;" target="_blank" title="Click to know more about N">N</a>^(<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a>) - <a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a>)/(<a href="https://interviewquestions.tuteehub.com/tag/12-269062" style="font-weight:bold;" target="_blank" title="Click to know more about 12">12</a>)`<br/>`(n)/(2)`<br/>`(n)/(4)`<br/>`(n)/(3)`</p>Answer :C</body></html>

Discussion

27973.	Mean of the following probability distribution is …………
Answer» <html><body><p>`(7)/(8)`<br/>`(<a href="https://interviewquestions.tuteehub.com/tag/19-280618" style="font-weight:bold;" target="_blank" title="Click to know more about 19">19</a>)/(8)`<br/>1<br/>`(<a href="https://interviewquestions.tuteehub.com/tag/51-324358" style="font-weight:bold;" target="_blank" title="Click to know more about 51">51</a>)/(8)`</p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :B</body></html>

Discussion

27974.	If X is a poisson variate such that P(X = 2) = 9P(X = 4) + 90P(X = 6) then find mean of X.
Answer» <html><body><p><br/></p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :<a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a></body></html>

Discussion

27975.	The period T and length l are increasing at the same rate is T = 2pi sqrt(l//g). Then the length l in terms of pi and g is
Answer» <html><body><p>`<a href="https://interviewquestions.tuteehub.com/tag/pi-600185" style="font-weight:bold;" target="_blank" title="Click to know more about PI">PI</a>//<a href="https://interviewquestions.tuteehub.com/tag/g-1003017" style="font-weight:bold;" target="_blank" title="Click to know more about G">G</a>`<br/>`pi g`<br/>`<a href="https://interviewquestions.tuteehub.com/tag/pig-1154561" style="font-weight:bold;" target="_blank" title="Click to know more about PIG">PIG</a>^(<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a>)`<br/>`pi^(2) // g`</p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :D</body></html>

Discussion

27976.	If vec(a), vec(b), vec(c) are the position vectors of vertices A, B, C of a triangle ABC, Show that the area of the triangle is (1)/(2) \|vec(b) xx vec(c) + vec(c) xx vec(a) + vec(a) xx vec(b)\|
Answer» <html><body><p><br/></p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :`- <a href="https://interviewquestions.tuteehub.com/tag/hat-1016178" style="font-weight:bold;" target="_blank" title="Click to know more about HAT">HAT</a>(i)`</body></html>

Discussion

27977.	Find the points on the curve x^(2)+y^(2)-2x-3=0 at which the tangents are parallel to the X-axis.
Answer» <html><body><p>`(0, pm <a href="https://interviewquestions.tuteehub.com/tag/sqrt-1223129" style="font-weight:bold;" target="_blank" title="Click to know more about SQRT">SQRT</a>(<a href="https://interviewquestions.tuteehub.com/tag/3-301577" style="font-weight:bold;" target="_blank" title="Click to know more about 3">3</a>))` <br/>`(<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a>, pm sqrt(3))` <br/>`(<a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a>,2), (1,-2)` <br/>(3, 0) </p>Answer :<a href="https://interviewquestions.tuteehub.com/tag/c-7168" style="font-weight:bold;" target="_blank" title="Click to know more about C">C</a></body></html>

Discussion

27978.	Each of the following defines a relation of N : x+y = 10 , x , y in N Determine which of the above relations are reflexive , symmetric and transitive .
Answer» <html><body><p><br/></p><a href="https://interviewquestions.tuteehub.com/tag/solution-25781" style="font-weight:bold;" target="_blank" title="Click to know more about SOLUTION">SOLUTION</a> :N/A</body></html>

Discussion

27979.	In howmanywayscan 52cardsbe dividedamong4playersso thateach mayhave 13is
Answer» <html><body><p>`(52!)/(<a href="https://interviewquestions.tuteehub.com/tag/13-271882" style="font-weight:bold;" target="_blank" title="Click to know more about 13">13</a>!^(<a href="https://interviewquestions.tuteehub.com/tag/4-311707" style="font-weight:bold;" target="_blank" title="Click to know more about 4">4</a>))`<br/>`(52!)/((13!^(4))4!)`<br/>`(52!)/((13!)^(<a href="https://interviewquestions.tuteehub.com/tag/5-319454" style="font-weight:bold;" target="_blank" title="Click to know more about 5">5</a>))`<br/>`""^(52)P_(13)`</p>Answer :A</body></html>

Discussion

27980.	If a=hat(i)-2hat(j)+hat(k), b=hat(i)+3hat(j)-2hat(k), c=2hat(i)+hat(j)-hat(k) " and "d=hat(i)+hat(j)+hat(k), then the volume (in cubic units) of the tetrahedron having (a times b) times c, b, d as its coterminuous edges is
Answer» <html><body><p>`15/2`<br/><a href="https://interviewquestions.tuteehub.com/tag/90-341351" style="font-weight:bold;" target="_blank" title="Click to know more about 90">90</a><br/>`21/2`<br/>`66/5`</p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :<a href="https://interviewquestions.tuteehub.com/tag/c-7168" style="font-weight:bold;" target="_blank" title="Click to know more about C">C</a></body></html>

Discussion

27981.	cos (alpha + beta + gamma ) + cos (alpha - beta - gamma) + cos ( beta - gamma- alpha ) + cos ( gamma - alpha - beta )=
Answer» <html><body><p>`2cos <a href="https://interviewquestions.tuteehub.com/tag/alpha-858274" style="font-weight:bold;" target="_blank" title="Click to know more about ALPHA">ALPHA</a> cos beta cos <a href="https://interviewquestions.tuteehub.com/tag/gamma-470142" style="font-weight:bold;" target="_blank" title="Click to know more about GAMMA">GAMMA</a>`<br/>`<a href="https://interviewquestions.tuteehub.com/tag/3-301577" style="font-weight:bold;" target="_blank" title="Click to know more about 3">3</a> cos alpha cos beta cos gamma`<br/>`4 cos alpha cos beta cos gamma`<br/>`6 cos alpha cos beta cos gamma`</p>Answer :<a href="https://interviewquestions.tuteehub.com/tag/c-7168" style="font-weight:bold;" target="_blank" title="Click to know more about C">C</a></body></html>

Discussion

27982.	A, B, C are the centres of three circles of equal radii which donot touch extranally pairwise whose centers are non-collinear. The radical centre of the circles for triangle ABC is
Answer» <html><body><p>circumcentre<br/>centroid<br/>orthocentre<br/>incentre</p>Answer :A</body></html>

Discussion

27983.	Derivative of sin x^(2) w.r.t. x^2 is
Answer» <html><body><p>`<a href="https://interviewquestions.tuteehub.com/tag/x-746616" style="font-weight:bold;" target="_blank" title="Click to know more about X">X</a>^(<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a>)`<br/>`cos x^2`<br/>`2 <a href="https://interviewquestions.tuteehub.com/tag/sin-1208945" style="font-weight:bold;" target="_blank" title="Click to know more about SIN">SIN</a> x`<br/>`sin x`</p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :B</body></html>

Discussion

27984.	find the order and degree of the differential equation:
Answer» <html><body><p><br/></p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :order=3, degree=2</body></html>

Discussion

27985.	Integrate the following : int(sqrtx+2)^2/x^4dx
Answer» <html><body><p></p><a href="https://interviewquestions.tuteehub.com/tag/solution-25781" style="font-weight:bold;" target="_blank" title="Click to know more about SOLUTION">SOLUTION</a> :`<a href="https://interviewquestions.tuteehub.com/tag/int-11513" style="font-weight:bold;" target="_blank" title="Click to know more about INT">INT</a>(sqrtx+<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a>)^2/(x^4)<a href="https://interviewquestions.tuteehub.com/tag/dx-960990" style="font-weight:bold;" target="_blank" title="Click to know more about DX">DX</a>`<br/> =`int(x+4+2xx(2sqrtx))/(x^4)dx`<br/> =`int(x^-3+4x^-4+4x^(-7/2))dx`<br/> =`x^-2/-2+4(x^-3)/-3+4x^(-5/2)/(-5/2)+<a href="https://interviewquestions.tuteehub.com/tag/c-7168" style="font-weight:bold;" target="_blank" title="Click to know more about C">C</a>`<br/> =`-1/2xx1/(x^2)-4/3xx1/(x^3)-8/5xx1/x^(5/2)+C`</body></html>

Discussion

27986.	Obtain the following integrals : int(2x-1)/(2x+3)dx
Answer» <html><body><p><br/></p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :`:.I=x-log\|(2x+3)^(<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a>)\|+<a href="https://interviewquestions.tuteehub.com/tag/c-7168" style="font-weight:bold;" target="_blank" title="Click to know more about C">C</a>`</body></html>

Discussion

27987.	Discuss the continuity of the function f, where f is defined by f(x)={{:(3," if "0 le xle 1),(4," if "1 lt x lt 3),(5," if "3 le x le 10):}.
Answer» <html><body><p><br/></p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :<a href="https://interviewquestions.tuteehub.com/tag/f-455800" style="font-weight:bold;" target="_blank" title="Click to know more about F">F</a> is not <a href="https://interviewquestions.tuteehub.com/tag/continuous-932035" style="font-weight:bold;" target="_blank" title="Click to know more about CONTINUOUS">CONTINUOUS</a> at x=1 and x=3.</body></html>

Discussion

27988.	If the vectors a=hat(i)+a hat(j)+a^(2) hat(k), b=hat(i)+b hat(j)+b^(2) hat(k) and c=hat(i)+chat(j)+c^(2) hat(k) are three non-coplanar vectors and \|(a,a^(2),1+a^(3)),(b,b^(2),1+b^(3)),(c,c^(2),1+c^(3))\|=0, then the value of abc is
Answer» <html><body><p>0<br/>1<br/>2<br/>`-1`</p>Solution :Since, a, <a href="https://interviewquestions.tuteehub.com/tag/b-387190" style="font-weight:bold;" target="_blank" title="Click to know more about B">B</a> and <a href="https://interviewquestions.tuteehub.com/tag/c-7168" style="font-weight:bold;" target="_blank" title="Click to know more about C">C</a> are non-coplanar vectoprs <a href="https://interviewquestions.tuteehub.com/tag/therefore-706901" style="font-weight:bold;" target="_blank" title="Click to know more about THEREFORE">THEREFORE</a> `[abc]<a href="https://interviewquestions.tuteehub.com/tag/ne0-2855274" style="font-weight:bold;" target="_blank" title="Click to know more about NE0">NE0</a>`<br/> `<a href="https://interviewquestions.tuteehub.com/tag/rarr-1175461" style="font-weight:bold;" target="_blank" title="Click to know more about RARR">RARR</a>""Delta=\|{:(1,a,a^2),(1,b,b^2),(1,c,c^2):}\|ne0rArrDeltane0` <br/> `"Now,"\|{:(1,a^2,1+a^3),(1,b,1+b^3),(1,c^2,1+c^3):}\|=0`<br/> `rArr""\|{:(1,a^2,1),(1,b,1),(1,c^2,1):}\|+\|{:(a,a^2,a^3),(b,b^2, b^3),(c,c^2,c^3):}\|=0` <br/> `rArr""Delta(1+abc)=0rArr""abc=-1[because Delta=ne]`</body></html>

Discussion

27989.	If ax ^2 + 2bx+ c=0 , a_1x^2+ 2b _1x +c_1=0havea commonroot, thenthe rootsof theequation( b^2 -ac )x^2+(2b b_1 - a a_1 - a_1 c ) x+ (b_1^2-a_1 c_1 ) =0 are
Answer» <html><body><p><a href="https://interviewquestions.tuteehub.com/tag/different-951434" style="font-weight:bold;" target="_blank" title="Click to know more about DIFFERENT">DIFFERENT</a> <br/><a href="https://interviewquestions.tuteehub.com/tag/equal-446400" style="font-weight:bold;" target="_blank" title="Click to know more about EQUAL">EQUAL</a> <br/><a href="https://interviewquestions.tuteehub.com/tag/zero-751093" style="font-weight:bold;" target="_blank" title="Click to know more about ZERO">ZERO</a> <br/> none</p>Answer :<a href="https://interviewquestions.tuteehub.com/tag/b-387190" style="font-weight:bold;" target="_blank" title="Click to know more about B">B</a></body></html>

Discussion

27990.	You say the code word, and the door opens. You walk in, and look around the empty room. It is a dead end, but you see a poem on the wall. It reads: As you dance each _______around, through once, once only, Me, when you shallhave found, do not hide your glee ! One of you notices that the code word fits in the blank of the poem. As you think about the poem, you see an arrow which directs your eyes downward. To your amazement, you find the whole floor filled with letters and symbols! You realize that you need to use the poem to find a solution to the puzzle under them. The floor looked like this: Rearrange the clues from the puzzle above, using the poem, to find a question and then answer it to get out of the cave. What is the answer which can take you out of the cave?
Answer» <html><body><p>7<br/>70<br/>18<br/>81<br/></p>Solution :D <br/> After decoding the poem, you <a href="https://interviewquestions.tuteehub.com/tag/realize-1178972" style="font-weight:bold;" target="_blank" title="Click to know more about REALIZE">REALIZE</a> that you must go around ‘H’ in the <a href="https://interviewquestions.tuteehub.com/tag/matrix-18320" style="font-weight:bold;" target="_blank" title="Click to know more about MATRIX">MATRIX</a> in the direction <a href="https://interviewquestions.tuteehub.com/tag/given-473447" style="font-weight:bold;" target="_blank" title="Click to know more about GIVEN">GIVEN</a> by arrow and note down the word formed. On <a href="https://interviewquestions.tuteehub.com/tag/finding-989059" style="font-weight:bold;" target="_blank" title="Click to know more about FINDING">FINDING</a> out all such words and combining the you will <a href="https://interviewquestions.tuteehub.com/tag/get-11812" style="font-weight:bold;" target="_blank" title="Click to know more about GET">GET</a> the following question <br/> squre/of/largest/one/digit/number/ <br/> So, theanswer is `=9^(2) =81 `</body></html>

Discussion

27991.	Find the value of the integral underset(0)overset(2)int x^(3//2)sqrt(2-x) dx
Answer» <html><body><p><br/></p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :`(<a href="https://interviewquestions.tuteehub.com/tag/pi-600185" style="font-weight:bold;" target="_blank" title="Click to know more about PI">PI</a>)/(<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a>)`</body></html>

Discussion

27992.	Match the following {:(,"Column-I",,"Column-II",),((A),"If A and B are otthogonal, then AB is",(p),"Zero matrix",),((B),"If A and B are nilpotent matrices of order r and s and A and B commute, then "(AB)^(r)"is",(q),"Nilpotent matrix",),((C),"If A is a hermitian matrix such that "A^(2)=0", then A is ",(r),"Unitary matrix",),((D),"If A and B are unitary matrices, then AB is",(s),"Orthogonal",):}
Answer» <html><body><p><<a href="https://interviewquestions.tuteehub.com/tag/p-588962" style="font-weight:bold;" target="_blank" title="Click to know more about P">P</a>><br/></p>Answer :A(s), <a href="https://interviewquestions.tuteehub.com/tag/b-387190" style="font-weight:bold;" target="_blank" title="Click to know more about B">B</a>(p,q), C(p,q),D(<a href="https://interviewquestions.tuteehub.com/tag/r-611811" style="font-weight:bold;" target="_blank" title="Click to know more about R">R</a> )</body></html>

Discussion

27993.	Given two independent events A and B such that P(A)=0.3,P(B)=0.6. find P(neither A nor B)
Answer» <html><body><p><<a href="https://interviewquestions.tuteehub.com/tag/p-588962" style="font-weight:bold;" target="_blank" title="Click to know more about P">P</a>></p><a href="https://interviewquestions.tuteehub.com/tag/solution-25781" style="font-weight:bold;" target="_blank" title="Click to know more about SOLUTION">SOLUTION</a> :<a href="https://interviewquestions.tuteehub.com/tag/given-473447" style="font-weight:bold;" target="_blank" title="Click to know more about GIVEN">GIVEN</a> that P (A) = 0.3 and P(<a href="https://interviewquestions.tuteehub.com/tag/b-387190" style="font-weight:bold;" target="_blank" title="Click to know more about B">B</a>) = 0.6therefore `P(A^c)`= 1-P(A) = 1-0.3=0.7<br/> `P(B^c)` = 1-P(B) = 1-0.6=0.4<br a="" b="" nor="" p=""/> =`P(A^cnnB^c)=P(A^c) P(B^c)`<br/> =`0.7xx0.4`=0.28</body></html>

Discussion

27994.	{:("Column A","x is a two digit number. The digits of the number differ by 6, and the squares of the digits differ by 60" ,"Column B"),(x , ,60):}
Answer» <html><body><p>If <a href="https://interviewquestions.tuteehub.com/tag/column-922494" style="font-weight:bold;" target="_blank" title="Click to know more about COLUMN">COLUMN</a> A is larger<br/>If column B is larger <br/>If the <a href="https://interviewquestions.tuteehub.com/tag/columns-922590" style="font-weight:bold;" target="_blank" title="Click to know more about COLUMNS">COLUMNS</a> are equal <br/>If there is not <a href="https://interviewquestions.tuteehub.com/tag/enough-446095" style="font-weight:bold;" target="_blank" title="Click to know more about ENOUGH">ENOUGH</a> information to decide</p>Answer :D</body></html>

Discussion

27995.	Evalute the following integrals int (2x^(3))/(1 + x^(8)) dx
Answer» <html><body><p><br/></p>Answer :`(<a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a>)/(<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a>)<a href="https://interviewquestions.tuteehub.com/tag/tan-1238781" style="font-weight:bold;" target="_blank" title="Click to know more about TAN">TAN</a>^(-1)(<a href="https://interviewquestions.tuteehub.com/tag/x-746616" style="font-weight:bold;" target="_blank" title="Click to know more about X">X</a>^(4))+C`</body></html>

Discussion

27996.	i Reduce the equation 3x + 4y - 12 = 0 into intercept form. ii. Find the distance of the above line from the origin. iii. Find the distance of the above line from the line 6x + 8y- 18 = 0.
Answer» <html><body><p><br/></p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :i. `(<a href="https://interviewquestions.tuteehub.com/tag/x-746616" style="font-weight:bold;" target="_blank" title="Click to know more about X">X</a>)/(4)+(y)/(3)=1`, ii. `(<a href="https://interviewquestions.tuteehub.com/tag/12-269062" style="font-weight:bold;" target="_blank" title="Click to know more about 12">12</a>)/(5)`, iii. `(3)/(5)`</body></html>

Discussion

27997.	If sinA+sinB=l and cosA-cosA-cosB=m, then cos(A-B)=
Answer» <html><body><p>`(<a href="https://interviewquestions.tuteehub.com/tag/l-535906" style="font-weight:bold;" target="_blank" title="Click to know more about L">L</a>^(<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a>)-m^(2))/(l^(2)+m^(2))`<br/>`(l^(2)+m^(2))/(l^(2)-m^(2))`<br/>`(<a href="https://interviewquestions.tuteehub.com/tag/2lm-1837669" style="font-weight:bold;" target="_blank" title="Click to know more about 2LM">2LM</a>)/(l^(2)+m^(2))`<br/>`(2lm)/(l^(2)-m^(2))`</p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :A</body></html>

Discussion

27998.	Let f(x)= int_(x)^(x+(pi)/(3))\|sin theta\|d theta(x in [0,pi])
Answer» <html><body><p>`f(x)` is stricity increasing inthis interval <br/>`f(x)` is <a href="https://interviewquestions.tuteehub.com/tag/differentiable-7726202" style="font-weight:bold;" target="_blank" title="Click to know more about DIFFERENTIABLE">DIFFERENTIABLE</a> in this interval<br/>Range of `f(x)` is `[2-sqrt(3)-<a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a>]`<br/>`f(x)` has a maxima at `x = pi/3`</p><a href="https://interviewquestions.tuteehub.com/tag/solution-25781" style="font-weight:bold;" target="_blank" title="Click to know more about SOLUTION">SOLUTION</a> :N//A</body></html>

Discussion

27999.	Findthe valueofsin^(-1)( sin "" (5pi)/(9 )cos "" (pi)/(9) + cos""(5 pi )/(9)sin""(pi) /(9))
Answer» <html><body><p><br/></p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :`(<a href="https://interviewquestions.tuteehub.com/tag/pi-600185" style="font-weight:bold;" target="_blank" title="Click to know more about PI">PI</a>)/(<a href="https://interviewquestions.tuteehub.com/tag/3-301577" style="font-weight:bold;" target="_blank" title="Click to know more about 3">3</a>)`</body></html>

Discussion

28000.	If (1!)^(2) + (2!)^(2) + (3!)^(2) + "…….." + (99!)^(2) is divided by 100, the remainder is
Answer» <html><body><p>27<br/>28<br/>17<br/>14</p>Answer :<a href="https://interviewquestions.tuteehub.com/tag/c-7168" style="font-weight:bold;" target="_blank" title="Click to know more about C">C</a></body></html>

Discussion

Explore topic-wise InterviewSolutions in Class 12.

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If a_1,a_2,a_3….a_r are in G.P then show that |{:(a_(r+1),a_(r+5),a_(r+9)),(a_(r+7),a_(r+11),a_(r+15)),(a_(r+11),a_(r+7),a_(r+21)):}| is independent of r

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In howmanywayscan 52cardsbe dividedamong4playersso thateach mayhave 13is

If a=hat(i)-2hat(j)+hat(k), b=hat(i)+3hat(j)-2hat(k), c=2hat(i)+hat(j)-hat(k) " and "d=hat(i)+hat(j)+hat(k), then the volume (in cubic units) of the tetrahedron having (a times b) times c, b, d as its coterminuous edges is

cos (alpha + beta + gamma ) + cos (alpha - beta - gamma) + cos ( beta - gamma- alpha ) + cos ( gamma - alpha - beta )=

A, B, C are the centres of three circles of equal radii which donot touch extranally pairwise whose centers are non-collinear. The radical centre of the circles for triangle ABC is

Derivative of sin x^(2) w.r.t. x^2 is

find the order and degree of the differential equation:

Integrate the following : int(sqrtx+2)^2/x^4dx

Obtain the following integrals : int(2x-1)/(2x+3)dx

Discuss the continuity of the function f, where f is defined by f(x)={{:(3," if "0 le xle 1),(4," if "1 lt x lt 3),(5," if "3 le x le 10):}.

If the vectors a=hat(i)+a hat(j)+a^(2) hat(k), b=hat(i)+b hat(j)+b^(2) hat(k) and c=hat(i)+chat(j)+c^(2) hat(k) are three non-coplanar vectors and |(a,a^(2),1+a^(3)),(b,b^(2),1+b^(3)),(c,c^(2),1+c^(3))|=0, then the value of abc is

If ax ^2 + 2bx+ c=0 , a_1x^2+ 2b _1x +c_1=0havea commonroot, thenthe rootsof theequation( b^2 -ac )x^2+(2b b_1 - a a_1 - a_1 c ) x+ (b_1^2-a_1 c_1 ) =0 are

Find the value of the integral underset(0)overset(2)int x^(3//2)sqrt(2-x) dx

Given two independent events A and B such that P(A)=0.3,P(B)=0.6. find P(neither A nor B)

{:("Column A","x is a two digit number. The digits of the number differ by 6, and the squares of the digits differ by 60" ,"Column B"),(x , ,60):}

Evalute the following integrals int (2x^(3))/(1 + x^(8)) dx

i Reduce the equation 3x + 4y - 12 = 0 into intercept form.﻿ ii. Find the distance of the above line from the origin.﻿ iii. Find the distance of the above line from the line 6x + 8y- 18 = 0.

If sinA+sinB=l and cosA-cosA-cosB=m, then cos(A-B)=

Let f(x)= int_(x)^(x+(pi)/(3))|sin theta|d theta(x in [0,pi])

Findthe valueofsin^(-1)( sin "" (5pi)/(9 )cos "" (pi)/(9) + cos""(5 pi )/(9)sin""(pi) /(9))

If (1!)^(2) + (2!)^(2) + (3!)^(2) + "…….." + (99!)^(2) is divided by 100, the remainder is

A die is thrown three times. Events A and B are defined as below: A : 4 on the third throw B : 6 on the first and 5 on the second throw Find the probability of A given that B has already occurred.

i Reduce the equation 3x + 4y - 12 = 0 into intercept form. ii. Find the distance of the above line from the origin. iii. Find the distance of the above line from the line 6x + 8y- 18 = 0.