InterviewSolution
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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.
| 11101. |
x sin^(-1) x |
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Answer» SOLUTION :`" Let " I = INT " x sin"^(-1)x dx "` lt brgt ` I=sin^(-1)x intx dx- int [(d)/(dx) (sin^(-1) x) intxdx ] dx` ` =sin^(-1) x. (x^(2))/(2)- int ((1)/(sqrt(1-x^(2))).(x^(2))/(2))dx` `=(x^(2))/(2).sin^(-1) x+ int ((1-1-x^(2))/(sqrt(1-x^(2))).(1)/(2))dx` `=(x^(2))/(2).sin^(-1) x-(1)/(2) int (1)/(sqrt(1-x^(2)))dx` `+(1)/(2) int (1-x^(2))/(sqrt(1-x^(2)))dx` ` =(x^(2))/(2).sin^(-1) x-(1)/(2) sin^(-1) x+(1)/(2) int sqrt(1-x^(2))dx` ` RARR I=(x^(2))/(2).sin^(-1) x-(1)/(2) sin^(-1) x` ` +(1)/(2) ((1)/(2) xsqrt(1-x^(2))+(1)/(2) sin^(-1) x)+C` ` rArr I = sin^(-1) x ((x^(2))/(2)-(1)/(4))+(1)/(4) xsqrt(1-x^(2))+C` `rArr I=(sin^(-1))/(4) (2x^(2) -1)+(1)/(4) x sqrt(1-x^(2))+C` |
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| 11102. |
Which of the following differential equations has y=x as one of its particular solution |
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Answer» `(d^(2)y)/(DX^(2))- x^(2)(DY)/(dx) + xy = x` |
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| 11103. |
Compute the integralI = int_(0)^(x) x sin^(m)x dx(m is naturalnumber) |
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| 11105. |
Show that the locus of the point of intersection of the stright lines x sin theta -y(cos theta-1) = a sin theta and x sin theta-y(cos theta+1)+ a sin theta =0 is a circle, find the equation of the circle. |
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| 11106. |
Ify=cos^-1((2x)/(1+x^2)),-1ltxlt1, Find (dy)/(dx) |
| Answer» SOLUTION :`y=cos^-1((2X)/(1+x^2))=pi/2-sin^-1((2x)/(1+x^2))=pi/2-2tan^-1xtherefore(DY)/(DX)=0-2/(1+x^2)=(-2)/(1+x^2)cos^-1x=pi/2-sin^-1x` | |
| 11107. |
The sum of the Y and Z intercepts made by the plane 3x + 4y -6z = 12 is .................. |
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Answer» 10 |
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| 11108. |
{:(" "Lt),(n rarr oo):} (2^(k)+4^(k)+6^(k)+....+(2n)^(k))/(n^(k+1))= |
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| 11109. |
The magnetic ............. |
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Answer» `:.` RELATIVE permeability `mu_(r)=mu/mu_(0)=B/(mu_(0) H)=10/(4pi xx10^(-7) xx250)=10^(5)/pi` |
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| 11111. |
If |veca + vecb| = |veca - vecb| then the vectors veca and vecb are adjacent sides of |
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Answer» a rectangle |
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| 11112. |
If P(n)be the statementn(n +1)+1isodd, thenwhichof thefollowingis even? |
| Answer» Answer :D | |
| 11113. |
Locus of P such that the chord of contact of P with respect to y^2= 4ax touches the hyperbola x^(2)-y^(2) = a^(2) as |
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Answer» `x^(2)+4y^(2)=4A^(2)` |
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| 11115. |
If int tan^(7)x dx = f(x) + log |cos x | +c then f(x) = |
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Answer» `(1)/(6) TAN^(6) X + (1)/(4) tan^(4)x + (1)/(2) tan^(2) x ` |
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| 11116. |
{:(" "Lt),(n rarr oo):} ((sqrt(1)+2sqrt(2)+3sqrt(3)+......+nsqrt(n))/(n^(5//2)))= |
| Answer» ANSWER :D | |
| 11117. |
Let y = f(x) be a differentiable curve satisfyingint_(2)^(x)f(t)dt=(x^(2))/(2)+int_(x)^(2)t^(2)f(t)dt, then int_(-pi//4)^(pi//4)(f(x)+x^(9)-x^(3)+x+1)/(cos^(2)x)dx equals : |
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Answer» 0 |
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| 11118. |
Fromthetopof a towerthe angleofdepressionof a pointon thegroundis 60^@if thedistanceof thispointto toweris (1)/( sqrt(3) +1) metres, thentheheightof thetower is |
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Answer» ` (4sqrt(3))/(2)` metres |
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| 11119. |
Find the value of k if the points (1,3) and (2,k) are coujuate with respect to the circlex^(2) + y^(2) = 35. |
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| 11120. |
Find the vertex and focusof x^(2)-6x-6y+6=0 |
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| 11122. |
Prove that the height of the cylinder of maximum volume, that can be inscribed in a sphere of radius R is (2R)/(3) . Also find the maximum volume . |
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| 11123. |
A variable chord ................ |
Answer»  `t_(1)t_(2)=-4` `h=(t_(1)^(2)+t_(2)^(2))/3, k=(2t_(1)+2t_(2))/3` `3H=(t_(1)+t_(2))^(2)+8` `3h=(9k^(2))/4 +8 IMPLIES y^(2)=1/9 (12x-32)` `implies y^(2) =4/3 (x-8/3)` |
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| 11124. |
If a gt 0 and a ne 1, 2 log_(x)a +log_(ax)a +3 log_(a^(2)x) a = 0, then x = |
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Answer» `a^(1//2)` |
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| 11125. |
If |z^(2) - 1| = |z|^(2)+ 1 , then z lies on |
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Answer» the real AXIS |
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| 11126. |
If bar(a)=(3,1,-2) and bar(b)=(1,3,-2) then (bar(a)" "^(hat)bar(b)) = ………… |
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Answer» `cos^(-1)""(2sqrt(6))/(7)` |
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| 11127. |
If ""^(12)C_(r+1)=""^(12)C_(3r-5), find r. |
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| 11128. |
If overline(a), overline(b), overline(c) are unit vectors such that overline(a)*overline(b)=(1)/(2), overline(b)*overline(c)=(1)/(sqrt(2) and overline(c)*overline(a)=(sqrt(3))/(2), then overline(a)*(overline(b)timesoverline(c))= |
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Answer» `(SQRT(sqrt(6)-2))/(2)` |
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| 11129. |
If a set A has n elements then number of relations defined on A is |
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Answer» `2^((N^(2)))` |
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| 11130. |
Two squares are choosen at random on a chess board. Show that the probability that they have a side in common is (1)/(18). |
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| 11131. |
{x in R : [x-|x|=5} is equal to |
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Answer» R, the set of all REAL NUMBERS |
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| 11132. |
Normals are drawn to the parabola y^(2)=4x from any point on the line y=2, then vertices of the triangle formed by corresponding tangents lie on a fixed rectangular hyperbola xy=-c^(2) then c^(2) is ________ |
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Answer» LET any POINT on `y=2` is `(h,2)` If normal passes through `(h,2)` `2+ht-2t-t^(3)=0` `t^(3)-t(h-2)-2=0` `t_(1),t_(2)` and `t_(3)` are points of this equation vertices lies on `xy=-2` |
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| 11133. |
Which one of the following function(s) is/are homogeneous? |
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Answer» `f(X,y) = (x-y)/(x^(2)+y^(2))` THUS, it is homogenous of degree `-1` b) `f(lambdax,lambday)=(lambdax)^(1//3)(lambday)^(-2//3)tan^(-1)x/y` `=lambda^(-1//3)x^(1//3)tan^(-1)x/y` `=lambda^(-1//3)f(x,y)` C) `f(lambdax,lambday) = lambdax("ln"sqrt(lambda^(2)(x^(2)+y^(2))-"ln "lambday))+lambdaye^(x//y)` `=lambdax["ln"((lambdasqrt(x^(2)+y^(2)))/(lambday))]+lambdaye^(x//y)` `lambda[x("ln "sqrt(x^(2)+y^(2))-"ln"y)+ye^(x//y)]` `=lambdaf(x,y)` Thus, it is homogeneous. d) `f(lambdax,lambday)=lambdax["ln "(2lambda^(2)x^(2)+lambda^(2)y^(2))(lambdaxlambda(x+y))]+lambda^(2)x^(2)tan(x+2y)/(3x-y)` `=lambda x["ln "(2x^(2)+y^(2))/(x(x+y))]+lambda^(2)x^(2)tan(x+2y)/(3x-y)` Thus, it is non-homogeneous. |
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| 11135. |
The random variable X has a probability distribution P(X) of the following form, where k is some number. P(X)={{:(k,",",if x=0),(2k,","," if x=1"),(3k,",","x=2 "),(0,",","otherwise"):} a. Determine the value of k b. Find P(X lt 2), IP(X le 2), P(X gt 2). |
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| 11136. |
lim_( xto0)sqrt(1-cos2x)/(sqrt2x) is |
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Answer» 1 |
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| 11137. |
If cos^(2)x-a|cosx|+b=0 has exactly two solutions in ((-pi)/(2),(3pi)/(2)) then which of following is correct |
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Answer» A=B |
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| 11138. |
Which of the following set of quantum numbers will have lowest energy of an electron ? |
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Answer» n=4, l=3,m=0,s=`+1/2` |
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| 11139. |
Find sin(pi/3-sin^(-1)(-1/2)) = |
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Answer» `1/2` |
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| 11140. |
Find the points of discontinuity of the function f(x) = x - [x] where [x] indicates the greatest integer not greater than x. Also write the set of value of x where the function is continuous. |
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| 11141. |
Find the nature of the triangle with vertices z_(1) , z_(2) , z_(3) satisfying (z_(1) - z_(3))/(z_(2) - z_(3)) = (1 + isqrt3)/(2) |
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| 11142. |
If P(A)= (3)/(10), P(B)= (2)/(5) and P(A cup B)= (3)/(5) thenP(A//B) + P(B//A) equals = ………. |
| Answer» Answer :D | |
| 11143. |
int(dx)/((x+1)^(2)(x^(2)+1))dx |
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| 11144. |
Formthe polynomialequationwhoseroot are 4+- sqrt(3) ,2 +- i |
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| 11145. |
Identify the axes on which the given points lie:(1,0,0),(0,1,0),(0,0,1) |
| Answer» SOLUTION :x-axis, y-axis, z-axis | |
| 11146. |
The solutionset of (5+4costheta )(2cos theta+1)=0 in the interval [0,2pi] |
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Answer» `{PI/3, (2pi)/3}` |
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| 11147. |
If log_(9)x +log_(4)y = (7)/(2) and log_(9) x - log_(8)y =- (3)/(2), then x +y equals |
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Answer» 35 |
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| 11149. |
Differentiate w.r.t x the function (3x^(2)-9x + 5)^(9) |
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| 11150. |
Ifthe marginal cost function a product is given by MC=10-4x+3x^(2) and fixed cost is Rs 500, then the cost function is |
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Answer» `10x-2x^(2)+x^(3)` |
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