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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.
| 27251. |
If a normal chord of a puint on the parabola y^(2) = 4ax, subtends a right angle at the vertex, then t = |
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Answer» 4AL +n=0 |
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| 27252. |
If int (sin^(2) alpha - sin^(2)x)/(" cos x - cos"alpha)dx = f(x) + Ax + B and B in R then |
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Answer» F(x) = 2 SIN x, A = COS `alpha` |
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| 27253. |
Find the area bounded by the curve (x-1)^2+y^2=1" and "x^2+y^2=1. |
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| 27254. |
Which of the following molecule is//are polar and non planar? |
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Answer» `XeO_(3)F_(2)` |
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| 27255. |
If x=y+y^2/(2!)+y^3/(3!)+... then show that y=x-x^2/2+x^3/3-x^4/4+…. |
| Answer» SOLUTION :`x=y+y^2/(2!)+y^3/(3!)=...implies1+x=1+y+y^2/(2!)+y^3/(3!)+...=e^yimpliesy=log_e(1+x)=x-x^2/2+x^3/3-x^4/4+...` | |
| 27256. |
Vertify mean value theorem for the following functions: f(x)= x + (1)/(x), x in [1, 3] |
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| 27257. |
For any non-zero vectors vec(a),vec(b)andvec(c),(vec(a)xxvec(b)).vec(c) is |
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Answer» `VEC(a).(vec(B)xxvec(C))` |
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| 27258. |
Consider triangle ABC where A=(4,4),B=(7,4),C=(4,7) then |
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Answer» The centriod of triangle ABC is (5,5) |
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| 27259. |
L_(1):2(x-1)+3(y+2)+(z-7)=0 and L_(1):2(x+1)-3(y+2)+(z+7)=0 are two planes. |
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Answer» `L_(1)andL_(2)` are parallel |
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| 27260. |
Find the mean and standard deviation for the following data. |
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| 27261. |
If the equation of base of an equilateral triangle is 2x - y = 1 and the vertex is (-1, 2), then the length of the side of the triangle is |
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Answer» `SQRT((20)/(3))` |
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| 27263. |
Differentiate the following functions with respect to x: x^(3) + y^(3)= sin (x + y) |
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| 27264. |
Find the graph of linear inequation in xy plane 2y+1 le 0 |
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| 27265. |
Let ** be a binary operation on the set Q of rational numbers as follows : a "*" b = a -b Find which of the binary operations are commutative and which are associative. |
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| 27266. |
Select the option having all extensive terms. |
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Answer» PH, electrode POTENTIAL, moles |
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| 27267. |
The vector and cartesian equations of the line which passes through the point (1,2,3) and is parallel to the vector hati-2hatj+3hatk are |
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Answer» `vecr=(hati+2hatj+3hatk)+lambda(hati+2hatj+3hatk),` |
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| 27268. |
Which of the following is an arithmetico geometric series ? |
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Answer» `1+3x+7x^2+15x^3+….` |
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| 27269. |
Integrate the following functions : int(4x+3)/(sqrt(2x^(2)+3x+1))dx |
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| 27270. |
Find the angle between two vectors vecaandvecb with magnitudes sqrt(3)and2, respectively having veca*vecb=sqrt(6). |
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| 27271. |
If (3x+4)/(x^(2)-3x+2)=A/(x-2)-B/(x-1) then (A, B) = |
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Answer» (7, 10) |
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| 27272. |
Let x,y,z be the distinctcommon rootsof equationa^10=1 and a^15=1such that :there realpart is positive and omega=|(1+x^2+x^4,1+xy+x^2y^2, 1+xz+y^2+z^2),(1+xy+y^2z^2, 1+y^2+y^4,1+xy+y^2z^2),(1+xz+x^2z^2, 1+yz+y^2z^2,1+z^2+z^4)| then : |
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Answer» `OMEGA`is purely real |
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| 27275. |
A fair coin is tossed 2n times. The probability of getting as many heads in the first n tosses as in the last n is |
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Answer» `(""^(2n)C_(N))/(2^(2n))` |
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| 27276. |
Find the value of n so that (a ^(n -1) + b ^(n +1))/( a ^(n) + b ^(n))may be the G.M. between a and b. |
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| 27277. |
Find the area of the region bonded by y=x(x-1)(x-2), the x-axis and x = 0 and x = 4. |
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| 27279. |
Prove that the following four points are coplanar. i) 4bar(i)+5bar(j)+bar(k), -bar(j)-bar(k), 3bar(i)+9bar(j)+4bar(k), -4bar(i)+4bar(j)+4bar(k) ii) -bar(a)+4bar(b)-3bar(c), 3bar(a)+2bar(b)-5bar(c), -3bar(a)+8bar(b)-5bar(c), -3bar(a)+2bar(b)+bar(c)" ("bar(a), bar(b), bar(c) are non-coplanar vectors) iii) 6bar(a)+2bar(b)-bar(c), 2bar(a)-bar(b)+3bar(c), -bar(a)+2bar(b)-4bar(c), -12bar(a)-bar(b)-3bar(c)" ("bar(a), bar(b), bar(c) are non-coplanar vectors) |
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| 27280. |
Statement-I If r=xhat(i)+yhat(j)+zhat(k), then equation rtimes(2hat(i)-hat(j)+3hat(k))=3hat(i)+hat(k) repesents a straight line. Statement-II Ifr=xhat(i)+yhat(j)+zhat(k), then equation rtimes(hat(i)+2hat(j)-3hat(k))=3hat(i)-hat(j)repesents a straight line. |
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Answer» STATEMENT I is true, Statement II is ALSO true, Statement-II is the CORRECT EXPLANATION of Statement-I. |
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| 27281. |
If a, b,c, in _N, a^(n) + b^(n) is divisible by c when n is odd but not when n is even, then value of c is |
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Answer» a+ B |
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| 27282. |
The maximum number of points on the parabola y^(2)=16x which re equidistant from a variable point P (which lie inside the parabola) are |
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| 27283. |
Evaluate : (i) intsin^(2)(x)/(2)dx (ii) int"tan"^(2)(x)/(2)dx (iii) intcos^(2)nxdx (iv) intcos^(5)xdx (v) intsin^(7)xdx (vi) intsin^(3)(2x+1)dx |
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Answer» Solution :(i) `int"SIN"^(2)(x)/(2)dx=(1)/(2)int2"sin"^(2)(x)/(2)dx` `=(1)/(2)int(1-cosx)dx=(1)/(2)dx-(1)/(2)intcosxdx` `=(1)/(2)x-(1)/(2)x+C`. (ii) `int"tan"^(2)(x)/(2)dx=int("sec"^(2)(x)/(2)-1)dx=int"sec"^(2)(x)/(2)dx-intdx` `=intsec^(2)tdt-intdx,"where"(x)/(2)=t` `=2tant-x+C=2"tan"(x)/(2)-x+C`. (iii) `intcos^(2)nxdx=(1)/(2)COS^(2)nxdx` `=(1)/(2)int(1+cos2nx)dx=(1)/(2)intdx+(1)/(2)intcos2nxdx` `=(x)/(2)+(1)/(4n)sin2nx+C`. (iv) `intcos^(5)xdx=intcos^(4)x*cosxdx` `=int(1-sin^(2)x)^(2)*cosxdx=int(1-t^(2))^(2)dt,"where"sinx=t` `=int(1+t^(4)-2t^(2))dt=intdt+int t^(4)dt-2int t^(2)dt` `=t+(t^(5))/(5)-(2t^(3))/(3)+C=sinx+(1)/(5)sin^(5)sin^(5)x-(2)/(3)sin^(3)x+C`. (v)`intsin^(7)xdx=fsin^(6)x*sinxdx` `=int(1-cos^(2)x)^(3)sinxdx` `=-(1-t^(2))dt," where"cosx=t` `=int(t^(6)-3t^(4)+3t^(2)-1)dt=(t^(7))/(7)-(3t^(5))/(5)+t^(3)-t+C` `(1)/(7)cos^(7)x-(3)/(5)cos^(5)x+cos^(3)x-cosx+C`. (VI) `intsin^(3)(2x+1)dx=int{1-cos^(2)(2x+1)}*sin(2x+1)dx` `=-(1)/(2)(1-t^(2))dt,"where"cos(2x+1)=t` `=-(1)/(2)intdt+(1)/(2)intt^(2)dt=-(1)/(2)t+(1)/(6)t^(3)+C` `=-(1)/(2)cos(2x+1)+(1)/(6)cos^(3)(2x+1)+C`. |
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| 27284. |
Using elementary transformations, find the inverseof the matrices [(6,-3),(-2,1)] |
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| 27285. |
Find the area lying between the curve y^(2) = 4x and the line y=2x |
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| 27287. |
If x_(n) = omega^(n) + (1)/(omega^(n)) then x_(1) x_(2) x_(3)…, x_(12) = |
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Answer» 4 |
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| 27288. |
Using Cofactors of elements of second row, evaluate Delta=|{:(5,3,8),(2,0,1),(1,2,3):}| |
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| 27289. |
Evaluate the following : [[2,-3,4],[-4,2,-3],[11,-15,20]] |
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Answer» Solution :`[[2,-3,4],[-4,2,-3],[11,-15,20]]` `2[[2,-3],[-15,20]]+3[[-4,-3],[11,20]]+4[[-4,2],[11,-15]]` =2(40-45)+3(-80+33)+4(60-22) =-10-141+152=-151+152=1 |
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| 27290. |
A tangents to the hyperbolax^(2)//a^(2))-y^(2)//b^(2)=1 cuts the elipsex^(2)//a^(2) +y^(2)//b^(2) =1in P and Q . The locus of midpoint of PQ is |
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Answer» `( X^(2)//a^(2) +y^(2) //B^(2)) ^(2) =x^(a)//a^(2)-y^(2)//b^(2)` |
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| 27291. |
Integrate the functions (2cosx-3sinx)/(6cosx+4sinx) |
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| 27292. |
A factory makes tennis rackets and cricket bats. Atennis racket takes 1. 5hours of machinetime and 3 hours of craftmans time in its making while a cricket bat takes 3hours of machine time and 1 hour of craftmans time. In a day, the factoryhas the availability of not more than 42 hours of machine time and 24 hoursof craftsmans time. If the profit on a racket and on a bat is Rs. 20 and Rs. 10 respectively, findthe number of tennis rackets and crickets bats that the factory mustmanufacture to earn the maximum profit. Make it as an L.P.P. and solvegraphically. |
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| 27293. |
(cos 8 A cos 5A-cos 12 A cos 9A)/(sin 8 A cos 5 A +cos 12Asin 9A)= |
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Answer» `tan 2A` |
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| 27294. |
Refers to question 13. Solve the liner progamming problem and deterimine profit to the manufacturer. |
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Answer» Maximise Z=100x+170y SUBJECT to `3x+2y le 3600, x+y ge 1800 x ge0, y=180  Hence the maximum profit to the MANUFACTURER is 138600. |
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| 27295. |
int( dx)/( sqrt( 2x - x^(2) ) ) = …...... +C. |
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Answer» `2 sin^(-1) ( X-1)` |
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| 27297. |
int_(1)^(4)(x^(2) - x)dx. |
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| 27298. |
Statement I In any triangle ABC, the square of the length of the bisector AD is bc(1-(a^(2))/((b+c)^(2))). Statement II In any triangle ABC length of bisector AD is (2bc)/((b+c))cos ((A)/(2)). |
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Answer» Both STATEMENT I and Statement II are correct and Statement II is the correct explanation of Statement I |
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| 27299. |
What are the solutions to 3x^(2)-33=18x? |
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Answer» `x=3pm2sqrt(3)` |
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| 27300. |
If the feasible region for a LPP is unbounded, maximum or minimum of the objective function Z = ax + by may or may not exist. |
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