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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.
| 8201. |
The point on the curve x^(2)=2y which is nearest to the point (0, 5) is ……….. |
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Answer» `(2sqrt(2), 4)` |
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| 8202. |
""^(n-2)C_(r)+2.""^(n-2)C_(r-1)+""^(n-2)C_(r-2) is equal to |
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Answer» `""^(N+1)C_(R)` |
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| 8203. |
Prove that(veca.(vecbxxvecc))veca=(vecaxxvecb)xx(vecaxxvecc). |
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| 8204. |
Evaluate the definite integral in exercise overset(3)underset(2) int (xdx)/(x^(2)+1) |
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| 8205. |
Consider a polynomial y = P(x) of the least degree passing through A(-1,1) and whose graph has two points of inflection B(1,2) and C with abscissa 0 at which the curve is inclined to the positive axis of abscissa at an angle of sec^(-1)sqrt(2) The equation P(x) =0 has |
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Answer» three distinct real roots p(1)=P(0)=0 `therefore P(x)=a(x^(2)-x)` or `P(x)=a(x^(3)/(3)-x^(2)/(3))` also given `(dy)/(dx)_(x=0)=sec^(-1)sqrt(2)=tan^(-1)1` HENCE P(0)=1 so B =1 thus `P(x)=a(x^(3)/(3)-x^(2)/(2))+1` `therefore P(x) =a(x^(4)/(12)-x^(3)/(6))=x+c` As P(1)=2 ,we have `a((1)/(12)-(1)/(6))+1+c=1` or `(a)/(12)+c=0` solving (1) and (2) we have `a =6 and c=1/2` `P(x) =6(x^(4)/(12)-x^(3)/(6))+x+1/2` `P(2)=5/2 land p(x)=1/2` `P(x) =6(x^(3)/(3))-(x^(2)/(2))+1=(x-1)^(2)(2x+1)` |
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| 8206. |
Consider a polynomial y = P(x) of the least degree passing through A(-1,1) and whose graph has two points of inflection B(1,2) and C with abscissa 0 at which the curve is inclined to the positive axis of abscissa at an angle of sec^(-1)sqrt(2) The value of P(2) ius |
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Answer» -1 p(1)=P(0)=0 `therefore P(x)=a(x^(2)-x)` or `P(x)=a(x^(3)/(3)-x^(2)/(3))` also given `(dy)/(dx)_(x=0)=sec^(-1)sqrt(2)=tan^(-1)1` Hence P(0)=1 so b =1 thus `P(x)=a(x^(3))/(3)-(x^(2))/(2)+1` `therefore P(x) =a(x^(4))/(12)-(x^(3))/(6)=x+c` As P(1)=2 ,we have `a(1)/(12)-(1)/(6)+1+c=1` or `(a)/(12)+c=0` SOLVING (1) and (2) we have `a =6 and c=1/2` `P(x) =6(x^(4))/(12)-(x^(3))/(6)+x+1/2` `P(2)=5/2and p(x)=1/2` `P(x) =6(x^(3))/(3)-(x^(2))/(2)+1=(x-1)^(2)(2x+1)` |
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| 8207. |
Consider a polynomial y = P(x) of the least degree passing through A(-1,1) and whose graph has two points of inflection B(1,2) and C with abscissa 0 at which the curve is inclined to the positive axis of abscissa at an angle of sec^(-1)sqrt(2) The value ofP(0) is |
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Answer» 1 p(1)=P(0)=0 `therefore P(x)=a(x^(2)-x)` or `P(x)=a(x^(3)/(3)-x^(2)/(3))` also given `(dy)/(dx)_(x=0)=SEC^(-1)SQRT(2)=TAN^(-1)1` Hence P(0)=1 so b =1 thus `P(x)=a(x^(3)/(3)-x^(2)/(2))+1` `therefore P(x) =a(x^(4)/(12)-x^(3)/(6))=x+c` As P(1)=2 ,we have `a((1)/(12)-(1)/(6))+1+c=1` or `(a)/(12)+c=0` SOLVING (1) and (2) we have `a =6 and c=1/2` `P(x) =6(x^(4)/(12)-x^(3)/(6))+x+1/2` `P(2)=5/2 land p(x)=1/2` `P(x) =6(x^(3)/(3))-(x^(2)/(2))+1=(x-1)^(2)(2x+1)` |
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| 8208. |
For some natureal number 'n', the sum of the fist 'n' natural numbers is 240 less than the sum of the first (n+5) natural numbers. Then n itself is the sum of how many natural numbers starting with 1. |
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| 8209. |
Evaluate : intsqrt(4ax-x^(2))dx. |
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| 8211. |
Find the optimal solutionof the aboveLPPand alsofind the value of Z_(max) from the graph of feasible region |
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| 8212. |
Find the correct statement in the following given four points A, B, C, D are coplanar only of the following condition is satisfied. |
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Answer» `vec(AB)+vec(BC)+vec(CA)=0` |
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| 8213. |
Integrate the following function : int(x)/(x^(2)+3x+2)dx |
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| 8214. |
Let f(x) be a polynomial function of second degree. If f(1) = f(-1) and a, b. c are in A.P., then f'(a), f'(b),f'(c) are in |
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Answer» G.P. |
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| 8215. |
Let f(x)=x(1)/(x-1)+(1)/(x)+(1)/(x+1) x lt 1 then |
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Answer» `f(X) LE 1` |
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| 8216. |
Number of integers satisfying the inequality log_2sqrtx-2log_(1//4)^2x+1gt0,is |
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| 8217. |
An isosceles triangle is inscribed in the circle x ^(2) + y ^(2) - 6x - 8y =0 with vertex at the origin and one of the equal sides along the axis ofx. Equation of the other side through the origin is |
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Answer» `7X -24Y =0` |
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| 8218. |
Three vectors vec(a),vec(b),vec(c) are such that vec(a)xxvec(b)=4(vec(a)xxvec(c))and|vec(a)|=|vec(b)|=1and|vec(c)|=(1)/(4). If the angle between vec(b)andvec(c)" is "(pi)/(3), then vec(b) is |
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Answer» `VEC(a)+4vec(C)` |
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| 8219. |
If1 , omega , omega^(2) are the cube roots of unity , then find the values of the following . ( i + omega )^(3 ) + ( 1 + omega^(2))^(3) |
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| 8220. |
((1 + ""^nC_1 + ""^nC_2 + ""^nC_3+…….+nC_n)^2)/(1 + ""^(2n)C_1 + ""^(2n)C_2 + ""^(2n)C_3 + ……… + ""^(2n)C_(2n)) = |
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Answer» 1 |
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| 8221. |
Divide 20 into two parts such that the product of one part and the cube of the other part is maximum. |
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| 8222. |
The solution of (dy)/(dx) = (x-y)^(2) is |
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Answer» `(x -y + 1) = c (1 -x + y) E^(2X)` |
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| 8223. |
int(1)/(1+cos^(2)x)dx=..... |
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Answer» `(1)/(sqrt(2))tan^(-1)(TANX)+c` |
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| 8224. |
If the equation 2^(2x)+a*2^(x+1)+a+1=0 has roots of opposite sign, then the exhaustive set of real values of a is |
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Answer» `(-OO,0)` `implies t^(2)+2a*t+(a+1)=0` Now, `t=1` should lie between the roots of above EQUATION. Let `f(t)=t^(2)+2a*t+(a+1)` `:.f(1) lt 0` and `f(0) gt 0` `implies a lt (-2)/(3)` and `a gt -1` `:.a in (-1,(-2)/(3))` |
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| 8225. |
The value of int_(0)^(pi) sin^(n) x cos^(2m+1) x dx is |
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Answer» `((2m+1)!)/( (n!)^(2) ) ` |
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| 8226. |
Show by an example that for AneO,BneO,AB=O. |
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| 8227. |
int log (2- 3x) dx = |
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Answer» `(x- (2)/(3)) `LOG |2 -3X| - x +c |
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| 8228. |
Find the centre and radius of the following circles : x^2 + y^2 + 6x -4y -12 = 0 |
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Answer» Solution :`x^2 + y^2 + 6X -4y -12 = 0` `therefore` 2g = 6, 2F = -4, c = -12 `therefore` g = 3, f = -2 `therefore` CENTRE of (-g, -f) = (-3, 2) and radius = `sqrt(g^2 + f^2 -c)` = `sqrt(9 + 4 + 12)` = 5 |
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| 8229. |
Let f(x)=(x^(2)-4)^(1//3), then f has a : |
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Answer» LOCAL maxima at x = 0 |
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| 8230. |
Twenty meters of wire is available to fence off a flower bed in the form of a sector. If the flower bed has the maximum surface then radius is |
| Answer» ANSWER :C | |
| 8231. |
Let X represent the difference between the number of head and the number of tails obtained when a coin is tossed 6 times. What are possible values of X? |
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| 8232. |
Consider the following complexes (I) [Cr(CO)_(x)], (II) [Cr(CO)_((x-1))PF_(3)] If PF_(3) is better pi accepter than CO, what be the order of bond length of CO in complexes (I) and (II) : |
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Answer» `IgtII` |
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| 8233. |
Find the coefficient of a^(5) b^(5)c^(5)d^(8) in the expansion of the following expression. (bcd + acd + abd+ abc)^(7) |
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| 8234. |
int(root(3)(1+root(4)(x)))/(sqrtx)dx is equal to : |
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Answer» `12(((1+root(4)(X))^(7//3))/(7)+((1+root(4)(x))^(4//3))/(4))+C` |
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| 8235. |
A soft drinks firm has two bottling plants, one located at P and the other located at Q.Each plant produces three different soft drinks A, B and C.The capacities of two plants in number of bottles per day, are as follows: A market survey indicates that during the month of April, there will be a demand for 24,000 bottles of A, 16,000 bottles of B and 48,000 bottles of C.The cost of running the two plants P and Q are respectively ₹6,000 and ₹ 4,000 per day.Find graphically, the number of days for which either of the two plants P and Q should be run in the month of April so as to minimise production cost while still meeting the market demand. |
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| 8236. |
The solution of (dy)/(dx) +(Tan y)/(1+x) = (1+x)e^(x)sec y is |
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Answer» `(SIN y)/(1+x) = e^(x) + c` |
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| 8237. |
I = int {log _(e) log _(e) x + (1)/( (log _(e) x ) ^(2))} dx is equal to: |
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Answer» `X log _(e) log _(e) x +C` |
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| 8238. |
Formation of real image using a biconves lens is shown below: If the whole set up is immersed in water without disturbing the object and the screen positions, what will one observe onthe secreen ? |
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Answer» IMAGE disappears |
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| 8239. |
If the equation ax ^(2) + 2 (a^(2) + ab 16) ay + by ^(2) + 2ax + 2by - 4 sqrt2=0 represents a circle, the radius of the circle is |
| Answer» ANSWER :A | |
| 8240. |
Locus of the poles of focal chord of a parabola is |
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Answer» the axis |
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| 8241. |
If A, B, C are three events, then which of the following is/are not correct?a.P (Exactly two of A, B and C occur)leP(AnnB)+P(BnnC)+P(CnnA)b.P(AuuBuuC)leP(A)+P(B)+P(C) c.P (Exactly one of A, B and C occur)leP(A)+P(B)+P(C)-P(BnnC)-P(CnnA)-P(AnnB)d.None of these |
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Answer» P (Exactly two of A, B and C occur) |
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| 8242. |
Find the sum of all four digit numbers (without repetition of digits) formed using the digits 1,2, 3, 4, 5. |
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| 8244. |
Let Delta=|(Ax,x^(2),1),(By,y^(2),1),(Cz,z^(2),1)| and Delta_(1)=|(A,B,C),(x,y,z),(zy,zx,xy)| then |
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Answer» 1.`Delta_(1)=-Delta` |
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| 8245. |
Ifveca.vecb=vecb.vecc=vecc.veca=0,then the value of|[veca,vecb,vecc]|is________ |
| Answer» Answer :a | |
| 8246. |
Which of the following statement (s) is (are) correct ? |
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Answer» Sum of the RECIPROCAL of all the n harmonic means inserted between a and b is equal to n times the harmonic mean between two GIVEN numbers a and b. |
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| 8247. |
Let f(x) be a twice differentiable function and f^(11)(0)=2, then Lim_(x to 0) (2f(x)-3f(2x)+f(4x))/(x^(2)) is |
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Answer» a |
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| 8248. |
Velocity-time graph for a particle, which is moving in straight line is given below. Displacement of particle between t=2 sec to t=5 sec is :- |
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Answer» 5m |
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| 8250. |
If p and q are two propositions, then ~(p harr q) is |
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Answer» <P>`~p ^^ ~Q` |
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