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.
| 301. |
If alpha,betagt0and alphaltbeta and ax^2+4gammaxy+betay^2+4p(x+y+1)=0 represents a pair of straight lines , then |
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Answer» <P>`alphaleplebeta` |
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| 302. |
Find the area of the parallelogram whose adjacent sides are determined bythe vecor veca= 3hati+hatj+4hatk and vecb= hat i-hatj+hatk |
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| 304. |
Consider the ragular hexagon ABCDEF with centre at O (origin). Five forces vec(AB), vec(AC), vec(AD), vec(AE), vec(AF) act at the vertex A of a regular hexagon ABCDEF. Then their resultant is |
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Answer» ` 3 vec(AO)`  `vec(AD) + vec(EB) + vec(FC) = 2 vec(AO) + 2 vec(OB) + 2 vec(OC)` `"" = 2 ( vec(AO) + vec(OB) ) + 2 vec(OC)` `"" = 2 vec(AB) + 2 vec(AB) ` `"" ( because vec(OC) = vec(AB))` `"" = 4 vec(AB)` `vecR = vec(AB) + vec(AC) + vec(AD) + vec(AE) + vec(AF)` `= vec(ED) + vec(AC) + vec(AD) + vec(AE) +vec(CD)` `( because vec(AB) = vec(ED) and vec(AF)= vec(CD))` `= ( vec(AC) + vec(CD)) + ( vec(AE) + vec(ED)) + vec(AD)` `= vec(AD) + vec(AD) + vec(AD) = 3 vec(AD) = 6 vec(AO)` |
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| 305. |
If A = {(x,y): x,y in R, y = (1/7)^(x)} and B={(x,y), x, y in R, y = 7x} then |
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Answer» `A cap B = PHI` |
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| 306. |
Two circles of unequal radii have four common tangents. A transverse common tangent meets the direct common tangents at the points P & Q. If length of direct tangent (between the point of contacts) is 8 then length of PQ is |
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Answer» So `PQ=8-a+b` ALSO `QD=QR=8-b` So `QP=8-b+a` `8-a+b=8-b+a` `impliesa=b` `PQ=8` 
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| 307. |
Find the number of ways of preparing a chain with 6 different coloured beads. |
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| 308. |
Moving further ahead, they reach the castle walls where Tintin sees this mysterious poster (shown below) pasted on the wall. He realised that an entrance through a secret tunnel lay behind it which can be opened by climbing the “spiraling green leaves”. He realises that the poster is hinting towards a word. So help Tintin crack the logic of the poster, which demands the 4th letter in the word. |
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Answer» H To get the alphabet corresponding to that particular square,Connect each white square to the nearest x white squares in that chosen SQUARE, where xcorresponds to the NUMBER in that squareFor the 6th square (the central square of the whole box) use the directions given to figurethe PATH. Hence the ANSWER is option A)H. |
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| 309. |
Prove that the equation(a+2h+b)x^2-2(a-b)xy+(a-2h+b)y^2=0represents a pair of lines each inclined at an angle of 45^@ to one or other of the lines given by , ax^2+2hxy+by^2=0 |
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| 310. |
A book store has m copies each of n different books. Find the number of ways of arranging these books in a shelf. |
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| 311. |
A company manufactures two types of screws A and B. All the screws have to pass through a threading machine and a slotting machine. A box of Type A screws requires 2 minutes on the threading machine and 3 minutes on the slotting machine. A box of type B screws requires 8 minutes of threading on the threading machine and 2 minutes on the slotting machine. In a week, each machine is available for 60 hours. On selling these screws, the company gets a profit of Rs. 100 per box on type A screws and Rs. 170 per box on type B screws. |
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| 312. |
There are n pairs of shoes in a closet. If r(ltn) are selected at random then the number of ways that among the selected shoes there are exactly 2 pairs is ""^(n)C_(2).""^(n-2)C_(r-4).2^(r-4) |
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| 313. |
There are n pairs of shoes in a closet. If r(ltn) are selected at random then the number of ways that among the selected shoes there is atleast one pair is ""^(2n)C_(1).""^(n-1)C_(r-2).2^(r-2) |
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| 314. |
There are n pairs of shoes in a closet. If r(ltn) are selected at random then the number of ways that among the selected shoes there is exactly one pair is ""^(n)C_(1).""^(n-1)C_(r-2).2^(r-2) |
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| 315. |
Which one of the following is independent of alpha in the hyperbola (0lt alphaltpi/2)x^2/(cos^2alpha)-y^2/(sin^2alpha)=1 |
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Answer» ECCENTRICITY |
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| 316. |
Two events A and B are such that P(B) = 0.55 and P(AB') = 0.15. The probability of occurrence of at least one of event is |
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Answer» `0.70` |
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| 317. |
Integrate the following functions: sin 4x sin8x |
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Answer» SOLUTION :sin 4X sin 8X `=1/2[cos(8x-4x)-cos(8x+4x)]` =1/2[cos 4x- cos12x] therefore` int sin4x sin 8x DX` =`1/2[(sin 4x)/4-sin(12x)/(12)]+c` |
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| 318. |
Consider the binary operation ** on the set A= {1,2,3,4,5} given by the following multiplication table Is ** commutative ? |
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Answer» Solution :The entries in the table are SYMMETRIC about the MAIN DIAGONAL. HENCE `**` is commutative. i.e., `a**b=b**a AA a,b in A` |
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| 319. |
Find the scalar and vector projection of veca on vecb. veca = hati-hatj-hatk,vecb = 3hati+hatj+3hatk. |
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Answer» SOLUTION :Scalar projection of `VECA` on `VECB` = `((veca.vecb)/|vecb|) vecb/|vecb| = 1/sqrt19 (3hati+hatj+3hatk)/sqrt19` `(-3hati+hatj+3hatk)/19` |
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| 320. |
ABC is a right-angled triangle in which angleB=90^(@) and BC=a. If n points L_(1),L_(2),…,L_(n) on AB is divided in n+1 equal parts and L_(1)M_(1), L_(2)M_(2),…,L_(n)M_(n) are line segments paralllel to BC and M_(1), M_(2),….,M_(n) are on AC, then the sum of the lengths of L_(1)M_(1), L_(2)M_(2),...,L_(n)M_(n) is |
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Answer» `(a(N+1))/(2)` `=1/(n+1)=(L_(1)M_(1))/a` `(AL_(2))/(AB)=(L_(2)M_(2))/(BC)` `rArr2/(n+1)=(L_(2)M_(2))/a` `rArrL_(2)M^(2)=(2a)/(n+1), ETC` HENCE. The required sum is `a/(n+1)+(2a)/(n+1)+(3a)/(n+1)+….+(na)/(n+1)` `=a/(n+1)(n(n+1))/2` `=(an)/2` 
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| 321. |
If A is a matrix of order 3xx3, then |3A|= ".........." |
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| 322. |
Two progressive transverse waves are described by : y_(1) = 3.0 cm sin [(4x-700t)rad] and y_(2) = 3.0 cm sin [(4x-700t - pi//3) rad]. |
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Answer» Amplitude of a RESULTANT wave is `3sqrt(3) cm` |
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| 323. |
{:(" " Lt),(n rarroo):} sum_(r=1)^(n)(r)/(n^(2)+r^(2))= |
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Answer» LOG 2 |
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| 324. |
Find the equation of the circle which passes through the origin, meets the x-axis orthogonally & cuts the circle x^(2) + y^(2) = a^(2) at an angle of 45^(@). |
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| 325. |
Find the number of 15^(th)roots of unity, which are also 25^(th) roots of unity . |
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| 326. |
Determine whether(t_n) is an arithmetic sequence if:t_n=an+b |
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Answer» Solution :`t_n=an+brArrt_(n+1)=a(n+1)+b` Now `t_(n+1)-t_a={a(n+1)+b}-{an+b}=a` (constant) `THEREFORE(t_n)` is an ARITHMETIC SEQUENCE. |
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| 327. |
The product of the perpendicular distances from the origin on the pair of straight lines 12 x^(2) + 25xy +12y^(2) + 10 x + 11y + 2 = 0 , is |
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Answer» `(1)/(25)` |
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| 328. |
Evaluation of definite integrals by subsitiution and properties of its : int_(0)^(1)(2x)/(5x^(2)+1)dx=.......... |
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Answer» `(1)/(5)LOG6` |
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| 330. |
Find the coordinates of the point where the line through (3,--4,-5) and (2, -3, 1) crosses the plane 2x + y + z = 7. |
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| 331. |
Find the sum of all 4-digited numbers that can be formed using the digits 0, 2, 3, 4, 6 without repetition. |
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| 332. |
Ifthe product of twoof therootsofx^4 - 5x^3 + 5x^2 + 5x -6=0is2 thenthe rootsare |
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Answer» `1,-2 ,4,-8` |
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| 333. |
There are n pairs of shoes in a closet. If r(ltn) are selected at random then the number of ways that among the selected shoes there is no pair is ""^(n)C_(r).2^(r) |
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| 334. |
Let A and B be two events such thatP(A cup B) ge 3//4 and 1//8 le P(A cap B) le 3//8Statement 1 : P(A) +P(B) ge 7//8Statement 2 : P(A) +P(B) le 11//8 |
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Answer» STATEMENT 1 and statement 2 are both false |
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| 335. |
Ifw = alpha+ibeta, where beta ne 0 and z ne 1, satisfies thecondition that ((w - bar(w) z)/(1-z)) is purely real, then the set of values of z is |
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Answer» `{Z : |z| =1}` |
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| 336. |
The sum of two non - integral roots of |(x,2,5),(3,x,3),(5,4,x)|=0 is : |
| Answer» Answer :B | |
| 337. |
The value of the integral int_(-3pi)^(3pi)|sin^(3)x|dx is equal to |
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Answer» `PI` |
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| 338. |
Volume of the tetrahedron with vertices P(-1, 2, 0), Q(2, 1, -3), R(1, 0, 1) and S(3, -2, 3) is |
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Answer» `1//3` |
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| 339. |
IF 0=2/(n-2)-6/(n+1), what is the value of n? |
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| 340. |
At break even point, we have |
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Answer» `(R(x))/(C(x)) =1` |
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| 341. |
If the sides of a cyclic quadrilateral are 3,3,4,4, show that a circle be inscribed in it. |
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Answer» Solution :Since, length of tangents from EXTERNAL point to a circle are equal. `THEREFORE` AP=AS………(i) BP= BQ ……(ii) CR = CQ ………….(iii) DR=DS…………..(iv) `therefore AB+ CD = (AP + PB) (CR + DR)` `=(AS + BQ) + (CR + DS) =(AS+DS) + (BQ+CR)`  `rArr AB + CD = AD + BC`.....(1) `therefore` A circle can be inscribed in a QUADRILATERA, if sides of a quadrilateral satisfies (1) Sides of quadrilateral are 3,3,4,4. If we take AB=3, CD=4, BC=3, AD=4 `therefore AB+CD = BC + AD=7` `therefore` Circle is inscribed in quadrilateral ABCD. If sum of opposite sides of a quadrilateral is equal. only then a cirlcle can be inscribed in a quadrilateral. |
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| 342. |
(2^(n) [1.3.5. . .(2n-1) ])/(n!)= |
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Answer» `""^(2N)C_n` |
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| 343. |
If the equation of the circle passing through the origin and the point of intersection of the two circlesx^(2)+ y^(2) - 4x - 6y - 3= 0, x^(2) + y^(2) + 4x - 2y - 4 = 0 " is " x^(2) + y^(2) + 2ax + 2by + c = 0then the ascending order of a,b,c is |
| Answer» Answer :A::C | |
| 344. |
Find all the solution of x,y in the equation 4(3sqrt(4x-x^(2))sin^(2)""((x+y)/(2))+2cos(x+y))=13+4 cos^(2)(x+y) |
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| 345. |
Ifbara=(1)/(sqrt(10)) (3bari+bark) and barb=(1)/(7)(2bari+3barj-6bark), then the value of (2bara-barb).[(bara xx barb)xx(bara+2barb)] |
| Answer» ANSWER :C | |
| 347. |
Express each of the following physical statements in the form of differential equation (i) radium decays at a rate proportional to the amount Q present (ii) The population P of a city increases at a rateproportional to the product of population and to the difference between 500000 and the population (iii) Fora certain substance the rateof changeof vaporpressurep with respect to temperature T is proportional to the vapor pressure and inversely proportional to the square of the temperature A saving amount pays 8% interest per year compounded continously in additionthe income from another investment is credited to the amount continously at the rate of Rs 400 per year |
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Answer» (ii) KP(5000-P)[`before` is a constant] (iiii) `K(P)/(T^(2))[before "k is a constant"]` (IV) `(2x)/(25)+400` |
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| 348. |
Find the number of ways of giving away 4 similar coins to 5 boys if each boy can be given any member (less than or equal to 4) of coins. |
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| 349. |
What amount of heat ( in kJ) is released in forming 31.2 g AsH_(3) by the following reaction ? (Given : At. Wt. As=75, H=1) Given :2As(s) +3H_(2)(g) to 2AsH_(3)(g)""DeltaH=-780 kJ/mol |
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Answer» SOLUTION :[0156] Moles of `AsH_(3)=(31.2)/(78)=0.4` HEAT liberated `=(780)/(2)xx0.4=056kJ` |
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| 350. |
If a fair coin is tossed 10 times, find the probability of Atleast six heads. |
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