28278 + Interview Questions in Maths in Class 12 Page 7 InterviewSolution

301.	If alpha,betagt0and alphaltbeta and ax^2+4gammaxy+betay^2+4p(x+y+1)=0 represents a pair of straight lines , then
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>>`alphaleplebeta`<br/>`plealpha`<br/>`p lealphaor p gebeta`<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> :D</body></html>

Discussion

302.	Find the area of the parallelogram whose adjacent sides are determined bythe vecor veca= 3hati+hatj+4hatk and vecb= hat i-hatj+hatk
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/sqrt-1223129" style="font-weight:bold;" target="_blank" title="Click to know more about SQRT">SQRT</a>(<a href="https://interviewquestions.tuteehub.com/tag/42-316129" style="font-weight:bold;" target="_blank" title="Click to know more about 42">42</a>)` <a href="https://interviewquestions.tuteehub.com/tag/sq-1223093" style="font-weight:bold;" target="_blank" title="Click to know more about SQ">SQ</a>. <a href="https://interviewquestions.tuteehub.com/tag/units-1438468" style="font-weight:bold;" target="_blank" title="Click to know more about UNITS">UNITS</a></body></html>

Discussion

303.	Solve (dy)/(dx) = (x+y+1)/(2x+2y+5)
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> :`2/3 (x+y+1) + 4/3 <a href="https://interviewquestions.tuteehub.com/tag/log-543719" style="font-weight:bold;" target="_blank" title="Click to know more about LOG">LOG</a> \|3x+3y +<a href="https://interviewquestions.tuteehub.com/tag/7-332378" style="font-weight:bold;" target="_blank" title="Click to know more about 7">7</a> \| = x+c`</body></html>

Discussion

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
Answer» <html><body><p>` 3 vec(AO)` <br/>`2 vec(AO)` <br/>`4 vec(AO)` <br/>`6 vec(AO)` </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> :Consider the regular hexagon ABCDEF with centre at O (origin) <br/> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/CEN_V_3DG_C01_E07_007_S01.png" width="80%"/> <br/> `vec(AD) + vec(EB) + vec(<a href="https://interviewquestions.tuteehub.com/tag/fc-456602" style="font-weight:bold;" target="_blank" title="Click to know more about FC">FC</a>) = 2 vec(AO) + 2 vec(OB) + 2 vec(OC)` <br/> `"" = 2 ( vec(AO) + vec(OB) ) + 2 vec(OC)` <br/> `"" = 2 vec(<a href="https://interviewquestions.tuteehub.com/tag/ab-360636" style="font-weight:bold;" target="_blank" title="Click to know more about AB">AB</a>) + 2 vec(AB) ` <br/> `"" ( because vec(OC) = vec(AB))` <br/> `"" = 4 vec(AB)` <br/> `vecR = vec(AB) + vec(AC) + vec(AD) + vec(AE) + vec(AF)` <br/> `= vec(ED) + vec(AC) + vec(AD) + vec(AE) +vec(<a href="https://interviewquestions.tuteehub.com/tag/cd-407381" style="font-weight:bold;" target="_blank" title="Click to know more about CD">CD</a>)` <br/> `( because vec(AB) = vec(ED) and vec(AF)= vec(CD))` <br/> `= ( vec(AC) + vec(CD)) + ( vec(AE) + vec(ED)) + vec(AD)` <br/> `= vec(AD) + vec(AD) + vec(AD) = 3 vec(AD) = 6 vec(AO)`</body></html>

Discussion

305.	If A = {(x,y): x,y in R, y = (1/7)^(x)} and B={(x,y), x, y in R, y = 7x} then
Answer» <html><body><p>`A cap <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/phi-599602" style="font-weight:bold;" target="_blank" title="Click to know more about PHI">PHI</a>`<br/>`A cap B` is singleton<br/>A = B<br/>`A cup B = <a href="https://interviewquestions.tuteehub.com/tag/r-611811" style="font-weight:bold;" target="_blank" title="Click to know more about R">R</a>` </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

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
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> :`PA=PR=8-a` <br/> So `PQ=8-a+b` <br/> <a href="https://interviewquestions.tuteehub.com/tag/also-373387" style="font-weight:bold;" target="_blank" title="Click to know more about ALSO">ALSO</a> `QD=QR=8-b` <br/> So `QP=8-b+a` <br/> `8-a+b=8-b+a` <br/> `impliesa=b` <br/> `PQ=8` <br/> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/FIT_JEE_FT1_P1_E01_067_S01.png" width="80%"/></body></html>

Discussion

307.	Find the number of ways of preparing a chain with 6 different coloured beads.
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/60-328817" style="font-weight:bold;" target="_blank" title="Click to know more about 60">60</a></body></html>

Discussion

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.
Answer» <html><body><p><a href="https://interviewquestions.tuteehub.com/tag/h-1014193" style="font-weight:bold;" target="_blank" title="Click to know more about H">H</a><br/>B<br/>E<br/>D<br/></p>Solution :The hint was the <a href="https://interviewquestions.tuteehub.com/tag/term-1241851" style="font-weight:bold;" target="_blank" title="Click to know more about TERM">TERM</a>, ‘Spiralling’ which indicated that, it was a square inside squarekind of spiral. Start from the outermost “SQUARE”,<br/> 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 <a href="https://interviewquestions.tuteehub.com/tag/number-582134" style="font-weight:bold;" target="_blank" title="Click to know more about NUMBER">NUMBER</a> in that squareFor the 6th square (the central square of the whole box) use the directions given to figurethe <a href="https://interviewquestions.tuteehub.com/tag/path-11833" style="font-weight:bold;" target="_blank" title="Click to know more about PATH">PATH</a>.<br/> Hence the <a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> is option A)H.</body></html>

Discussion

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
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/therefore-706901" style="font-weight:bold;" target="_blank" title="Click to know more about THEREFORE">THEREFORE</a> (a+2h+b)x^2-2(a-b)<a href="https://interviewquestions.tuteehub.com/tag/xy-747762" style="font-weight:bold;" target="_blank" title="Click to know more about XY">XY</a>+(a-2h+b)y^2=0`</body></html>

Discussion

310.	A book store has m copies each of n different books. Find the number of ways of arranging these books in a shelf.
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> :`(lfloormn)/((lfloorm)^<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/ways-25480" style="font-weight:bold;" target="_blank" title="Click to know more about WAYS">WAYS</a></body></html>

Discussion

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.
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> :Maximize <a href="https://interviewquestions.tuteehub.com/tag/z-750254" style="font-weight:bold;" target="_blank" title="Click to know more about Z">Z</a> = 100x + 170y subject to constraints `x+4y le 1800, 3x+2y le <a href="https://interviewquestions.tuteehub.com/tag/3600-1859327" style="font-weight:bold;" target="_blank" title="Click to know more about 3600">3600</a>" and "x ge <a href="https://interviewquestions.tuteehub.com/tag/0-251616" style="font-weight:bold;" target="_blank" title="Click to know more about 0">0</a>, y ge 0`</body></html>

Discussion

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)
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/n-568463" style="font-weight:bold;" target="_blank" title="Click to know more about N">N</a>)C_(<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a>).""^(n-2)C_(r-4).2^(r-4)`</body></html>

Discussion

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)
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> :`=""^(2n)C_(r)-""^(<a href="https://interviewquestions.tuteehub.com/tag/n-568463" style="font-weight:bold;" target="_blank" title="Click to know more about N">N</a>)C_(r)2^(r)`</body></html>

Discussion

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)
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/n-568463" style="font-weight:bold;" target="_blank" title="Click to know more about N">N</a>)C_(<a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a>).""^(n-1)C_(r-<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^(r-2)`</body></html>

Discussion

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
Answer» <html><body><p><a href="https://interviewquestions.tuteehub.com/tag/eccentricity-964854" style="font-weight:bold;" target="_blank" title="Click to know more about ECCENTRICITY">ECCENTRICITY</a> <br/><a href="https://interviewquestions.tuteehub.com/tag/abscissa-845962" style="font-weight:bold;" target="_blank" title="Click to know more about ABSCISSA">ABSCISSA</a> of <a href="https://interviewquestions.tuteehub.com/tag/foci-993966" style="font-weight:bold;" target="_blank" title="Click to know more about FOCI">FOCI</a> <br/><a href="https://interviewquestions.tuteehub.com/tag/directrix-955115" style="font-weight:bold;" target="_blank" title="Click to know more about DIRECTRIX">DIRECTRIX</a> <br/>vertex.</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

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
Answer» <html><body><p>`0.70`<br/>`0.20`<br/>`0.35`<br/>`0.30`</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

317.	Integrate the following functions: sin 4x sin8x
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> :sin <a href="https://interviewquestions.tuteehub.com/tag/4x-319255" style="font-weight:bold;" target="_blank" title="Click to know more about 4X">4X</a> sin <a href="https://interviewquestions.tuteehub.com/tag/8x-340330" style="font-weight:bold;" target="_blank" title="Click to know more about 8X">8X</a> <br/> `=1/2[cos(8x-4x)-cos(8x+4x)]` <br/> =1/2[cos 4x- cos12x] <br/> therefore` int sin4x sin 8x <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/> =`1/2[(sin 4x)/4-sin(12x)/(<a href="https://interviewquestions.tuteehub.com/tag/12-269062" style="font-weight:bold;" target="_blank" title="Click to know more about 12">12</a>)]+c`</body></html>

Discussion

318.	Consider the binary operation on the set A= {1,2,3,4,5} given by the following multiplication table Is commutative ?
Answer» <html><body><p></p>Solution :The entries in the table are <a href="https://interviewquestions.tuteehub.com/tag/symmetric-657979" style="font-weight:bold;" target="_blank" title="Click to know more about SYMMETRIC">SYMMETRIC</a> about the <a href="https://interviewquestions.tuteehub.com/tag/main-552371" style="font-weight:bold;" target="_blank" title="Click to know more about MAIN">MAIN</a> <a href="https://interviewquestions.tuteehub.com/tag/diagonal-950665" style="font-weight:bold;" target="_blank" title="Click to know more about DIAGONAL">DIAGONAL</a>. <a href="https://interviewquestions.tuteehub.com/tag/hence-484344" style="font-weight:bold;" target="_blank" title="Click to know more about HENCE">HENCE</a> `` is commutative. <br/> i.e., `ab=b**a AA a,b in A`</body></html>

Discussion

319.	Find the scalar and vector projection of veca on vecb. veca = hati-hatj-hatk,vecb = 3hati+hatj+3hatk.
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> :Scalar projection of `<a href="https://interviewquestions.tuteehub.com/tag/veca-3257210" style="font-weight:bold;" target="_blank" title="Click to know more about VECA">VECA</a>` on `<a href="https://interviewquestions.tuteehub.com/tag/vecb-3257249" style="font-weight:bold;" target="_blank" title="Click to know more about VECB">VECB</a>` <br/> = `((veca.vecb)/\|vecb\|) vecb/\|vecb\| = 1/sqrt19 (3hati+hatj+3hatk)/sqrt19` <br/> `(-3hati+hatj+3hatk)/<a href="https://interviewquestions.tuteehub.com/tag/19-280618" style="font-weight:bold;" target="_blank" title="Click to know more about 19">19</a>`</body></html>

Discussion

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
Answer» <html><body><p>`(a(<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/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a>))/(2)`<br/>`(a(n-1))/(2)`<br/>`(an)/(2)`<br/>none of these </p>Solution :`(AL_(1))/(<a href="https://interviewquestions.tuteehub.com/tag/ab-360636" style="font-weight:bold;" target="_blank" title="Click to know more about AB">AB</a>)=(L_(1)M_(1))/(BC)` <br/> `=1/(n+1)=(L_(1)M_(1))/a` <br/> `(AL_(2))/(AB)=(L_(2)M_(2))/(BC)` <br/> `rArr2/(n+1)=(L_(2)M_(2))/a` <br/> `rArrL_(2)M^(2)=(2a)/(n+1), <a href="https://interviewquestions.tuteehub.com/tag/etc-975753" style="font-weight:bold;" target="_blank" title="Click to know more about ETC">ETC</a>` <br/> <a href="https://interviewquestions.tuteehub.com/tag/hence-484344" style="font-weight:bold;" target="_blank" title="Click to know more about HENCE">HENCE</a>. The required sum is <br/> `a/(n+1)+(2a)/(n+1)+(3a)/(n+1)+….+(na)/(n+1)` <br/> `=a/(n+1)(n(n+1))/2` <br/> `=(an)/2` <br/> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/CEN_ALG_C05_E10_021_S01.png" width="80%"/></body></html>

Discussion

321.	If A is a matrix of order 3xx3, then \|3A\|= ".........."
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> :27.\|A\|</body></html>

Discussion

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].
Answer» <html><body><p>Amplitude of a <a href="https://interviewquestions.tuteehub.com/tag/resultant-1187362" style="font-weight:bold;" target="_blank" title="Click to know more about RESULTANT">RESULTANT</a> wave is `3sqrt(<a href="https://interviewquestions.tuteehub.com/tag/3-301577" style="font-weight:bold;" target="_blank" title="Click to know more about 3">3</a>) cm`<br/><a href="https://interviewquestions.tuteehub.com/tag/resultantis-2991334" style="font-weight:bold;" target="_blank" title="Click to know more about RESULTANTIS">RESULTANTIS</a> a standing wave.<br/>Resultant is a progressive wave<br/>The particle will be <a href="https://interviewquestions.tuteehub.com/tag/oscillating-2900383" style="font-weight:bold;" target="_blank" title="Click to know more about OSCILLATING">OSCILLATING</a> in xy-plane.</p>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>::D</body></html>

Discussion

323.	{:(" " Lt),(n rarroo):} sum_(r=1)^(n)(r)/(n^(2)+r^(2))=
Answer» <html><body><p><a href="https://interviewquestions.tuteehub.com/tag/log-543719" style="font-weight:bold;" target="_blank" title="Click to know more about LOG">LOG</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/>log 4<br/>`log sqrt(2)`<br/>`log sqrt(<a href="https://interviewquestions.tuteehub.com/tag/6-327005" style="font-weight:bold;" target="_blank" title="Click to know more about 6">6</a>)`</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

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^(@).
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/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>) + y^(2) +- asqrt(2)x = <a href="https://interviewquestions.tuteehub.com/tag/0-251616" style="font-weight:bold;" target="_blank" title="Click to know more about 0">0</a>`</body></html>

Discussion

325.	Find the number of 15^(th)roots of unity, which are also 25^(th) roots of unity .
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/5-319454" style="font-weight:bold;" target="_blank" title="Click to know more about 5">5</a></body></html>

Discussion

326.	Determine whether(t_n) is an arithmetic sequence if:t_n=an+b
Answer» <html><body><p></p>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)<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>(t_n)` is an <a href="https://interviewquestions.tuteehub.com/tag/arithmetic-15417" style="font-weight:bold;" target="_blank" title="Click to know more about ARITHMETIC">ARITHMETIC</a> <a href="https://interviewquestions.tuteehub.com/tag/sequence-1201556" style="font-weight:bold;" target="_blank" title="Click to know more about SEQUENCE">SEQUENCE</a>.</body></html>

Discussion

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
Answer» <html><body><p>`(1)/(25)`<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>)/(25)`<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>)/(25)`<br/>`(<a href="https://interviewquestions.tuteehub.com/tag/4-311707" style="font-weight:bold;" target="_blank" title="Click to know more about 4">4</a>)/(25)`</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

328.	Evaluation of definite integrals by subsitiution and properties of its : int_(0)^(1)(2x)/(5x^(2)+1)dx=..........
Answer» <html><body><p>`(1)/(<a href="https://interviewquestions.tuteehub.com/tag/5-319454" style="font-weight:bold;" target="_blank" title="Click to know more about 5">5</a>)<a href="https://interviewquestions.tuteehub.com/tag/log6-1077593" style="font-weight:bold;" target="_blank" title="Click to know more about LOG6">LOG6</a>`<br/>`(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>)log5`<br/>`(1)/(2)log6`<br/>`(1)/(5)<a href="https://interviewquestions.tuteehub.com/tag/log3-1077583" style="font-weight:bold;" target="_blank" title="Click to know more about LOG3">LOG3</a>`</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

329.	int_(-pi//2)^(pi//2)cos^(3)theta(1+sin theta)^(2)d theta=
Answer» <html><body><p>`<a href="https://interviewquestions.tuteehub.com/tag/5-319454" style="font-weight:bold;" target="_blank" title="Click to know more about 5">5</a>/8`<br/>`8/5`<br/><a href="https://interviewquestions.tuteehub.com/tag/0-251616" style="font-weight:bold;" target="_blank" title="Click to know more about 0">0</a><br/>`(5)/(<a href="https://interviewquestions.tuteehub.com/tag/16-276476" style="font-weight:bold;" target="_blank" title="Click to know more about 16">16</a>)`</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/b-387190" style="font-weight:bold;" target="_blank" title="Click to know more about B">B</a></body></html>

Discussion

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.
Answer» <html><body><p><br/></p>Answer :`therefore` The <a href="https://interviewquestions.tuteehub.com/tag/required-1185621" style="font-weight:bold;" target="_blank" title="Click to know more about REQUIRED">REQUIRED</a> <a href="https://interviewquestions.tuteehub.com/tag/point-1157106" style="font-weight:bold;" target="_blank" title="Click to know more about POINT">POINT</a> is 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>,y,z)=(<a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a>,-2,7).</body></html>

Discussion

331.	Find the sum of all 4-digited numbers that can be formed using the digits 0, 2, 3, 4, 6 without repetition.
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> :389970</body></html>

Discussion

332.	Ifthe product of twoof therootsofx^4 - 5x^3 + 5x^2 + 5x -6=0is2 thenthe rootsare
Answer» <html><body><p>`1,-<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/4-311707" style="font-weight:bold;" target="_blank" title="Click to know more about 4">4</a>,-8`<br/>`+- 1,2,3`<br/>`+- 2i ,2,3`<br/>` -3/2 ,-1/ 2, 2 +- <a href="https://interviewquestions.tuteehub.com/tag/sqrt-1223129" style="font-weight:bold;" target="_blank" title="Click to know more about SQRT">SQRT</a>(3)`</p>Answer :B</body></html>

Discussion

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)
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/n-568463" style="font-weight:bold;" target="_blank" title="Click to know more about N">N</a>)C_(<a href="https://interviewquestions.tuteehub.com/tag/r-611811" style="font-weight:bold;" target="_blank" title="Click to know more about R">R</a>)xx2^(r)`</body></html>

Discussion

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
Answer» <html><body><p><a href="https://interviewquestions.tuteehub.com/tag/statement-16478" style="font-weight:bold;" target="_blank" title="Click to know more about STATEMENT">STATEMENT</a> 1 and statement <a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a> are both false <br/>Statement 1 and <a href="https://interviewquestions.tuteehub.com/tag/statement2-652468" style="font-weight:bold;" target="_blank" title="Click to know more about STATEMENT2">STATEMENT2</a> are both <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/>Statement 1 is true and statement 2 is false <br/>Statement1 is false and statement2 is true </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

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
Answer» <html><body><p>`{<a href="https://interviewquestions.tuteehub.com/tag/z-750254" style="font-weight:bold;" target="_blank" title="Click to know more about Z">Z</a> : \|z\| =<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/>`{ z:z=bar(z) }`<br/>`{ z : z <a href="https://interviewquestions.tuteehub.com/tag/ne-1112263" style="font-weight:bold;" target="_blank" title="Click to know more about NE">NE</a> 1}`<br/>`{ z : \|z\| = 1, z <a href="https://interviewquestions.tuteehub.com/tag/ne1-2188195" style="font-weight:bold;" target="_blank" title="Click to know more about NE1">NE1</a>}`</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

336.	The sum of two non - integral roots of \|(x,2,5),(3,x,3),(5,4,x)\|=0 is :
Answer» <html><body><p><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/>`-5`<br/>`-<a href="https://interviewquestions.tuteehub.com/tag/18-278913" style="font-weight:bold;" target="_blank" title="Click to know more about 18">18</a>`<br/><a href="https://interviewquestions.tuteehub.com/tag/none-580659" style="font-weight:bold;" target="_blank" title="Click to know more about NONE">NONE</a> of these</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

337.	The value of the integral int_(-3pi)^(3pi)\|sin^(3)x\|dx is equal to
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>`<br/>`8pi`<br/>1<br/>8</p>Answer :D</body></html>

Discussion

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
Answer» <html><body><p>`1//3`<br/>`2//3`<br/>`1//4`<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/b-387190" style="font-weight:bold;" target="_blank" title="Click to know more about B">B</a></body></html>

Discussion

339.	IF 0=2/(n-2)-6/(n+1), what is the value of n?
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> :`7/2` or 3.5</body></html>

Discussion

340.	At break even point, we have
Answer» <html><body><p>`(<a href="https://interviewquestions.tuteehub.com/tag/r-611811" style="font-weight:bold;" target="_blank" title="Click to know more about R">R</a>(x))/(C(x)) =<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/>`R(x) = 2C(x)` <br/>`C(x) lt R(x)` <br/>`p(x) lt <a href="https://interviewquestions.tuteehub.com/tag/0-251616" style="font-weight:bold;" target="_blank" title="Click to know more about 0">0</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> :N/A</body></html>

Discussion

341.	If the sides of a cyclic quadrilateral are 3,3,4,4, show that a circle be inscribed in it.
Answer» <html><body><p></p>Solution :Since, length of tangents from <a href="https://interviewquestions.tuteehub.com/tag/external-981194" style="font-weight:bold;" target="_blank" title="Click to know more about EXTERNAL">EXTERNAL</a> point to a circle are equal. <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>` AP=AS………(i) <br/> BP= BQ ……(ii) <br/> CR = CQ ………….(iii) <br/> <a href="https://interviewquestions.tuteehub.com/tag/dr-959219" style="font-weight:bold;" target="_blank" title="Click to know more about DR">DR</a>=DS…………..(iv) <br/> `therefore AB+ CD = (AP + <a href="https://interviewquestions.tuteehub.com/tag/pb-597752" style="font-weight:bold;" target="_blank" title="Click to know more about PB">PB</a>) (CR + DR)` <br/> `=(AS + BQ) + (CR + DS) <br/> =(AS+DS) + (BQ+CR)` <br/> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/AAK_T3_MAT_C08_SLV_093_S01.png" width="80%"/> <br/> `rArr AB + CD = AD + BC`.....(1) <br/> `therefore` A circle can be inscribed in a <a href="https://interviewquestions.tuteehub.com/tag/quadrilatera-2965178" style="font-weight:bold;" target="_blank" title="Click to know more about QUADRILATERA">QUADRILATERA</a>, if sides of a quadrilateral satisfies (1) <br/> Sides of quadrilateral are 3,3,4,4. <br/> If we take AB=3, CD=4, BC=3, AD=4 <br/> `therefore AB+CD = BC + AD=7` <br/> `therefore` Circle is inscribed in quadrilateral ABCD. <br/> If sum of opposite sides of a quadrilateral is equal. only then a cirlcle can be inscribed in a quadrilateral.</body></html>

Discussion

342.	(2^(n) [1.3.5. . .(2n-1) ])/(n!)=
Answer» <html><body><p>`""^(<a href="https://interviewquestions.tuteehub.com/tag/2n-300431" style="font-weight:bold;" target="_blank" title="Click to know more about 2N">2N</a>)C_n`<br/>`""^(2n)P_C`<br/>`""^(<a href="https://interviewquestions.tuteehub.com/tag/3n-310768" style="font-weight:bold;" target="_blank" title="Click to know more about 3N">3N</a>)C_n`<br/>`(2n[<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/n-568463" style="font-weight:bold;" target="_blank" title="Click to know more about N">N</a>-1)2])/(n!)`</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

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» <html><body><p>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><br/>b,c,a<br/>b,a,c<br/>a,c,b</p>Answer :A::C</body></html>

Discussion

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)
Answer» <html><body><p><br/></p>Answer :`(<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/2n-300431" style="font-weight:bold;" target="_blank" title="Click to know more about 2N">2N</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> pm (2pi)/3-2)`</body></html>

Discussion

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» <html><body><p><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/><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/>`-5`<br/>`-3`</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

346.	{:(" lim"),(x rarr 0):}((sinh 2x)/(2x))^(1/x^(2))=
Answer» <html><body><p><a href="https://interviewquestions.tuteehub.com/tag/0-251616" style="font-weight:bold;" target="_blank" title="Click to know more about 0">0</a><br/>`<a href="https://interviewquestions.tuteehub.com/tag/e-444102" style="font-weight:bold;" target="_blank" title="Click to know more about E">E</a>^(1/3)`<br/>`e^(2/3)`<br/>`e^(4/3)`</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

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
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) kQ[`before` <a href="https://interviewquestions.tuteehub.com/tag/k-527196" style="font-weight:bold;" target="_blank" title="Click to know more about K">K</a> <a href="https://interviewquestions.tuteehub.com/tag/decay-945588" style="font-weight:bold;" target="_blank" title="Click to know more about DECAY">DECAY</a> constant]<br/> (ii) KP(5000-P)[`before` is a constant] <br/> (iiii) `K(P)/(T^(<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a>))[before "k is a constant"]` <br/> (<a href="https://interviewquestions.tuteehub.com/tag/iv-501699" style="font-weight:bold;" target="_blank" title="Click to know more about IV">IV</a>) `(2x)/(25)+400`</body></html>

Discussion

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.
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/70-333629" style="font-weight:bold;" target="_blank" title="Click to know more about 70">70</a></body></html>

Discussion

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
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> :[0156] <br/> Moles of `AsH_(<a href="https://interviewquestions.tuteehub.com/tag/3-301577" style="font-weight:bold;" target="_blank" title="Click to know more about 3">3</a>)=(31.2)/(78)=0.4` <br/> <a href="https://interviewquestions.tuteehub.com/tag/heat-21102" style="font-weight:bold;" target="_blank" title="Click to know more about HEAT">HEAT</a> liberated `=(<a href="https://interviewquestions.tuteehub.com/tag/780-335876" style="font-weight:bold;" target="_blank" title="Click to know more about 780">780</a>)/(2)xx0.4=056kJ`</body></html>

Discussion

350.	If a fair coin is tossed 10 times, find the probability of Atleast six heads.
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/193-1800975" style="font-weight:bold;" target="_blank" title="Click to know more about 193">193</a>)/(<a href="https://interviewquestions.tuteehub.com/tag/512-1895092" style="font-weight:bold;" target="_blank" title="Click to know more about 512">512</a>)`</body></html>

Discussion

Explore topic-wise InterviewSolutions in Class 12.

If alpha,betagt0and alphaltbeta and ax^2+4gammaxy+betay^2+4p(x+y+1)=0 represents a pair of straight lines , then

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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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

If A = {(x,y): x,y in R, y = (1/7)^(x)} and B={(x,y), x, y in R, y = 7x} then

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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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

A book store has m copies each of n different books. Find the number of ways of arranging these books in a shelf.

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)

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)

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)

Which one of the following is independent of alpha in the hyperbola (0lt alphaltpi/2)x^2/(cos^2alpha)-y^2/(sin^2alpha)=1

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

Integrate the following functions: sin 4x sin8x

Consider the binary operation ** on the set A= {1,2,3,4,5} given by the following multiplication table Is ** commutative ?

Find the scalar and vector projection of veca on vecb. veca = hati-hatj-hatk,vecb = 3hati+hatj+3hatk.

If A is a matrix of order 3xx3, then |3A|= ".........."

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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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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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

Evaluation of definite integrals by subsitiution and properties of its : int_(0)^(1)(2x)/(5x^(2)+1)dx=..........

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Find the coordinates of the point where the line through (3,--4,-5) and (2, -3, 1) crosses the plane 2x + y + z = 7.

Find the sum of all 4-digited numbers that can be formed using the digits 0, 2, 3, 4, 6 without repetition.

Ifthe product of twoof therootsofx^4 - 5x^3 + 5x^2 + 5x -6=0is2 thenthe rootsare

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)

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

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

The sum of two non - integral roots of |(x,2,5),(3,x,3),(5,4,x)|=0 is :

The value of the integral int_(-3pi)^(3pi)|sin^(3)x|dx is equal to

Volume of the tetrahedron with vertices P(-1, 2, 0), Q(2, 1, -3), R(1, 0, 1) and S(3, -2, 3) is

IF 0=2/(n-2)-6/(n+1), what is the value of n?

At break even point, we have

If the sides of a cyclic quadrilateral are 3,3,4,4, show that a circle be inscribed in it.

(2^(n) [1.3.5. . .(2n-1) ])/(n!)=

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

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)

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)]

{:(" lim"),(x rarr 0):}((sinh 2x)/(2x))^(1/x^(2))=

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.

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

If a fair coin is tossed 10 times, find the probability of Atleast six heads.

Consider the binary operation on the set A= {1,2,3,4,5} given by the following multiplication table Is commutative ?