Explore topic-wise InterviewSolutions in Class 12.

This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your Class 12 knowledge and support exam preparation. Choose a topic below to get started.

28151.

If alpha, beta are the irrational roots of the equation x^(5)-5x^(4)+9x^(3)-9x^(2)+5x-1=0 then the roots of the equation (alpha+beta)x^(2)+2alphabetax-alphabeta=0are

Answer» <html><body><p>`-<a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a>,(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>)` <br/>`(3+-sqrt(3))/(<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/>`(1+-isqrt(3))/(2)`<br/>`1,-(1)/(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</body></html>
Discussion
28152.

Let f and g be differentiable functions on R such that fog is the identity function. If for some a,b in R,g'(a)=5 and g(a)=b, then f'(b) is equal to :

Answer» <html><body><p>`2/5`<br/>`1/5`<br/>1<br/>5</p>Answer :D</body></html>
Discussion
28153.

Evaluate the following determinants. [[1,1,1],[1,1,1],[1,1,1]]

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> :`[[1,1,1],[1,1,1],[1,1,1]]`=<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/> as the <a href="https://interviewquestions.tuteehub.com/tag/row-1191712" style="font-weight:bold;" target="_blank" title="Click to know more about ROW">ROW</a> are <a href="https://interviewquestions.tuteehub.com/tag/identical-496701" style="font-weight:bold;" target="_blank" title="Click to know more about IDENTICAL">IDENTICAL</a>.</body></html>
Discussion
28154.

Let x be a non-zero real number. A determinant is chosen from the set of all determinants of order 2 with entries x or -x only. The probability that the value of the determinant is non-zero is

Answer» <html><body><p>`(3)/(<a href="https://interviewquestions.tuteehub.com/tag/16-276476" style="font-weight:bold;" target="_blank" title="Click to know more about 16">16</a>)`<br/>`(1)/(<a href="https://interviewquestions.tuteehub.com/tag/4-311707" style="font-weight:bold;" target="_blank" title="Click to know more about 4">4</a>)`<br/>`(1)/(2)`<br/>`(1)/(3)`</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
28155.

If (m_(1),1//m_(1)), i=1,2,3,4 are concyclic points, then the value of m_(1)m_(2)m_(3)m_(4)" is"

Answer» <html><body><p><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/>`-1`<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/>`<a href="https://interviewquestions.tuteehub.com/tag/oo-583684" style="font-weight:bold;" target="_blank" title="Click to know more about OO">OO</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
28156.

Show that the circles x^(2) +y^(2) + 2ax + c=0 and x ^(2) + y^(2)+ 2by + c=0to touch each other if(1)/(a^(2)) + (1)/( b^(2)) = (1)/( c )

Answer» <html><body><p><br/></p>Answer :i.e. if ` (1)/( 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>)) + (1)/( <a href="https://interviewquestions.tuteehub.com/tag/b-387190" style="font-weight:bold;" target="_blank" title="Click to know more about B">B</a>^(2)) = (1)/( <a href="https://interviewquestions.tuteehub.com/tag/c-7168" style="font-weight:bold;" target="_blank" title="Click to know more about C">C</a> ) ` which is <a href="https://interviewquestions.tuteehub.com/tag/true-713260" style="font-weight:bold;" target="_blank" title="Click to know more about TRUE">TRUE</a></body></html>
Discussion
28157.

If f(x) = (x-1)/(x+1), x ne -1, 1, then "fof"^(-1) is

Answer» <html><body><p><a href="https://interviewquestions.tuteehub.com/tag/identity-1036134" style="font-weight:bold;" target="_blank" title="Click to know more about IDENTITY">IDENTITY</a> <a href="https://interviewquestions.tuteehub.com/tag/function-11303" style="font-weight:bold;" target="_blank" title="Click to know more about FUNCTION">FUNCTION</a><br/>Even function<br/>Odd function <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</body></html>
Discussion
28158.

Let an object be placed at some height h cm and let P and Q two points of observation which are at a distance 10 cm a part on a line inclined at angle 15° to the horizontal. If the angles of elevation of the object from P and Q are 30^@ and 60^@ respectively then find h.

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> :`5sqrt(<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/cm-919986" style="font-weight:bold;" target="_blank" title="Click to know more about CM">CM</a>`</body></html>
Discussion
28159.

Let A = N xx N and ** be the binary opertion on A defined by (a,b) ** (c,d) = (a + c, b+d) Show that ** is commutative and associative. Find the identity element for ** on A, if any.

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/identity-1036134" style="font-weight:bold;" target="_blank" title="Click to know more about IDENTITY">IDENTITY</a> <a href="https://interviewquestions.tuteehub.com/tag/element-969236" style="font-weight:bold;" target="_blank" title="Click to know more about ELEMENT">ELEMENT</a> does not <a href="https://interviewquestions.tuteehub.com/tag/exist-979486" style="font-weight:bold;" target="_blank" title="Click to know more about EXIST">EXIST</a>.</body></html>
Discussion
28160.

Find the probability distribution of (i) number of heads in two tosses of a coin.  (ii) number of tails in the simultaneous tosses of three coins. (iii) number of heads in four tosses of a coin.

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> :`(##NCERT_GUJ_MAT_XII_P2_C13_E04_004_A01##)` <br/> `(##NCERT_GUJ_MAT_XII_P2_C13_E04_004_A02##)`</body></html>
Discussion
28161.

Using the second Guldin theorem, find the coordinates of the centre of gravity of the figure bounded by the x-axis and one are of the cycloid: x=a (t -sin t), y = a (1- cos t).

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/5a-326262" style="font-weight:bold;" target="_blank" title="Click to know more about 5A">5A</a>)/(<a href="https://interviewquestions.tuteehub.com/tag/6-327005" style="font-weight:bold;" target="_blank" title="Click to know more about 6">6</a>)`</body></html>
Discussion
28162.

cot^(-1)((sqrt(1+x^(2))-1)/(x))=

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>)/(2)-(<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)<a href="https://interviewquestions.tuteehub.com/tag/cot-936468" style="font-weight:bold;" target="_blank" title="Click to know more about COT">COT</a>^(-1)x`<br/>`cot^(-1)x`<br/>`-(1)/(2)<a href="https://interviewquestions.tuteehub.com/tag/tan-1238781" style="font-weight:bold;" target="_blank" title="Click to know more about TAN">TAN</a>^(-1)x`<br/>`(pi)/(2)-(1)/(2)tan^(-1)x`</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
28163.

In the cartesian plane, O is the origin of the coordinate axes. A person starts at O and walks a distance of 3 units in the NORTH - EAST direction and reaches the point P. From P he walks 4 units distance parallel to NORTH - WEST direction and reaches the point Q. Express the vector bar(OQ) interms of bar(i) and bar(j) (Observe angleXOP=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/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</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>(2))(-<a href="https://interviewquestions.tuteehub.com/tag/bar-892478" style="font-weight:bold;" target="_blank" title="Click to know more about BAR">BAR</a>(i)+7bar(j))`</body></html>
Discussion
28164.

If eccentricity of conjugate hyperbola of the given hyperbola : |sqrt((x-1)^(2)+(y-2)^(2))-sqrt((x-5)^(2)+(y-5)^(2))|=3 is e', then value of 8e' is :

Answer» <html><body><p>12<br/>14<br/>17<br/>10</p>Answer :D</body></html>
Discussion
28165.

Prove statement "tan"^(-1)((a-b)/(1+ab)) +"tan"^(-1)((b-c)/(1+bc)) ="tan"^(-1)a-"tan"^(-1) c.

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> :"<a href="https://interviewquestions.tuteehub.com/tag/tan-1238781" style="font-weight:bold;" target="_blank" title="Click to know more about TAN">TAN</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>)((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>)/(1+ab)) +"tan"^(-1)((b-<a href="https://interviewquestions.tuteehub.com/tag/c-7168" style="font-weight:bold;" target="_blank" title="Click to know more about C">C</a>)/(1+bc))<br/>`="tan"^(-1) a- "tan"^(-1)b+"tan"^(-1)b-"tan"^(-1)c`<br/>`"tan"^(-1)a-"tan"(-1)c`</body></html>
Discussion
28166.

Find x and y :[[x+3],[2-y]]=[[1],[-3]]

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> :`[[x+<a href="https://interviewquestions.tuteehub.com/tag/3-301577" style="font-weight:bold;" target="_blank" title="Click to know more about 3">3</a>],[2-y]]=[[<a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a>],[-3]]`<br/>`:. x+3=1,2-y=-3`<br/>`:.x=-2,y=5`</body></html>
Discussion
28167.

Construct Collection of all integers of multiples of 3 in the form of set and describe it with the help of proposition.

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> :`D ={<a href="https://interviewquestions.tuteehub.com/tag/0-251616" style="font-weight:bold;" target="_blank" title="Click to know more about 0">0</a>,+-<a href="https://interviewquestions.tuteehub.com/tag/3-301577" style="font-weight:bold;" target="_blank" title="Click to know more about 3">3</a>,+- <a href="https://interviewquestions.tuteehub.com/tag/6-327005" style="font-weight:bold;" target="_blank" title="Click to know more about 6">6</a>}` <brge :x="" a="" all="" integers="" is="" multiples="" of="" set=""></brge></body></html>
Discussion
28168.

There are 30 boys and 20 girls in a class. The mean and variance of their marks in maths are, respectively, 65 and 100. If 5 grace marks are added to the score of each students, then the revised mean and variance will be respectively.

Answer» <html><body><p>`70, 100` <br/>` 70, "variance " gt 100` <br/>` 65, "variance " <a href="https://interviewquestions.tuteehub.com/tag/lt-537906" style="font-weight:bold;" target="_blank" title="Click to know more about LT">LT</a> 100` <br/>` 65, 100` </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
28169.

Find the variance of the number obtained on a throw of an unbiased die.

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/35-308504" style="font-weight:bold;" target="_blank" title="Click to know more about 35">35</a>)/(<a href="https://interviewquestions.tuteehub.com/tag/12-269062" style="font-weight:bold;" target="_blank" title="Click to know more about 12">12</a>)`</body></html>
Discussion
28170.

If A = {x|x inN, xle5}, B = {x|x in Z, x^(2) – 5x +6=0}, then the number of onto functions from A to B is

Answer» <html><body><p>30<br/>2<br/>32<br/>23</p>Answer :A</body></html>
Discussion
28171.

int sec^(2)x*cosec^2(x)dx=.....+c

Answer» <html><body><p>`tanx+cotx`<br/>`tanx-cotx`<br/>`sec^(<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a>)x+"<a href="https://interviewquestions.tuteehub.com/tag/cosec-426601" style="font-weight:bold;" target="_blank" title="Click to know more about COSEC">COSEC</a>"^(2)x`<br/>`cotx-tanx`</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
28172.

Let function f(x) be defined as f(x) = |sin^(-1)x| + cos^(-1) (1/x) .Then which of the following is /are TRUE.

Answer» <html><body><p>f(<a href="https://interviewquestions.tuteehub.com/tag/x-746616" style="font-weight:bold;" target="_blank" title="Click to know more about X">X</a>) is injective in its domain. <br/>f(x) is <a href="https://interviewquestions.tuteehub.com/tag/many-554478" style="font-weight:bold;" target="_blank" title="Click to know more about MANY">MANY</a> - one in its domain. <br/>Range of f is <a href="https://interviewquestions.tuteehub.com/tag/singleton-1210377" style="font-weight:bold;" target="_blank" title="Click to know more about SINGLETON">SINGLETON</a> set <br/>sgn (f(x)) =1 , where sgn x <a href="https://interviewquestions.tuteehub.com/tag/denotes-948116" style="font-weight:bold;" target="_blank" title="Click to know more about DENOTES">DENOTES</a> signum function of x. </p>Answer :A::D</body></html>
Discussion
28173.

Using differentials, find the approximate value of each of the up to 3 places of decimal. (0.0999)^((1)/(10))

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> :0.999</body></html>
Discussion
28174.

A set of values of theta for which the system of equations (sin 3theta ) x +4y+3z=0,2x+7y+7z=0 has non -trivial solutions is

Answer» <html><body><p>`(n+<a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a>)^(pi)/(2)+(-1)^(n)(pi)/(<a href="https://interviewquestions.tuteehub.com/tag/4-311707" style="font-weight:bold;" target="_blank" title="Click to know more about 4">4</a>)` (here n is any <a href="https://interviewquestions.tuteehub.com/tag/integer-11854" style="font-weight:bold;" target="_blank" title="Click to know more about INTEGER">INTEGER</a>) <br/>`(n-1)^(pi)/(2)+(-1)^(n)(pi)/(4)` (here n is any integer) <br/>`(npi)/(2)+(-1)^(n)(pi)/(<a href="https://interviewquestions.tuteehub.com/tag/6-327005" style="font-weight:bold;" target="_blank" title="Click to know more about 6">6</a>)` ( here n is any integer ) <br/>`npi +(-1)^(n)(pi)/(6)` ( here n is any integer ) </p>Answer :D</body></html>
Discussion
28175.

For Delta ABC,if 81 + 144 a ^(4) + 16b ^(4) + 9c ^(4) =144 abc, (where notations have their usual meaning), then :

Answer» <html><body><p>`a <a href="https://interviewquestions.tuteehub.com/tag/gt-1013864" style="font-weight:bold;" target="_blank" title="Click to know more about GT">GT</a> b gt <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/>`A lt B lt C`<br/>Area of `Delta ABC = (3 <a href="https://interviewquestions.tuteehub.com/tag/sqrt3-3056952" style="font-weight:bold;" target="_blank" title="Click to know more about SQRT3">SQRT3</a>)/(8)`<br/>Triangle ABC is <a href="https://interviewquestions.tuteehub.com/tag/right-1188951" style="font-weight:bold;" target="_blank" title="Click to know more about RIGHT">RIGHT</a> angled </p>Answer :B::C::D</body></html>
Discussion
28176.

Solve system of linear equations , using matrix method if exists 2/x-3/y+3/z=10 1/x+1/y+1/z=10 3/x-1/y+2/z=13

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> :`x=1/2,y=1/3,z=1/5`</body></html>
Discussion
28177.

If |x-5| lt 1 then the range of f(x) = (x)/(X+10) is

Answer» <html><body><p>`(2/3 , 3/8)`<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> , <a href="https://interviewquestions.tuteehub.com/tag/oo-583684" style="font-weight:bold;" target="_blank" title="Click to know more about OO">OO</a>)`<br/>`(3/7, 3/4)`<br/>`(<a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a>, oo)`</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
28178.

If the lengths of tangents drawn to the circlesx^(2) + y^(2) -8x + 40 = 0 , 5x^(2) + 5y^(2) - 25x + 80 = 0 , x^(2) + y^(2) - 8x + 16y+ 160 = 0from the point P are equal, then P =

Answer» <html><body><p>`(<a href="https://interviewquestions.tuteehub.com/tag/8-336412" style="font-weight:bold;" target="_blank" title="Click to know more about 8">8</a>, (<a href="https://interviewquestions.tuteehub.com/tag/15-274069" style="font-weight:bold;" target="_blank" title="Click to know more about 15">15</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/>`(-8,(15)/(2))`<br/>`(8, (-15)/(2))`<br/>`(-8, (-15)/(2))` </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
28179.

Study the following statements. I. The vertex of the parabola x=ly^(2)+my+n is (n-m^(2)/(4 l), -m/(2l)) II. The focus of the parabola y=l x^(2) +mx+n is (n+(1-m^(2))/(4l), -m/(2l)) III. The pole of the line lx+my+n=0 with respect to the parabola x^(2)=4ay is (-(2 al)/m, n/m) Then the correct option among the following is

Answer» <html><body><p>A.All the three <a href="https://interviewquestions.tuteehub.com/tag/statement-16478" style="font-weight:bold;" target="_blank" title="Click to know more about STATEMENT">STATEMENT</a> are <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/>B.Statement I &amp; <a href="https://interviewquestions.tuteehub.com/tag/ii-1036832" style="font-weight:bold;" target="_blank" title="Click to know more about II">II</a> are true but III is false<br/><a href="https://interviewquestions.tuteehub.com/tag/c-7168" style="font-weight:bold;" target="_blank" title="Click to know more about C">C</a>.Statement I &amp; III are true but II is false<br/>D.Statement II &amp; III are true but I is false</p>Answer :C</body></html>
Discussion
28180.

Maximum slope of the curve y=-x^(3)+3x^(2)+9x-27 is ………….

Answer» <html><body><p>0<br/>12<br/>16<br/>32</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
28181.

Integrate the functions 1/(xsqrt(ax-x^(2))) [Hint: Put x =a/t]

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/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a>)/(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-<a href="https://interviewquestions.tuteehub.com/tag/x-746616" style="font-weight:bold;" target="_blank" title="Click to know more about X">X</a>)/(x))+<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
28182.

If the chord of contact of a point P with respect to thecirclesx ^(2) + y ^(2)= a ^(2)cut the circle at A and B such thatangle AOB =90 ^(@).Find the locus of P.

Answer» <html><body><p><br/></p>Answer :` <a href="https://interviewquestions.tuteehub.com/tag/therefore-706901" style="font-weight:bold;" target="_blank" title="Click to know more about THEREFORE">THEREFORE</a> (x_1.y_1) ` <a href="https://interviewquestions.tuteehub.com/tag/lies-1073086" style="font-weight:bold;" target="_blank" title="Click to know more about LIES">LIES</a> on the circle `<a href="https://interviewquestions.tuteehub.com/tag/x-746616" style="font-weight:bold;" target="_blank" title="Click to know more about X">X</a> ^(2) +y^(2)=<a href="https://interviewquestions.tuteehub.com/tag/2a-300249" style="font-weight:bold;" target="_blank" title="Click to know more about 2A">2A</a>^(2) `</body></html>
Discussion
28183.

The solution of cos x(dy)/(dx) + y = sin x is

Answer» <html><body><p>`y(sec <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/tan-1238781" style="font-weight:bold;" target="_blank" title="Click to know more about TAN">TAN</a> x) = sec x + Tan x + x + <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/>`y(sec x + Tan x) = sec x + Tan x - x + c`<br/>`y(sec x + Tan x) = sec x - Tan x - x + c`<br/>`y(sec x - Tan x) = sec x + Tan x + x - c`</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
28184.

Which of the following is correct combination

Answer» <html><body><p>(i) (<a href="https://interviewquestions.tuteehub.com/tag/ii-1036832" style="font-weight:bold;" target="_blank" title="Click to know more about II">II</a>) (<a href="https://interviewquestions.tuteehub.com/tag/q-609558" style="font-weight:bold;" target="_blank" title="Click to know more about Q">Q</a>)<br/>(III) (i) (S)<br/>(II) (iv) (S)<br/>(IV) (iii) (<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> :<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
28185.

Which of the following is correct combination

Answer» <html><body><p>(<a href="https://interviewquestions.tuteehub.com/tag/ii-1036832" style="font-weight:bold;" target="_blank" title="Click to know more about II">II</a>) (ii) (P)<br/>(i) (ii) (Q) <br/>(I) (ii) (<a href="https://interviewquestions.tuteehub.com/tag/r-611811" style="font-weight:bold;" target="_blank" title="Click to know more about R">R</a>)<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>) (<a href="https://interviewquestions.tuteehub.com/tag/iii-497983" style="font-weight:bold;" target="_blank" title="Click to know more about III">III</a>) (R)</p>Answer :C</body></html>
Discussion
28186.

If line (x-2)/(3)=(y-4)/(4)=(z+2)/(1)is parallel to planesmux+3y-2z+d=0and x-2lambda y+z=0,then value oflambdaand mu are

Answer» <html><body><p>`mu=4, lambda=-(2)/(3)`<br/>`mu=-6, lambda=-2`<br/>`mu=(-<a href="https://interviewquestions.tuteehub.com/tag/10-261113" style="font-weight:bold;" target="_blank" title="Click to know more about 10">10</a>)/(3), lambda=(-<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/>`mu=(-10)/(3), lambda=(1)/(2)`</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> :`3xxmu+4xx3+1xx(-2)=<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/> `3mu=2-12` <br/> `mu=(-10)/(3) and3xx1+4xx(-2lambda)+1xx1=0` <br/> `-8lambda=-4,""lambda=(1)/(2)`</body></html>
Discussion
28187.

bar(a)=a_(1)hati+a_(2)hatj+a_(3)hatk,bar(b)=b_(1)hati+b_(2)hatj+b_(3)hatk,bar( c )=c_(1)hati+c_(2)hatj+c_(3)hatk are three non zero vectors. The unit vector bar( c ) is perpendicular to bar(a) and bar(b). The angle between bar(a) and bar(b) is (pi)/(6) then, |{:(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3)):}| = .............

Answer» <html><body><p>0<br/>1<br/>`(1)/(<a href="https://interviewquestions.tuteehub.com/tag/4-311707" style="font-weight:bold;" target="_blank" title="Click to know more about 4">4</a>)|<a href="https://interviewquestions.tuteehub.com/tag/bar-892478" style="font-weight:bold;" target="_blank" title="Click to know more about BAR">BAR</a>(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>)|bar(<a href="https://interviewquestions.tuteehub.com/tag/b-387190" style="font-weight:bold;" target="_blank" title="Click to know more about B">B</a>)|^(2)`<br/>`(3)/(4)|bar(a)|^(2)|bar(b)|^(2)` </p>Answer :C</body></html>
Discussion
28188.

The solution of y dx - x dy + log x dx = 0 is

Answer» <html><body><p>`y - <a href="https://interviewquestions.tuteehub.com/tag/log-543719" style="font-weight:bold;" target="_blank" title="Click to know more about LOG">LOG</a> x - 1 = <a href="https://interviewquestions.tuteehub.com/tag/cx-428873" style="font-weight:bold;" target="_blank" title="Click to know more about CX">CX</a>`<br/>`x + log y + 1 = cx`<br/>`y + log x + 1 = cx`<br/>`y + log x - 1 = <a href="https://interviewquestions.tuteehub.com/tag/c-7168" style="font-weight:bold;" target="_blank" title="Click to know more about C">C</a> x`</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> :C</body></html>
Discussion
28189.

Out of 8 given points .3 are collinear.How many different straight lines can be drawn by joining any two points from those 8 points ?

Answer» <html><body><p>26<br/>28<br/>27<br/>25</p>Answer :A</body></html>
Discussion
28190.

(sin 7 theta+ 6 sin 5 theta+17sin 3 theta+12sin theta)/(sin 6 theta+5 sin 4 theta+12sin 2theta)

Answer» <html><body><p>`<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/cos-935872" style="font-weight:bold;" target="_blank" title="Click to know more about COS">COS</a> <a href="https://interviewquestions.tuteehub.com/tag/theta-1412757" style="font-weight:bold;" target="_blank" title="Click to know more about THETA">THETA</a>`<br/>`cos theta`<br/>`2 <a href="https://interviewquestions.tuteehub.com/tag/sin-1208945" style="font-weight:bold;" target="_blank" title="Click to know more about SIN">SIN</a> theta`<br/>`sin theta`</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
28191.

Find x if abs[[2,4],[5,1]]=abs[[2x,4],[6,x]]

Answer» <html><body><p></p>Solution :The given equation may be <a href="https://interviewquestions.tuteehub.com/tag/written-732709" style="font-weight:bold;" target="_blank" title="Click to know more about WRITTEN">WRITTEN</a> as <br/> 2-20 = `2x^2 - 24 <a href="https://interviewquestions.tuteehub.com/tag/implies-1037962" style="font-weight:bold;" target="_blank" title="Click to know more about IMPLIES">IMPLIES</a> -<a href="https://interviewquestions.tuteehub.com/tag/18-278913" style="font-weight:bold;" target="_blank" title="Click to know more about 18">18</a> = 2x^2 - 24 implies 2x^2 = 6 implies x^2 = <a href="https://interviewquestions.tuteehub.com/tag/3-301577" style="font-weight:bold;" target="_blank" title="Click to know more about 3">3</a>`</body></html>
Discussion
28192.

If f(x)={((sin([x]+x))/([x]+x),x!=0),(1,x=0):} when [.] denotes the greatest integer function, then:

Answer» <html><body><p>`lim_(xto0)(f(x)=<a href="https://interviewquestions.tuteehub.com/tag/sin1-3032522" style="font-weight:bold;" target="_blank" title="Click to know more about SIN1">SIN1</a>`<br/>`lim_(xto0)f(x)=1`<br/>`lim_(xto0)f(x)` does not <a href="https://interviewquestions.tuteehub.com/tag/exist-979486" style="font-weight:bold;" target="_blank" title="Click to know more about EXIST">EXIST</a><br/>`lim_(xto0)f(x)` <a href="https://interviewquestions.tuteehub.com/tag/exists-979838" style="font-weight:bold;" target="_blank" title="Click to know more about EXISTS">EXISTS</a> but `f(x)` is not <a href="https://interviewquestions.tuteehub.com/tag/continuous-932035" style="font-weight:bold;" target="_blank" title="Click to know more about CONTINUOUS">CONTINUOUS</a> at x=0</p>Answer :C</body></html>
Discussion
28193.

A square is inscribed in the circlex^(2)+y^(2)-4x+6y-5=0 whose sides are parallel to co-ordinate axes then vetices of square are

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>,<a href="https://interviewquestions.tuteehub.com/tag/0-251616" style="font-weight:bold;" target="_blank" title="Click to know more about 0">0</a>),(5,-<a href="https://interviewquestions.tuteehub.com/tag/6-327005" style="font-weight:bold;" target="_blank" title="Click to know more about 6">6</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>,0),(-1,-6)<br/>(5,1),(5,-6),(-,1),(-1,-6)<br/>(5,-1),(5,6),(-1,0),(1,-6)<br/>(0,5),(-6,5),(0,-1),(6,1)</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
28194.

(1-omega +omega^2)(1+omega-omega^2)=4

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> :L.H.S.`=(1-omega+omega^2)(1+omega-omega^2)`<br/>`= (-omega-omega)(-omega^2-omega^2)(:' 1+omega+omega^2=0)`<br/>`(-2omega-2omega^2)=4omega^3=4=`R.H.S.</body></html>
Discussion
28195.

z = x + iy and w = (1 - iz)/(z-i) , then |w| = 1 implies in the complex plane

Answer» <html><body><p>z lies on the imaginary <a href="https://interviewquestions.tuteehub.com/tag/axis-889931" style="font-weight:bold;" target="_blank" title="Click to know more about AXIS">AXIS</a> <br/>z lies on the real axis <br/>z lies on the unit circle <br/>z lies on the <a href="https://interviewquestions.tuteehub.com/tag/parabola-1146268" style="font-weight:bold;" target="_blank" title="Click to know more about PARABOLA">PARABOLA</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
28196.

Let f(x) = x^3 + ax^2 + bx + c and g(x) = x^3 + bx^2 + cx + a, where a, b, c are integers. Suppose that the following conditions hold- (a) f(1) = 0, (b) the roots of g(x) = 0 are the squares of the roots of f(x) = 0. Find the value of: a^(2013) + b^(2013) + c^(2013)

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/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a>`</body></html>
Discussion
28197.

Evaluate the following determinants. [[1,0,0],[0,1,0],[0,0,1]]

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> :`[[<a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a>,0,0],[0,1,0],[0,0,1]]=1[[1,0],[0,1]]`=1-0=1</body></html>
Discussion
28198.

Removesecondterm( secondhigherpowerof x )fromthe equation x^3-6x^2 +4x -7=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> :`x^3 -8x-15=0`</body></html>
Discussion
28199.

If A is the set of students of a school then write, which of following relations are Universal, Empty or neither of the two. R_(1)={(a,b):a,b " are ages of students and" |a-b| gt 0} R_(2)={(a,b):a,b " are weights ofstudents, and "|a-b|lt0} R_(3)={(a,b):a,b " are students studying in same class"}

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> :`R_(1)` : is universal <a href="https://interviewquestions.tuteehub.com/tag/relation-1183220" style="font-weight:bold;" target="_blank" title="Click to know more about RELATION">RELATION</a>. <br/> `R_(2)`: is <a href="https://interviewquestions.tuteehub.com/tag/empty-2611346" style="font-weight:bold;" target="_blank" title="Click to know more about EMPTY">EMPTY</a> relation. <br/> `R_(<a href="https://interviewquestions.tuteehub.com/tag/3-301577" style="font-weight:bold;" target="_blank" title="Click to know more about 3">3</a>)`: is <a href="https://interviewquestions.tuteehub.com/tag/neither-1113494" style="font-weight:bold;" target="_blank" title="Click to know more about NEITHER">NEITHER</a> universal nor empty</body></html>
Discussion
28200.

int_(0)^(2)[x^(2)]dx=

Answer» <html><body><p><a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a>)`5-sqrt2+sqrt3`<br/>2)`5-sqrt2-sqrt3`<br/>3)`-5-sqrt2-sqrt3`<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>)`5+sqrt2-sqrt3`</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