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InterviewSolution
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.
| 401. |
x+2y+4z=12 y+2z=-1 3x+2y+4z=4 |
| Answer» | |
| 402. |
xa^3+ya^2+za=0 In the equation above,x,y and z are constants. IF the equations has roots -6,0 and 4, which of the following is a factor of xa^3+ya^2+za? |
| Answer» <html><body><p>a-2<br/>a+4<br/>a-6<br/>a+6</p>Answer :D</body></html> | |
| 403. |
A letter is known to have come from either 'MAHARASTRA' or 'MADRAS' on the post mark only conseutive letter 'RA' can be read clearly. What is the chance that the letter came from 'MAHARASTRA'. |
| 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/10-261113" style="font-weight:bold;" target="_blank" title="Click to know more about 10">10</a>)/(<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> | |
| 404. |
If f(x)=sqrt("cosec"^2x-2sinx cosx - 1/(tan^2x)) x in ((7pi)/4,2pi), then f.((11pi)/6)= |
| Answer» <html><body><p>`(1-sqrt3)/2`<br/>`(sqrt3-1)/2`<br/>`(1+sqrt3)/2`<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><a href="https://interviewquestions.tuteehub.com/tag/solution-25781" style="font-weight:bold;" target="_blank" title="Click to know more about SOLUTION">SOLUTION</a> :`f(x)=sqrt("cosec"^2x-cot^2x-2sin x cos x)` <br/> `=sqrt((cosx-sinx)^2)` <br/> <img src="https://doubtnut-static.s.llnwi.net/static/physics_images/VMC_JEE_MN_PT_03_E03_012_S01.png" width="80%"/> <br/>f(x)=cos x -sin x <br/> `<a href="https://interviewquestions.tuteehub.com/tag/rarr-1175461" style="font-weight:bold;" target="_blank" title="Click to know more about RARR">RARR</a>` f.(x)=-sin x - cos x <br/> `f.((11pi)/<a href="https://interviewquestions.tuteehub.com/tag/6-327005" style="font-weight:bold;" target="_blank" title="Click to know more about 6">6</a>)=-[sin (11pi)/6 + cos(11pi)/6]` <br/> `rArr f.((11pi)/6)=-[(-1)/2+sqrt3/2]=(1-sqrt3)/2`</body></html> | |
| 405. |
The longest distance of the point (a, 0) from the curve 2x^2+y^2=2x is |
| Answer» <html><body><p>`1+a`<br/>`|1-a|`<br/>`<a href="https://interviewquestions.tuteehub.com/tag/root-1190914" style="font-weight:bold;" target="_blank" title="Click to know more about ROOT">ROOT</a>()(1-2a+2a^2)`<br/>`root()(1-2a+3a^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> | |
| 406. |
The set of points where the function f given by f(x) = |2x – 1| sin x is differentiable is |
| Answer» <html><body><p>R<br/>`R-{(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>)}`<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/>None of these</p>Answer :B</body></html> | |
| 407. |
There are 5 bags, each containing 5 white balls and 3 black balls. Also, there are 6 bags, each containing 2 white balls and 4 black balls. A white balls is drawn at random. Find the probability that this white ball is from a bag of the first group. |
| 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>></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> :Let `E_1` = event of selecting a bag from the first group, <br/> `E_2` = event of selecting a bag from the second group, and <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> = event of drawing a <a href="https://interviewquestions.tuteehub.com/tag/white-742716" style="font-weight:bold;" target="_blank" title="Click to know more about WHITE">WHITE</a> ball.<br/> Then, `P(E_1)=5/11and P(E_2)=6/11`. <br/> `P(E//E_1)`= probability of <a href="https://interviewquestions.tuteehub.com/tag/getting-2670847" style="font-weight:bold;" target="_blank" title="Click to know more about GETTING">GETTING</a> a white ball, given that it is from a bag of the first group <br/> `=5/8`. <br/> `P(E//E_2)` = probability of getting a white ball, given that it is from a bag of the second group <br/> `=2/6=1/3` <br/> Probability of getting the ball from a bag of the first group, given that it is white <br/> `P(E_1//E)` <br/> `=(P(E//E_1).P(E_1))/(P(E//E_1).P(E_1)+P(E//E_2).P(E_2))`[by Bayes's theorem] <br/> `=((5/8xx5/11))/((5/8xx5/11)+(1/3xx6/11))=75/123`.</body></html> | |
| 408. |
If veca, vecb and vecc are non-zero vectors, then vecaxxvecb = vecaxxvecc |
| Answer» <html><body><p>`<a href="https://interviewquestions.tuteehub.com/tag/vecb-3257249" style="font-weight:bold;" target="_blank" title="Click to know more about VECB">VECB</a>` = `<a href="https://interviewquestions.tuteehub.com/tag/vecc-3257279" style="font-weight:bold;" target="_blank" title="Click to know more about VECC">VECC</a>`<br/>`<a href="https://interviewquestions.tuteehub.com/tag/veca-3257210" style="font-weight:bold;" target="_blank" title="Click to know more about VECA">VECA</a>||(vecb-vecc)<br/>`vecb||vecc`<br/>`vecbbotvecc`</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> | |
| 409. |
Find the vector cartesian equation of the plane passing through the points (1, -2, 3) and (-1, 2, -1) and is parallel to the line vecr=(2hati-hatj+hatk)+t(2hati+3hatj+4hatk) |
| 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> :N/A</body></html> | |
| 410. |
IF a,b,care thenumberof4digitednumberthat canbeformedusingthe digits2,4,5,7,8that aredivisibleby3,4,5 respectively thenascendingorderof 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/>c,b,a<br/>c,a,b</p>Answer :C</body></html> | |
| 411. |
If veca and vecb are two nonzero vectors such that |vecaxxvecb|=veca.vecb then find the angle between veca and vecb. |
| 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/45-316951" style="font-weight:bold;" target="_blank" title="Click to know more about 45">45</a>^(@)`</body></html> | |
| 412. |
Match the statements/expressions given in List I with the values given in List II. |
| 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>>`{:(a,b,c,d),(s,r,<a href="https://interviewquestions.tuteehub.com/tag/q-609558" style="font-weight:bold;" target="_blank" title="Click to know more about Q">Q</a>,p):}`<br/>`{:(a,b,c,d),(q,s,r,p):}`<br/>`{:(a,b,c,d),(s,r,p,q):}`<br/>`{:(a,b,c,d),(q,s,p,r):}`<br/></p>Solution :`y=<a href="https://interviewquestions.tuteehub.com/tag/cos-935872" style="font-weight:bold;" target="_blank" title="Click to know more about COS">COS</a> (3 cos^(-1)x)` <br/> `rArr""(3 sin (3 cos^(-1)x))/(sqrt(1-x^(2)))` <br/> `rArr""sqrt(1-x^(2))y'=3 sin (3 cos ^(-1)x)` <br/> `rArr""(-x)/(sqrt(1-x^(2)))y'+sqrt(1+x^(2))y''=<a href="https://interviewquestions.tuteehub.com/tag/3cos-310909" style="font-weight:bold;" target="_blank" title="Click to know more about 3COS">3COS</a> (3cos ^(-1) x)<a href="https://interviewquestions.tuteehub.com/tag/cdot-407575" style="font-weight:bold;" target="_blank" title="Click to know more about CDOT">CDOT</a>(-3)/(sqrt(1-x^(2)))` <br/> `rArr""-xy'+(1-x^(2))y''=-9y` <br/> `rArr""(1)/(y)[(x^(2)-1)y''+xy']=9`</body></html> | |
| 413. |
Let triangle ABC be right angled at C.If tanA+tanB2, then- |
| Answer» <html><body><p>`/_A = 30^(@)`<br/><a href="https://interviewquestions.tuteehub.com/tag/triangle-1427233" style="font-weight:bold;" target="_blank" title="Click to know more about TRIANGLE">TRIANGLE</a> <a href="https://interviewquestions.tuteehub.com/tag/abc-360912" style="font-weight:bold;" target="_blank" title="Click to know more about ABC">ABC</a> must be <a href="https://interviewquestions.tuteehub.com/tag/isoscles-2751988" style="font-weight:bold;" target="_blank" title="Click to know more about ISOSCLES">ISOSCLES</a> <br/>sides of the triangle ABC are 3,4,5<br/>triangle must be scalene</p>Answer :B</body></html> | |
| 414. |
If int (3 cos x - 2 sin x )/(4 sin x + 5 cos x )dx = Ax + B log | 5cos x + 4 sin x | then (A, B ) = |
| Answer» <html><body><p>`((<a href="https://interviewquestions.tuteehub.com/tag/7-332378" style="font-weight:bold;" target="_blank" title="Click to know more about 7">7</a>)/(41), (22)/(41)) `<br/>`((22)/(41), (7)/(41))` <br/>`((<a href="https://interviewquestions.tuteehub.com/tag/15-274069" style="font-weight:bold;" target="_blank" title="Click to know more about 15">15</a>)/(41), (7)/(21))`<br/>`((7)/(21), (15)/(41))` </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> | |
| 415. |
If S is defined on R by (x,y) inR hArr xy ge 0 . Then S is ........... |
| Answer» <html><body><p>an <a href="https://interviewquestions.tuteehub.com/tag/equivalence-452629" style="font-weight:bold;" target="_blank" title="Click to know more about EQUIVALENCE">EQUIVALENCE</a> <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/><a href="https://interviewquestions.tuteehub.com/tag/reflexive-2982335" style="font-weight:bold;" target="_blank" title="Click to know more about REFLEXIVE">REFLEXIVE</a> only <br/><a href="https://interviewquestions.tuteehub.com/tag/symmetric-657979" style="font-weight:bold;" target="_blank" title="Click to know more about SYMMETRIC">SYMMETRIC</a> only <br/><a href="https://interviewquestions.tuteehub.com/tag/transitive-2310545" style="font-weight:bold;" target="_blank" title="Click to know more about TRANSITIVE">TRANSITIVE</a> only</p>Solution :N/A</body></html> | |
| 416. |
If for a continuous function f(x), int_(-pi)^(t) (f(x)+x)dx=pi^(2)-t^(2), forall t ge -pi, thenf(-(pi)/(3)) 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/>`(pi)/(2)` <br/>`(pi)/(<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/>`(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>)` </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> :1</body></html> | |
| 417. |
If A and B are coefficients of x^(n)in the expansions of (1+x)^(2n) and (1+x)^(2n-1) respectively, then A/B is equal to |
| Answer» <html><body><p>4<br/>2<br/>9<br/>6</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> | |
| 418. |
Find the direction cosines of the line whose direction ratios are 12, 4, -8. |
| 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/6-327005" style="font-weight:bold;" target="_blank" title="Click to know more about 6">6</a>)/(<a href="https://interviewquestions.tuteehub.com/tag/11-267621" style="font-weight:bold;" target="_blank" title="Click to know more about 11">11</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>)/(11),(-<a href="https://interviewquestions.tuteehub.com/tag/9-340408" style="font-weight:bold;" target="_blank" title="Click to know more about 9">9</a>)/(11)`</body></html> | |
| 419. |
Show that if f :R {(7)/(5)} to R - {(3)/(5)} is defined by f (x) = (3x +4)/( 5x -7) and g :R - {(3/(5)} to R - {(7)/(5)} is defined by g (x) = (7x +4)/(5x -3), then fog = I _(A) andgof =I _(B), where, A = R - {(3)/(5)}, B+R -{(7)/(5)},I_(A)(x) =x, AA x in A, I_(B)|(x) =x , AA x in B are called identity functions on sets A and B, respectively. |
| 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 _(A)`</body></html> | |
| 420. |
Given that x is a real number satisfying(5x^(2)-26x+5)/(3x^(2)-10x+3) lt 0, then |
| Answer» <html><body><p>`x <a href="https://interviewquestions.tuteehub.com/tag/lt-537906" style="font-weight:bold;" target="_blank" title="Click to know more about LT">LT</a> (1)/(5)` <br/>`(1)/(5) lt x lt <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/>`x gt 5` <br/>`(1)/(5) lt x lt (1)/(3) or 3 lt x lt 5` </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> | |
| 421. |
Find the eccentricity of the ellipse (a) whose latus rectum is equal to |
| 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/3-301577" style="font-weight:bold;" target="_blank" title="Click to know more about 3">3</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>)`</body></html> | |
| 422. |
int_(0)^(1) (x^(5)dx)/(1+x^(4))= |
| Answer» <html><body><p>`(2-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>)`<br/>`(2+pi)/(4)`<br/>`(4+pi)/(<a href="https://interviewquestions.tuteehub.com/tag/8-336412" style="font-weight:bold;" target="_blank" title="Click to know more about 8">8</a>)`<br/>`(4-pi)/(8)`</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> | |
| 423. |
Let A and B be independent events with P(A) = 0 . 3 and P(B) = 0 . 4, . FindP(Acap B) |
| 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) 0.12, (<a href="https://interviewquestions.tuteehub.com/tag/ii-1036832" style="font-weight:bold;" target="_blank" title="Click to know more about II">II</a>) 0.58, (<a href="https://interviewquestions.tuteehub.com/tag/iii-497983" style="font-weight:bold;" target="_blank" title="Click to know more about III">III</a>) 0.3, (<a href="https://interviewquestions.tuteehub.com/tag/iv-501699" style="font-weight:bold;" target="_blank" title="Click to know more about IV">IV</a>) 0.4</body></html> | |
| 424. |
Decide whether each statement Must Be True, Could Be True, or Will Never Be True. pqgt 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/could-410026" style="font-weight:bold;" target="_blank" title="Click to know more about COULD">COULD</a> Be <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> | |
| 425. |
{:("Column A","Kate ate 1/3 of a cake, Fritz ate 1/5 of remaining cake, and what was left was eaten by Emily","Column B"),("Fraction of the cake eaten by Emily",,5//7):} |
| Answer» <html><body><p>If <a href="https://interviewquestions.tuteehub.com/tag/column-922494" style="font-weight:bold;" target="_blank" title="Click to know more about COLUMN">COLUMN</a> A is larger<br/>If column <a href="https://interviewquestions.tuteehub.com/tag/b-387190" style="font-weight:bold;" target="_blank" title="Click to know more about B">B</a> is larger <br/>If the columns are <a href="https://interviewquestions.tuteehub.com/tag/equal-446400" style="font-weight:bold;" target="_blank" title="Click to know more about EQUAL">EQUAL</a> <br/>If there is not <a href="https://interviewquestions.tuteehub.com/tag/enough-446095" style="font-weight:bold;" target="_blank" title="Click to know more about ENOUGH">ENOUGH</a> information to decide</p>Answer :B</body></html> | |
| 426. |
|((a+b)^(2),ca,bc),(ca,(b+c)^(2),ab),(bc,ab,(c+a)^(2))|= |
| Answer» <html><body><p>`(ab+bc+ca)^(3)`<br/>`abc(a+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>)^(3)`<br/>`<a href="https://interviewquestions.tuteehub.com/tag/2abc-1836722" style="font-weight:bold;" target="_blank" title="Click to know more about 2ABC">2ABC</a>(a+b+c)^(3)`<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>(ab+bc+ca)^(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> :C</body></html> | |
| 427. |
The x-coordinate of the incentre of the triangle where the midpoints of the sides are (0, 1) (1, 1) and (1, 0) is |
| Answer» <html><body><p>`2+sqrt2`<br/>`1+sqrt2`<br/>`2-sqrt2`<br/>`1-sqrt2`</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> | |
| 428. |
Ify = A (x) e^(-intpdx) isa solution of (dy)/(dx) +P(x)y = Q(x) ,then A'(x) = |
| Answer» <html><body><p>`<a href="https://interviewquestions.tuteehub.com/tag/e-444102" style="font-weight:bold;" target="_blank" title="Click to know more about E">E</a>^(intpdx)`<br/>`<a href="https://interviewquestions.tuteehub.com/tag/q-609558" style="font-weight:bold;" target="_blank" title="Click to know more about Q">Q</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>)e^(-intpdx)`<br/>`<a href="https://interviewquestions.tuteehub.com/tag/int-11513" style="font-weight:bold;" target="_blank" title="Click to know more about INT">INT</a> Q (x)e^(intpdx) dx`<br/>`Q(x) e^(intpdx)`</p>Answer :D</body></html> | |
| 429. |
If the lines (x-1)/-3 = (y-2)/(2k) = (z-3)/2 and (x-1)/(3k) = (y-1)/1 = (z-6)/-5 are perpendicular, then find the value of k. |
| Answer» <html><body><p><br/></p>Answer :The direction <a href="https://interviewquestions.tuteehub.com/tag/ratios-1177874" style="font-weight:bold;" target="_blank" title="Click to know more about RATIOS">RATIOS</a> of the two lines are -3, 2k, 2 and 3k, <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 respectively <br/> <a href="https://interviewquestions.tuteehub.com/tag/since-644476" style="font-weight:bold;" target="_blank" title="Click to know more about SINCE">SINCE</a> the lines are perpendicular, `-3xx3k+2kxx1+2xx-5=0` <br/> `rArr` -9k+2k-10=0 <br/> `rArr` 7k=-10 `rArr = (-10)/7`</body></html> | |
| 430. |
Statement 1 : (A hArr ~B)) a tautology to A hArr B Statement 2: A vv (~A ^^ ~B)) a tautology |
| Answer» <html><body><p>Statement 1 and statement 2 are both false<br/>Statement 1 and staement 2 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/>statement 1 is false and statement 2 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> | |
| 431. |
If I _(1) = int _(0) ^(1) 2 ^(x ^(2)) dx, I _(2) = int _(0) ^(1) 2 ^(x ^(3)) dx, I _(3) = int _(1) ^(2) 2 ^(x ^(3)) dx and I _(4 ) = int _(1) ^(2) 2 ^(x ^(3)) dx then- |
| Answer» <html><body><p>`I _(<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a>) gt I _(<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/>`I _(1) gt I _(2)`<br/>`I _(3) =I_(<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/>`I _(3) gt I _(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> | |
| 432. |
LeT p(X,Y) be the midpoint of the line joining (1,0) to a point on the curve y^(2)=|(x+1,x+2),(x+3,x+5)|. The locus of P is symmetrical about |
| Answer» <html><body><p>X-axis<br/>Y-axis<br/>`y=1`<br/>`X+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> | |
| 433. |
Find number of three digit numbers equal to the sum of the factorials of their digits. |
| 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> | |
| 434. |
When |x|lt (1)/(2) , the coefficient of x^(4)in the expansion of(3x^(2) - 5x + 3)/((x - 1)(2x +1) (x +3))is |
| Answer» <html><body><p>`(<a href="https://interviewquestions.tuteehub.com/tag/the-ratio-frac-vectorsumofinducedemfpercoilarhitmeticsumofinducedemfpercoil-722-334499" style="font-weight:bold;" target="_blank" title="Click to know more about 722">722</a>)/(<a href="https://interviewquestions.tuteehub.com/tag/27-298706" style="font-weight:bold;" target="_blank" title="Click to know more about 27">27</a>)`<br/>`(<a href="https://interviewquestions.tuteehub.com/tag/724brbr-1918440" style="font-weight:bold;" target="_blank" title="Click to know more about 724">724</a>)/(27)`<br/>`(-722)/(27)`<br/>`(-724)/(27)`</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> | |
| 435. |
Differentiate x^(sin x), x gt 0 w.r.t x |
| 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/sin-1208945" style="font-weight:bold;" target="_blank" title="Click to know more about SIN">SIN</a> x-1).sin x + x^(sin x). <a href="https://interviewquestions.tuteehub.com/tag/cos-935872" style="font-weight:bold;" target="_blank" title="Click to know more about COS">COS</a> x.log x`</body></html> | |
| 436. |
Find the number of 4- letter words that can be formed using the letters of the word. MIRACLE. How many of them begin with an vowel |
| 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/360-309472" style="font-weight:bold;" target="_blank" title="Click to know more about 360">360</a></body></html> | |
| 437. |
Let a=2^(log_35 , b=3^(log_5 2, c=4 the identify the correct option :- |
| Answer» <html><body><p>ab=<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/>ab <a href="https://interviewquestions.tuteehub.com/tag/gt-1013864" style="font-weight:bold;" target="_blank" title="Click to know more about GT">GT</a> c<br/>ac =b<br/>ab `<a href="https://interviewquestions.tuteehub.com/tag/le-540308" style="font-weight:bold;" target="_blank" title="Click to know more about LE">LE</a>` c</p></body></html> | |
| 438. |
Find the number of 4- letter words that can be formed using the letters of the word. MIRACLE. How many of them begin and end with vowels |
| 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/120-270396" style="font-weight:bold;" target="_blank" title="Click to know more about 120">120</a></body></html> | |
| 439. |
Find the number of 4-letter words that can be formed using the letters of the word MIRACLE. How many of them end with a consonant ? |
| 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/480-1879936" style="font-weight:bold;" target="_blank" title="Click to know more about 480">480</a></body></html> | |
| 440. |
The xy-plane above shows the two points of intersection of thegraphs of a linear function and a quadratic function. The leftmost point of intersection has coordinates (a, b) and the rightmost point of intersection has coordinates (c, d) . If the vertex of the graph of the quadraticfunction is at (2, -27) , what is the value of b-d ? |
| 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/36-309156" style="font-weight:bold;" target="_blank" title="Click to know more about 36">36</a></body></html> | |
| 441. |
Let f(x) be a non-positive continuous function and F(x)=int_(0)^(x)f(t)dt AA x ge0 and f(x) ge cF(x) where c lt 0 and let g:[0, infty) to R be a function such that (dg(x))/(dx) lt g(x) AA x gt 0 and g(0)=0 The total number of root(s) of the equation f(x)=g(x) is/ are |
| Answer» <html><body><p>`infty`<br/>1<br/>2<br/>0</p>Solution :`<a href="https://interviewquestions.tuteehub.com/tag/f-455800" style="font-weight:bold;" target="_blank" title="Click to know more about F">F</a>(x) le0` and `F^(')(x)=f(x)` <br/> Now, `f(x) ge cF(x)` <br/> or `e^(-cx)F^(')(x) -ce^(-cx)F(x) ge0` <br/> <a href="https://interviewquestions.tuteehub.com/tag/thus-2307358" style="font-weight:bold;" target="_blank" title="Click to know more about THUS">THUS</a>, `e^(-cx)F(x)` is an increasing function <br/> `therefore e^(-cx) F(x) ge e^(-c(0))F(0)` <br/> or `e^(-cx)F(x) ge` <br/> or `F(x) ge0` [as `f(x) ge cF(x)` and c is <a href="https://interviewquestions.tuteehub.com/tag/positive-1159908" style="font-weight:bold;" target="_blank" title="Click to know more about POSITIVE">POSITIVE</a>. <br/> Also, `(dg(x))/(dx) lt g (x) <a href="https://interviewquestions.tuteehub.com/tag/aa-844885" style="font-weight:bold;" target="_blank" title="Click to know more about AA">AA</a> x gt 0` <br/> or `(d/(dx)) e^(-x)g(x) lt 0` <br/> Thus, `e^(-x)g(x)` has <a href="https://interviewquestions.tuteehub.com/tag/one-585732" style="font-weight:bold;" target="_blank" title="Click to know more about ONE">ONE</a> solution, `x=0` <br/></body></html> | |
| 442. |
Let f(x) be a non-positive continuous function and F(x)=int_(0)^(x)f(t)dt AA x ge0 and f(x) ge cF(x) where c lt 0 and let g:[0, infty) to R be a function such that (dg(x))/(dx) lt g(x) AA x gt 0 and g(0)=0 The number of solution(s) of the equation |x^(2)+x-6|=f(x)+g(x) is/are |
| 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><br/>1<br/>0<br/>3</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/x-746616" style="font-weight:bold;" target="_blank" title="Click to know more about X">X</a>^(2)+x-6|=f(x) + <a href="https://interviewquestions.tuteehub.com/tag/g-1003017" style="font-weight:bold;" target="_blank" title="Click to know more about G">G</a>(x)` or `|x^(2)+x-6|=g(x)` <br/> Thus, no solution exists.</body></html> | |
| 443. |
Let f(x) be a non-positive continuous function and F(x)=int_(0)^(x)f(t)dt AA x ge0 and f(x) ge cF(x) where c lt 0 and let g:[0, infty) to R be a function such that (dg(x))/(dx) lt g(x) AA x gt 0 and g(0)=0 The solution set of inequation g(x)(cos^(-1)x-sin^(-1)) le0 |
| Answer» <html><body><p>`[-1,1/sqrt(<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/sqrt(2),1]`<br/>`[0,1/sqrt(2)]`<br/>`[0,1/sqrt(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> :`<a href="https://interviewquestions.tuteehub.com/tag/g-1003017" style="font-weight:bold;" target="_blank" title="Click to know more about G">G</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/cos-935872" style="font-weight:bold;" target="_blank" title="Click to know more about COS">COS</a>^(-1)x-sin^(-1)x) le0` <br/> or `(cos^(-1)x-sin^(-1)x) ge0` or `x in [-1, 1/sqrt(2)]`</body></html> | |
| 444. |
There are 50 stations on a railway line. The number of different kinds of single 2nd class tickets must be printed so as to enable a passenger to go from one station to another station is |
| Answer» <html><body><p>`""^(<a href="https://interviewquestions.tuteehub.com/tag/50-322056" style="font-weight:bold;" target="_blank" title="Click to know more about 50">50</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>)`<br/>2500<br/>2450<br/>`50!`</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> | |
| 445. |
If the vertices A, B, C of a DeltaABC have position vectors (1, 2, 3), (-1, 0, 0), (0, 1, 2) respectively, then angleABC angleABC is the angle between the vectors BA and BC), is equal to |
| Answer» <html><body><p>`(pi)/(2)`<br/>`(pi)/(4)`<br/>`cos^(-1)((10)/(sqrt(102)))`<br/>`cos^(-1)((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>))`</p>Solution :WE aregiventhe points `A (1,2,3),B(-1,0,0)` and`C (0,1,2)` Also , itgiventhat` angleABC `is theanglebetweenthevectorsBAand BChereBA= PVofofA -PV of B<br/> `=( <a href="https://interviewquestions.tuteehub.com/tag/hati-2693493" style="font-weight:bold;" target="_blank" title="Click to know more about HATI">HATI</a> + 2 hatj+3 hatk )- (-hati+ 0 hatj + 0 hatk )`<br/> `=[ hati-(-hati )+(2hatj -0 )+ (3 hatk -0 )] = 2 hati+ 2 hatj+ 3hatk` <br/> ` <a href="https://interviewquestions.tuteehub.com/tag/implies-1037962" style="font-weight:bold;" target="_blank" title="Click to know more about IMPLIES">IMPLIES</a>| BA|= sqrt((2) ^(2)+(2)^(2)+(3)^(2))=sqrt(4+4+9)=sqrt(17)` <br/>`implies BC=PVofC-PV of B ` <br/> `=(0 hati +1 hatj + 2 hatk)-(-hati +0hatj+0hatk)=hati +hatj+2hatk` <br/> `implies |BC|=sqrt((1)^(2) +(1)^(2)+(2)^(2))=sqrt(1+1+4)= sqrt(6)` <br/>Now , `BA.BC =(2 hati + 2 hatj + 3 hatk ).(hati + hatj + 2 hatk )`<br/> `=2xx1+2xx1+3xx2=10` <br/> ` thereforecos theta= (BA.BC)/(|BA||BC|)implies cos (angle <a href="https://interviewquestions.tuteehub.com/tag/abc-360912" style="font-weight:bold;" target="_blank" title="Click to know more about ABC">ABC</a>)=(10)/(sqrt(17)sqrt(6))` <br/> `impliesangleABC= cos ^(-1) ((10)/(sqrt(102)))`</body></html> | |
| 446. |
In the figure, the area of the quadrilateral ABCD is 75. What is the area of parallelogram EFGH? |
| Answer» <html><body><p>96<br/>153<br/>157<br/>171</p>Answer :D</body></html> | |
| 447. |
Integrate the following functions : int(dx)/(x(x^(5)+1)) |
| 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> :`log|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>)/(<a href="https://interviewquestions.tuteehub.com/tag/5-319454" style="font-weight:bold;" target="_blank" title="Click to know more about 5">5</a>)log|x^(5)+1|+c`</body></html> | |
| 448. |
Vertices of a parallelogram are (0, 0), ((1)/(m-n), (m)/(m-n)), ((-1)/(m-n), (m)/(m-n)) and (0, 1) are m,n are the roots of the equation 441x^(2)+42x-8=0. If area of the parallelogram is A then A is equal to |
| 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> :`3.5`</body></html> | |
| 449. |
Four rotten oranges are accidentally mixed with 16 good ones. Three oranges are drawn at random from the mixed lot. Let X be the number of rotten oranges drawn. Find the mean and variance of X. |
| 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/mean-1091459" style="font-weight:bold;" target="_blank" title="Click to know more about MEAN">MEAN</a> "=(3)/(5), "<a href="https://interviewquestions.tuteehub.com/tag/variance-1443227" style="font-weight:bold;" target="_blank" title="Click to know more about VARIANCE">VARIANCE</a> "=(<a href="https://interviewquestions.tuteehub.com/tag/68-331600" style="font-weight:bold;" target="_blank" title="Click to know more about 68">68</a>)/(<a href="https://interviewquestions.tuteehub.com/tag/125-271180" style="font-weight:bold;" target="_blank" title="Click to know more about 125">125</a>)`</body></html> | |
| 450. |
Equation of circle which touch X-axies at (3,0) and making Y-intercept of length 8 units is |
| Answer» <html><body><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>^(<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)-6x+-10y+9=0`<br/>`x^(2)+y^(2)-6x+-10y-9=0`<br/>`x^(2)+y^(2)+16x+110y+9=0`<br/>None</p>Answer :A</body></html> | |