28278 + Interview Questions in Maths in Class 12 Page 79 InterviewSolution

3901.	The straight lines y=x=2 and y=6x+3 are parallel to two sides of the rhombus ABCD. If the vertex A lies on y-axis and the diagonals of the rhombus intersect at (1,2) find the coordinat of A.
Answer» ANSWER :`(0,0) or (0, (5)/(2))`

Discussion

3902.	If tanalpha,tanbeta are the roots of the equation x^(2)+px+q=0(pne0),then
Answer» `sin^(2)(alpha+beta)+p sin(alpha+beta)cos(alpha+beta)+qcos^(2)(alpha+beta)=q` `TAN(alpha+beta)=(q)/(p-1)` `cos(alpha+beta)=1-q` `sin(alpha+beta)=-p` Solution :Since `tanalpha,tanbeta` are the ROOTS of the equation `x^(2)+px+q=0`. `thereforetanalpha+tanbeta=-p,tanalphatanbeta=q` `thereforetan(alpha+beta)=(tanalpha+tanbeta)/(1-tanalphatanbeta)=(p)/(q-1)` Also ,when `tan(alpha+beta)=(p)/(q-1)`. L.H.S. of the EXPRESSION given in `=cos^(2)(alpha+beta)[tan^(2)(alpha+beta)+ptan(alpha+beta)+q]` `=(1)/(1+tan^(2)(alpha+beta))[(p^(2))/((q-1)^(2))+(p^(2))/(q-1)+q]` `=((q-1)^(2))/((q-1)^(2)-p^(2))[(p^(2)+p^(2)(q-1)+q(q-1)^(2))/((q-1)^(2))]` `=(q{p^(2)+(q-1)^(1)})/(p^(2)+(q-1)^(2))` =q = R.H.S.of i.e., Relation given in (a) is also SATISFIED.

Discussion

3903.	Find the value of k. If f(x) = {{:(kx+1", if "xlepi),(cosx",if "x>pi):} is continuous at x=pi.
Answer» ANSWER :`K=(-2)/PI`

Discussion

3904.	Using elementary row transformations , find the inverse of [{:(2,5),(1,3):}]
Answer» ANSWER :`thereforeA^(-1)=[{:(3,-5),(-1,2):}]`

Discussion

3905.	(p)/(q) + (q)/(p) = (c)/(a) - (a)/(c)
Answer» `(3^(9) 2^(4))/(7^(7))` `(3^(10) 2^(4))/(7^(7))` `(3^(8) 2^(4))/(7^(7))` `(3^(7) 2^(4))/(7^(7))` ANSWER :2

Discussion

3906.	int(x)/(sqrt(1+x^(2)+sqrt((1+x^(2))^(3)))) dx=....+c
Answer» `(1)/(2) log\|+sqrt(1+x^(2))\|` `2 sqrt(1+sqrt(1+x^(2)))` `2(1+sqrt(1+x^(2)))` None of these Answer :B

Discussion

3907.	The points (-3,2) and (-3,1) are the end points of latusrectum of a parabola then find the equation of parabola.
Answer» ANSWER :`RARR (2y-3)^(2) = (4x+11)`

Discussion

3908.	Resolve (2x^(2)+3)/((x^(2)+1)(x^(2)+2)(x^(2)+3)) into partial fractions.
Answer» ANSWER :`:.` PARTIAL fractions are, `(1)/(2(x^(2)+1))+(1)/(x^(2)+2)-(3)/(2(x^(2)+3))`

Discussion

3909.	There are 5 green balls of different shades and 4 red balls of identical shades. No. of ways of arranging them in a row so that · no two red balls are together is
Answer» 1800 1100 900 500 Answer :A

Discussion

3910.	There are 5 green balls of different shades and 4 red balls of identical shades. No. of ways of arranging them in a row so that · no two green balls are together is
Answer» 70 90 120 140 Answer :C

Discussion

3911.	Let a_1=0 and a_1,a_2,a_3 …. , a_nbe real numbers such that \|a_i\|=\|a_(i-1) + 1\| for all I then the A.M.Of the numbera_1,a_2 ,a_3…., a_nhas the value A where :
Answer» `A LT -1/2` `A lt -1` `A GE -1/2` A=-2 ANSWER :C

Discussion

3912.	There are 5 green balls of different shades and 4 red balls of identical shades. No. of ways of arranging them in a row so that · green and red balls come alternatively is
Answer» 120 140 180 200 Answer :A

Discussion

3913.	In a triangle ABC I_1, I_2,I_3 are excentre of triangle then show thatII_(1). II_(2). II_(3)=16R^(2)r.
Answer» ANSWER :`II_(1).II_(2). II_(3) =64 R^(3). (r)/(4R)=16R^(2)r`

Discussion

3914.	Ifveca=hati-hatj,vecb=hati-hatj-4hatk,vecc=3hatj-hatkandvecd=2hati+5hatj+hatk, verify that (i)(vecaxxvecb)xx(veccxxvecd)=[veca,vecb,vecd]vecc-[veca,vecb,vecc]vecd(ii)(vecaxxvecb)xx(veccxxvecd)=[veca,vecc,vecd]vecb-[vecb,vecc,vecd]veca
Answer» ANSWER : ` -24hati+24hatj-40hatk `

Discussion

3915.	If (2,1) is limiting point of the coaxa system of which x^(2) + y^(2) - 6x - 4y -3 = 0is a member, then the other limiting point is
Answer» (-5,-6) (5,6) (3,5) (-8,-13) ANSWER :A

Discussion

3916.	To the circle x^(2)+y^(2)-8x-4y+4=0 tangent at the point theta=(pi)/4 is
Answer» `x+y+2-4sqrt(2)=0` `x-y+2-4sqrt(2)=0` `x+y+4+4sqrt(2)=0` `x-y-2-4sqrt(2)=0` ANSWER :A

Discussion

3917.	For all positive integral values of n, 3^(2n)-2n+1 is divisible by
Answer» 2 4 8 12 Answer :A

Discussion

3918.	Let f: R of R be a function defined by f(x) =x^(3) + px^(2) + 7x + 4 cos x where p in R. If f is invertible, p lies in
Answer» `(0, INFTY)` `[-3,3]` `(-infty, 0)` `[5,11]` ANSWER :B

Discussion

3919.	The number of ways of dividing 15 men and 15 women into 15 couples each consisting a man and a woman is
Answer» `15!` 1840 1820 2005 Answer :A

Discussion

3920.	Chords of he hyperbolax^(2)//a^(2) -y^(2)//b^(2) =1 are at a constantdistance k from the centre . The equation to the locus of their poles is
Answer» ` (x^(2))/(a^(4)) +(y^(2))/(B^(4)) =(1)/(k^(2))` ` (x^(2))/(a^(4)) +(y^(2))/(b^(4)) =k^(2) ` ` (x^(2))/(a^(4))+(y^(2))/(b^(4))=(1)/(L^(4))` ` (x^(2))/(a^(4))+(y^(2))/(b^(4)) = k^(4) ` Answer :A

Discussion

3921.	A laboratory blood test is 99% effective in detecting a certain disease when it is in fact present. However, the test also yields a false positive result for0 . 5 % of the healthy person tested (i.e., if a healthy person is tested, then with probability 0 . 005, the test will imply he has the disease). If 0 . 1 % of the population actually has the disease, what is the probahility that a person has disease given that his test result is positive ?
Answer» ANSWER :`(22)/(133)`

Discussion

3922.	Evalute the following integrals int (3x-2) sqrt(2x^(2) - x + 1 dx)
Answer» Answer :`(1)/(2) (2x^(2) - x + 1)^(3//2) - (5)/(4 sqrt(2)) ( x - (1)/(4)) sqrt((x - (1)/(4))^(2) + (7)/(16)) - (35)/(64 sqrt(2)) " SINH"^(-1) ((4x - 1)/(sqrt(7))) + c `

Discussion

3923.	Find k, if f(x) = [(x^2-9) , x!=3] , [k , x=3]]is continuous at x=3,
Answer» 6 0 2 1 Answer :A

Discussion

3924.	A teacher the united states wishes to purchase textbooks forher classroom when she goes on a trip to Canada, where they are on sale for 45 Canadian dollars each. At the time of purchase one Canadian dollar can be exchanged for 0.76 U.S. dollars. Assuming she is able to exchange her U.S. dollars for Canadian dollars at no cost, what is the exact cost, in U.S. dollars, to purchase 30 books?
Answer» `$849` `$1026` `$1350` `1776` ANSWER :B

Discussion

3925.	If the equation of the circle which passes through the point (1,1) and cuts both the circles x^2+y^2 -4x -6y+4 =0 and x^2+y^2 +6x-4y +15 =0orthogonally is x^2 +y^2 +2 gx +2fy +c =0 then 5g +2f +c =
Answer» 0 1 3 2 Answer :D

Discussion

3926.	It the A.M., is thrice the G.M. of two positive numbers . Show that numbers are in the ratio (3 pm 3 sqrt(2))/(3 - 2 sqrt(2))
Answer» Solution :` (a + b)/(2sqrt(AB)) = 3` Using componendo and DIVIDENDO, ` rArr((SQRT(a) + sqrt(b))^(2))/((sqrt(a) - sqrt(b))^(2)) = 2 `

Discussion

3927.	If a, b, c are real, then both the roots of the equation(x-b) (x-c )+(x-c) (x-a) +(x-a) (x-b) =0 are always
Answer» POSITIVE NEGATIVE REAL imaginary Answer :C

Discussion

3928.	If 28x -5y=36and 15x+5y+18=68, whatis the value of x ?
Answer» 1 2 3 4 Solution :Stary by WRITING the second equatin in the same form as the first, then use combination to solve for x: ` 28x-5y=26` `(+15 +5y=50)/({:(43x, ""=86),(x, ""=2 ):}` Choice (B) is correct. If you feel more comfortable USING substitution, you can maximize efficiency by solving one equation for 5y and substituting that VALUE into the other equation: `15x + 5y =50` `5y =50-15x` `28x -(50-15x ) =36` `43x -50 =36` `43x =86` `x =2` Note that the arithmetic is fundamentally the same, but the setup using combination is quicker and visually easier to follow.

Discussion

3929.	An expression of the form (a+b+c+d+ .... ) consisting of sum of many distinct symbols is called a multinomial. Show that (a+b+c)^n is the sum of all terms of the form n!/p!q!e!a^pb^qc^r where p, q and r range over all possible triples of non negative integers such that p+q+r = n.
Answer» <P> Solution :`(a+b+c)^N` = `sum_(p=0)^n "^nCp a^p (b+c)^(n-p)` = `sum(n!)/(p!(n-p)!) a^pxx"^(n-p)C_q b^q c^(n-p-q)` = `sum(n!)/((p!)(n-p1))XX (n-p!)/((q!)(n-p-q!)` `sum(n!)/((p!q!r!)) a^pb^qc^r (therefore n = p+q+r)`

Discussion

3930.	A point lying on the plane that passes through the point hat(i)-hat(j)+hat(k),hat(i)- 2hat(j)+3 hat(k)and hat(i) + 2hat(j)-3hat(k) is
Answer» `-hat(i)+2 hat(J)-3HAT(K)` `-hat(i)+hat(j)-hat(k)` `hat(i)+hat(j)-hat(k)` `4hat(i)+2HAT(j) +3hat(k)` ANSWER :C

Discussion

3931.	Translate "Time and tide waits for none" propositions into symbolic form, stating the prime components
Answer» Solution :Let p : TIME WAITS for none. Q :TIDE waits for none.`:.`ANSWER is `p^^q`.

Discussion

3932.	Two non negative integers are chosen at random, find the probability that the sum of the squares is divisible by 11.
Answer» ANSWER :`(1)/(121)`

Discussion

3933.	If vec(a), vec(b) and vec(c) are three vectors such that vec(a) times vec(b)=vec(c) and vec(b) times vec(c)=vec(a)," prove that "vec(a), vec(b), vec(c) are mutually perpendicular and abs(vec(b))=1 and abs(vec(c))=abs(vec(a)).
Answer» ANSWER :96 SQ. UNITS

Discussion

3934.	An ideal choke takes a current of 10 amp when connected to an AC supply of 125 volt and 50 Hz. A pure resistor under the same condition takes a current of 12.5 amp. If the two are connected to an AC supply of 100sqrt(2)volt and 40 Hz, then the current in series combination of above resistor and inductor is N × 10 then N is.
Answer» Solution :`R = 125/12.5 = 10 Omega` `X_(L) = omegaL = 2 pi f L = V/I = 125/10 = 12.5` `2 pi fL = 12.5` `2piL = (12.5)/(50) = 0.25` `X_(L) = (2piL)f = 0.25 xx 40 = 10 Omega` Impedance of the circuit `Z = SQRT(R^(2)+X_(L)^(2)) = 10sqrt(2)OHM` `:. "CURRENT" = (100sqrt(2))/(10sqrt(2)) = 10 amp`.

Discussion

3935.	If (x^(4)+3x+1)/((x+1)^(2)(x-1))=Ax+B+C/(x+1)+D/(x+1)^(2)+E/(x-1) " then "A+D=
Answer» 2 2 `3//2` 0 Answer :C

Discussion

3936.	Which of the following statements is correct? (a) Every L.P.P admits an optimal solution (b)A L.P.P admits unique optimal solution (c) If a L.P.P adimits two optimal solutions it has an infinite number of optimal solutions (d)None of these
Answer» EVERY L.P.P ADMITS an OPTIMAL solution A L.P.P admits unique optimal solution If a L.P.P adimits two optimal soluctions it has an idfinite NUMBER of optimal solutions None of these Answer :C

Discussion

3937.	Solve \|(x-1)/(3+x2x-8x^(2))\|+\|1-x\|=(x-1)^(2)/(\|3+2x=8x^(2)\|) +1
Answer» Answer :`X = {0,2,(1 PM sqrt129)/(16),(3 pm sqrt73)/(16)}`

Discussion

3938.	Evalute the following integrals int "cosec"^(2) x sin 2 x dx
Answer» ANSWER :`2log\|sinx\|+c`

Discussion

3939.	Find the value of x if , \|{:(3,x),(x,1):}\|=\|{:(3,2),(4,1):}\|
Answer» ANSWER :` x=+-2sqrt 2 `

Discussion

3940.	Integrate the function in Exercise. e^(2x)sinx
Answer» ANSWER :`(E^(2X))/(5)(2sinx-cosx)+C`

Discussion

3941.	There are 5 letters and 5 addressed envelopes. If the letters are put at random in the envelopes , the probability that all the letters may be placed in wrongly addressed envelopes is
Answer» `119//120` `1//120` `11//30` `11//120` ANSWER :A

Discussion

3942.	There are 5 letters and 5 addressed envelopes. If the letters are put at random in the envelopes, the probability that atleast one letter may be placed in wrongly addressed envelope is
Answer» `(119)/(120)` `(120)/(343)` `(1)/(1155)` `(139)/(140)` ANSWER :B

Discussion

3943.	The means and variance of n observation x_1, x_2, x_3,....x_n are 5 and 0 respectively . Ifsum_(i=1)^(n) x_(i)^(2) = 400, then find the value of n
Answer» SOLUTION :16

Discussion

3944.	Find the anti derivative F of f defined by f (x) = 4x^(3) - 6, where F (0) = 3
Answer» ANSWER :`X^(4)-6x+3`

Discussion

3945.	f:N rarrN , f(x)=x+(-1)^(x-1) then f^(-1)(x)= .......
Answer» XY `X-1` `x-(-1)^(x-1)` `x+(-1)^(x-1)` SOLUTION :N/A

Discussion

3946.	A candidate is required to anwer 6 questions by choosing atleast one question from each section where 1^(st) section consists of 4 questions, 2^(nd) section consists of 3 questions and 3^(rd) section consists of 2 questions. The number of ways can he make up his choice is
Answer» 76 80 95 63 Answer :A

Discussion

3947.	The sum of the coefficients in the binomial expansion of (1/x + 2x)^(6) is equal to
Answer» 1024 729 243 512 Answer :B

Discussion

3948.	Solve the following equations by matrix method. If A = [(2,-1,1),(-1,2,-1),(1,-1,2)] verify that A^(3) - 6A^(2) + 9A = 4 I = 0 and hence, find A^(-1).
Answer» ANSWER :`(1)/(4){:[( 3,1,-1),(1,3,1),(-1,1,3)]:}`

Discussion

3949.	Differentiate the following w.r.t.x. sin^(-1)((a+bcosx)/(b+acosx)),bgtagt1
Answer» ANSWER :`-(SQRT(B^(2)-a^(2)))/(b+acosx)`

Discussion

3950.	Let x_1,x_2…..x_(20 )be 20 observations and d_1=2( x_i -5), I = 1,2,……20 . If the mean and variance of d_1,d_2, …….,d_(20)are 20 and 12 respectively, then the mean and variance of x_1,x_2,……,x_(20)are respectively,
Answer» 10 and 3 15 and 4 15 AND3 10 and 4 Answer :C

Discussion

Explore topic-wise InterviewSolutions in .

The straight lines y=x=2 and y=6x+3 are parallel to two sides of the rhombus ABCD. If the vertex A lies on y-axis and the diagonals of the rhombus intersect at (1,2) find the coordinat of A.

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Let a_1=0 and a_1,a_2,a_3 …. , a_nbe real numbers such that |a_i|=|a_(i-1) + 1| for all I then the A.M.Of the numbera_1,a_2 ,a_3…., a_nhas the value A where :

There are 5 green balls of different shades and 4 red balls of identical shades. No. of ways of arranging them in a row so that · green and red balls come alternatively is

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To the circle x^(2)+y^(2)-8x-4y+4=0 tangent at the point theta=(pi)/4 is

For all positive integral values of n, 3^(2n)-2n+1 is divisible by

Let f: R of R be a function defined by f(x) =x^(3) + px^(2) + 7x + 4 cos x where p in R. If f is invertible, p lies in

The number of ways of dividing 15 men and 15 women into 15 couples each consisting a man and a woman is

Chords of he hyperbolax^(2)//a^(2) -y^(2)//b^(2) =1 are at a constantdistance k from the centre . The equation to the locus of their poles is

Evalute the following integrals int (3x-2) sqrt(2x^(2) - x + 1 dx)

Find k, if f(x) = [(x^2-9) , x!=3] , [k , x=3]]is continuous at x=3,

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It the A.M., is thrice the G.M. of two positive numbers . Show that numbers are in the ratio (3 pm 3 sqrt(2))/(3 - 2 sqrt(2))

If a, b, c are real, then both the roots of the equation(x-b) (x-c )+(x-c) (x-a) +(x-a) (x-b) =0 are always

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An expression of the form (a+b+c+d+ .... ) consisting of sum of many distinct symbols is called a multinomial. Show that (a+b+c)^n is the sum of all terms of the form n!/p!q!e!a^pb^qc^r where p, q and r range over all possible triples of non negative integers such that p+q+r = n.

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Translate "Time and tide waits for none" propositions into symbolic form, stating the prime components

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Solve |(x-1)/(3+x2x-8x^(2))|+|1-x|=(x-1)^(2)/(|3+2x=8x^(2)|) +1

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There are 5 letters and 5 addressed envelopes. If the letters are put at random in the envelopes , the probability that all the letters may be placed in wrongly addressed envelopes is

There are 5 letters and 5 addressed envelopes. If the letters are put at random in the envelopes, the probability that atleast one letter may be placed in wrongly addressed envelope is

The means and variance of n observation x_1, x_2, x_3,....x_n are 5 and 0 respectively . Ifsum_(i=1)^(n) x_(i)^(2) = 400, then find the value of n

Find the anti derivative F of f defined by f (x) = 4x^(3) - 6, where F (0) = 3

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A candidate is required to anwer 6 questions by choosing atleast one question from each section where 1^(st) section consists of 4 questions, 2^(nd) section consists of 3 questions and 3^(rd) section consists of 2 questions. The number of ways can he make up his choice is

The sum of the coefficients in the binomial expansion of (1/x + 2x)^(6) is equal to

Solve the following equations by matrix method. If A = [(2,-1,1),(-1,2,-1),(1,-1,2)] verify that A^(3) - 6A^(2) + 9A = 4 I = 0 and hence, find A^(-1).

Differentiate the following w.r.t.x. sin^(-1)((a+bcosx)/(b+acosx)),bgtagt1

Let x_1,x_2…..x_(20 )be 20 observations and d_1=2( x_i -5), I = 1,2,……20 . If the mean and variance of d_1,d_2, …….,d_(20)are 20 and 12 respectively, then the mean and variance of x_1,x_2,……,x_(20)are respectively,