28278 + Interview Questions in Maths in Class 12 Page 5 InterviewSolution

201.	lim_(x to oo)[ sqrt(x^(2) + 2x -1)-x]is equal to
Answer» `OO` `1/2` 4 1 Answer :D

Discussion

202.	Match the following :
Answer» <P>`{:(P,Q,R,S),(2,3,4,1):}` `{:(P,Q,R,S),(4,1,3,2):}` `{:(P,Q,R,S),(1,4,2,3):}` `{:(P,Q,R,S),(3,2,1,4):}` ANSWER :A

Discussion

203.	If f(x)=((7x+1)sinx)/(e^(x)logx) " and "f^(')(x)=f(x)g(x), then g^(')(x)=
Answer» `1/(x^(2)logx)+1/(XLOGX)^(2)-cosec^(2)x-49/(7x+1)^(2)` `1/(x^(2)logx)+1/(logx)-cosec^(2)x-49/(7x+1)^(2)` `1/(xlogx)^(2)+1/(logx)-cosec^(2)x-49/(7x+1)^(2)` `1/(x^)(x^(2)logx)x+1/(xlogx)^(2)+cosec^(2)x+49/(7x+1)^(2)` Answer :A

Discussion

204.	Find the equation of the chord joining point P(alpha) and Q(beta) on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1.
Answer» ANSWER :`-(B^(2))/(a^(2))`

Discussion

205.	Can the inverse of the following matric be found ? [[1,2],[2,4]]
Answer» SOLUTION :`ABSA = [[1,2],[2,4]]` =4-4=0 `THEREFORE A^-1` EXISTS

Discussion

206.	X wants to put 5 different rings into three different pockets is such that to pocket is empty. Then the probabaility of such event occuring is (1)/(P) ,[P]=_______ ([] is the greatest integer function).
Answer» ANSWER :1

Discussion

207.	Integrate the following functions cos sqrtx/sqrtx
Answer» Solution :LET.` t =sqrtx`. Then `DT = 1/(2sqrtx) dx` `GT 1/sqrtx dx = 2dt` therefore` int (COS sqrtx)/sqrtx dx = int costxx2dt` =`2 sint t+c = 2sin sqrtx+c`

Discussion

208.	Foot of the perpendicular drawn from the point (1,3,4) to the plane 2x-y+z+3=0 is
Answer» (1,2,-3) (-1,4,3) (-3,5,2) (0,-4,-7) ANSWER :B

Discussion

209.	If the matrices [(3x+7,5),(y+1,2-3x)]=[(5,y-2),(8,4)], then the values of x and y are :
Answer» `x=-1/3,y=7` `x=-1/3,y=-2/3` `x=-2/3,y=7` `x=5,y=-2/3`. ANSWER :C

Discussion

210.	Using elementary row transformations , find the inverse of [{:(1,3),(2,7):}]
Answer» ANSWER :`thereforeA^(-1)=[{:(7,-3),(-2,1):}]`

Discussion

211.	Smallest ear ossicle is :
Answer» INCUS Stapes Malleus Lagena Answer :A

Discussion

212.	If the point P denotes the complexnumber z=x+ iy in the Argand plane and if (z-i)/(z-1) is a purelly imaginary number, find the locus of P.
Answer» Solution :We note that the quotient `(Z-i)/(z-1)` is not DEFINED if `z=1` Sine `z=x I y` `(z-i)/(z-1)=(xiy-i)/(x+iy-1)` `=(x+i(y-1))/(x-1+iy)=([(x+i(y-1)][(x-1)-iy)])/([(x-1)-iy])` `=((x^(2)+y^(2)-x-y)/((x-1)^(2)+y^(2)))+i((1-x+y)/((x-1)^(2)+y^(2)))` `(z-i)/(z-1)` is purelyimaginry if Re part =0 `HARR z ne 1 and (x^(2)+y^(2)-x-y)/((x-1)^(2)+y^(2))=0` `harr x^(2)+y^(2)-x-y=0` and `(x,y) ne (1,0)` `:.` The locus of P is the CIRCLE `x^(2)+y^(2)-x-y=0` excluding the pint (1,0)

Discussion

213.	Write down the power set of{a,{a},{a,b}}
Answer» <P> SOLUTION :LET A ={a,{a},{a,B}} `:. P(A)={{a},{{a}},{{a,b}},{a},{a}` `{{a}.{a,b}},{a,{a,b},A,PHI}`

Discussion

214.	He imprisons them in his prison and decides to test their cleverness. They are kept in two different cells, which are located on opposite sides of the prison, so that they cannot com- municate in any way. Max's cell's window has twelve steel bars, while Jenny's cell's window has eight. The first day of their imprisonment, Mr. Giovanni tells first Max and then Jenny that he has decided to give them a riddle to solve. The rules are simple, and solving the riddle is the only hope the two have to escape. ● In the prison there are no bars on any window, door or passage, except for windows in the to logicians' cells, which are the only barred ones (this implies that each cell has at least one bar on its window). ● Mr. Giovanni will ask the same question to Max every morning: "Are there eighteenor twenty bars in my castle?" ● If Max doesn't answer, the same question will then be asked to Jenny the night of the same day. ● If either of them answers correctly, and is able to explain the logicalreasoning behind their answer, Mr. Giovanni will immediately free both of them and never bother them again. ● If either of them answers wrong, Mr. Giovanni will throw away the keys of the cells and hold Max and Jenny prisoners for the rest of their lives. ● Both Max and Jenny know these rules. As soon as either Max or Jenny answer, the decision is made. Only if they don't give an answer does the question pass on to the other person.What’s the minimum number of days they will need to escape? They soon find the answer. Impressed that they could escape, Mr. Giovanni makes them another offer. Mr. Giovanni is an avid fan of chess, and hence gives them two problems. If they solve both the problems, Mr. Giovanni offers to not only free all the Pokémon he has captured till date, but alsoto give Max 5 of his strongest Pokémon, which can help Max easily defeat all the gym leaders.
Answer» Solution :The explanation: Let's start on the time of release and follow the thought process. Max learns that Jenny has 8 bars on the morning of the 4th day. To avoid long lists of "he knows she knows" let's use some shorthand. M represents Max and R represents Jenny "M12: R=6,8" means "In the CASE that Max has 12 bars, Max knows that Jenny has 6 or 8 bars". On the NEXT indent level, "R6" and "R8" describes both possible cases. Here's the thought process of Max on the morning of the 4th day, just before he announces that there are 20 bars in total. The logic starts LIKE this: Max knows Jenny has 6 or 8 bars. If Jenny had 6 bars, she would think Max had 12 or 14 bars. If Jenny had 6 bars and assumed Max had 12, Max would think... etc. `M12: R=6,8 - R6: M=12,14 - - M14: R=4,6 - - - R4: M=14,16 - - - - M16: R=2,4 - - - - - R2: M=16,18 - - - - - - M18`: If M had 18 bars, he would have answered "20" on the first morning - - - - - - M16: Since M didn't answer day 1, R would answer "18" on the first evening. - - - - - R4: That didn't happen, so M would answer "20" on second morning - - - - M14: That didn't happen, so R would answer "18" on second evening- - R6: That didn't happen, so M would answer "20" on the third morning - - M12: That didn't happen, so R would answer "18" on the third evening - R8: None of the above happened, so this is the only remaining choice Max announces that 20 is the answer on the fourth morning.

Discussion

215.	If the pair of lines a x^(2)+2 h x y+b y^(2)=0 is rotated about the origin through 90^(0), then their equation in the new position is given by
Answer» `AX^(2)-2hxy-by^(2)=0` `ax^(2)-2hxy+by^(2)=0` `BX^(2)+2hxy+ay^(2)=0` `bx^(2)-2hxy+ax^(2)=0` ANSWER :D

Discussion

216.	Numebr of circles touching all the lines x+y-1=0, x-y=1=0 and y+1=0 are
Answer» 0 2 4 infinite Answer :C

Discussion

217.	Evaluation of definite integrals by subsitiution and properties of its : int_(0)^(1)(e^(t))/(t+1)dt=a then int_(b-1)^(b)(e^(-t))/(t-b-1)dt=...........
Answer» `AE^(-B)` `-ae^(-b)` `be^(-b)` NONE of these ANSWER :B

Discussion

218.	Prove that\|(2ab,a^(2),b^(2)),(a^(2),b^(2),2ab),(b^(2),2ab,a^(2))\|=-(a^(3)+b^(3))^(2).
Answer» ANSWER :AB = 152 `I_(3): x =1 , y=-1 z =-(1)/(2)`

Discussion

219.	If the sum of odd terms and the sum of even terms in (x + a)^nare p and q respectively then p^2 - q^2 =
Answer» `(x^2 +a^2)^N` `(x^2- a^2)^n` `(a^2 - x^2)^n` `x^2 - a^2` ANSWER :B

Discussion

220.	Write the value of A if int(dx)/((x+1)(x+2))=Alog\|x+1\|-log\|x+2\|+C
Answer» SOLUTION :`INT(DX)/((x+1)(x+2))=int (1/(x+1)-1/(x+2))dx=In \| x+1\| -In \| x+2 \|+cthereforeA=1`

Discussion

221.	Find the derivative of x=tan(e^(-y)) with respect to x.
Answer» ANSWER :A::B

Discussion

222.	Evaluate, int_(0)^(1)[2x]dx where [.]is the greatest integer funtion .
Answer» ANSWER :`(1)/(2)`

Discussion

223.	How many times a fair coin must be tossed, so that the probabillity of getting at least one tail is more than 90 %
Answer» ANSWER :Coin must be TOSSED at least 4 TIMES

Discussion

224.	If alpha,beta,gamma are direction angles of a line, then
Answer» `0lealpha,beta,gammale(PI)/(2)` `0lealpha,beta,gammalepi` `0LTALPHA,beta,gammalt(pi)/(2)` `0ltalpha,beta,gammaltpi` ANSWER :B

Discussion

225.	Let (x, y) be such that sin^(-1)(ax)+cos^(-1)y+cos^(-1)(bxy)=(pi)/(2) .
Answer» <P> ANSWER :[A - p] ; [B - Q] ; [C - p] ; [D - s]

Discussion

226.	If a normal to the hyperbola x^(2) - 4y^(2) = 4 having equal positive intercepts on the axes is a tangent to the ellipse (x^(2))/(a^(2))-(y^(2))/(b^(2))=1then the distance between the foci of the hyperbola(x^(2))/(a^(2))-(y^(2))/(b^(2))=1is
Answer» `(10)/SQRT(3)` `(5)/sqrt(3)` `10sqrt(3)` `5sqrt(3)` ANSWER :a

Discussion

227.	Find the shortest distance between the lines (x+1)/(7)=(y+1)/(-6)=(z+1)/(1) and (x-3)/(1)=(y-5)/(-2)=(z-7)/(1).
Answer» ANSWER :`=2sqrt(29)`

Discussion

228.	Findthe area boundedby theellipse(x^2)/( a^2) +(y^2)/(b^2) =1and thecordinatesx=0andx = ae,whereb^2= a^2 ( 1- e^2) ande lt 1 .
Answer» ANSWER :`ab [E SQRT(1-e^2) + SIN^(-1)e]`

Discussion

229.	A firm has to transport 1200 packages using large vans which can carry 200 packages each and small vans which can take 80 packages each. The cost for engaging each large van is 400 and each small van is 200. Not more than 3000 is to be spent on the job and the number of large vans cannot exceed the number of small vans. Formulate this problem, a LPP given that the objective is to minimise cost.
Answer» SOLUTION :Let the firm has x number or large vans and y number of small vans. From the gives, information we have following corresponding constraint table. Thus, we see that objective function for minimum cost is Z=400x+200y. Subject to constraints `200x+80y GE 2000["pakage constranit"]` `RIGHTARROW 5x+2y ge 30....(i)` and `400x+200y LE 3000["cost constraint"]` `Rightarrow 2x+y le 15 ...(ii)` and `x le y ..["van constraint"]...(iii)` and `x ge 0, y ge 0 ["non negative constraints"]...(iv)` Thus, REQUIRED LPP to minimise cost is minimise `Z=400x+200y, "subject to " 5x+2y ge 30` `2x+y le 15` `x le y` `x ge 0, y ge 0`

Discussion

230.	One number is selected at random from 1 to 500. Find the probability that it is a perfect square.
Answer» ANSWER :`(11)/(250)`

Discussion

231.	Choose the correct answer int_(-pi/2)^(pi/2) (x^3+x cosx+tan^5 x+1) dx =
Answer» 0 2 `PI` 1 Answer :C

Discussion

232.	calculate number of moles of HNO_(3) in 126 amu of HNO_(3)?
Answer» `(2)/(N_(A))` 2 1 `(1)/(N_(A))` ANSWER :A

Discussion

233.	Integration of some particular functions : int(dx)/(sqrt(("log"(1)/(2))^(2)-x^(2)))dx=....+c
Answer» `SIN^(-1)((X)/(log2))` `sin^(-1)((x)/(log(1)/(2)))` `COS^(-1)((x)/(log2))` `cos^(-1)((log2)/(x))` ANSWER :A

Discussion

234.	If bara,barb,barc are three non-zero, non-coplanar vectors and alphabara+betabarb+gammabarc=0 where alpha,beta,gamma are scalers then
Answer» `alpha=0,beta=0,gamma=1` `alpha=0,beta=0,gamma=0` `alpha=1,beta=0,gamma=0` `alpha=1,beta=1,gamma=1` ANSWER :B

Discussion

235.	Evaluate: int_(0)^(2pi)x^(2)sinnxdx, where n is positive integer.
Answer» ANSWER :`-(4PI^(2))/(N)`

Discussion

236.	Find the particular solution of the differential equation : dy/dx + y cot x = 4x cosec x, (x ≠ 0), given, that y = 0, when x= pi/2
Answer» Answer :`y = x^(2) - (pi^(2))/(4 SIN x)(sin x NE 0)`

Discussion

237.	If a pair of conjugate diameters meet the hyperbola and its conjugate in P and Q and O be the centre of the hyperbola, then OP^(2) - OQ^(2) equals
Answer» `a^(2) - B^(2)` `(a^(2) -b^(2))/(a^(2) + b^(2))` `(a^(2)b^(2))/(a^(2) + b^(2))` `a^(2) + b^(2)` SOLUTION :N/A

Discussion

238.	if A.M.,G.M. and H.M. in series are equal then
Answer» the distribution is symmetric all the VALUES are same the distribution is uninormal NONE of these Answer :B

Discussion

239.	A bag contains 6 white and 6 black balls. One by one the balls are drawn from the bag with replacement then the probability that 3rd time a white ball is drawn in 7th draw is:
Answer» `5/16` `5/12` `15/64` `15/128` SOLUTION :In first 6 DRAWS 2 white balls are drawn and 7th DRAW to be a white ball. Required probability `=""^(6)C_(2)(1/2)^(2)(1/2)^(4) xx 1/2 = 15/128`

Discussion

240.	Determine the value of z when z^6=sqrt(3)+i
Answer» ANSWER :0,1,2,3,4,5

Discussion

241.	The vertices of a polygon in a feassible region are (2,-3), (3,3) and (-4,2), The maximimum value of the objective function F=2x+3y is
Answer» 10 12 15 25 Answer :C

Discussion

242.	The value of .^(n)C_(0) xx .^(2n)C_(r) - .^(n)C_(1)xx.^(2n-2)C_(r)+.^(n)C_(2)xx.^(2n-4)C_(r)+"…." is equal to
Answer» `.^(n)C_(r-n) XX 2^(2n-r)` if `r ge n` 0, if `r lt n` `.^(n)C_(r-n) xx 2^(n-r)` if `r ge n` `.^(-n)C_(r-n) xx 2^(2n-r)` if `r lt n` SOLUTION :`.^(n)C_(0)xx.^(2n-r)C_(r)-.^(n)C_(1) xx .^(2n-2)C_(r)+.^(n)C_(2)xx.^(2n-4)C_(r)+"...."` = Coefficient of `X^(r)` in `(.^(n)C_(0) (1+x)^(2n)-.^(n)C_(1) (1+x)^(2n-2) + .^(n)C_(2)(1+x)^(2n-4)+"…..")` = Coefficient of `x^(r)` in `(.^(n)C_(0)((1+x)^(2))^(n) - .^(n)C_(1)((1+x)^(2))^(n-1)+.^(n)C_(2)((1+x)^(2))^(n-2)+"....")` `=` Coefficient of `x^(r)` in `((1+x)^(2)-1)^(n)` = Coefficient of `x^(r)` in `(2X+x^(2))^(n)` General term, `T_(p+1) = .^(n)C_(p)(2x)^(n-p)(x^(2))^(p) = .^(n)C_(p)2^(n-p)x^(n+p)` For `x^(r ), n+p=r`, So, `p = r-n`. `:.` Coefficient of `x^(r) = .^(n)C_(r-n) xx 2^(2n-r)` This is non-zero if `r ge n` and zero if `r lt n`.

Discussion

243.	Select the correct answer :Order of differential equation2x^2(d^2y/(dx^2))-3(dy/(dx))+y=0
Answer» `1` `0` `2` `3` Answer :C

Discussion

244.	intsqrt(1+x^(2))dx=...
Answer» `(1+2x^(2))/(SQRT(1+x^(2)))+C` `sqrt(1+x^(2))+c` `3(1+x^(2))^((3)/(2))+c` `(1)/(3)(1+x^(2))^((3)/(2))+c` Answer :D

Discussion

245.	If cosalpha+cosbeta+cosgamma=0=sinalpha+sinbeta+singamma then x^(sin(2alpha-beta-gamma)).x^(sin(2beta-gamma-alpha).x^(sin(2gamma-alpha-beta)=
Answer» 0 1 x `x^3` ANSWER :B

Discussion

246.	If x is real, then minimum vlaue of (3x ^(2) + 9x +17)/(3x ^(2) +9x+7) is:
Answer» 41 1 `17/7` `1/4` ANSWER :A

Discussion

247.	The mid points of the sides AB and AC of a triangle aBC are (2, -1) and (-4, 7) respectively, then the length of BC is
Answer» 10 20 25 30 Answer :B

Discussion

248.	If alpha,beta gt 0 and alpha lt and ax^(2)+4gammaxy+betay^(2)+4p(x+y+1)=0 represent a pair of straight lines, then
Answer» `a le p le BETA` `p le alpha` `p GE alpha` `p le alpha` or `p ge beta` ANSWER :D

Discussion

249.	If pi=(tan(3^(n+1)theta)-tan theta) and Q=sum_(r=0)^(n) (sin(3^(r )theta))/(cos(3^(r+1)theta)), then
Answer» `P=2Q` `P=3Q` `2P=Q` `3P=Q` ANSWER :A

Discussion

250.	int e^(sin^(-1)x){ 1 + (x)/(sqrt(1 - x^(2))) }dx =
Answer» `x e^(sin^(-1)x)` + c `e^(sin^(-1)x) + c ` `(1)/(SQRT(1 - x^(2))) e^(sin^(-1)x) + c` `sqrt(1 - x^(2))e^(sin^(-1)x)` + c Answer :A

Discussion

Explore topic-wise InterviewSolutions in .

lim_(x to oo)[ sqrt(x^(2) + 2x -1)-x]is equal to

Match the following :

If f(x)=((7x+1)sinx)/(e^(x)logx) " and "f^(')(x)=f(x)g(x), then g^(')(x)=

Find the equation of the chord joining point P(alpha) and Q(beta) on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1.

Can the inverse of the following matric be found ? [[1,2],[2,4]]

X wants to put 5 different rings into three different pockets is such that to pocket is empty. Then the probabaility of such event occuring is (1)/(P) ,[P]=_______ ([] is the greatest integer function).

Integrate the following functions cos sqrtx/sqrtx

Foot of the perpendicular drawn from the point (1,3,4) to the plane 2x-y+z+3=0 is

If the matrices [(3x+7,5),(y+1,2-3x)]=[(5,y-2),(8,4)], then the values of x and y are :

Using elementary row transformations , find the inverse of [{:(1,3),(2,7):}]

Smallest ear ossicle is :

If the point P denotes the complexnumber z=x+ iy in the Argand plane and if (z-i)/(z-1) is a purelly imaginary number, find the locus of P.

Write down the power set of{a,{a},{a,b}}

If the pair of lines a x^(2)+2 h x y+b y^(2)=0 is rotated about the origin through 90^(0), then their equation in the new position is given by

Numebr of circles touching all the lines x+y-1=0, x-y=1=0 and y+1=0 are

Evaluation of definite integrals by subsitiution and properties of its : int_(0)^(1)(e^(t))/(t+1)dt=a then int_(b-1)^(b)(e^(-t))/(t-b-1)dt=...........

Prove that|(2ab,a^(2),b^(2)),(a^(2),b^(2),2ab),(b^(2),2ab,a^(2))|=-(a^(3)+b^(3))^(2).

If the sum of odd terms and the sum of even terms in (x + a)^nare p and q respectively then p^2 - q^2 =

Write the value of A if int(dx)/((x+1)(x+2))=Alog|x+1|-log|x+2|+C

Find the derivative of x=tan(e^(-y)) with respect to x.

Evaluate, int_(0)^(1)[2x]dx where [.]is the greatest integer funtion .

How many times a fair coin must be tossed, so that the probabillity of getting at least one tail is more than 90 %

If alpha,beta,gamma are direction angles of a line, then

Let (x, y) be such that sin^(-1)(ax)+cos^(-1)y+cos^(-1)(bxy)=(pi)/(2) .

If a normal to the hyperbola x^(2) - 4y^(2) = 4 having equal positive intercepts on the axes is a tangent to the ellipse (x^(2))/(a^(2))-(y^(2))/(b^(2))=1then the distance between the foci of the hyperbola(x^(2))/(a^(2))-(y^(2))/(b^(2))=1is

Find the shortest distance between the lines (x+1)/(7)=(y+1)/(-6)=(z+1)/(1) and (x-3)/(1)=(y-5)/(-2)=(z-7)/(1).

Findthe area boundedby theellipse(x^2)/( a^2) +(y^2)/(b^2) =1and thecordinatesx=0andx = ae,whereb^2= a^2 ( 1- e^2) ande lt 1 .

One number is selected at random from 1 to 500. Find the probability that it is a perfect square.

Choose the correct answer int_(-pi/2)^(pi/2) (x^3+x cosx+tan^5 x+1) dx =

calculate number of moles of HNO_(3) in 126 amu of HNO_(3)?

Integration of some particular functions : int(dx)/(sqrt(("log"(1)/(2))^(2)-x^(2)))dx=....+c

If bara,barb,barc are three non-zero, non-coplanar vectors and alphabara+betabarb+gammabarc=0 where alpha,beta,gamma are scalers then

Evaluate: int_(0)^(2pi)x^(2)sinnxdx, where n is positive integer.

Find the particular solution of the differential equation : dy/dx + y cot x = 4x cosec x, (x ≠ 0), given, that y = 0, when x= pi/2

If a pair of conjugate diameters meet the hyperbola and its conjugate in P and Q and O be the centre of the hyperbola, then OP^(2) - OQ^(2) equals

if A.M.,G.M. and H.M. in series are equal then

A bag contains 6 white and 6 black balls. One by one the balls are drawn from the bag with replacement then the probability that 3rd time a white ball is drawn in 7th draw is:

Determine the value of z when z^6=sqrt(3)+i

The vertices of a polygon in a feassible region are (2,-3), (3,3) and (-4,2), The maximimum value of the objective function F=2x+3y is

The value of .^(n)C_(0) xx .^(2n)C_(r) - .^(n)C_(1)xx.^(2n-2)C_(r)+.^(n)C_(2)xx.^(2n-4)C_(r)+"…." is equal to

Select the correct answer :Order of differential equation2x^2(d^2y/(dx^2))-3(dy/(dx))+y=0

intsqrt(1+x^(2))dx=...

If cosalpha+cosbeta+cosgamma=0=sinalpha+sinbeta+singamma then x^(sin(2alpha-beta-gamma)).x^(sin(2beta-gamma-alpha).x^(sin(2gamma-alpha-beta)=

If x is real, then minimum vlaue of (3x ^(2) + 9x +17)/(3x ^(2) +9x+7) is:

The mid points of the sides AB and AC of a triangle aBC are (2, -1) and (-4, 7) respectively, then the length of BC is

If alpha,beta gt 0 and alpha lt and ax^(2)+4gammaxy+betay^(2)+4p(x+y+1)=0 represent a pair of straight lines, then

If pi=(tan(3^(n+1)theta)-tan theta) and Q=sum_(r=0)^(n) (sin(3^(r )theta))/(cos(3^(r+1)theta)), then

int e^(sin^(-1)x){ 1 + (x)/(sqrt(1 - x^(2))) }dx =