28278 + Interview Questions in Maths in Class 12

1.	Let lim_(x to) (1+(P(x))/(x^(5)))^((1)/(x^(3)-tan^(3)x)) exists and is equal to e^(9//7), where P(x) is a polynormial function. The degree of polynomial is
Answer» 8 9 10 11 Solution :`UNDERSET(xto0)lim(1+(P(x))/(x^(5)))^((1)/(x^(3)-tan^(3)x))=E^(9//7)` `:.P(x)` must be of degree greater than or EQUAL to 6 `i.e.P(x)=ax^(6)+bx^(7)+. . . . .. . . . . . .. ` `underset(xto0)lime^(underset(xto0)lim(1)/((x^(3)-tan^(3)x))(1+(P(x))/(x^(2))-1))=e^(9//7)` `underset(xto0)lim((x^(3))/(x-tanx))((x^(2))/(x^(2)+tan^(2)x+xtanx))(P(x))/(x^(5).x^(5))=(9)/(7)` `(-3)(2)underset(xto0)lim(P(x))/(x^(10))=(9)/(7)` `underset(xto0)lim(P(x))/(x^(10))=(-3)/(14)` Hence degree of P(x) is 10

Discussion

2.	If f(x)=f(pi + e - x) and int_(e)^(pi)f(x)dx=(2)/(e + pi), then int_(e)^(pi)xf(x)dx is equal to
Answer» `PI - e` `(pi + e)/(2)` 1 `(pi-e)/(2)` ANSWER :C

Discussion

3.	Find (dy)/(dx)," if "y= sin^(-1)x +sin^(-1)sqrt(1-x^(2)), 0 lt x lt 1.
Answer» ANSWER :`0`

Discussion

4.	The probability distribution of x is Find the value of k
Answer» 1)0.1 2)0.4 3)0.3 4)0.2 Answer :D

Discussion

5.	If A=[a_(ij)]_(nxxn)such that a_(ij)=0,for i nej then , A is …….. (a_(ij)nea_(jj))(ngt1)
Answer» a COLUMN matrix a ROW matrix a DIAGONAL matrix a scalar matrix. Answer :C

Discussion

6.	Find the area bounded by the curves y= cos x and y= sin x between the ordinates x=0 and x= (3pi)/(2)
Answer» ANSWER :`4 sqrt2-2`

Discussion

7.	For the reaction C_(2)H_(6)(g)hArrC_(2)H_(4)(g)+H_(2)(g),DeltaG^(@)=22.38KJ mol^(-1)" at "900K. If pure C_(2)H_(6) is passed over a suitable catalyst at a temperature of 900 K and a pressure of 1.0 atmosphere, then calculate X. Where X=100xx"mole percent of hydrogen present at equilibrium". [Antilog(1.299=0.05)]
Answer» Solution :`DELTAG^(@)=-RTlnK_(p)" or "DeltaG^(@)=-RT.2.303logK_(p)` Or `K_(p)="antilog"[-(DeltaG^(@))/(2.303RT)]="antilog"[-(22.38xx10^(3)J)/((2.303)(8.314)(900))]` `K_(p)="antilog"[-1.299]` `K_(p)=0.050` `{:("Now,"""C_(2)H_(6)(g)hArrC_(2)H_(4)(g)+H_(2)(g)),("At equilibrium,"""(C-Calpha)""Calpha""Calpha):}` where 'C' is the initial concentration of `C_(2)H_(6).` Total moles at equilibrium `=C-Calpha+Calpha+Calpha=C+Calpha=C(1+alpha)` THEREFORE, the partial PRESSURE of `C_(2)H_(6)=(1-alpha)/(1+alpha).P` partial pressure of `H_(2)=(alpha)/(1+alpha).P` `K_(P)=0.050=([(alpha)/(1+alpha).P]^(2))/([(1-alpha)/(1+alpha)].P)=(alpha^(2))/((1+alpha)(1-alpha)).P=(alpha^(2))/(1-alpha^(2)).P` Then, `K_(p)=0.050=(alpha^(2))/(1+alpha^(2)).1" or "alpha=0.2182` Mole percent of `H_(2)=(alpha)/(1+alpha)xx100=(0.2182)/(1.2182)xx100=17.91` `X=17.91xx100=1791` Ans.

Discussion

8.	Jasperwantsto measurethealtiude of hiskite. Hetiesthe kitestringto a spikedrivenintothegroundand measuresthe anglebetweenthe stringand theground. Thenhe createstwosimilartrianglesbyadjustingthedistancebetweenan-8 footpoleand thespikeuntilthe anglecreatedby apieceofstringis thesameas theanglehe measuredpreviously. thelengthof thestringto thekiteis 85feetandthelengthof thestringto thepoleis 17feet. which ofthe follpowingis closestto theheight, in feet, thatthekiteisabovethe ground?
Answer» 25 40 102 110 Answer :B

Discussion

9.	Draw the graph of y=sin^(-1)("log"_(e)x). Also find the point of inflection.
Answer» Solution :We have `y=f(X) =sin^(-1)("LOG"_(e)x)` `Heref(x) is defined if-1le" log"_(e)XLE1` `or ""e^(-1)lexle e` `f(x) = sin^(-1)("log"_(e)x)=0` `therefore"log"_(e)x=0` `therefore""x=1` So the graph meets the x-axis at (1,0). `f'(x)=1/(xsqrt(1-(log_(e)x))^(2))gt0," hence f(x) is invreasing".` `f'(x)=(sqrt(1-(log_(e)x)^(2))-(log_(e)x)/(sqrt((1-(log_(e)x)^(2)))))/(x^(2)(1-(log_(e)x)^(2)))` `f'(x)=sqrt(1-(log_(e)x)^(2))-(log_(e)x)/(sqrt((1-(log_(e)x)^(2))))=0` `therefore""(log_(e)x)^(2)+log_(e)x-1=0` `therefore""log_(e)x=(-1+sqrt5)/2` `therefore""x=e^((-1+sqrt5)/2)` Hence the graph of the FUNCTION is as shown in the FOLLOWING figure. In the figure, the graph has his point of infection at point A.

Discussion

10.	Let f(x) be twice differentiable on [1, 3], and let f(1)=f(3). Further if \|f''(x)\| le 2, then for all x in [1, 3] :
Answer» `-1 le F'(x) le 1` `-4 lt f'(x) lt 4` `\|f'(x)\| GT 2` `\|f'(x)\| lt 4` Answer :D

Discussion

11.	int (("cosx")/(x) - "sinx.logx")dx =
Answer» (log x) sinx + c (log x )(COS x) + c `-` (log x).(cosx) + c `-`(log x) sin x + c Answer :B

Discussion

12.	If A=[{:(3,5),(1,2):}],B=adjAandC=3A, then (\|adjB\|)/(\|C\|)=.......
Answer» `(1)/(3)` `(1)/(9)` `(1)/(4)` 1 Answer :B

Discussion

13.	If I_(n) = int(sin^(n))dx, then nI_(n)-(n-1)I_(n-1) equals to
Answer» `SIN^(n-1)x cosx` `COS^(n-1)x sinx` `-sin^(n-1) x cosx` `-cos^(n-1)x sinx` Answer :C

Discussion

14.	Given three identical boxes I, II and III, each containing two coins. In box I both coins are gold coins, in box II both are silver coins and in box III there is one gold and one silver coin. A person chooses a box at random and takes out a coin. If the first coin is gold, what is the probability that the other coin in the box is gold.
Answer» ANSWER :`(1)/(3)`

Discussion

15.	Answer questions 4,5 and 6 by appropriately matching the information given in the three columns of the following table. Column l : Functions Column ll : Integration of the function with constants alpha,betaandgamma Column III : Sum of alpha,betaandgamma Which of the following options is the only CORRECT combination ?
Answer» (II) (ii) (Q) (II) (i) (P) (II)(III) (Q) (III) (ii) (Q) Answer :6

Discussion

16.	Answer questions 4,5 and 6 by appropriately matching the information given in the three columns of the following table. Column l : Functions Column ll : Integration of the function with constants alpha,betaandgamma Column III : Sum of alpha,betaandgamma Which of the following options is the only CORRECT combination?
Answer» (I) (IV) (P) (I) (iv) (Q) (I) (III) (P) (I) (iii) (Q) ANSWER :5

Discussion

17.	Evaluate int cos ec^(4) x dx
Answer» ANSWER :`-(COSEC^(2)xcotx)/(3)-(2)/(3)cotx+c`

Discussion

18.	The numberof waysinwhich6 menand4 ladiescansitarounda roundtableso thatno twoladiescome together is
Answer» ANSWER :`7!XX""^8P_4`

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19.	Find the derivative of y = e^(2x)log (3x + 4)
Answer» ANSWER :B::C::D

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20.	Find the number of ordered pair of real numbers (x, y) satisfying the equation: 5x(1+1/(x^(2)+y^(2)))=12 & 5y(1-1/(x^(2) + y^(2))) =4
Answer» ANSWER :(2,1)

Discussion

21.	Answer questions 4,5 and 6 by appropriately matching the information given in the three columns of the following table. Column l : Functions Column ll : Integration of the function with constants alpha,betaandgamma Column III : Sum of alpha,betaandgamma Which of the following options is the only INCORRECT combinations?
Answer» ANSWER :(A)

Discussion

22.	Match the relation defined on set A={a,b,c} in column I with the corresponding type is columnII
Answer» SOLUTION :NA

Discussion

23.	Iim_(n to oo) (1^(99) + 2^(99) + …..+ n^(99))/(n^(100)) equals :
Answer» 100 `1/99` `1/100` 99 Answer :C

Discussion

24.	The sum of coefficitents in the expansion of (1 + 3x -3x^(2))^(1143) is equal to
Answer» `-1` 0 1 `2^(1143)` ANSWER :C

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25.	If n is a natural number, then
Answer» `1^(2)+2^(2)+…..+n^(2)lt(n^(3))/(3)` `1^(2)+2^(2)+….+n^(2)=(n^(3))/(3)` `1^(2)+2^(2)+….+n^(2) GTN^(3)` `1^(2)+2^(3)+….+n^(2) gt(n^(3))/(3)` ANSWER :D

Discussion

26.	A variable line is drawn through the origin O. Two points A and B same side of O are taken on the line such thatOA=1 and OB=2 unit. . Through points A and B two lines are drawn making equal angle alphawith the line AB. Then the locus of the point of intersection of the lines, is:
Answer» `X^(2)+y^(2)=(9+tan^(2)ALPHA)/(4)` `x^(2)+y^(2)=(9-tan^(2)alpha)/(4)` `x^(2)+y^(2)=(9+tan^(2)alpha)/(2)` `x^(2)+y^(2)=(9+2tan^(2)alpha)/(4)` ANSWER :A

Discussion

27.	Evaluate the following lim_(xto1) (1+2x-3x^2+4x^3-5x^4)
Answer» SOLUTION :`lim_(xto1)(1+2x-3x^2+4x^3-5x^4)` 1+2-3+4-5=7-8=-1

Discussion

28.	The probability that a student is not a swimmer is (4)/(5). The probability that out of 5 students exactly 4 are swimmers is ………..
Answer» `((1)/(5))^(3)` `4((1)/(5))^(4)` `""_(5)C_(4)((4)/(5))^(4)` `((4)/(5))^(4)` ANSWER :B

Discussion

29.	If int (x^(2)-x+1)/(x^(2)+1)e^(cot^(-1)x)dx=A(x)e^(cot^(-1)x)+c, then A(x) is equal to :
Answer» `-X` x `SQRT(1-x)` `sqrt(1+x)` ANSWER :2

Discussion

30.	Let y(x) be the solution of the differential equation . (x log x) (dy)/(dx) + y = 2x log x, (x ge 1). Then y (e) is equal to
Answer» E 0 2 2e Answer :3

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31.	The statement phArr q is not equivalent to
Answer» `(pvvq)RARR (p^^q)` `(p^^q)rArr(pvvq)` `(pvvq)HARR (p^^q)` `~(pvvq)VV(p^^q)` ANSWER :B

Discussion

32.	If A=[[1, 2, 3], [2, 3, 2], [1, 2, 2]], then
Answer» `A_(12)+A_(22)+A_(32)=0` `A_(13)+A_(23)+A_(33)=1` `A_(11)+A_(21)=A_(32)` `A_(11)+A_(21)=2A_(32)` Answer :C

Discussion

33.	Find x and y :[[2x-y],[x+y]]=[[3],[-9]]
Answer» SOLUTION :`[[2X,-y],[X,+y]]=[[3],[-9]]` `:.2x-y=3` `(x+y=-9)/(3x=-6)` `x=-2` `:. Y=-9+2=-7`

Discussion

34.	(1 + x+x^2)^8 = a_0 + a_1x +…….+a_16 x^16 then a_0 - a_2 + a_4 - a_6 + ……..+a_16 =
Answer» 1 2 3 4 Answer :A

Discussion

35.	For any square matrix A, show that AA' is symmetric.
Answer» ANSWER :THUS (AA')'=AA'

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36.	Evaluate the limit . underset(n to 00)("Lt") (1+2^(4)+3^(4)+…….+n^(4))/(n^(5))
Answer» ANSWER :`(1)/(5)`

Discussion

37.	The tangent to the curvey=(1+x^2)^2at x=-1 has slope ______.
Answer» 4 -4 8 -8 Answer :D

Discussion

38.	(Transportation Problem) A catering agency has two kitchens to prepare food at two places A and B. From these places 'Mid-day Meal' is to be supplied to threee different schools situated at P,Q,R. Themonthly requirments of the schools are respectively 40,40 and 50 food packets.A packet contains lunch for 1000 students.Preparing capacity of kitchen A and B are 60 and 70 packets per month respectively.The transpportation cost per packet for the kitchen to schools s given below: How many packets from kitechen should be transported to schools so that the cost of transportation is minimum? Also find the minimum cost.
Answer» ANSWER :MINIMUM cost is₹300 at the POINT I (10, 0).

Discussion

39.	Solve sqrt((x-3)(2-x)) lt sqrt(4x^(2)+12x+11).
Answer» ANSWER :`X in [2, 3]`

Discussion

40.	Compute the indicated products: (i) [(a,b),(-b,a)][(a,-b),(b,a)] (ii) [(1),(2),(3)][(2,3,4)] (iii) [(1,-2),(2,3)][(1,2,3),(2,3,1)] (iv) [(2,3,4),(3,4,5),(4,5,6)][(1,-3,5),(0,2,4),(3,0,5)] (v) [(2,1),(3,2),(-1,1)][(1,0,1),(-1,2,1)] (vi) [(3,-1,3),(-1,0,2)][(2,-3),(1,0),(3,1)]
Answer» Answer :`(i) [(a^(2)+b^(2),0),(0,a^(2)+b^(2))] (II)[(2,3,4),(4,6,8),(6,9,12)] (III)[(-3,-4,1),(8,13,9)]` `(IV)[(14,0,42),(18,-1,56),(22,-2,70)] (V)[(1,2,3),(1,4,5),(-2,2,0)] (vi) [(14,-6),(4,5)]`

Discussion

41.	If a=2hati+2hatj+3hatk, b=-hati+2hatj+hatk and c=3hati+hatj such that a + lambda b is perpendicular to c, then the value of lambda is
Answer» 2 4 6 8 Solution :The givenvectorsare ` a = 2 hati+ 2 hatj + 3hatk, B=- hati+ 2hatj +hatk` ` andC=3hati+ hatj` Now` (a+ lamda b) BOT c` ` implies( a + LAMDAB).c =0` `[ :' `SCALAR PRODUCTOF twoperpendicularvectorsis zero] ` implies[( 2 hati + 2 hatj+ 3 hatk )+lamda (-hati + 2 hatj + hatk ) ].(3 hati+ hatj )=0 ` `implies [(2 - lamda) hati +(2+ 2 lamda ) hatj +(3+ lamda )hatk ] .(3 hati+ hatj) =0` ` implies(2- lamda )3+(2+2lamda )1+(3+lamda )0=0` `implies6-3lamda+ 2 +2 lamda =0` `implies8-lamda =0` `implies lamda =8` hence , therequied valueof ` lamda ` is 8 .

Discussion

42.	Discuss the relative position of the fol- lowing pair of circles. x^(2) + y^(2) + 6x + 6y + 14 = 0 x^(2) + y^(2) - 2x -4y -4 = 0.
Answer» ANSWER :ONE LIES COMPLETELY OUTSIDE the other

Discussion

43.	A vector vec( r ) has length 21 and directi9on ratio 2,-3,6. Find the direction cosines and components of vec( r ) given that vec( r ) makes an acute angle with X- axis.
Answer» Answer :`(2)/(7),(-3)/(7),(6)/(7)` COMPONENTS : `6hati,-9hatj,18hatk`

Discussion

44.	If a and b are respective coefficients of x^m and x^n in the expansion of (1+ x)^(m+n) then
Answer» a + B = m+ N a = 2b a = b b = 2a Answer :C

Discussion

45.	If y= log_(e)( log_(pi)x) , ( x gt 1) then ( d^2 y)/( dx^2) = …....
Answer» `- ((X .log_(e)x)^2) /( log_(e)(EX) )` `(log_(e) (ex) )/( ( x.log_(e) x)^2)` `- (log_(e)(ex) )/( (x.log_(e) x)^(2) )` `(log_(e)((e )/( x)))/( (x.log_(pi)x)^2)` Answer :C

Discussion

46.	Find the value of lambda so that the three vectors are co-planar. (2,-1,1), (1,2,-3) and (3,λ,5)
Answer» Solution :Let `VECA = (2,-1,1), vecb = (1,2,-3), vecc = (3,lambda,5)` If `veca,vecb,vecc` are COPLANAR then `vecaxxvecb.vecc = 0`

Discussion

47.	int tanx/sqrt(sinx) dx
Answer»

Discussion

48.	if f(x)={{:((8^(x)-4^(x)-2^(x)+1)/(x^(2)),xgt0),( x^(2) , x le 0):} is continuousat x=0 , thenthe valueof lamdais
Answer» `4 log _(E)2` `2log_(e)2` `log_(e)2` NONEOF these Answer :C

Discussion

49.	Write the first three terms in the expansion of (2-(y)/(3))^(6)
Answer» ANSWER :`64-64y + (80)/(3) y^(2)`

Discussion

50.	(d)/(dx)[tan^(-1){(secx+tan^2x}]=
Answer» `(COSX)/(1+cos^(2)x)` `(SINX)/(1+sin^(2)x)` `(sin2x)/(1+sin^(2)x)` `(cosx)/(1+sin^(2)x)` ANSWER :D

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Let lim_(x to) (1+(P(x))/(x^(5)))^((1)/(x^(3)-tan^(3)x)) exists and is equal to e^(9//7), where P(x) is a polynormial function. The degree of polynomial is

If f(x)=f(pi + e - x) and int_(e)^(pi)f(x)dx=(2)/(e + pi), then int_(e)^(pi)xf(x)dx is equal to

Find (dy)/(dx)," if "y= sin^(-1)x +sin^(-1)sqrt(1-x^(2)), 0 lt x lt 1.

The probability distribution of x is Find the value of k

If A=[a_(ij)]_(nxxn)such that a_(ij)=0,for i nej then , A is …….. (a_(ij)nea_(jj))(ngt1)

Find the area bounded by the curves y= cos x and y= sin x between the ordinates x=0 and x= (3pi)/(2)

Draw the graph of y=sin^(-1)("log"_(e)x). Also find the point of inflection.

Let f(x) be twice differentiable on [1, 3], and let f(1)=f(3). Further if |f''(x)| le 2, then for all x in [1, 3] :

int (("cosx")/(x) - "sinx.logx")dx =

If A=[{:(3,5),(1,2):}],B=adjAandC=3A, then (|adjB|)/(|C|)=.......

If I_(n) = int(sin^(n))dx, then nI_(n)-(n-1)I_(n-1) equals to

Evaluate int cos ec^(4) x dx

The numberof waysinwhich6 menand4 ladiescansitarounda roundtableso thatno twoladiescome together is

Find the derivative of y = e^(2x)log (3x + 4)

Find the number of ordered pair of real numbers (x, y) satisfying the equation: 5x(1+1/(x^(2)+y^(2)))=12 & 5y(1-1/(x^(2) + y^(2))) =4

Match the relation defined on set A={a,b,c} in column I with the corresponding type is columnII

Iim_(n to oo) (1^(99) + 2^(99) + …..+ n^(99))/(n^(100)) equals :

The sum of coefficitents in the expansion of (1 + 3x -3x^(2))^(1143) is equal to

If n is a natural number, then

A variable line is drawn through the origin O. Two points A and B same side of O are taken on the line such thatOA=1 and OB=2 unit. . Through points A and B two lines are drawn making equal angle alphawith the line AB. Then the locus of the point of intersection of the lines, is:

Evaluate the following lim_(xto1) (1+2x-3x^2+4x^3-5x^4)

The probability that a student is not a swimmer is (4)/(5). The probability that out of 5 students exactly 4 are swimmers is ………..

If int (x^(2)-x+1)/(x^(2)+1)e^(cot^(-1)x)dx=A(x)e^(cot^(-1)x)+c, then A(x) is equal to :

Let y(x) be the solution of the differential equation . (x log x) (dy)/(dx) + y = 2x log x, (x ge 1). Then y (e) is equal to

The statement phArr q is not equivalent to

If A=[[1, 2, 3], [2, 3, 2], [1, 2, 2]], then

Find x and y :[[2x-y],[x+y]]=[[3],[-9]]

(1 + x+x^2)^8 = a_0 + a_1x +…….+a_16 x^16 then a_0 - a_2 + a_4 - a_6 + ……..+a_16 =

For any square matrix A, show that AA' is symmetric.

Evaluate the limit . underset(n to 00)("Lt") (1+2^(4)+3^(4)+…….+n^(4))/(n^(5))

The tangent to the curvey=(1+x^2)^2at x=-1 has slope ______.

Solve sqrt((x-3)(2-x)) lt sqrt(4x^(2)+12x+11).

Compute the indicated products: (i) [(a,b),(-b,a)][(a,-b),(b,a)] (ii) [(1),(2),(3)][(2,3,4)] (iii) [(1,-2),(2,3)][(1,2,3),(2,3,1)] (iv) [(2,3,4),(3,4,5),(4,5,6)][(1,-3,5),(0,2,4),(3,0,5)] (v) [(2,1),(3,2),(-1,1)][(1,0,1),(-1,2,1)] (vi) [(3,-1,3),(-1,0,2)][(2,-3),(1,0),(3,1)]

If a=2hati+2hatj+3hatk, b=-hati+2hatj+hatk and c=3hati+hatj such that a + lambda b is perpendicular to c, then the value of lambda is

Discuss the relative position of the fol- lowing pair of circles. x^(2) + y^(2) + 6x + 6y + 14 = 0 x^(2) + y^(2) - 2x -4y -4 = 0.

A vector vec( r ) has length 21 and directi9on ratio 2,-3,6. Find the direction cosines and components of vec( r ) given that vec( r ) makes an acute angle with X- axis.

If a and b are respective coefficients of x^m and x^n in the expansion of (1+ x)^(m+n) then

If y= log_(e)( log_(pi)x) , ( x gt 1) then ( d^2 y)/( dx^2) = …....

Find the value of lambda so that the three vectors are co-planar. (2,-1,1), (1,2,-3) and (3,λ,5)

int tanx/sqrt(sinx) dx

if f(x)={{:((8^(x)-4^(x)-2^(x)+1)/(x^(2)),xgt0),( x^(2) , x le 0):} is continuousat x=0 , thenthe valueof lamdais

Write the first three terms in the expansion of (2-(y)/(3))^(6)

(d)/(dx)[tan^(-1){(secx+tan^2x}]=