28278 + Interview Questions in Maths in Class 12

1.	Consider the expansion of (x + 3)^(8). (i) Write general term. (ii) Hence find the third term.
Answer» ANSWER :(i) `""^(8)C_(3) x^(8 - R) 3^(r)`, (II)`252x^(6)`

Discussion

2.	A parallelogram is constructed on the vectors 3bara + barb and bara - 4barb, where abs(bara) = 6, abs(barb) = 8 and barauarrdarrbarb. The length of its longer diagonal is
Answer» 40 64 32 48 Answer :D

Discussion

3.	Does the following graph represent a function or a relation?
Answer» Solution :No MATTER where you try to DRAW a VERTICAL line, it only hits the graph once, so this is a FUNCTION. The point (2, 1) is not filled in, indicating that the graph does not include the point (2, 1). However, notice that (2, 2) is completely filled in, because that point is included in the graph.

Discussion

4.	Show that the points (-6,1) and (2,3) are conjugate points with respect ot the circle
Answer» ANSWER :` (-6, 1) and (2, 3)` are conjugate w.r.tcircle.

Discussion

5.	The solution of the differential equation (1+y^2)+(x-e^(tan^-1 y))(dy)/(dx)=0, is
Answer» `x E^("TAN"^(-1)y)="Tan"^(-1)y+k` `x e^("2TAN"^(-1)y)=e^("Tan"^(-1)y)+k` `(x-2)=KE^(-"Tan"^(-1)y)` `2x " "e^("Tan"^(-1)y)=e^(2"Tan"^(-1)y)+k` ANSWER :4

Discussion

6.	Let P, Q, R and S be statement and suppose that P rarr Q rarr R rarr P. If ~S rarr R, then
Answer» `S RARR ~Q` `~Q rarr S` `~S rarr ~Q` `Q rarr ~S` ANSWER :B

Discussion

7.	Find (dy)/(dx) in the following : y= sin^(-1)((1-x^(2))/(1+x^(2))), 0 lt x lt 1.
Answer» ANSWER :`(-2)/(1+x^(2))`

Discussion

8.	One moel of N_(2) and 3.0 moles of PCl_(5) were placed in a 100-lotre vessel and heated to 227^(@)C. The equilibrium pressure was 2.05 atm. Assuming ideal behaviour, calculate X. Where X=1000xxK_(p) of reaction at 227^(@)C.
Answer» Solution :The reaction is `underset((g))(PCl_(5))hArrunderset((g))(PCl_(3))+underset((g))(Cl_(2))` `{:("INTIAL concn.","3moles",0,0),("Concn. at equilbrium",(3-3alpha),3alpha,3alpha where alpha"degree of dissociation of"PXl_(5)):}` Total MOLES of gases in the VESSEL `=n=N_(2)(1"MOLE")+PCl_(5)underset("moles")((3-3alpha))+PCl_(3)underset("moles")((3alpha))+Cl_(2)underset("moles")((3alpha))` `Or n=4+3alpha` Using the ideal gas equation `n=(PV)/(RT)=(2.05xx100)/(0.082xx500K)=5.0` moles Or `4+3alpha=5or 3alpha=1or alpha=1//3=0.333` (degree of dissociation of `PCl_(5))` Partial pressure of `PCl_(5)=2/5xx2.05=0.41atm.` Partial pressure of `PCl_(3)=1/5xx2.05=0.41atm.` Partial pressure of `Cl_(2)=1/5xx2.05=0.41` `K_(p)=((0.41atm)^(2))/((0.82atm))=0.205atm.` `X=0.205xx1000=205`

Discussion

9.	By using the properties of definite integrals evaluate the integrals in exercise. overset((pi)/(4))underset(0)int log (1+tan x)dx
Answer» ANSWER :`I=(PI)/(8)LOG2`

Discussion

10.	Evaluate the product (3veca-5vecb)*(2veca+7vecb).
Answer» ANSWER :`6\|veca\|^(2)+11veca,vecb-35\|vecb\|^(2)`

Discussion

11.	Let A and B be independent events with P(A) = 0.3 and P(B) = 0.4. Find, P(AnnB)
Answer» <P> SOLUTION :`P(ANNB)`=P(A)P(B) =`0.3xx0.4`=0.12

Discussion

12.	Let triangle ABC is right triangle right angled at C such that A lt B and r=8, R=41 . Q. Area of DeltaABC is :
Answer» 720 1440 360 480 Answer :A

Discussion

13.	In the given sets, working operations is defined, check whether is binary or not ? Justify your answer. (i) In Z^(+), ab=a-b (ii) In Z^(+), ab=ab (iii) In R, ab=ab^(2) (iv) In Z^(+), ab=\|a-b\| (v) In Z^(+), ab=a (vi) In Z^(+), a*b=a-3b
Answer» ANSWER :(II),(iii),(IV),(v) are BINARY

Discussion

14.	A men's basketball league assigns every player a two-digit number for the back of his jersey. If the league uses only the digits 1-5, what is the maximum number of players that can join the league such that no player has a number with a repeated digit (e.g., 22), and no two players have the same number?
Answer» ANSWER :20

Discussion

15.	Find the angle between the vectors hati-2hatj+3hatkand3hati-2hatj+hatk
Answer» ANSWER :`COS^(-1)((5)/(7))`

Discussion

16.	If 2x + 3y = 11 and 3x + 2y = 9, then x + y =
Answer» 4 7 8 9 Answer :A

Discussion

17.	The x intercept of the circle x^(2)+y^(2)+8x-9=0 is
Answer» 8 10 7 20 Answer :B

Discussion

18.	Find the matrix X so that , X[{:(1,2,3),(4,5,6):}]=[{:(-7,-8,-9),(2,4,6):}].
Answer» ANSWER :`=[{:(1,-2),(2,0):}]`

Discussion

19.	IF Z ne +-1 is a complex number and Arg ((Z-1)/(Z+1))= (pi)/(4) then the locus of Z in the Arg and plane is
Answer» `X^(2)+y^(2)-2y-1=0` `x^(2)+y^(2)+2y-1=0` `x^(2)+y^(2)-2x+1=0` `x^(2)+y^(2)+2x+1=0` ANSWER :A

Discussion

20.	Number of distinct normals that can be drawn from ((11)/(4),(1)/(4)) to the parabola y^(2)=4x is
Answer» 3 2 1 4 Answer :B

Discussion

21.	If f(x) = int_(e)^(e^(x) )log((x)/( log t))dt, then the value of (3f'(3)) / e
Answer» `- 3 LOG 3` `3 log 3` `e^(3) - e` `e^(2) -1` ANSWER :D

Discussion

22.	Integration by partial fraction : int(x^(2)+1)/(x^(4)+1)dx=.....
Answer» `(1)/(SQRT(2))tan^(-1)((x^(2)-1)/(2X))+c` `(1)/(sqrt(2))tan^(-1)((x^(2)-1)/(sqrt(2x)))+c` `(1)/(sqrt(2))tan^(-1)((x^(2)-1)/(2sqrt(x)))+c` `(1)/(sqrt(2))tan^(-1)((x^(2)-1)/(sqrt(2)x))+c` Answer :D

Discussion

23.	Evalute the following integrals int (1)/(sin x + sqrt(3)cos x )dx
Answer» Answer :`(1)/(2) " LOG "\|(SQRT(3) tan ""(X)/(2) +1)/(sqrt(3) - tan ""(x)/(2)) \| + C `

Discussion

24.	If veca=2hati+2hatj+3hatk,vecb=-hati+2hatj+hatkandvecc=3hati+hatjare such thatveca+lambdavecb isperpendicular to vecc , then find the value of lambda.
Answer» ANSWER :8

Discussion

25.	Probability of solving specific problem independently by A and B are (1)/(2) and (1)/(3) respectively. If both try to solve the problem independently, find the probability that (i) the problem is solved (ii) exactly one of them solves the problem.
Answer» ANSWER :(i) `(2)/(3)`, (II) `(1)/(2)`

Discussion

26.	Consider A and B as 2xx2 matrices with determinant equal to 1 then tr(AB)-tr(A).tr(B)+tr(AB^(-1))+2 is_______
Answer» Solution :`B^(2)-tr(B).B+l=0` `impliesAB-(tr(B)A+AB^(-1)=0` `:. Tr(AB)-tr(A)tr(B)+tr(AB^(-1))=0`

Discussion

27.	Define Feasible region in LPP.
Answer» ANSWER :The COMMON region DETERMINED by all the constraints including non - negative constraints `X,y ge 0` of a linear programming problem.

Discussion

28.	The value of C in mean value theorem for the function f(x)=x^(2) in [2, 4] is
Answer» 1)3 2)2 3)4 4)`7//2` ANSWER :A

Discussion

29.	int_(0)^(pi/2) cos 2x dx
Answer» SOLUTION :`int_(0)^(pi//2) cos 2X dx=[(sin 2x)/(2)]_(0)^(pi//2)` `=(1)/(2)[sin 2x]_(0)^(pi//2)` `=(1)/(2) [(sin 2XX .(pi)/(2))-sin(0)]=(1)/(2) (0-0)=0`

Discussion

30.	The sum of the fifth powers of the roots of the equation x^(4) - 7x^(2) + 4x - 3 =0 is
Answer» 99 `-140` `-99` 140 Answer :2

Discussion

31.	If f(x) =[tan^2x], what is f ' (0)?
Answer» SOLUTION :F(X) = `[tan^2x]f(0)=underset(hto0)lim([tan^2(0+h)]-[tan^2(0)])/h=underset(hto0)lim(0-0)/h=0

Discussion

32.	Evaluate: int sec^3 ( 2x ) dx.
Answer» SOLUTION :`1/4 SEC (2X) TAN (2x) + 1/4 log\|sec (2x) + tan (2x)\| + C `

Discussion

33.	Let M be a 3xx3 matrix satisfying M^(3)=0. Then which of the following statement(s) are true:
Answer» `\|(1)/(2)M^(2)+M+I\|ne0` `\|(1)/(2)M^(2)-M+I\|=0` `\|(1)/(2)M^(2)+M+I\|=0` `\|(1)/(2)M^(2)-M+I\|ne0` ANSWER :A::D

Discussion

34.	y"+(y')^(2) + 2y = 0
Answer» ANSWER :ORDER 2; DEGREE 1

Discussion

35.	If 2x+3y=1 and 3x+4y=k are conjugate lines w.r. the circle x^(2)+y^(2)=4 then k=
Answer» 36 72 24 144 Answer :B

Discussion

36.	Let a function f: R to R, where R is the set of real nos. satisfying the equation f(x+y) = f(x) + f(y) AA x, y if f(x) is continuous at x = 0, then
Answer» f(x) is discontinuous `AA K in R -{1}` f(x) is continuous `AA k in R ` f(x) is continuous `AA k in R -{1,2}` NONE of these Answer :B

Discussion

37.	Find the projection of the point (7,-5,3) on xy-plane,
Answer» SOLUTION :(7,-5,0),

Discussion

38.	Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are hati+2hatj-hatk and -hati+hatj+hatk respectively, in the ratio 2 : 1. (i) internally(ii) externally
Answer» Answer :(i) `R=-(1)/(3)hati+(4)/(3)HATJ+(1)/(3)hatk` (ii) `=-3hati+3hatk`

Discussion

39.	If a=(1)/(sqrt(10))(3hati+hatk) and b=(1)/(7)(2hati+3hatj-6hatk), then the value of (2a-b).[(axxb)xx(a+2b)] is
Answer» `-3` 5 3 `-5` Solution :GIVEN , `a = 1/(SQRT(10)) (hati + hatk)`and `b = 1/(7) (2hati + 3hatj - 6hatk)` `:. (2a-b) .[(a xx b) xx (a+2B)]` `= (2a - b).{(a xx b)xx a + (a xx b) xx 2b }` `= (2a - b) .{(a.a) b - (b.a) a+ 2 (a.b) b - 2(b.b)a}` `= (2a - b) .{1(b)- (0) a + 2(0) b - 2 (1)a}` [ `:' a .b = 0` and ` a.a = b = 1`] `= (2a - b) (b - 2a) = - (4\|a\|^(2) - 4A. b + \|b\|^(2))` `= - {4 - 0 + 1} = - 5`

Discussion

40.	If the letters of the word SACHIN are arranged in all possible ways and these words are written out as in dictoionary, then the word SACHIN appers at serial number is
Answer» 601 600 603 602 Answer :A

Discussion

41.	Coefficient of x^n in (1+x)/(1!) +((1+x)^2)/(2!) + ((1+x)^3)/(3!) + .......=
Answer» `E/(N!)` `1/(e.n!)` `e/(n!) -1` `(EN)/(n!)` ANSWER :A

Discussion

42.	If(1 -x +6 x ^ 2 ) /(x - x ^ 3 )= (A)/(x)+(B)/( 1 - x )+ (C )/(1 +x ) ,then Ais equal to
Answer» ` 1 ` 2 3 4 Solution : ` ( 1- X+6x ^ 2 )/( x (1 -x ^ 2 ) )=(A( 1 -x ^ 2 ) +B(x )(1 + x ) + C(x) (1 - x ))/(x(1 - x )(1 + x)) ` ` rArr1- x+6x ^ 2= A (1 - x ^ 2 )+ Bx ( 1 + x ) + Cx( 1 - x ) … (1) ` Substituting`x = 0 `in equation(1) ` I =A(-0 )+ B(0) +C(0) ` ` RARR A = 1`

Discussion

43.	If veca = hati+2hatj-hatk, vecb = hati+hatj+2hatk,vecc = 2hati-hatj then
Answer» `vecabotvecb` `vecbbotvecc` `vecabotvecc` no PAIR of VECTORS are perpendicular Answer :C

Discussion

44.	Assertion(A ) :Theequationwhoserootsarethesquearesof therootsofx^4 +x^3+2x^2 +x+1=0isx^4 +3x^3 +4x^2 +3x+1=0 Reason(R ): theequationwhoserootsarethe squaresof the rootsof f (x )=0is obtainedbyeliminatingsquaresrootfromf( sqrt(x))=0
Answer» both A and R true and R is the CORRECT EXPLANATION of A both A and R are true but R is not correct explanation of A A is true but R is FALSE A is false but R is true Answer :1

Discussion

45.	If F_1" and "F_2 be the feet of perpendicular from the foci S_1" and "S_2 of an ellipse (x^2)/(5)+(y^2)/(3)=1 on the tangent at any point P on the ellipse then (S_1F_1)*(S_2F_2) is
Answer» 2 3 4 5 Answer :B

Discussion

46.	Find the mean and variance of the random variable X which follows the following distribution
Answer» ANSWER :3, 1

Discussion

47.	Let A and E be two events with positive probabilites Statement 1 : P(E//A)ge P(A//E) P(E)Statement 2 : P(A//E)ge P(A cap E)
Answer» both STATEMENTS are true both statements are FALSE STATEMENT 1 is true, statement 2 is false statement 1 is false, statement 2is true Answer :A

Discussion

48.	If f(x)=x+{-x}+[x], where [x] and {x} denotes greatest integer function and fractional part function respectively, then find the number of points at whichf(x) is both discontinuous and non-differentiable in[-2,2].
Answer» ANSWER :5

Discussion

49.	An instructor has a question bank consisting of 300 easy "True" // "False" questions, 200 difficult "True" // "False" questions, 500 easy multiple choice questions and 400 difficult multiple choice questions. If a question is selected at random from the question bank, what is the probability that it will be an easy question given that it is a multiple choice question?
Answer» ANSWER :`(5)/(9)`

Discussion

50.	A small block B is placed on block A of mass 5kg and length 20 cm. Initially block B in near the right end of block A .A constant horizontal force of 10N is applied to the block A All surfaces are smooth . Find the time elapsed (in sec) before blocks B separates from A.
Answer» ANSWER :0.45

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Consider the expansion of (x + 3)^(8). (i) Write general term. (ii) Hence find the third term.

A parallelogram is constructed on the vectors 3bara + barb and bara - 4barb, where abs(bara) = 6, abs(barb) = 8 and barauarrdarrbarb. The length of its longer diagonal is

Does the following graph represent a function or a relation?

Show that the points (-6,1) and (2,3) are conjugate points with respect ot the circle

The solution of the differential equation (1+y^2)+(x-e^(tan^-1 y))(dy)/(dx)=0, is

Let P, Q, R and S be statement and suppose that P rarr Q rarr R rarr P. If ~S rarr R, then

Find (dy)/(dx) in the following : y= sin^(-1)((1-x^(2))/(1+x^(2))), 0 lt x lt 1.

One moel of N_(2) and 3.0 moles of PCl_(5) were placed in a 100-lotre vessel and heated to 227^(@)C. The equilibrium pressure was 2.05 atm. Assuming ideal behaviour, calculate X. Where X=1000xxK_(p) of reaction at 227^(@)C.

By using the properties of definite integrals evaluate the integrals in exercise. overset((pi)/(4))underset(0)int log (1+tan x)dx

Evaluate the product (3veca-5vecb)*(2veca+7vecb).

Let A and B be independent events with P(A) = 0.3 and P(B) = 0.4. Find, P(AnnB)

Let triangle ABC is right triangle right angled at C such that A lt B and r=8, R=41 . Q. Area of DeltaABC is :

In the given sets, working operations ** is defined, check whether ** is binary or not ? Justify your answer. (i) In Z^(+), a**b=a-b (ii) In Z^(+), a**b=ab (iii) In R, a**b=ab^(2) (iv) In Z^(+), a**b=|a-b| (v) In Z^(+), a*b=a (vi) In Z^(+), a**b=a-3b

Find the angle between the vectors hati-2hatj+3hatkand3hati-2hatj+hatk

If 2x + 3y = 11 and 3x + 2y = 9, then x + y =

The x intercept of the circle x^(2)+y^(2)+8x-9=0 is

Find the matrix X so that , X[{:(1,2,3),(4,5,6):}]=[{:(-7,-8,-9),(2,4,6):}].

IF Z ne +-1 is a complex number and Arg ((Z-1)/(Z+1))= (pi)/(4) then the locus of Z in the Arg and plane is

Number of distinct normals that can be drawn from ((11)/(4),(1)/(4)) to the parabola y^(2)=4x is

If f(x) = int_(e)^(e^(x) )log((x)/( log t))dt, then the value of (3f'(3)) / e

Integration by partial fraction : int(x^(2)+1)/(x^(4)+1)dx=.....

Evalute the following integrals int (1)/(sin x + sqrt(3)cos x )dx

If veca=2hati+2hatj+3hatk,vecb=-hati+2hatj+hatkandvecc=3hati+hatjare such thatveca+lambdavecb isperpendicular to vecc , then find the value of lambda.

Probability of solving specific problem independently by A and B are (1)/(2)﻿ and﻿ (1)/(3) respectively. If both try to solve the problem independently, find the probability﻿ that﻿ (i) the problem is solved (ii) exactly one of them solves the problem.﻿

Consider A and B as 2xx2 matrices with determinant equal to 1 then tr(AB)-tr(A).tr(B)+tr(AB^(-1))+2 is_______

Define Feasible region in LPP.

The value of C in mean value theorem for the function f(x)=x^(2) in [2, 4] is

int_(0)^(pi/2) cos 2x dx

The sum of the fifth powers of the roots of the equation x^(4) - 7x^(2) + 4x - 3 =0 is

If f(x) =[tan^2x], what is f ' (0)?

Evaluate: int sec^3 ( 2x ) dx.

Let M be a 3xx3 matrix satisfying M^(3)=0. Then which of the following statement(s) are true:

y"+(y')^(2) + 2y = 0

If 2x+3y=1 and 3x+4y=k are conjugate lines w.r. the circle x^(2)+y^(2)=4 then k=

Let a function f: R to R, where R is the set of real nos. satisfying the equation f(x+y) = f(x) + f(y) AA x, y if f(x) is continuous at x = 0, then

Find the projection of the point (7,-5,3) on xy-plane,

Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are hati+2hatj-hatk and -hati+hatj+hatk respectively, in the ratio 2 : 1. (i) internally(ii) externally

If a=(1)/(sqrt(10))(3hati+hatk) and b=(1)/(7)(2hati+3hatj-6hatk), then the value of (2a-b).[(axxb)xx(a+2b)] is

If the letters of the word SACHIN are arranged in all possible ways and these words are written out as in dictoionary, then the word SACHIN appers at serial number is

Coefficient of x^n in (1+x)/(1!) +((1+x)^2)/(2!) + ((1+x)^3)/(3!) + .......=

If(1 -x +6 x ^ 2 ) /(x - x ^ 3 )= (A)/(x)+(B)/( 1 - x )+ (C )/(1 +x ) ,then Ais equal to

If veca = hati+2hatj-hatk, vecb = hati+hatj+2hatk,vecc = 2hati-hatj then

Assertion(A ) :Theequationwhoserootsarethesquearesof therootsofx^4 +x^3+2x^2 +x+1=0isx^4 +3x^3 +4x^2 +3x+1=0 Reason(R ): theequationwhoserootsarethe squaresof the rootsof f (x )=0is obtainedbyeliminatingsquaresrootfromf( sqrt(x))=0

If F_1" and "F_2 be the feet of perpendicular from the foci S_1" and "S_2 of an ellipse (x^2)/(5)+(y^2)/(3)=1 on the tangent at any point P on the ellipse then (S_1F_1)*(S_2F_2) is

Find the mean and variance of the random variable X which follows the following distribution

Let A and E be two events with positive probabilites Statement 1 : P(E//A)ge P(A//E) P(E)Statement 2 : P(A//E)ge P(A cap E)

If f(x)=x+{-x}+[x], where [x] and {x} denotes greatest integer function and fractional part function respectively, then find the number of points at whichf(x) is both discontinuous and non-differentiable in[-2,2].

A small block B is placed on block A of mass 5kg and length 20 cm. Initially block B in near the right end of block A .A constant horizontal force of 10N is applied to the block A All surfaces are smooth . Find the time elapsed (in sec) before blocks B separates from A.

In the given sets, working operations is defined, check whether is binary or not ? Justify your answer. (i) In Z^(+), ab=a-b (ii) In Z^(+), ab=ab (iii) In R, ab=ab^(2) (iv) In Z^(+), ab=|a-b| (v) In Z^(+), a*b=a (vi) In Z^(+), a**b=a-3b

Probability of solving specific problem independently by A and B are (1)/(2) and (1)/(3) respectively. If both try to solve the problem independently, find the probability that (i) the problem is solved (ii) exactly one of them solves the problem.