28278 + Interview Questions in Maths in Class 12

1.	Let ** be the binary operation on N defined by a""b = H.C.F of a and b . Is * commutative ? Is ** associative ? Does there exist identity for this binary operation on N ?
Answer» SOLUTION :N/A

Discussion

2.	1 + omega + omega^(2) + ….. + omega^(300)
Answer» 0 `-OMEGA^(2)` `-omega` `1` ANSWER :D

Discussion

3.	A coins is tossed three times,where E:head on third toss,F: heads on first two tosses find P(E/F)
Answer» Solution :Here,S = {HHH,HHT,HTH,HTT,THH,THT,TTH,TTT} E ={HHH,HTH,THH,TTH}, F={HHH,HHT} `ENNF={HHH}, therefor P(EnnF)=1/8 and P(F)=2/8` THUS,P(E/F) = `(P(EnnF))/(P(F))`=1/8/2/8=1/2

Discussion

4.	Fortheequilibrium x^3 +3x^2 -x-2=0ifs_1,s_2 ,s_3havetheirusualnotaionthen
Answer» `s_1 lt_3lt s_2` `s_1lt s_2lt s_3` `s_2 LT s_1 lt s_3` `s_3 lt s_1 lt s_2` ANSWER :B

Discussion

5.	Polychromatic lightdescribed at a place by the equation E=100[sin(0.5pixx10^(15)t)+cos(pixx10^(15)t)+sin(2pixx10^(15)t)] where E is in V/m and t in sec, falls on a metal surface having work function 2.0 eV. The maximum kinetic energy of the photoelectron is [Take h = Planck's constant = 6.4xx10^(-34)J-s]
Answer» zero 1 eV 2 eV 3 eV Solution :most energetic photon FREQUENCY = `(2pixx10^(15))/(2pi)=10^(15)Hz` `hv-phi=K_(max)` `(6.4xx10^(-34)xx10^(15))/(1.6xx10^(-19))-2EV=K_(max)` `K_(max)=2eV`

Discussion

6.	Find the coefficient of x^n in the expansion of (1+ 2x + 3x^2 + 4x^3 + …..)^2
Answer» ANSWER :`""^((n+3))C_3`

Discussion

7.	If alpha and beta are the roots of the equation x^2-2x+4 =0, then alpha^(12)+ beta^(12)=
Answer» `2^(12)` `2^(10)` `2^(13)` `-2^(13)` ANSWER :C

Discussion

8.	A die is tossed thrice. Find the probability of getting an odd number at least once.
Answer» ANSWER :`(7)/(8)`

Discussion

9.	Find thearea of theregion boundedby thecurvesy^2 =x+1 and y^2=- x+1
Answer» ANSWER :`8/3` SQ. UNIT

Discussion

10.	Find the number of ways of selecting a cricket team of 11 players from 7 batsmen and 6 bowlers such that there will be atleast 5 bowlers in the team.
Answer» ANSWER :63

Discussion

11.	If force F, density D and area A are taken as fundamental quantities then dimensional formula of frequency is :
Answer» `[F^(+1/2)D^(-1/2)A^(-1)]` `[F^(1/2)D^(1/2)A^(1)]` `[FDA^(1//2)]` [FDA]

Discussion

12.	vec a , vec b , vec care three vectors such that\|vec a \| = 5 \| vec b \| =8, \|vec c \| = 3 if vec a + vec b + vec c = 8 hati+ 6hatj , find the value ofvec a , vec b +vec b .vec c + vec c .vec a
Answer» ANSWER :`1`

Discussion

13.	If log_(e)4 = 1.3868, then log_(e) 4.01 =
Answer» 1.3968 1.3898 1.3893 none ANSWER :C

Discussion

14.	If veca,vecb,vecc are non-coplanar vectors and vecu and vecv are any two vectors. Prove that vecuxxvecv=(1)/([vecavecbvecc])\|{:(vecu.veca,vecv.veca,veca),(vecu.vecb,vecv.vecb,vecb),(vecu.vecc,vecv.vecc,vecc):}\|
Answer»

Discussion

15.	Ifthe coinc ax^(2) + 2hxy + by^(2) + 2gx + 2fy + c = 0be a hyperbola , and the equation of the conjugate hyperbola is ax^(2) + 2hxy + by^(2) + 2gx + lambda = 0 , then lambda is equal to
Answer» `Delta/(AB - h^(2))` `C + Delta/(ab - h^(2))` `c - (2 Delta)/(ab - h^(2))` `-c` SOLUTION :N/A

Discussion

16.	If a, b are the roots of x^(2)+x+1=0, then a^(2)+b^(2) is
Answer» ab `a^(3)+B^(3)` 2AB `a^(-2)+b^(-2)` Answer :D

Discussion

17.	Let x= hat(i)+hat(j) and y=3 hat(i)-2 hat(k). Then, the vector r of magnitude sqrt(21) satisfying r xx x =y xx x and r xx y=x xx y, is
Answer» `-hat(i)+4hat(J)-2 hat(k)` `-hat(i)-4 hat(j)-2 hat(k)` `4 hat(i)+hat(j)-2 hat(k)` `4 hat(i)-hat(j)-2 hat(k)` ANSWER :C

Discussion

18.	The value for [axx(b+c),bxx(c-2a),cxx(a+3b)] is equal to
Answer» `[abc]^(2)` `7[abc]^(2)` `-5[AXXB" "bxxc" "cxxa]` none of these Answer :B

Discussion

19.	The position of reflection of the point (4, 1) about the line y = x - 1 is
Answer» (1, 2) (3, 4) (-1, 0) (2, 3) ANSWER :D

Discussion

20.	If (.^(20)C_(1))/(1)+(.^(20)C_(3))/(2)+(.^(20)C_(5))/(3)+.......+(.^(20)C_(19))/(10)=(K(2^(20-1)))/(21), then Kis equal to :
Answer» Solution :`(.^(20)C_(1))/(1)+(.^(20)C_(3))/(2)+(.^(20)C_(5))/(3)+......+(.^(20)C_(19))/(10)` `=underset(r=1)overset(10)SIGMA(1)/(r).^(20)C_(2r-1)=(2)/(21)underset(r=1)overset(10)Sigma(21)/(2r).^(20)C_(2r-1)` `=(2)/(21)underset(r=1)overset(10)Sigma.^(21)C_(2r)=(2)/(21)[.^(21)C_(2)+.^(21)C_(4)+.^(21)C_(20)]` `=(2)/(21)(2^(20)-1)`

Discussion

21.	Find an approximate value of the following correctedto 4 decimal places. (1.02)^(3//2)-(0.98)^(3//2)
Answer» ANSWER :`=0.059998`

Discussion

22.	The radius of the cone is increasing at the rate of 4 cm/se. Its height is decreasing at the rate of 3 cm/se. When its radius is 3 cm and height is 4 cm. Find the rate of change of its curved surface area.
Answer» ANSWER :`20 pi cm^(2)//SE`.

Discussion

23.	If(x - 4 )/( x^ 2 - 5x+6)canbeexpandedintheascendingpowersofx,thenthe coefficientofx ^ 3is
Answer» ` ( - 73 )/(648) ` `(73)/(648) ` `(71)/(648) ` ` ( - 71)/(648)` Solution : `(x -4) / ( x ^ 2- 5x+ 6 ) ` `=(2 ) /((x - 2 )) - (1)/((x - 3 )) ` `therefore(2) /((x - 2 )) - (1)/((x-3))= (2)/((-2) (1 - (x ) /(2)) )+(1)/(3(1 -(x)/(3)) ` =` (1 ) /(3) (1 -(x )/(3)) ^( -1)- (1 -(x)/(2)) ^(-1) ` `=(1)/(3) [ 1+(x)/(3)+((x)/(3)) ^ 2+ (x/3)^ 3 +... ] ` ` - [ 1+(x )/(2)+ (x/2) ^2+(x/2 ) ^ 3+... ] ` `therefore`CO - efficientof`x ^ 3` inaboveexpansion is ` (1)/(3)(1/3) ^3- (1/2) ^3 = (1)/(81)- (1)/(8)= ( -73)/(648) `

Discussion

24.	A(2,-3) and B(-2,1) are the vertices of a triangle A B C . If the centroid of this triangle moves on the line 2 x+3 y=1, then the locus of the vertex C is the line
Answer» `2x+3y=9` `2x-3y=7` `3x+2y=5` `3x-2y=3` ANSWER :A

Discussion

25.	Evaluate the following integrals int x^2 (1-1/x^2) dx
Answer» SOLUTION :`INT X^2 (1-1.x^2)DX = int(x^2-1) dx = x^3/3 -x +C`

Discussion

26.	Find lambda + mu if (2hat(i) + 6hat(j) + 27 hat(k)) xx (hat(i) + lambda hat(j) + mu hat(k)) = vec(0).
Answer» ANSWER :`LAMBDA + MU = (33)/(2)`

Discussion

27.	Find the maximum or minimum values of the following functions: (i)x^(3)-2x^(2)+x+3 (ii) x^(3)-6x^(2)+9x+4 (iii) (x+1)(x-2)^(2)+1 (iv) 2x^(3)-9x^(2)+12x+1
Answer» ANSWER :(i) Min value = 3, max value = `85/27` (ii) Min value = 4, max value = 8 (iii) Min value= 1, max value = 5 (IV) Min value = 5, max value = 6

Discussion

28.	If x^(2) + y^(2) =t- (1)/(t) and x^(4) + y^(4) = t^(2) + (1)/(t^(2)) " then " x^(3)y (dy)/(dx)= ……
Answer» `-1` 0 1 None of these Answer :C

Discussion

29.	Let f(x) = int_(0)^(x) sqrt(6-mu^(2) ) du. Then the real roots of the equation x^(2) - f'(x)=0 are
Answer» `x= pmsqrt6` `x = pm sqrt3` `x= pm sqrt2` `x = pm 1` ANSWER :C

Discussion

30.	If a circle of radius 2 touches X-axis at (1,0) then its centre may be
Answer» (1,2) an (1,-2) (1,2) and (2,1) (-1,2)(1,-2) (-1,2)(-1,-2) ANSWER :A

Discussion

31.	Which of the following statement is true Statement - I Coefficient of x^3 in e^(5x) is (5^2)/(3!) Statement - II sum_(n=1)^(oo)(""^(n)C_0+""^nC_1+""^(n)C_2+.......+""^nC)/(""^(n)P_n)=e^2-1
Answer» only I only II both I and II NEITHER I nor II ANSWER :B

Discussion

32.	Evaluate the following integrals int e^(x) sin 3 x cos 3x dx
Answer» `(1)/(2)e^(x)[(1)/(26)(SIN 5x+5cos 5x)+(1)/(2)(sin x-cosx)]+c` `(1)/(2)e^(x)[(1)/(26)(sin 5x-5cos 5x)+(1)/(2)(sin x + cosx)]+c` `(1)/(2)e^(x)[(1)/(26)(sin 5x-5cos 5x)+(1)/(2)(sin x-cosx)]+c` `(1)/(2)e^(x)[(1)/(26)(sin 5x-5cos 5x)-(1)/(2)(sin x-cosx)]+c` ANSWER :C

Discussion

33.	If rho (A) =r then which of the following is correct?
Answer» all the MINORS of order in which do not VANISH A' has at least ONE MINOR of order r which does not vanish and all higher order minors vanish A' has at least one (r+1) order minor which vanish all (r+1) and higher order minors should not vanish Answer :A::B::C::D

Discussion

34.	If a force F =500-100t, then impulse as a function of time will be :-
Answer» `500t-50t^(2)` ` 50t-10` `50-t^(2)` `100T^(2)` ANSWER :A

Discussion

35.	Solve the following differential equations. (dy)/(dx)=(-3x-2y+5)/(2x+3y-5)
Answer» `3x^(2) + 4xy + 3Y^(2) - 10 x - 10y = c` `3x^(2) + 4xy - 3y^(2) + 10 x + 10y = c` `3x^(2) - 4xy + 3y^(2) - 10 x - 10y = c` `3x^(2) - 4xy + 3y^(2) + 10 x + 10y = c` Answer :A

Discussion

36.	Determine whether a*b =a^2 +b^2 "on" N operations as defined by are binary operations on the sets specified in each case. Give reasons if it is not a binary operation.
Answer» SOLUTION :for all `a, B in N , a b = a^2+b^^2 in N` ` :. ` is a BINARY OPERATION on N.

Discussion

37.	Assume that each born child is equally likely to be a boy or a girl. If a family has two children,what is the conditional probability that both are girls given that atleast one is a girl
Answer» Solution :Let C be the event taht out of the two children in the family atleast one is a girl.Then C={GB,BG,GG}.`rArr AnnC={GG}` THEREFORE `P(AnnC)`=1/4and P (C)=3/4 Hence,the requried probability

Discussion

38.	Find the pole of x-2y + 22 = 0with respect to x^(2) + y^(2) - 5 x + 8y + 6 =0
Answer» ANSWER :` (2,-3) `

Discussion

39.	Assume that each born child is equally likely to be a boy or a girl. If a family has two children,what is the conditional probability that both are girls given that the youngest is a girl
Answer» Solution :Let A be the event that both CHILDREN are girls and B be the event that the YOUNGEST CHILD is a girl. Then A={GG}and B={GB,GG}.therefore `AnnB`={GG} `rArr` `P(AnnB)=1/4 and P(B) = 2/4 HENCE,the required probability =P(A/B0=`(P(AnnB))/P(B)`=1/4/2/4=1/2

Discussion

40.	Solve 3x+8 gt2, when (i) x is an integer. (ii) x is a real number.
Answer» ANSWER :i.The solution SET is {-1, 0,1,2,3,…….} ii. The solution set is (-2, `oo`)

Discussion

41.	If x = 6 and y=-2 then x-2y=9. The contrapositive of this statement is
Answer» If `x-2y NE 9` then `XNE 6 or y ne -2` If `x-2y ne 9` then `x ne 6 and y ne -2` If `x-2y =9` then `x=6 and y=-2` None of these Answer :A

Discussion

42.	Area of a rectangle having vertices A,B,C and D with positions vectors - hat i +1/2 hat j + 4 hat k, hat i + 1/2 hat j + 4 hat k, hat i - 1/2 hat j + 4 hat k and - hat i - 1/2 hat j + 4 hat k, respectively is
Answer» `(1)/(2)` 1 2 4 Answer :C

Discussion

43.	Real part of 1/(1-costheta+isinthet a) is
Answer» `-1/2` `1/2` `1/2tantheta//2` 2 Answer :B

Discussion

44.	Evaluate int(x^(2)+1)/(x^(4)+1)dx
Answer» `(1)/(SQRT(2)) tan^(-1) ((X^(2) -1)/(sqrt(2x)) ) + C` `sqrt(2) SIN^(-1)((x^(2) -1)/(sqrt(2)x)) + c` `(1)/(sqrt(2)) sinh^(-1) ((x^(2) -1)/(sqrt(2)x) ) + c` `sqrt(2) cosh^(-1) ((x^(2) -1)/(sqrt(2)x)) + c ` Answer :A

Discussion

45.	Statement-1: ~(pharr~q) is equivalent to (pharrq). Statement-2: ~(pharr~q) is a tautology.
Answer» Statement-1 is TRUE, statement-2 is true: Statement-2 is not a CORRECT EXPLANATION for statement-1 Statement-1 is true, statement-2 is false Statement-1 is true, statement-2 is true Statement-1 is true, statement-2 is true, statement-2 is correct explanation for statement-1 Answer :B

Discussion

46.	If x=int_(2)^(sint) sin^(-1) theta thetaand y=int_(n)^(sqrt(t))(sintheta^(2))/(theta)d theta (dy)/(dx) is equal to
Answer» `(SIN t)/(2T^(2))` `(2t^(2))/(tan t)` `(tan t)/(t^(2))` NONE of these ANSWER :A

Discussion

47.	int(x^(2)-1)/(x^(4)+1)dx=
Answer» `(1)/(2 SQRT(2)) LOG \| (x^(2) - sqrt(2)x +1)/(x^(2) + sqrt(2)x +1)\| + C` `(1)/(sqrt(2)) log \| (x^(2) - sqrt(2)x +1)/(x^(2) + sqrt(2)x +1)\| + c` `(1)/(2 sqrt(2)) log \| (x^(2) + sqrt(2)x +1)/(x^(2) - sqrt(2)x +1)\| + c` `(1)/(2 sqrt(2)) log \| (x^(2) - sqrt(2)x -1)/(x^(2) - sqrt(2)x +1)\| + c` Answer :A

Discussion

48.	Evaluate P(A uu B) If 2 P(A) = P(B) = 5/13 and P(A//B) = 2/5.
Answer» ANSWER :`(11)/(26)`

Discussion

49.	Assume that each bornchild is equally likely to be a boy or a girl. If a family has two childeren what is the conditional probability that both gives both are girls given that i. the youngest is a girl ii.Atleast one is a girl
Answer» ANSWER :(i) `(1)/(2)` (II) `(1)/(3)`

Discussion

50.	f : R^(+)to R^(+), f(x)=(log x)/(sqrt(x)). Find the intervals in which f(x) is increasing or decreasing.
Answer» ANSWER :increase in `(0, e^(2))`, decrease in `(e^(2), OO)`

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Let ** be the binary operation on N defined by a"*"b = H.C.F of a and b . Is ** commutative ? Is ** associative ? Does there exist identity for this binary operation on N ?

1 + omega + omega^(2) + ….. + omega^(300)

A coins is tossed three times,where E:head on third toss,F: heads on first two tosses find P(E/F)

Fortheequilibrium x^3 +3x^2 -x-2=0ifs_1,s_2 ,s_3havetheirusualnotaionthen

Find the coefficient of x^n in the expansion of (1+ 2x + 3x^2 + 4x^3 + …..)^2

If alpha and beta are the roots of the equation x^2-2x+4 =0, then alpha^(12)+ beta^(12)=

A die is tossed thrice. Find the probability of getting an odd number at least once.

Find thearea of theregion boundedby thecurvesy^2 =x+1 and y^2=- x+1

Find the number of ways of selecting a cricket team of 11 players from 7 batsmen and 6 bowlers such that there will be atleast 5 bowlers in the team.

If force F, density D and area A are taken as fundamental quantities then dimensional formula of frequency is :

vec a , vec b , vec care three vectors such that|vec a | = 5 | vec b | =8, |vec c | = 3 if vec a + vec b + vec c = 8 hati+ 6hatj , find the value ofvec a , vec b +vec b .vec c + vec c .vec a

If log_(e)4 = 1.3868, then log_(e) 4.01 =

If veca,vecb,vecc are non-coplanar vectors and vecu and vecv are any two vectors. Prove that vecuxxvecv=(1)/([vecavecbvecc])|{:(vecu.veca,vecv.veca,veca),(vecu.vecb,vecv.vecb,vecb),(vecu.vecc,vecv.vecc,vecc):}|

Ifthe coinc ax^(2) + 2hxy + by^(2) + 2gx + 2fy + c = 0be a hyperbola , and the equation of the conjugate hyperbola is ax^(2) + 2hxy + by^(2) + 2gx + lambda = 0 , then lambda is equal to

If a, b are the roots of x^(2)+x+1=0, then a^(2)+b^(2) is

Let x= hat(i)+hat(j) and y=3 hat(i)-2 hat(k). Then, the vector r of magnitude sqrt(21) satisfying r xx x =y xx x and r xx y=x xx y, is

The value for [axx(b+c),bxx(c-2a),cxx(a+3b)] is equal to

The position of reflection of the point﻿ (4, 1) about the line y = x - 1 is﻿

If (.^(20)C_(1))/(1)+(.^(20)C_(3))/(2)+(.^(20)C_(5))/(3)+.......+(.^(20)C_(19))/(10)=(K(2^(20-1)))/(21), then Kis equal to :

Find an approximate value of the following correctedto 4 decimal places. (1.02)^(3//2)-(0.98)^(3//2)

The radius of the cone is increasing at the rate of 4 cm/se. Its height is decreasing at the rate of 3 cm/se. When its radius is 3 cm and height is 4 cm. Find the rate of change of its curved surface area.

If(x - 4 )/( x^ 2 - 5x+6)canbeexpandedintheascendingpowersofx,thenthe coefficientofx ^ 3is

A(2,-3) and B(-2,1) are the vertices of a triangle A B C . If the centroid of this triangle moves on the line 2 x+3 y=1, then the locus of the vertex C is the line

Evaluate the following integrals int x^2 (1-1/x^2) dx

Find lambda + mu if (2hat(i) + 6hat(j) + 27 hat(k)) xx (hat(i) + lambda hat(j) + mu hat(k)) = vec(0).

Find the maximum or minimum values of the following functions: (i)x^(3)-2x^(2)+x+3 (ii) x^(3)-6x^(2)+9x+4 (iii) (x+1)(x-2)^(2)+1 (iv) 2x^(3)-9x^(2)+12x+1

If x^(2) + y^(2) =t- (1)/(t) and x^(4) + y^(4) = t^(2) + (1)/(t^(2)) " then " x^(3)y (dy)/(dx)= ……

Let f(x) = int_(0)^(x) sqrt(6-mu^(2) ) du. Then the real roots of the equation x^(2) - f'(x)=0 are

If a circle of radius 2 touches X-axis at (1,0) then its centre may be

Which of the following statement is true Statement - I Coefficient of x^3 in e^(5x) is (5^2)/(3!) Statement - II sum_(n=1)^(oo)(""^(n)C_0+""^nC_1+""^(n)C_2+.......+""^nC)/(""^(n)P_n)=e^2-1

Evaluate the following integrals int e^(x) sin 3 x cos 3x dx

If rho (A) =r then which of the following is correct?

If a force F =500-100t, then impulse as a function of time will be :-

Solve the following differential equations. (dy)/(dx)=(-3x-2y+5)/(2x+3y-5)

Determine whether a**b =a^2 +b^2 "on" N operations as defined by * are binary operations on the sets specified in each case. Give reasons if it is not a binary operation.

Assume that each born child is equally likely to be a boy or a girl. If a family has two children,what is the conditional probability that both are girls given that atleast one is a girl

Find the pole of x-2y + 22 = 0with respect to x^(2) + y^(2) - 5 x + 8y + 6 =0

Assume that each born child is equally likely to be a boy or a girl. If a family has two children,what is the conditional probability that both are girls given that the youngest is a girl

Solve 3x+8 gt2, when (i) x is an integer. (ii) x is a real number.

If x = 6 and y=-2 then x-2y=9. The contrapositive of this statement is

Area of a rectangle having vertices A,B,C and D with positions vectors - hat i +1/2 hat j + 4 hat k, hat i + 1/2 hat j + 4 hat k, hat i - 1/2 hat j + 4 hat k and - hat i - 1/2 hat j + 4 hat k, respectively is

Real part of 1/(1-costheta+isinthet a) is

Evaluate int(x^(2)+1)/(x^(4)+1)dx

Statement-1: ~(pharr~q) is equivalent to (pharrq). Statement-2: ~(pharr~q) is a tautology.

If x=int_(2)^(sint) sin^(-1) theta thetaand y=int_(n)^(sqrt(t))(sintheta^(2))/(theta)d theta (dy)/(dx) is equal to

int(x^(2)-1)/(x^(4)+1)dx=

Evaluate P(A uu B) If 2 P(A) = P(B) = 5/13 and P(A//B) = 2/5.

Assume that each bornchild is equally likely to be a boy or a girl. If a family has two childeren what is the conditional probability that both gives both are girls given that i. the youngest is a girl ii.Atleast one is a girl

f : R^(+)to R^(+), f(x)=(log x)/(sqrt(x)). Find the intervals in which f(x) is increasing or decreasing.

Let ** be the binary operation on N defined by a"*"b = H.C.F of a and b . Is commutative ? Is associative ? Does there exist identity for this binary operation on N ?

The position of reflection of the point (4, 1) about the line y = x - 1 is