28278 + Interview Questions in Maths in Class 12

1.	Differentiate w.r.t x the function ("cos"^(-1) (x)/(2))/(sqrt(2x + 7)) where -2 le x le 2
Answer» Answer :`-[(cos^(-1) ((x)/(2)))/((2X+ 7)^((3)/(2))) + (1)/(SQRT(2x + 7) sqrt(4-x^(2)))]`

Discussion

2.	Let a sequence x_(1),x_(2),x_(3),… of complex numbers be defined by x_(1)=0, x_(n+1)=x_(n)^(2)-i for alln gt 1, where i^(2)=-1. Find the distance of x_(2000) from x_(1997) in the complex plane.
Answer» ANSWER :`SQRT(5)`

Discussion

3.	How many numbers with no more than three digits can be formed using only the digits 1 through 7 with no digit used more than once in a given number?
Answer» 259 249 257 252 Answer :A

Discussion

4.	Derive the equation of the plane in the intercept form.
Answer» ANSWER :1

Discussion

5.	Integration of some particular functions : int(dx)/(sqrt(x^(2)-2x+3))=...+c
Answer» `(1)/(2)tan^(-1)((x-1)/(2))` `tan^(-1)((x-1)/(2))` `log\|x-1+sqrt(x^(2)-2x+3)\|+C` `log\|x-1-sqrt(x^(2)-2x+3)\|+c` ANSWER :C

Discussion

6.	Find dy/dx if x^(3)+x^(2)y+xy^(2)+y^(3)=81
Answer» ANSWER :`dy/dx=(-(3X^(2)+2xy+y^(2)))/((X^(2)+2xy+3y^(2)))`

Discussion

7.	The surface area of a cube is decreasing at the rate of 15 sq. cm/sec. Find the rate length of the edge is 5 cm.
Answer» SOLUTION :Let s be the surface area of a cube. Let X be the length of each side of the cube. `then s = 6x^2 rArr ds/dt = 12x dx/dt` Given that `ds/dt = 15 SQ. cm/sec. and x = 5 cm`. Then - 15 = 12 xx 5 dx/dt` `rArr dx/dt = - 15/60 = - 1/4 = -0 cdot 25 cm/sec`. therefore The edge is decreasing at the rate of 0 cdot 25 cm/sec`.

Discussion

8.	A land in the form of a circular sector has been fenced by wire of 40 metre length. The area of the land will be maximum whenthe radius of the circular sector (in metre) is-
Answer» 25 20 10 15 Answer :C

Discussion

9.	Let a,b and c be three non-coplanar vectors. The vector equation of a line which passes through the point of intersection of two lines, one joining the points a+2b-5c, -a-2b-3c and the other joining the points -4c, 6a-4b+4c is
Answer» `r=2a -4b+3c+mu(a-6b+4c)` `r=3a+6b-c+mu(a+2b+c)` `r=2a+3b-c+mu(a+B+c)` `r=-2b+3c+mu(a-4b+3c)` ANSWER :B

Discussion

10.	Find X and Y if, X+Y=[(5,2),(0,9)] and X-Y=[(3,6),(0,-1)].
Answer» ANSWER :`X=[(4,4),(0,4)]` `Y=[(1,-2),(0,5)]`

Discussion

11.	Sum the series (1)/(3.6) +(1.3)/(3.6.9) +(1.3.5)/(3.6.9.12)+…
Answer» SOLUTION :N/A

Discussion

12.	Determine whether the relation R in the set A = {1,2,3,…..13,14} defined as R = {(x, y):3x -y=0} is reflexive symmetric and transitive.
Answer» Answer :(i) Neither reflexive nor symmetric nor transitive. (ii) Neither reflexive nor symmetric but transitive. (iii) Reflexive and transitive but not symmetric. (iv) Reflexive, symmetric and transitive. (V) (a) Reflexive, symmetric and transitive. (B) Reflexive, symmetric and transitive. (c ) Neither reflexive nor symmetric nor transitive. (d) Neither reflexive nor symmetric but transitive. (E) Neither reflexive nor symmetric nor transitive.

Discussion

13.	Find the value of c for which A(2,0),B(0,14//3) ,C(4,5) and D(0,c)are concylic.
Answer» ANSWER :`75/72`

Discussion

14.	Silver has work function of 4.7 eV when ultraviolet light of wavelength 100 nm is incident upon it, a potential of 7.7 volt is required to stop the photoelectrons from reaching the collector plate. What will be the minimum de-Broglie wavelength of photoelectrons when the wavelength of incident radiations is increased by 100% ?
Answer» 3.3 Å 5.6 Å 10 Å 12.27 Å Solution :`7.7 = E-4.7 implies E = 12.4 eV` When the wavelength is increased by 100% then energy of incident photon wil be `6.2 eV` then `K_("max") = E - 4.7 = 6.2 - 4.7 = 1.5 eV` `:. lambda_(dB) = SQRT((150)/(V)) = sqrt((150)/(1.5))` Å = 10 Å.

Discussion

15.	If veca,vecb and vecc are three non-coplannar vectors, then prove that (\|hataxx(hatbxxhatc)\|)/sinA=(\|hatbxx(hatcxxhata)\|)/sinB=(\|hatcxx(hataxxhatb)\|)/sin C = (prod\|hata xx(hatbxx hatc)\|)/(\|sum sinalpha cosbeta cosgamma hatn_(1)\|)
Answer» Solution :Since `veca,vecb and VECC` are non - coplanar, vectors `VECAXXVECB,vecb xxveccandveccxxveca` are also non-coplanar. Let `vecd=l(vecbxxvecc)+vecm(veccxxveca)+vecn(vecaxxvecb)` now multiplying both SIDES of (i) scalarly by `veca` we have `veca.vecd=lveca.(vecbxxvecc)+mveca.(veccxxveca)+nveca.(vecaxxvecb)=l[vecavecc veca]([veca vecc veca]=0=[veca veca vecb])` `l=(veca.vecd)//[veca vecb vecc]` putting these values oif l,nm and n and (i) , we get the required RELATION.

Discussion

16.	A = {x : cos x gt - 1//2, 0 le x le pi}, B = {x : sin x gt 1//2,pi//3 le x le pi} then
Answer» `A cap B = [PI/3, (2PI)/3]` `A cap B = [- pi/3, (2pi)/3]` `A cup B = [- (5 pi)/6, (5PI)/6]` none Answer :A

Discussion

17.	x^(2) e^(x)
Answer» Solution :` " LET I=" int x^(2) E^(x) dx` `I=x^(2) int e^(x) dx- int [(d)/(dx)(x^(2)) int e^(x) dx]dx` `=x^(2)e^(x) -int (2xe^(2))dx` ` rArr I= x^(2) e^(x) -{ 2X int e^(x) dx-2 int [(d)/(dx)(x) int e^(x) dx ] dx }` `=x^(2) e^(x) -2xe^(x) +2 int e^(x) dx` `=x^(2)e^(x) -2xe^(x) +2E^(x) +C` `rArr I=e^(x)(x^(2)-2x+2)+C`

Discussion

18.	If a=hati-2hatj-3hatk, b=2hati+hatj-k,c=hati+3hatj-2hatk, then [(axxb)xx(bxxc)(bxxc)xx(cxxa)(cxxa)xx(axxb)]=
Answer» 160000 `-8000` 400 `-40` ANSWER :A

Discussion

19.	(d)/(dx)[cot^(-1)((cot^(-1)x-1)/(2cotx))]=
Answer» 2 1 `-1` `-(1)/(2)` ANSWER :A

Discussion

20.	Equation of the parabola with focus (-4,0) and vertex at the origin is
Answer» `y^2 = 16 x` `y^2 = 16X = 0` `x^2= 16Y` `x^2 + 16y = 0` Answer :B

Discussion

21.	If (x+1)/((x-a)(x-3))=2/(x-a)+b/(x-3), " then "(a, b)=
Answer» (7, -1) (-4, 1) (4, 1) (-4, -1) ANSWER :A

Discussion

22.	Let M be a 2 × 2 symmetric matrix with integer entries. Them M is invertible if
Answer» the first column of M is the transpose of the second row of M the second row of M is the transpose of the first column of M M is a diagonal matrix with NONZERO entries in the main diagonal the product of entries in the main diagonal of M is not the SQUARE of an integer Answer :C::D

Discussion

23.	Find the middle term (s) in the expansion of((3)/(p^3) + 5p^4)^20
Answer» ANSWER :`T_11 = ""^20C_10.3^10.5^10.p^10`

Discussion

24.	A point P is taken on the right half of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 having its foci as S_1 and S_2. If the internal angle bisector of the angle angleS_1PS_2 cuts the x-axis at poin Q(alpha, 0) then range of alpha is
Answer» `[-a, a]` `[0, a]` `[0, a]` `[-a, 0]` ANSWER :C

Discussion

25.	Given that the regression equation of y on x is y = a + 1/(m)x, find the value of m when r = 0.5 , sigma_(x)^2=1/4sigma_(y)^2 .
Answer» ANSWER :`m=1`

Discussion

26.	IFalphaandbetaaretherootsof theequationax ^2+bx+c=0and theequationhavingroots(1-alpha)/( alpha ) and(1- beta )/( beta) ispx^2+qx +r=0thenr=
Answer» `a+2b` `ab+bc +CA` `a+b+C` `ABC` ANSWER :C

Discussion

27.	Solve the equation tan x + (cosx)/(sqrt(1+sin2x))=2.
Answer» Solution :`X = npi + ALPHA`, where `n int Z` and `tan alpha = (1+-sqrt(5))/(2)`

Discussion

28.	Compute the following: [[2,1],[3,2],[-1,1]] [[1,0,1],[-1,2,1]]
Answer» SOLUTION :`[[2,1],[3,2],[-1,1]], [[1,0,1],[-1,2,1]]=[[2-1, 0+2, 2+1],[3-2, 0+4, 3+2],[-1-1, 0+2, -1+1]]=[[1,2,3],[1,4,5],[-2,2,0]]`

Discussion

29.	Show thatRe(z_1z_2)=Rez_1Rez_2-Im z_1Imz_2Im(z_1z_2)=Re z_1 Im z_2+Re z_2 Im z_1
Answer» SOLUTION :LET `z_1=a+ib,z_2=c+id` `:. z_1z_2=(a+ib),(c+id)` `=ac+iad+ibc+i^2bc` `=(ac-bd)+i(ad+bc)` `:."Re"(z_1z_2)=ac-bd="Re"z_1."Re"z_2-"IM" z_1."Im"z_2` `"Again,Im"z_1z_2=ad+bc="Re" z_1."Im"z_2,"Re"z_2`

Discussion

30.	On theset Z of allintegers , consider the relation R={(a,b):(a-b) is divisible by 3}. Show thatR isanequivalencerelationon Z. Also findthepartitioning of Z intomutuallydisjointequivalenceclasses .
Answer» Solution :the relationR on Z satisfiesthe followingproperties : (i) Reflexivity Let ` a in Z` then,`(a-a)=0,` whichisdivisibleby 3 . `thereforea Ra AAa in Z.` So,R isreflexive .(ii)SYMMETRY Let` a ,bin Z` suchthat`a ,R,b` then `a R bimplies(a-b) ` isdivisibleby 3 `implies -(a-b)` isdivisibleby 3 `implies (b-a) ` is divisible by 3 `impliesb R a .` `thereforea R b impliesbRa AAa,bin Z .` So,R issymmetric . (iii)Transitivity Leta,b,c `in Z ` such thata R bandb R c. then `a R b,bRc implies (a-b)` isdivisibleby3 and(b-c)isdivisibleby 3 `implies [(a-b)+(b-c)] `isdivisibleby 3 `implies(a-c)` is DIVISIBLEBY 3. thus,`a R b ,B R cimplies aR cAA a,b,cin Z.` ` therefore ` R isequivalencerelation on Z. Now ,letusconsider [0],[1] and [2] we have : `[0]={x in Z : x R O }` ` ={x in Z: (x-0)` is divisibleby 3} `={. . . . . .,-6,-3,0,3,6,9,. . . . }.` `therefore [0] {. . . .,-6,-3,0,3,6,9,....}.` Similarly ,`[1] ={x INZ: xR 1}` `={x inz : (x-1) ` is divisibleby 3} `={. . . . .,-5,-2,1,4,7,10,. . . . . .,}.` and,`[2] ={x inZ: x R 2}.` `={x in Z : (x-2)` is divisibleby3} `={. . . ,-4,-1,2,5,8,11,. . .}.` ` therefore [2] ={. .. ..,-4,-1,2,5,8,11,. . . .}.` CLEARLY[0] ,[1]and [2]aremutuallydisjoint and`Z=[0] cup[1]cup [2].`

Discussion

31.	Write the derivative of sin^-1x with respect to cos^-1x.
Answer» SOLUTION :`(DU)/dx=1/SQRT(1-x^2)`and `(DV)/dx=(-1)/sqrt(1-x^2)` Thus `(du)/(dv)=(((du)/dx))/(((dv)/dx))=-1`

Discussion

32.	A plane cutting the axes in P,Q,R passes through (alpha,beta,beta-lambda,lambda-alpha). If O is origin, then locus of center of sphere OPQR is
Answer» `alphax+betay+lambdaz=4` `(alpha-beta)X+(beta-lambda)y+(y-alpha)z=0` `(alpha-beta)yz+(beta-y)zx+(lambda-alpha)xy=2xyz` `(1/alpha^(2)+1/beta^(2)+1/lambda^(2))(x^(2+y^(2)+z^(2)))=XYZ` ANSWER :C

Discussion

33.	Integrate the following functions cotx log(sinx)
Answer» Solution :Let t = log(sinx). Then DT = 1/sinx cosx DX = cotxdx THEREFORE `INT cotx log(sinx)dx = int t dt = t^2/2+c = [log(sinx)]^2/2 +c`

Discussion

34.	If A+B+C=(3pi)/(2), prove that cos 2A+ cos 2B+ cos 2C=1-4 sin A sin B sin C .
Answer» `1-4 SIN A sin B sin C ` `1-4 cos A cos B cos C ` `4 sin A sin B sin C ` `1+ 2 cos A cos B cos C ` ANSWER :A

Discussion

35.	Evaluate the following integrals. int_(0)^(2)\|x^(2)+2x-3\|dx
Answer» 1 2 3 4 Answer :D

Discussion

36.	The relation between pressure p and volume V is given by pV^(1/4)= constant. If the percentage decrease in volume is 1/2, then the percentage increase in pressure is
Answer» `-1/8` `1/16` `1/8` `1/2` ANSWER :C

Discussion

37.	A function f(x) is defined as follows :f(x)={(x sin ""1/x "," x ne 0),(0 "," x=0):} Discuss its continuity at x=0
Answer» Solution :At x=0 f(0)=0 R.H.L `=UNDERSET(xrarr0^+)limf(x)=underset(hrarr0)limf(0+h)` `=underset(hrarr0)limhsin"" (1)/(h)` `=0xx`(a definite value ) =0 `(therefore)"SIN" (1)/(h) ` ALWAYS lies between -1 and 1) gt L.H.L`=underset(xrarr0^-)lim f(x)=underset(hrarr0)limf(0-h)` ` =underset(hrarr0)lim(-h)sin (1/-h)=underset(hrarr0)(lim) h sin ""1/h` `=0xx` (a definite value )=0 `therefore`R.H.L = f(0)=L.H.L `therefore`f(x) is continuous at x=0. Prove that(x) is CONTINOUS at x=2.

Discussion

38.	How many factors does 210 have ?
Answer» Solution : ` :.`We can CHOOSE at least one 2,3,5,7 to be a factor of 210. `:."The number of factors. = ""^4C_1+ ""^4C_2 + ""^4C_3+ ""^4C_4= 2^2-1=15`(Including 215 itself and EXCLUDING 1).

Discussion

39.	If total numberof runs secored is n matches is (n+1)/(4) (2^(n+1) -n-2)wheren ge 1 , and the runs scored in thek^(th)match is given by k.2^(n+1 - k) , where1 lek le n, nis
Answer» 8 9 7 6 Answer :3

Discussion

40.	If x^(2)=y^(2) and (x-y)^(2)=2x, then which of the following is a possible value of y?
Answer» `64` `16` `8` `4` ANSWER :D

Discussion

41.	If (sqrt3 + i) = (a + ib) (c + id) then tan^(-1) (b)/(a) + tan^(-1) (d)/(c) =
Answer» `2n pi + (pi)/(3) , n in Z` `n pi + (pi)/(6) , n in Z` `2 n pi + (pi)/(6) , n in Z` `2n pi + (pi)/(6) , n in Z` Answer :B

Discussion

42.	Let N be number of ways four different integers be chosen from the set {1,2,3,4, . .104, 105} so that their sum is divisible by 4, then [(N)/(10^(5))] is equal to : ([.] denote greatest integer function).
Answer» ANSWER :7

Discussion

43.	A bag contains 2n + 1 coins . It is known that n of these coins have a head on both sides, whereas the remaining n + 1 coins are fair . A coin is picked up at random from the beg and tossed . If the probability that the toss results in a head is (31)/(42), then n is equal to
Answer» 10 11 12 13 Answer :A

Discussion

44.	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 (i) the youngest is a girl, (ii) at least one is a girl?
Answer» ANSWER :`(i) (1)/(2), (II) (1)/(3)`

Discussion

45.	Compute the limit underset(n rarr oo)("lim") ((1)/(sqrt(4n^(2)-1)) + (1)/(sqrt(4n^(2)-2^(2))) +……+ (1)/(sqrt(4n^(2)-n^(2))))
Answer» ANSWER :`(PI)/(6)`

Discussion

46.	Find the number of onto functions that can be defined from a set A={a_1,a_2,…..,a_n) onto another set B= (x,y) such that a_1 is always mapped to x
Answer» ANSWER :`2^(n-1)-1`

Discussion

47.	The numberof waysof dividing 12 boys into2 groups of 7,5 boysrespectivelyis
Answer» `(8!)/(6!5!)` `(9!)/(5!4!)` `(10!)/(3!2!)` `(12!)/(7!5!)` Answer :D

Discussion

48.	A and B are two events such that P(A) ne0 , find P (B/A)if A is a subset of B.
Answer» 0 1 `1/2` NONE of these Answer :B

Discussion

49.	If the plane ax + by + cz = 5 passes through the points (1, 2, 1), (1, 1,0), (- 2, 2, - 1) then the decreasing order of a, b, c is
Answer» a, B, c b, c, a c, a, b c, b, a Answer :C

Discussion

50.	State the geometrival interpretation of int _c^(d) phi (y) dy
Answer» ANSWER :9 square units (ii) `(1)/(3) (8-2sqrt2) `square units

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Differentiate w.r.t x the function ("cos"^(-1) (x)/(2))/(sqrt(2x + 7)) where -2 le x le 2

Let a sequence x_(1),x_(2),x_(3),… of complex numbers be defined by x_(1)=0, x_(n+1)=x_(n)^(2)-i for alln gt 1, where i^(2)=-1. Find the distance of x_(2000) from x_(1997) in the complex plane.

How many numbers with no more than three digits can be formed using only the digits 1 through 7 with no digit used more than once in a given number?

Derive the equation of the plane in the intercept form.

Integration of some particular functions : int(dx)/(sqrt(x^(2)-2x+3))=...+c

Find dy/dx if x^(3)+x^(2)y+xy^(2)+y^(3)=81

The surface area of a cube is decreasing at the rate of 15 sq. cm/sec. Find the rate length of the edge is 5 cm.

A land in the form of a circular sector has been fenced by wire of 40 metre length. The area of the land will be maximum whenthe radius of the circular sector (in metre) is-

Let a,b and c be three non-coplanar vectors. The vector equation of a line which passes through the point of intersection of two lines, one joining the points a+2b-5c, -a-2b-3c and the other joining the points -4c, 6a-4b+4c is

Find X and Y if, X+Y=[(5,2),(0,9)] and X-Y=[(3,6),(0,-1)].

Sum the series (1)/(3.6) +(1.3)/(3.6.9) +(1.3.5)/(3.6.9.12)+…

Determine whether the relation R in the set A = {1,2,3,…..13,14} defined as R = {(x, y):3x -y=0} is reflexive symmetric and transitive.

Find the value of c for which A(2,0),B(0,14//3) ,C(4,5) and D(0,c)are concylic.

If veca,vecb and vecc are three non-coplannar vectors, then prove that (|hataxx(hatbxxhatc)|)/sinA=(|hatbxx(hatcxxhata)|)/sinB=(|hatcxx(hataxxhatb)|)/sin C = (prod|hata xx(hatbxx hatc)|)/(|sum sinalpha cosbeta cosgamma hatn_(1)|)

A = {x : cos x gt - 1//2, 0 le x le pi}, B = {x : sin x gt 1//2,pi//3 le x le pi} then

x^(2) e^(x)

If a=hati-2hatj-3hatk, b=2hati+hatj-k,c=hati+3hatj-2hatk, then [(axxb)xx(bxxc)(bxxc)xx(cxxa)(cxxa)xx(axxb)]=

(d)/(dx)[cot^(-1)((cot^(-1)x-1)/(2cotx))]=

Equation of the parabola with focus (-4,0) and vertex at the origin is

If (x+1)/((x-a)(x-3))=2/(x-a)+b/(x-3), " then "(a, b)=

Let M be a 2 × 2 symmetric matrix with integer entries. Them M is invertible if

Find the middle term (s) in the expansion of((3)/(p^3) + 5p^4)^20

A point P is taken on the right half of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 having its foci as S_1 and S_2. If the internal angle bisector of the angle angleS_1PS_2 cuts the x-axis at poin Q(alpha, 0) then range of alpha is

Given that the regression equation of y on x is y = a + 1/(m)x, find the value of m when r = 0.5 , sigma_(x)^2=1/4sigma_(y)^2 .

IFalphaandbetaaretherootsof theequationax ^2+bx+c=0and theequationhavingroots(1-alpha)/( alpha ) and(1- beta )/( beta) ispx^2+qx +r=0thenr=

Solve the equation tan x + (cosx)/(sqrt(1+sin2x))=2.

Compute the following: [[2,1],[3,2],[-1,1]] [[1,0,1],[-1,2,1]]

Show thatRe(z_1z_2)=Rez_1Rez_2-Im z_1Imz_2Im(z_1z_2)=Re z_1 Im z_2+Re z_2 Im z_1

On theset Z of allintegers , consider the relation R={(a,b):(a-b) is divisible by 3}. Show thatR isanequivalencerelationon Z. Also findthepartitioning of Z intomutuallydisjointequivalenceclasses .

Write the derivative of sin^-1x with respect to cos^-1x.

A plane cutting the axes in P,Q,R passes through (alpha,beta,beta-lambda,lambda-alpha). If O is origin, then locus of center of sphere OPQR is

Integrate the following functions cotx log(sinx)

If A+B+C=(3pi)/(2), prove that cos 2A+ cos 2B+ cos 2C=1-4 sin A sin B sin C .

Evaluate the following integrals. int_(0)^(2)|x^(2)+2x-3|dx

The relation between pressure p and volume V is given by pV^(1/4)= constant. If the percentage decrease in volume is 1/2, then the percentage increase in pressure is

A function f(x) is defined as follows :f(x)={(x sin ""1/x "," x ne 0),(0 "," x=0):} Discuss its continuity at x=0

How many factors does 210 have ?

If total numberof runs secored is n matches is (n+1)/(4) (2^(n+1) -n-2)wheren ge 1 , and the runs scored in thek^(th)match is given by k.2^(n+1 - k) , where1 lek le n, nis

If x^(2)=y^(2) and (x-y)^(2)=2x, then which of the following is a possible value of y?

If (sqrt3 + i) = (a + ib) (c + id) then tan^(-1) (b)/(a) + tan^(-1) (d)/(c) =

Let N be number of ways four different integers be chosen from the set {1,2,3,4, . .104, 105} so that their sum is divisible by 4, then [(N)/(10^(5))] is equal to : ([.] denote greatest integer function).

A bag contains 2n + 1 coins . It is known that n of these coins have a head on both sides, whereas the remaining n + 1 coins are fair . A coin is picked up at random from the beg and tossed . If the probability that the toss results in a head is (31)/(42), then n is equal to

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 ﻿ (i) the youngest is a girl, (ii) at least one is a girl?﻿

Compute the limit underset(n rarr oo)("lim") ((1)/(sqrt(4n^(2)-1)) + (1)/(sqrt(4n^(2)-2^(2))) +……+ (1)/(sqrt(4n^(2)-n^(2))))

Find the number of onto functions that can be defined from a set A={a_1,a_2,…..,a_n) onto another set B= (x,y) such that a_1 is always mapped to x

The numberof waysof dividing 12 boys into2 groups of 7,5 boysrespectivelyis

A and B are two events such that P(A) ne0 , find P (B/A)if A is a subset of B.

If the plane ax + by + cz = 5 passes through the points (1, 2, 1), (1, 1,0), (- 2, 2, - 1) then the decreasing order of a, b, c is

State the geometrival interpretation of int _c^(d) phi (y) dy

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 (i) the youngest is a girl, (ii) at least one is a girl?