28278 + Interview Questions in Maths in Class 12 Page 40 InterviewSolution

1951.	If n(A)=10, then no of different functions from A to A is :
Answer» `ul(\|10)` `10^(10)` `2^(10)` `2^(10)-1` Answer :B

Discussion

1952.	Find the order and degree (if any) of each of the differential equations given below:{:((i)(dy)/(dx)-tanx=0,(ii)((dy)/(dx))^(2)+y=e^(x)),((iii)(d^(2)y)=sin3x+cos3x,(iv)(y")^(2)+cosy'=0),((v)y+2y'+siny=0,(vi)(d^(4)y)/(dx^(4))+sin ((d^(3)y)/(dx^(3)))=0),((vii)y''+y^(2)+e^(y')=0,(viii)3(d^(2)y)/(dx^(2))+5((dy)/(dx))^(2)=log x):}
Answer» Solution :(i) The given equation is `(dy)/(dx)-tanx=0.` In the this equation, the highest-order derivative is `(dy)/(dx)` whose power is 1. `therefore` its order = 1 and degree =1. (ii) The given equation is `((dy)/(dx))^(2)+y=e^(X).` In this equation, the highest-order derivative is `(dy)/(dx)` whose power is 2. `therefore` its order =1 and degree =2. (III) The given equation is `(d^(2)y)/(dx^(2))=sin3x+cos3x.` In this equation, the highest-order derivative is `(d^(2)y)/(dx^(2))` and its power is 1. `therefore` its order = 2 and degree =1. (iv) The given equation is `((d^(2)y)/(dx^(2)))+cos((dy)/(dx))=0.` In this equation, the highest-order dervative is `(d^(2)y)/(dx^(2)),` so its order is 2. It has a term cos `((dy)/(dx)),` so its degree is not DEFINED. (v) The given equation is `(d^(2)y)/(dx^(2))+2(dy)/(dx)+siny=0.` In this equation, the highest-order derivative is `(d^(2)y)/(dx^(2))` and its power is 1. `therefore` its order = 2 and degree =1. (vi) The given equation is `(d^(4)y)/(dx^(4))+sin((d^(3)y)/(dx^(3)))=0.` In this equation, the highest-order derivative is `(d^(4)y)/(dx^(4)),` so its order is 4. It has a term `sin((d^(3)y)/(dx^(3))),` so its degree is not defined. (vii) The given equation is `(d^(3)y)/(dx^(3))+y^(2)+e^((dy//dx))=0.` In this equation, the highest-order derivative is `(d^(3)y)/(dx^(3)),` so its order is 3. (viii) The given equation is `3(d^(2)y)/(dx^(2))+5((dy)/(dx))^(2)=logx.` In this equation, the highest-order derivative is `(d^(2)y)/(dx^(2))` and its power is 1. `therefore` its order =2 and degree =1.

Discussion

1953.	A pole stands at a point A on the boundary of a circular park of radius a and subtends an angle alpha at another point B on the boundary. If the chord AB subtends an angle alpha at the centre of the path, the height of the pole is
Answer» `2a COS (alpha//2) TAN alpha` `2a SIN (alpha//2) COT alpha` `2a sin (alpha//2) tan alpha` `2a cos (alpha//2) cot alpha` Answer :C

Discussion

1954.	findthe areaof theregionboundedby thetwo parabolasy=x^2and y^2 =x
Answer» ANSWER :`1/3`

Discussion

1955.	Discuss the continuity of the cosine functions.
Answer»

Discussion

1956.	Let f(x)=lim_( n to oo) ([x^2]+[(2x)^2]+... + [(nx)^2])/n^3 then the set of all points of continuity of f([x] denotes the greatest integer function)
Answer» `(-OO,oo) ~ {0}` `(-oo,oo) ~ I` `(-oo,oo)` `(-oo,oo) ~ {0,1}` ANSWER :C

Discussion

1957.	From the figure, which of the following could be the value of b?
Answer» 20 40 50 70 Answer :B::C::D

Discussion

1958.	Therepeated rootof theequation 4x^3 -12x^2 -15x -4=0 is
Answer» `5/2` `-1/2` `1/3` `-1/3` ANSWER :B

Discussion

1959.	If omega a complex cube root of unity ,then (2-omega)(2-omega^(2))+2(3-omega)(2-omega^2)+........+(n-1)(n-omega)(2-omega^2)=
Answer» `(N(n-1))/(4)` `(n(n+1))/(4)` `(n(n+1)(2n+1))/(4)` `(n(n+1)(n^+3n+4))/(4)` ANSWER :D

Discussion

1960.	Evaluate:int_(0)^(2a)x^(2) sqrt(2ax-x^(2))dx.
Answer» ANSWER :`PIA^(4)`

Discussion

1961.	If P(A) = 0.8, P(B) = 0.5 and P (B\|A) = 0.4, find P(A cup B)
Answer» ANSWER :The events (E and F) are independent, and EVENT (E and G) and (F and G) are dependent.

Discussion

1962.	Ifalpha, beta, gammaare therootsofx^3 +px^2 +qx +r=0then find ( beta + gamma- 3 alpha )( gamma+ alpha + beta - 3 gamma)
Answer» ANSWER :`3p^3 -16 PQ +64r`

Discussion

1963.	For any two events A, B show that P(A nn B) - P(A) P(B) = P(A^(C)) P(B) - P(A^(C) nn B) = P(A) P(B^(C)) - P(A nn B^(C))
Answer» <P> ANSWER :`P(A NN B) - P(A).P(B)`

Discussion

1964.	If AB=21, B-=(-2,1,-8) and the direction cosines of AB are 6/7, 2/7, 3/7 , then the co-ordinates of points in line PQ nearer to the origin at a distance of 14 units from A are
Answer» `(-16,-7,-1)` `(-20, -5,17)` `(16,7,1)` `(20, 5,17)` ANSWER :C

Discussion

1965.	Out of 10000 families with 4 children each, find the number of families all of whose children are daughters.
Answer» ANSWER :625

Discussion

1966.	Two events A and B wll be independent,if a)A and B are mutually exclusive b) P(A'B')=[1-P(A)] [1-P(B)] c)P(A)= P(B) d)P(A)+P(B)=1
Answer» <P>A and B are MUTUALLY EXCLUSIVE `P(A'B')`=[1-P(A)] [1-P(B)] P(A)= P(B) P(A)+P(B)=1 Answer :B

Discussion

1967.	The transformed equation of xy + 2x -5y - 11 = 0 when the origin is shifted to the point (2, 3) is,
Answer» xy-5x-3y + 16 = 0 xy+5x+3y - 16 = 0 xy+5x-3y - 16 = 0 xy-5x+3y + 16 = 0 Answer :C

Discussion

1968.	If p(x) isa polynomial with integer coefficients and a,b,c are three distinct integers, then show that it is impossible to have p(a)=b,p(b)=c and p(c)=a
Answer» <P> ANSWER :`p(C)=a`

Discussion

1969.	[x^2]is differentiable on (-1,1):
Answer» ANSWER :T

Discussion

1970.	The product of lenghts of the perpendicular from point (2, 3) on the lines given by 2x^(2)+6xy-y^(2)=0 is
Answer» `(7)/(9sqrt(5))` `(7)/(3sqrt(5))` `(7sqrt(5))/(9)` `(7sqrt(5))/(3)` ANSWER :D

Discussion

1971.	The value of cos "" (2pi)/(15) cos "" (4pi)/(15) cos "" (8pi)/(15) cos "" (14pi)/(15)is
Answer» `1/16` `1/8` `1/12` `1/4` ANSWER :A

Discussion

1972.	A circle of radius 4 drawn on a chord of the parabola y^(2)=8x as diameter touches the axis of the parabola. Then the slope of the chord is
Answer» `(1)/(2)` `(3)/(4)` 1 2 Answer :C

Discussion

1973.	Consider the function defined implicitly by the equation y^3-3y+x=0 on various intervals in the real line. If x in (-oo,-2) uu (2,oo), the equation implicitly defines a unique real-valued defferentiable function y=f(x). If x in (-2,2), the equation implicitly defines a unique real-valud diferentiable function y-g(x) satisfying g_(0)=0. The area of the region bounded by the curve y=f(x), the X-axis and the line x=a and x=b, where -oo lt a lt b lt -2 is
Answer» `int_(a)^(B)(X)/(3[{F(x)}^(2)-1])dx+by(b)-af(a)` `-int_(a)^(b)(x)/(3[{f(x)}^(2)-1])dx-by(b)+af(a)` `int_(a)^(b)(x)/(3[{f(x)}^(2)-1])dx-by(b)+af(a)` `-int_(a)^(b)(x)/(3[{f(x)}^(2)-1])dx+by(b)=af(a)` ANSWER :A

Discussion

1974.	Consider the function defined implicitly by the equation y^3-3y+x=0 on various intervals in the real line. If x in (-oo,-2) uu (2,oo), the equation implicitly defines a unique real-valued defferentiable function y=f(x). If x in (-2,2), the equation implicitly defines a unique real-valud diferentiable function y-g(x) satisfying g_(0)=0. int_(-1)^(1)g'(x)dx is equal to
Answer» `2G(-1)` 0 `-2g(1)` `2g(1)` ANSWER :D

Discussion

1975.	If n(A) = 5, then number of relations that are both reflexive and symmetric is
Answer» `2^(10)` `2^(15)` `2^(6)` `2^(20)` ANSWER :A

Discussion

1976.	A factory manufactures two types of screws, A and B, each type requiring the use of two machines, an automatic and a hand-operated. It takes 4 minutes on the automatic and 6 minutes on hand-operated machines to manufacture a packet of screws 'A', while it takes 6 minutes on the automatic and 3 minutes on the hand-operated machines to manufacture a packet of screws 'B'. Each machine is available for at the most 4 hours on any day. The manufacturer can sell a packet of screws 'A' at a profit of 70 paise and screws 'B' at a profit of Rs. 1. Assuming that he can sell all the screws he manufactures, how many packets of each type should the factory owner produce in a day in order to maximise his profit ? Formulate the above L.P.P. and solve it graphically and find the maximum profit.
Answer» ANSWER :30 packets of type-A and 20 packets of type B, Maximum profit = Rs. 41

Discussion

1977.	The order of the differential equation 3x^(2) (d^(2)y)/(dx^(2))-5(dy)/(dx) + y = 0 is
Answer» 2 1 0 not defined Answer :A

Discussion

1978.	W (x,y,z) = xy + yz , x = u - v ,y = uv , z = u +v,u,v in R. Find (delw)/(delu), (del w)/(delv) and evaluate them at (1/2,1)
Answer» ANSWER :`=-3/2`

Discussion

1979.	State the converse, inverse and contrapositive of The square of an integer is a natural number propositions. Stating it as a conditional, wherever necessary.
Answer» Solution :If a NUMBER is an integer, then its square is a natural number. Con: If the square of a number is a natural number, then it is an integer. INV :If a number is not an integer, then its square is not a natural number. CONT: If the square of a number is not a natural number then it is not an integer.

Discussion

1980.	I = int(sin^(10)x-cos^(8)xsin^(2)x+sin^(8)xcos^(2)x-cos^(10)x)/(1-2sin^(2)xcos^(2)x) dx is equal to
Answer» `(1)/(2) sin 2x + C` `-(1)/(2) sin 2x + C` `-(1)/(2) sin x + C` `-sin^(2) x + C` ANSWER :B

Discussion

1981.	Sum of the root of the equation 2 sin^2 theta + sin^2 2theta =2, 0 le theta le pi//2 is
Answer» `pi/2` `3pi//4` `7pi//2` `5pi//12` Solution :`4sin^2 THETA cos^2theta =2 (1-sin^2 theta)` `rArr (2 sin^2 theta -1) cos^2 theta =0` `rArr sin^2 theta =1//2` or `cos^2 theta =0` `rArr theta =pi//4` or `theta=pi//2`

Discussion

1982.	If (b+c-2a)/a , (c+a-2b)/b , (a+b-2c)/c are in A.P., then a,b,c are in :
Answer» A.P. G.P H.P. None of these Answer :C

Discussion

1983.	Using integration, find the area of the region bounded by : (i) (1,0), (4,5) and (6,3) (ii) (1,0) ,(2,2) and (3,1) (iii) (-1,2), (1,5) and (3,4) (iv) (2,3), (3,5) and (3,4) (v) (-1,0) ,(1,3) and (3,2) (vi) (1,3) , (2,5) and (3,4) (vii)(4,1), (6,6) and (8,4) (viii) (2,5), (4,7) and (6,2) (ix) (-2,1) ,(0,4) and (2,3) (x) (2,1), (3,4) and (5,2).
Answer» Answer :`(i) 7 (II) 3/2 (iii) 4 (iv) 3/2 (v) 4 (VI) 3/2 (vii) 7 (viii)7 (ix)4 (x)4` (sq. UNITS).

Discussion

1984.	If (x^(2)-x+p)(11y^(2)-4y+2)=(9)/(2) have exactly one ordered pair of (x, y) then find p.
Answer» Solution :If `(x^(2)-x+p)(11Y^(2)-4y+2)`…………… `((4P-1)/(4)) ((88-16)/(44)) = (9)/(2)` `((4p-1)72)/(2xx88) = (9)/(2) implies 4p - 1 = 11 implies p =3`

Discussion

1985.	If a**b = a +bon R - {1}, then a^(-1) is ........
Answer» `a^3` `1/a` `(-a)/(a+1)` `1/a^2` SOLUTION :N/A

Discussion

1986.	Let f(x) is a real valued function defined by f(x)=x^(2)+x^(2) int_(-1)^(1) tf(t) dt+x^(3) int_(-1)^(1)f(t) dt then which of the following hold (s) good?
Answer» ` int_(-1)^(1) tf(t) dt=(10)/(11)` `f(1)+f(-1)=(30)/(11)` `int_(-1)^(1)t f (t) dt gt INT _(-1)^(1) f(t) dt` `f(1)-f(-1)=(20)/(11)` ANSWER :B::D

Discussion

1987.	Prove that the feet of the perpendicular from the origin on the lines x+y=4,x+5y=26, 15x-27y=424 are collinear.
Answer» SOLUTION :NA

Discussion

1988.	Prove that if a plane has the intercepts a, b, c and is at a distance of p units from the origin,then (1)/(a^2)+(1)/(b^2)+(1)/(c^2)=(1)/(p^2)
Answer» ANSWER :HENCE PROVED `(1)/(a^2)+(1)/(b^2)+(1)/(c^2)=(1)/(p^2)`.

Discussion

1989.	Find the co-ordinates of the vertex and focus the equation of the directrix and axis of the following parabolas.
Answer» ANSWER :x-1=0

Discussion

1990.	If P(A) = 0.5, P(B) = 0.6 and P(A cup B) = 0.8 then find P( A \| B) and P( B \| A).
Answer» ANSWER :`(1)/(2),(3)/(5)`

Discussion

1991.	Find the number of critical points are the following functions in their respective intervals provided. (i) min(x, cosx),x epsilon[-pi, pi] (ii) min ({x}, {-x}), x epsilon[-3, 3], where {.} denotes the fractional part.
Answer» Answer :(i) The NUMBER of CRITICAL POINTS are to be one, between `(0, pi/2)`. (II) As 3 and -3 are not critical points.

Discussion

1992.	If O is the orthocentre of the triangle formed by A(1, -3), B(7, 2), C(2, 5) then the distance between the orthocentres of DeltaBOC, DeltaAOB is
Answer» `sqrt(65)` `2sqrt(65)` `(1)/(2) sqrt(65)` NONE ANSWER :A

Discussion

1993.	If lim_(xrarr0) (f(x))/(x^(2))=a and lim_(xrarr0) (f(1-cosx))/(g(x)sin^(2)x)=b (where b ne 0), then lim_(xrarr0) (g(1-cos2x))/(x^(4)) is
Answer» `(4a)/(b)` `(a)/(4b)` `(a)/(b)` none of these Solution :`underset(xrarr0)(LIM)(F(1-cosx))/(g(X)sin^(2)x)` `""=underset(xrarr0)(lim)(f(2SIN^(2).(x)/(2)))/(g(x)(2sin^(2).(x)/(2)))xx((2sin^(2).(x)/(2))^(2))/(4(sin^(2)(x)/(2))(cos^(2).(x)/(2)))` `""=underset(xrarr0)(lim)(a)/(g(x))xxtan^(2).(x)/(2)` `""a underset(xrarr0)(lim)(((x)/(2))^(2))/(g(x))xx(tan^(2).(x)/(2))/(((x)/(2))^(2))` `""=a underset(xrarr0)(lim)(x^(2))/(4g(x))` `therefore""underset(xrarr0)(lim)(x^(2))/(g(x))=(4b)/(a)` Now, `underset(xrarr0)(lim)(g(2sin^(2))x)/(x^(4))` `""underset(xrarr0)(lim)(g(sin^(2)x))/((2sin^(2)x)^(2))xx((2sin^(2)x)^(2))/(x^(4))` `""=(a)/(4b)xx4=(a)/(b)`

Discussion

1994.	A pair of dice is thrown at a time. X is the maximum of the two numbersshown on the dice. Then mean of X is
Answer» `(151)/(36)` `(161)/(36)` `(141)/(36)` `(131)/(36)` ANSWER :B

Discussion

1995.	Let f:R to ((-1)/2 , 1/2) be an odd function such that lim_( xto0) f(x) exists. Then, lim_( x to 0) 1/(2f(x)-1) equals
Answer» 0 `1/2` 2 `-1` ANSWER :D

Discussion

1996.	Let be a binary opertion on the set Q of rational numbers as follows:a b = (a-b) ^(2)commutative andassociative.
Answer»

Discussion

1997.	I: The foot of the perpendicular from (1, 3, 4) to 2x – y +z + 3 = 0 is (-1,4, 3) II: The image of (1, 3, 4) in the plane 2x – y +z+ 3 = 0 is (-3, 5,2)
Answer» only I is TRUE only II is true both I and II are true neither I nor II are true Answer :C

Discussion

1998.	If (a_(1) + ib_(1)) (a_(2) + ib_(2)) … (a_(n) + ib_(n)) = A + iB then Tan^(-1) ((b_(1))/(a_(1))) + Tan^(-1) ((b_(2))/(a_(2))) + …. + Tan^(-1) ((b_(n))/(a_(n))) =
Answer» `Tan^(-1) ((A)/(B))` tan^(-1) ((B)/(A))` `Tan^(-1) ((2A)/(B))` `NPI + Tan^(-1) ((B)/(A))` Answer :B

Discussion

1999.	If (G, ^()) is a group such that a ^()b=b^**a for two element a and b, then
Answer» `a^(-1)B^(-1)=b^(-1)a^(-1)` `a^()b=a^(-1)b^(-1)` `a^(-1)b=a^b^(-1)` NONE of these Answer :A

Discussion

2000.	Solve the equation x^4 -4x^2 +8x +35 =0giventhat2 + I sqrt(3)isaroot
Answer» ANSWER :`2+- I SQRT(3),-2 +-i`

Discussion

Explore topic-wise InterviewSolutions in .

If n(A)=10, then no of different functions from A to A is :

A pole stands at a point A on the boundary of a circular park of radius a and subtends an angle alpha at another point B on the boundary. If the chord AB subtends an angle alpha at the centre of the path, the height of the pole is

findthe areaof theregionboundedby thetwo parabolasy=x^2and y^2 =x

Discuss the continuity of the cosine functions.

Let f(x)=lim_( n to oo) ([x^2]+[(2x)^2]+... + [(nx)^2])/n^3 then the set of all points of continuity of f([x] denotes the greatest integer function)

From the figure, which of the following could be the value of b?

Therepeated rootof theequation 4x^3 -12x^2 -15x -4=0 is

If omega a complex cube root of unity ,then (2-omega)(2-omega^(2))+2(3-omega)(2-omega^2)+........+(n-1)(n-omega)(2-omega^2)=

Evaluate:int_(0)^(2a)x^(2) sqrt(2ax-x^(2))dx.

If P(A) = 0.8, P(B) = 0.5 and P (B|A) = 0.4, find﻿ P(A cup B)﻿

Ifalpha, beta, gammaare therootsofx^3 +px^2 +qx +r=0then find ( beta + gamma- 3 alpha )( gamma+ alpha + beta - 3 gamma)

For any two events A, B show that P(A nn B) - P(A) P(B) = P(A^(C)) P(B) - P(A^(C) nn B) = P(A) P(B^(C)) - P(A nn B^(C))

If AB=21, B-=(-2,1,-8) and the direction cosines of AB are 6/7, 2/7, 3/7 , then the co-ordinates of points in line PQ nearer to the origin at a distance of 14 units from A are

Out of 10000 families with 4 children each, find the number of families all of whose children are daughters.

Two events A and B wll be independent,if a)A and B are mutually exclusive b) P(A'B')=[1-P(A)] [1-P(B)] c)P(A)= P(B) d)P(A)+P(B)=1

The transformed equation of xy + 2x -5y - 11 = 0 when the origin is shifted to the point (2, 3) is,

If p(x) isa polynomial with integer coefficients and a,b,c are three distinct integers, then show that it is impossible to have p(a)=b,p(b)=c and p(c)=a

[x^2]is differentiable on (-1,1):

The product of lenghts of the perpendicular from point (2, 3) on the lines given by 2x^(2)+6xy-y^(2)=0 is

The value of cos "" (2pi)/(15) cos "" (4pi)/(15) cos "" (8pi)/(15) cos "" (14pi)/(15)is

A circle of radius 4 drawn on a chord of the parabola y^(2)=8x as diameter touches the axis of the parabola. Then the slope of the chord is

If n(A) = 5, then number of relations that are both reflexive and symmetric is

The order of the differential equation 3x^(2) (d^(2)y)/(dx^(2))-5(dy)/(dx) + y = 0 is

W (x,y,z) = xy + yz , x = u - v ,y = uv , z = u +v,u,v in R. Find (delw)/(delu), (del w)/(delv) and evaluate them at (1/2,1)

State the converse, inverse and contrapositive of The square of an integer is a natural number propositions. Stating it as a conditional, wherever necessary.

I = int(sin^(10)x-cos^(8)xsin^(2)x+sin^(8)xcos^(2)x-cos^(10)x)/(1-2sin^(2)xcos^(2)x) dx is equal to

Sum of the root of the equation 2 sin^2 theta + sin^2 2theta =2, 0 le theta le pi//2 is

If (b+c-2a)/a , (c+a-2b)/b , (a+b-2c)/c are in A.P., then a,b,c are in :

If (x^(2)-x+p)(11y^(2)-4y+2)=(9)/(2) have exactly one ordered pair of (x, y) then find p.

If a**b = a +bon R - {1}, then a^(-1) is ........

Let f(x) is a real valued function defined by f(x)=x^(2)+x^(2) int_(-1)^(1) tf(t) dt+x^(3) int_(-1)^(1)f(t) dt then which of the following hold (s) good?

Prove that the feet of the perpendicular from the origin on the lines x+y=4,x+5y=26, 15x-27y=424 are collinear.

Prove that if a plane has the intercepts a, b, c and is at a distance of p units from the origin,then (1)/(a^2)+(1)/(b^2)+(1)/(c^2)=(1)/(p^2)

Find the co-ordinates of the vertex and focus the equation of the directrix and axis of the following parabolas.

If P(A) = 0.5, P(B) = 0.6 and P(A cup B) = 0.8 then find P( A | B) and P( B | A).

Find the number of critical points are the following functions in their respective intervals provided. (i) min(x, cosx),x epsilon[-pi, pi] (ii) min ({x}, {-x}), x epsilon[-3, 3], where {.} denotes the fractional part.

If O is the orthocentre of the triangle formed by A(1, -3), B(7, 2), C(2, 5) then the distance between the orthocentres of DeltaBOC, DeltaAOB is

If lim_(xrarr0) (f(x))/(x^(2))=a and lim_(xrarr0) (f(1-cosx))/(g(x)sin^(2)x)=b (where b ne 0), then lim_(xrarr0) (g(1-cos2x))/(x^(4)) is

A pair of dice is thrown at a time. X is the maximum of the two numbersshown on the dice. Then mean of X is

Let f:R to ((-1)/2 , 1/2) be an odd function such that lim_( xto0) f(x) exists. Then, lim_( x to 0) 1/(2f(x)-1) equals

Let ** be a binary opertion on the set Q of rational numbers as follows:a ** b = (a-b) ^(2)commutative andassociative.

I: The foot of the perpendicular from (1, 3, 4) to 2x – y +z + 3 = 0 is (-1,4, 3) II: The image of (1, 3, 4) in the plane 2x – y +z+ 3 = 0 is (-3, 5,2)

If (a_(1) + ib_(1)) (a_(2) + ib_(2)) … (a_(n) + ib_(n)) = A + iB then Tan^(-1) ((b_(1))/(a_(1))) + Tan^(-1) ((b_(2))/(a_(2))) + …. + Tan^(-1) ((b_(n))/(a_(n))) =

If (G, ^(**)) is a group such that a ^(**)b=b^**a for two element a and b, then

Solve the equation x^4 -4x^2 +8x +35 =0giventhat2 + I sqrt(3)isaroot

If P(A) = 0.8, P(B) = 0.5 and P (B|A) = 0.4, find P(A cup B)

Let be a binary opertion on the set Q of rational numbers as follows:a b = (a-b) ^(2)commutative andassociative.

If (G, ^()) is a group such that a ^()b=b^**a for two element a and b, then