28278 + Interview Questions in Maths in Class 12 Page 22 InterviewSolution

1051.	In a certain college, 4% of ·boys and 1 % of girls are taller than 1.75 metres. Furthermore, 60% of the students are girls. If a student is selected at random and is taller than 1.75 metres, what is the probability that the selected student is a girl?
Answer» SOLUTION :LET `E_1and E_2` be the EVENTS of selecting a boy and a girl respectively. Then, `P(E_1)=40/100=2/5,and P(E_2)=60/100=3/5`. Let E = EVENT that the student selected is taller than 1.75 m. Then `P(E//E_1)=4/100=1/25and P(E//E_2)=1/100`. Probability that the selected student is a girl, givne that she is taller than 1.75 m `=P(E_2//E)` `=(P(E//E_2).P(E_2))/(P(E//E_1).P(E_1)+P(E//E_2.P(E_2))`

Discussion

1052.	Evalute the following integrals int (dx)/(6x^(2) - 5x + 1)
Answer» ANSWER :`LOG\|(2x-1)/(3x-1)\|+C`

Discussion

1053.	The set of values of the parameter ‘a’ for which the function, f(x) = 8ax – a sin 6x – 7x – sin 5x increases & has no critical points for all x in R, is
Answer» `[-1,1]` `(-OO,-6)` `(6,+oo)` `[6, +oo)` ANSWER :C

Discussion

1054.	Show that for all values of lambda , the lines joining the origin to the points common to x^2+2hxy-y^2+gx+fy=0and fx -gy= lambda are at right angles .
Answer»

Discussion

1055.	A bag contains 4 red, 5 black and 6 blue balls. Find the probability that two balls drawn at random simultaneously from the bag are a red and a black ball.
Answer» ANSWER :`(4)/(21)`

Discussion

1056.	The sum 1/(1!9!) + 1/(3!7!) + ... + 1/(7!3!) + 1/(9!1!) can be written in the form 2^a/(b!) Find a and b.
Answer» Solution :1/(1!9!) + 1/(3!7!) + ... + 1/(7!3!) + 1/(9!1!)` `1/(10!)((10!)/(1!9!) + (10!)/(3!7!) + .... + (10!)/(9!1!))` `1/(10!) ("^10C_1 + ^10C_3 + .... + ^10C_9)` `1/(10!) 2^(10-1)` `2^9/(10!)` = `2^a/(B!)` where a = 9, b = 10

Discussion

1057.	Find the acceleration of rod A and wedgeB in the arrangement shown in figure if the mass of rod equal that of the wedge and the friction between all contact surfaces is negligible Take angle ofwedge as 45^(@) & g=9.8 m//s^(2)
Answer» ANSWER :`4.90`

Discussion

1058.	If alpha, beta , gamma are the roots of x^(3) - 2x^(2) + 3x + 5 = 0 then the equation whose roots beta^(2) gamma^(2), gamma^(2) alpha^(2), alpha^(2) beta^(2)is
Answer» `y^(3) - 29y^(2) - 50y - 625 = 0 ` `2Y^(3) - 39y^(2) - 70y + 125 = 0 ` `y^(4) - 24y^(2) + 65y - 55 = 0 ` `5Y^(5) - 12y^(2) + 68y - 155 = 0 ` Answer :1

Discussion

1059.	Locus of the points of intersection of perpendicular tangents drawn one to each of the circles x^(2)+y^(2)-4x+6y-37=0, x^(2)+y^(2)-4x+6y-37=0, x^(2)+y^(2)-4x+6y-20=0 is
Answer» `X^(2)+y^(2)-4x+6y=0` `x^(2)+y^(2)-4x+6y-50=0` `x^(2)+y^(2)-4x+6y-57=0` `x^(2)+y^(2)-4x+6y-70=0` ANSWER :D

Discussion

1060.	Obtain Maclaurin's series for f(x) = log sec x
Answer» ANSWER :`F(X) = (x^(2))/(2) + (x^(2))/(12)`

Discussion

1061.	Let vec(a),vec(b) and vec(c )be three non-coplaner vectors and vec(p),vec(q),vec(r) be three vectors such that vec(p)=2vec(a)-vec(b)+vec(c ),vec(q)=vec(a)-3vec(b)+2vec(c),vec(r)=vec(a)+vec(b)-vec(c ). If [vec(a)vec(b)vec(c)]=2 then [vec(p)vec(q)vec( r)] equals
Answer» 6 -6 3 None of these Solution : `"Area of 1 traingle" =(1)/(2)xx2pixxpi=pi^(2)"" "Area of 1 semicircle" =(1)/(2)(pi((1)/(2))^(2))=(pi)/(8)` `underset(xrarroo)(Lt)(underset(0)overset(x)(int)F(t)DT)/(underset(0)overset(x)(int)G(t)dt)=underset(xrarroo)(Lt)(pi^(2).[(x)/(2pi)]+underset([(x)/(2pi)])overset((x)/(2pi))(int)COS^(-1)(COSX)dx)/((pi)/(8)[x]+underset([x])overset(x)(int)sqrt({x}-{x}^(2)).dx)` `underset(xrarroo)(Lt)(pi^(2)((x)/(2pi))-pi^(2).{(x)/(2pi)}+int)/((pi)/(8)x-(pi)/(8){x}+int)=underset(xrarroo)(Lt)((pi)/(2)+(("finite quantity"))/(x))/((pi)/(8)+(("finite quantity"))/(x))=((pi//2))/((pi//8))=4`

Discussion

1062.	Prove that the sequence with the general term (a) x_1=(1-(-1)^(n))/(n) (b) x_n=1/n sin [(2n-1)pi/2]
Answer» Answer :For `a gt 1" PUT "rootn(a)=1+alpha_n (alpha_n gt 0)` and,with the aid of the inequality `a=(1+alpha_(n))^(n) gt nalpha_(n)`, prove that `alpha_n` is an INFINITESIMAL. For `a LT 1` put `rootn(a)=(1)/(1+alpha_(n)) (alpha_n gt 0)` and make USE of the inequality `1/a=(1+alpha_(n))^(n) gt nalpha_n`

Discussion

1063.	Test differentiability and continuity of the following functions. \|1-1/x\| at x = 1
Answer» 0.25 0.5 0.75 1 Answer :B

Discussion

1064.	int_(0)^(pi) (theta sin theta)/(1 +cos^2 theta) d theta is equal to
Answer» `(pi^2)/(2)` `(pi^3)/(3)` `pi^2` `(pi^2)/(4)` ANSWER :D

Discussion

1065.	If (1+i) is a root of the equation x^(3) -5x ^(2) +9x -6 =0, then its other two roots are-
Answer» `-1, (2-i)` `1, (-2+i)` `1,(2-i)` `1, -2-i` ANSWER :C

Discussion

1066.	Fill int the blanks choosing correct answer from the bracket. Ifa = b cosC , then _____ angle is a right angle.
Answer» A B C Answer :B

Discussion

1067.	Whichof the following statement is correct
Answer» `N_(2)^(+)` is havingbond of 2.5 To GET`N^(+)` from `N_(2)^(-)`, ELECTRON(s) are removed from antibondingorbitals `B_(2)` molecule is paramagetic with `mu` VALUE of1.73Bm. In thechange of `O_(2) to O_(2)^(+)`the bondlengthincrease Answer :A

Discussion

1068.	If a line makes angles pi/3 and pi/4 with the x - axis and y - axisrespectively, then the angle made by the linewith the z - axis is
Answer» `pi/2` `pi/4` `(5PI)/12` `pi/3` ANSWER :D

Discussion

1069.	The rootsof48x^3 - 44 x^2 + 12 x -1=0are in
Answer» A.P G.P H.P A.G.P Answer :C

Discussion

1070.	Integrate the following functions : intx^(2)sqrt(8-x^(6))dx
Answer» ANSWER :`(1)/(3)[(X^(3))/(2)SQRT(8-x^(6))+4sin^(-1)""(x^(3))/(2sqrt2)]+c`

Discussion

1071.	If g(x)=x^2-1 and gof (x)=x^2+4x+3 , then f(1/2) is equal (f (x) gt 0AA x in R) :
Answer» `3/2` `2` `5/2` None of these SOLUTION :`G[f(N)]=x^2+4n+3` `RARR g[f(1/2)]=1/4+4xx1/2+3 rArr [f(1/2)^2 -1]=5+1/4` `rArr [f(1/2)]^2 =25/4 rArr f(1/2)=5/2`

Discussion

1072.	Find the asymptotes of the following curves : y = (x^(2)-6x+3)/(x-3)
Answer» ANSWER :x=1 `y = x-3`

Discussion

1073.	ABCD is a rectangular field with AB = a and BC = b. A lamp post of height h at A subtends an angle alpha at P, the middle point of CD and another lamp post of equal heigh at D subtends an angle beta at Q, the middle point of BC. If PQ subtends an angle theta at A, then cot^(2) alpha cot^(2) beta cos^(2) theta = k^(2), where k =
Answer» `(a^(2) + B^(2))//2H^(2)` `(a^(2)-b^(2))//2h^(2)` `2h^(2)//(a^(2) + b^(2))` `2(a^(2) + b^(2))H^(2)` ANSWER :A

Discussion

1074.	I=(xcosx+1)/(sqrt(2x^(3)e^(sinx)+x^(2)))dx (4)/(5)Alog\|sqrt(2xe^(sinx)+1-1)/(sqrt(2xe^(sinx)+1+1))\|+C then A is equal to.
Answer» ANSWER :1.25

Discussion

1075.	Let f(x)={{:(((e^"[x]"-e^"{x}")e^(-x)+A),"," x lt 0),("2 sin {x}"/"tan {x}",","x gt 0),(2,","x =0):} The value of A so that f is continous at x=0 is ([x] is greatest integer function and {x} is the fractional part of x) is
Answer» `E^(-1)` `3-e^(-1)` `2-e^(-1)` `2` ANSWER :B

Discussion

1076.	If xyz= m and det p [{:( x,y,z),(z,x,y),(y,z,x) :}] where P is an orthogonal matrix the value of x^(-10 ) y^(-12),z^(-12) +x^(12), y^(12) , z^(-10 )can be
Answer» 1 `m^(-12) ` `m^(-10 ) ` ` m^(10 ) ` ANSWER :B

Discussion

1077.	Find the values of the following integrals (ii) int_(0)^(pi) cos^(3)x sin^(4) x dx
Answer» 0 1 16 `(3PI)/(16)` ANSWER :A

Discussion

1078.	Two cards are drawn successively one by one with out replacement from a pack of cards. The mean of number of kings is
Answer» `(1)/(13)` `(2)/(13)` `(3)/(13)` `(4)/(13)` ANSWER :B

Discussion

1079.	Find the unit vector perpendicular to each of the vectors vec(a)+vec(b)" and "vec(a)-vec(b)" where "vec(a)=3hat(i)+2hat(j)+2hat(k)" and "vec(b)=hat(i)+2hat(j)-2hat(k).
Answer» ANSWER :`(2HAT(i)-2hat(j)+hat(k))/3`

Discussion

1080.	How many two digit even number of distinct digits can be formed with the digits 1,2,3,4,5?
Answer» Solution :Two digit even numbers of distinct digits are to be FORMED with the digits 1,2,3,4,5. Here the even numbers must be END with 2 or 4. When 2 is placed in the UNIT place, the tenth place can be FILLED up by other 4 digits in 4 different ways. SIMILARLY, when 4 is placed in the unit place, the tenth place can be filled up in 4 different ways. `:.` The total number of two digit even numbers` =4+4=8.`

Discussion

1081.	For the matrix A=[{:(3,2),(1,1):}] , find the numbers a and b such that A^2+aA+bI=O
Answer» ANSWER :A=4

Discussion

1082.	Find all points of discontinuity of f where f is defined by f(x)={(2x+3,xle2),(2x-3,x>2):}
Answer» Solution :`f(x)={(x,ifxle1),(5, ifx>1):}}` For `xgt1,f(x)=5` which is a constant FUNCTION and THEREFORE conti nuous. Hence f(x) is continuous at x=2.

Discussion

1083.	The solution of (x^(2) - y^(2)) dx + 2xy dy = 0 is
Answer» `X^(2) + y^(2) = CX` `x^(2) - y^(2) = cx` `x^(2) + y^(2) = CY` `x^(2) + y^(2) = cx^(2)` ANSWER :A

Discussion

1084.	If ((x+1)^(2))/(x(x^(2)+1))=(A)/(x)+(Bx+C)/(x^(2)+1) then cos^(-1)(A/C)=
Answer» `pi/6` `pi/4` `pi/3` `pi/2` ANSWER :C

Discussion

1085.	If cos (A -B) =5/3,tan A tan B =2, then which one of the following is true ?
Answer» `SIN (A+B) =1/5` `sin (A+B) =- 1/5` `COS (A-B) =1/5` `cos (A+B) =-1/5` ANSWER :D

Discussion

1086.	Consider a binary operation on N defined as ab=a^3+b^3. Choose the correct answer.a) both associative and commutative b)commutative but not associative c) associative but not commutative d) neither commutative nor associative
Answer» `` both ASSOCIATIVE and commulative `` COMMUTATIVE but not associative `` associative but not commutative `` NEITHER commutative nor associative Answer :B

Discussion

1087.	If int (1)/(cos^(6) x + sin^(6) x) dx = tan^(-1) f(x) + C then f(x) =
Answer» tan X - COT x tan x + cot x SEC x + tan x sec x - TANX ANSWER :A

Discussion

1088.	If sqrt(x)+sqrt(y)=sqrt(10), show that (dy)/(dx)+sqrt(y/x)=0
Answer» ANSWER :`0`

Discussion

1089.	Classify 10 kg measures as scalar and vector.
Answer» Solution :The measure 10 KG has only MAGNITUDE and THEREFORE it is a scalar.

Discussion

1090.	Thetangentat a point(1,1)to thecurvef(x)= x^2+ bx - bmakesa trinaglein thefirstquadrant withaxes . Ifthe areaofthistriangleis 2Sq, unitsthenthe valueof b is ……
Answer» `-1` `-2` `-3` `1` ANSWER :C

Discussion

1091.	The system of linear equations : x+y+z=6,x+2y+3z=1 and x+2y+az=6 has no solutions when :
Answer» `b= 3 a ne 10` `b=2 a=3` `a=3 b ne 10` `a= 2 b ne 3` ANSWER :C

Discussion

1092.	The solution of the differential equation (1+e^(x))y(dy)/(dx) = e^(x) when y=1 and x = 0 is
Answer» `E^(y^(2)//2) = SQRT(e)(1+e^(x))` `e^(y^(2)//2) = e(1+e^(x))` `2.e^(y^(2)//2) = sqrt(e)(1+e^(x))` `2.e^(y^(2)) = e(1+e^(x))` ANSWER :C

Discussion

1093.	A flash light has 10 batteries out of which 4 are dead. If 3 batteries are selected without replacement and tested, then the probability that all 3 are dead is
Answer» 1)`1/30` 2)`2/8` 3)`1/15` 4)`1/10` ANSWER :A

Discussion

1094.	If a=hati+2hatj+3hatk and b=hatixx(axxhati)+hatjxx(axx hatj)+hatk+(a xx hatk), then length of b is equal to
Answer» `SQRT(12)` `2sqrt(12)` `3sqrt(14)` `2sqrt(14)` Solution :We have , `a=hat(i)+2hat(j)+3hat(k)` `b=hat(i)xx(axxhat(i))+hat(j)xx(axxhat(j))+hat(k)xx(axxhat(k))` Now , `hat(i)xx(axxhat(i))=(hat(i).hat(i))a-(hat(i).a)hat(i)` `=a-a_(1)hat(i)""["LET" (a=a_(1)hat(i)+a_(2)hat(j)+a_(3)hat(k))]` Similarly , `hat(j)xx(axxhat(i))=a-a_(2)hat(j) and hat(k)xx(axxhat(k))` `therefore b=3a-a=2a=2(hat(i)+2hat(j)+3hat(j))` `rArr \|b\|=sqrt(4+16+36)=sqrt(56)=2sqrt(14)` .

Discussion

1095.	The shaded region shown in fig. is given by the inequation
Answer» 1)`14x + 5Y GE 70, y ge 14 and x-y ge 5` 2)`14x + 5y le 70, y le 14 and x-y ge 5` 3)`14x + 5y ge 70, y le 14 and x-y ge 5` 4)`14x + 5y ge 70, y le 14 and x-y le 5` Answer :D

Discussion

1096.	Let A, B be matrics of order 3x3 such that A' =-A and B'=B then matrix lamdaAB+3BA is skew symmetric if lamda =
Answer» 3 -3 3,-3 None Answer :A

Discussion

1097.	Two lines given by the joint equation ax^(2)(b-c)-xy(ab-bc)+cy^(2)(a-b)=0 are
Answer» `a(b-C)x-c(a-b)y=0, x+y=0` `x+y=0, x-y=0` `a(b-c)x-c(a-b)y=0, x-y=0` NONE of these Answer :C

Discussion

1098.	Family of curves y=e^x(A cos x + B sinx) represents the differential equation :
Answer» ANSWER :`y" - 2Y' + 2y = 0`

Discussion

1099.	Equation of plane passing through (x_(1),y_(1),z_(1)) and parallel to two lines with direction Ratios a_(1),b_(1),c_(1) and a_(2),b_(2),c_(2) is
Answer» `\|{:(X-a_(1),y-b_(1),Z-c_(1)),(a_(1)-a_(2),b_(1)-b_(2),c_(1)-c_(2)),(1,1,):}\|=0` `\|{:(x-x_(1),y-y_(1),z-c_(1)),(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)):}\|=0` `\|{:(x,y,z),(x-x_(1),y-y_(1),z-z_(1)),(a_(1)-a_(2),b_(1)-b_(2),c_(1)-c_(2)):}\|=0` `a_(1)a_(2)(x-x_(1))+b_(1)b_(2)(y-y_(1))+c_(1)c_(2)(z-z_(1))=0` Answer :B

Discussion

1100.	The perimeter of the triangle with vertices at (1,0,0),(0,1,0)and (0,0,1) is
Answer» 3 2 `2sqrt(2)` `3sqrt(2)` ANSWER :D

Discussion

Explore topic-wise InterviewSolutions in .

In a certain college, 4% of ·boys and 1 % of girls are taller than 1.75 metres. Furthermore, 60% of the students are girls. If a student is selected at random and is taller than 1.75 metres, what is the probability that the selected student is a girl?

Evalute the following integrals int (dx)/(6x^(2) - 5x + 1)

The set of values of the parameter ‘a’ for which the function, f(x) = 8ax – a sin 6x – 7x – sin 5x increases & has no critical points for all x in R, is

Show that for all values of lambda , the lines joining the origin to the points common to x^2+2hxy-y^2+gx+fy=0and fx -gy= lambda are at right angles .

A bag contains 4 red, 5 black and 6 blue balls. Find the probability that two balls drawn at random simultaneously from the bag are a red and a black ball.

The sum 1/(1!9!) + 1/(3!7!) + ... + 1/(7!3!) + 1/(9!1!) can be written in the form 2^a/(b!) Find a and b.

Find the acceleration of rod A and wedgeB in the arrangement shown in figure if the mass of rod equal that of the wedge and the friction between all contact surfaces is negligible Take angle ofwedge as 45^(@) & g=9.8 m//s^(2)

If alpha, beta , gamma are the roots of x^(3) - 2x^(2) + 3x + 5 = 0 then the equation whose roots beta^(2) gamma^(2), gamma^(2) alpha^(2), alpha^(2) beta^(2)is

Locus of the points of intersection of perpendicular tangents drawn one to each of the circles x^(2)+y^(2)-4x+6y-37=0, x^(2)+y^(2)-4x+6y-37=0, x^(2)+y^(2)-4x+6y-20=0 is

Obtain Maclaurin's series for f(x) = log sec x

Let vec(a),vec(b) and vec(c )be three non-coplaner vectors and vec(p),vec(q),vec(r) be three vectors such that vec(p)=2vec(a)-vec(b)+vec(c ),vec(q)=vec(a)-3vec(b)+2vec(c),vec(r)=vec(a)+vec(b)-vec(c ). If [vec(a)vec(b)vec(c)]=2 then [vec(p)vec(q)vec( r)] equals

Prove that the sequence with the general term (a) x_1=(1-(-1)^(n))/(n) (b) x_n=1/n sin [(2n-1)pi/2]

Test differentiability and continuity of the following functions. |1-1/x| at x = 1

int_(0)^(pi) (theta sin theta)/(1 +cos^2 theta) d theta is equal to

If (1+i) is a root of the equation x^(3) -5x ^(2) +9x -6 =0, then its other two roots are-

Fill int the blanks choosing correct answer from the bracket. Ifa = b cosC , then _____ angle is a right angle.

Whichof the following statement is correct

If a line makes angles pi/3 and pi/4 with the x - axis and y - axisrespectively, then the angle made by the linewith the z - axis is

The rootsof48x^3 - 44 x^2 + 12 x -1=0are in

Integrate the following functions : intx^(2)sqrt(8-x^(6))dx

If g(x)=x^2-1 and gof (x)=x^2+4x+3 , then f(1/2) is equal (f (x) gt 0AA x in R) :

Find the asymptotes of the following curves : y = (x^(2)-6x+3)/(x-3)

I=(xcosx+1)/(sqrt(2x^(3)e^(sinx)+x^(2)))dx (4)/(5)Alog|sqrt(2xe^(sinx)+1-1)/(sqrt(2xe^(sinx)+1+1))|+C then A is equal to.

Let f(x)={{:(((e^"[x]"-e^"{x}")e^(-x)+A),"," x lt 0),("2 sin {x}"/"tan {x}",","x gt 0),(2,","x =0):} The value of A so that f is continous at x=0 is ([x] is greatest integer function and {x} is the fractional part of x) is

If xyz= m and det p [{:( x,y,z),(z,x,y),(y,z,x) :}] where P is an orthogonal matrix the value of x^(-10 ) y^(-12),z^(-12) +x^(12), y^(12) , z^(-10 )can be

Find the values of the following integrals (ii) int_(0)^(pi) cos^(3)x sin^(4) x dx

Two cards are drawn successively one by one with out replacement from a pack of cards. The mean of number of kings is

Find the unit vector perpendicular to each of the vectors vec(a)+vec(b)" and "vec(a)-vec(b)" where "vec(a)=3hat(i)+2hat(j)+2hat(k)" and "vec(b)=hat(i)+2hat(j)-2hat(k).

How many two digit even number of distinct digits can be formed with the digits 1,2,3,4,5?

For the matrix A=[{:(3,2),(1,1):}] , find the numbers a and b such that A^2+aA+bI=O

Find all points of discontinuity of f where f is defined by f(x)={(2x+3,xle2),(2x-3,x>2):}

The solution of (x^(2) - y^(2)) dx + 2xy dy = 0 is

If ((x+1)^(2))/(x(x^(2)+1))=(A)/(x)+(Bx+C)/(x^(2)+1) then cos^(-1)(A/C)=

If cos (A -B) =5/3,tan A tan B =2, then which one of the following is true ?

Consider a binary operation ** on N defined as a**b=a^3+b^3. Choose the correct answer.a) both associative and commutative b)commutative but not associative c) associative but not commutative d) neither commutative nor associative

If int (1)/(cos^(6) x + sin^(6) x) dx = tan^(-1) f(x) + C then f(x) =

If sqrt(x)+sqrt(y)=sqrt(10), show that (dy)/(dx)+sqrt(y/x)=0

Classify 10 kg measures as scalar and vector.

Thetangentat a point(1,1)to thecurvef(x)= x^2+ bx - bmakesa trinaglein thefirstquadrant withaxes . Ifthe areaofthistriangleis 2Sq, unitsthenthe valueof b is ……

The system of linear equations : x+y+z=6,x+2y+3z=1 and x+2y+az=6 has no solutions when :

The solution of the differential equation (1+e^(x))y(dy)/(dx) = e^(x) when y=1 and x = 0 is

A flash light has 10 batteries out of which 4 are dead. If 3 batteries are selected without replacement and tested, then the probability that all 3 are dead is

If a=hati+2hatj+3hatk and b=hatixx(axxhati)+hatjxx(axx hatj)+hatk+(a xx hatk), then length of b is equal to

The shaded region shown in fig. is given by the inequation

Let A, B be matrics of order 3x3 such that A' =-A and B'=B then matrix lamdaAB+3BA is skew symmetric if lamda =

Two lines given by the joint equation ax^(2)(b-c)-xy(ab-bc)+cy^(2)(a-b)=0 are

Family of curves y=e^x(A cos x + B sinx) represents the differential equation :

Equation of plane passing through (x_(1),y_(1),z_(1)) and parallel to two lines with direction Ratios a_(1),b_(1),c_(1) and a_(2),b_(2),c_(2) is

The perimeter of the triangle with vertices at (1,0,0),(0,1,0)and (0,0,1) is

Consider a binary operation on N defined as ab=a^3+b^3. Choose the correct answer.a) both associative and commutative b)commutative but not associative c) associative but not commutative d) neither commutative nor associative