28278 + Interview Questions in Maths in Class 12 Page 10 InterviewSolution

451.	ABCD is a parallelogram . If L arid M and the middle points of BC and CD respec tively, then find lambda , if AM =lambda AD - LM
Answer» ANSWER :`(3)/(2)`

Discussion

452.	If I_(1)=int_(0)^(pi//4)(tanx)^(cosx)dx, I_(2)=int_(0)^(pi//4)(cotx)^(tanx)dx I_(3)=int_(0)^(pi//4)(tanx)^(tanx)dx, I_(4)=int_(0)^(pi//4)(cotx)^(cotx)dx then
Answer» `I_(1) lt I_(3)` `I_(2) lt I_(4)` `I_(1) lt I_(4)` `I_(3) lt I_(2)` ANSWER :A::B::C::D

Discussion

453.	dIiscuss the global maxima/minima of followingfunction in the given interval f(x) = \|x^(2) - 4x +3\| in [0.5]. (b) f(x) = 3x^(4) - 2x^(3)-6x^(2)+6x+1 in [0,2]. (c) f(x) = sqrt((1-x^(2))(1+2x^(2)) in [-1,1] (d) f(x)=sinxsin2x in (-infty, infty).
Answer» Answer :(a) Global maxima, `F(5)=8`; Global minima `f(1) = f(3) = 0` (b) Global minima 1 and Global maxima 21. (c) Global minima 0 and Global maxima `3/sqrt8` (d) Global minima `-4/3 SQRT3` and Global maxima `4/3 sqrt3`.

Discussion

454.	Compute the area of the region bounded by the straight lines x = 0, x = 2 and the curves y=2^(x) and y=2x-x^(2).
Answer» ANSWER :`(3)/(LN 2)-(4)/(3)`

Discussion

455.	A class consistsof 80 students, 25 of them are girls. If 10 of the students are rich and 20 of the studentsare fair complexioned, then the probabilityof selecting a fair complexioned rich girl from the class (assuming three traits as independent) is
Answer» `(1)/(10)` `(1)/(32)` `(5)/(512)` `(7)/(512)` ANSWER :C

Discussion

456.	Find the area of the region {(x,y): x^(2)-x-1 le y le -1}
Answer» ANSWER :`(1)/(6)` SQ UNITS

Discussion

457.	1+(w^2x)/(1!)+(wx^2)/(1!)+(x^3)/(3!) + (w^2x^4)/(4!) +(wx^5)/(5!) +(wx^5)/(5!) +(x^6)/(6!) + .... oo =
Answer» `e^x` `e^(WX)` `e^(OMEGA^(2)x)` `e^(omega^2)` ANSWER :C

Discussion

458.	If x and y are connected parametrically by the equations without eliminating the parameter, find (dy)/(dx) x=a (theta- sin theta), y= a (1 + cos theta)
Answer» ANSWER :`"TAN"(THETA)/(2)`

Discussion

459.	The point of intersection of the lines represented by r = (hat(i) + 2 hat(j)) + lambda[2 hat(i) + 3hat(j) + 4hat(k)] and r = (-hat(i) - 3hat(j) + 7 hat(k)) + mu(hat(i) + 2hat(j) - hat(k)) is
Answer» `3HAT(i) + 5hat(J) + 3hat(K)` `5hat(i) + 8hat(j) + 7hat(k)` `-HAT(i) - hat(j) - 5hat(k)` `- 3hat(i) - 4hat(j) - 9hat(k)` ANSWER :A

Discussion

460.	int(e^(-x))/(1+e^(x))dx=....
Answer» `LOG(1+e^(X))-x-e^(-x)+C` `log(1+e^(x))+x-e^(-x)+c` `log(1+e^(x))-x+e^(-x)+c` `log(1+e^(x))+x+e^(-x)+c` ANSWER :A

Discussion

461.	If the volume of a shpere increases at the rate of 2pi cm^3/s, then the rate of increase of its radius (in cm/s), when the volume is 288pi cm^3, is
Answer» `1/36` `1/72` `1/18` `1/9` ANSWER :B

Discussion

462.	If three events of a sample space are E, F and G, then P(Enn F nnG) is equal to
Answer» <P>`P(E).P(F\|E).P(G\|Enn F)` `P(E).P(F\|E).P(G\|F)` `P(E).P(E\|F).P(E\|FnnG)` NONE of these Answer :A

Discussion

463.	The products of lengths of perpendicuylars from anypoint of hyperbola x^(2)-y^(2)=8 to its asymptotes, is
Answer» 2 3 4 8 Answer :C

Discussion

464.	Let P, Q, R be three s on the circle x^2+y^2=25. L, M, N are points on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1. PL, QM, NR are perpendicular to x-axis, with each segment not intersecting the x-axis. Further none of these points lie on coordinate axes and P, Q, R have been so chosen that area of triangle PQR is maximum. Area of triangle LMN is : (in square units)
Answer» `45sqrt(3)` `(75sqrt(3))/(4)` `25sqrt(3)` `15sqrt(3)` ANSWER :D

Discussion

465.	Let P, Q, R be three s on the circle x^2+y^2=25. L, M, N are points on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1. PL, QM, NR are perpendicular to x-axis, with each segment not intersecting the x-axis. Further none of these points lie on coordinate axes and P, Q, R have been so chosen that area of triangle PQR is maximum. Normal to the ellipse at L, M and N are:
Answer» Concurrent at a point Such that they all pass through origin Sides of an equilateral TRIANGLE with non-zero area Such that two of them are NECESSARILY perpendicular Answer :A

Discussion

466.	Let f(x)=x^(2)-3x +4, the value of x which satisfiesf(1)+f(x)=f(1) f(x) is
Answer» 1 2 1 and 2 1 and 0 ANSWER :C

Discussion

467.	Evaluate int(sin^(4)x)/(cos^(6)x)dx
Answer» ANSWER :`(1)/(5)TAN^(5)x+c`

Discussion

468.	If the plane ax + by = 0 is rotated about its line of intersection with the plane z = 0 through an angle α, then prove that the equation of the plane in its new position isax+by pm (sqrt(a^2+b^2)tan alpha)z=0
Answer» ANSWER :`THEREFORE ax+by PM z tan alpha.sqrt(a^2+b^2)=0`

Discussion

469.	Prove that \|{:(18,,40,,89),(40 ,,89,,198),( 89,, 198,,440):}\| = 3 abc -a^(3) -b^(3)-c^(3)
Answer» Solution :`Delta = \|{:(b+C,,a-b,,a),(c+a,,b-c,,b),(a+b,,c-a,,c):}\|` `=\|{:(b+c,,-b,,a),(c+a,,-c,,b),(a+b,,-a,,c):}\|"""[APPLYING "C_(2) toC_(2)-C_(3)"]"` `=\|{:(c,,-b,,a),(a,,-c,,b),(b,,-a,,c):}\|"""[Applying "C_(1) toC_(1)+C_(2)"]"` `=\|{:(c,,a,,b),(a,,b,,c),(b,,c,,a):}\|"""[INTERCHANGING " C_(2) " and "C_(3)"]"` `=3abc -a^(3)-b^(3)-c^(3)`

Discussion

470.	int" x"^(3)sin3xdx=
Answer» 1)`-(x^(3).COS3X)/3+(x^(2)sin3x)/3+(2xcos3x)/9-(2sin3x)/27+C` 2)`-(x^(3)cos3x)/3-(x^(2)sin3x)/3+(2xcos3x)/9-(2sin3x)/27+C` 3)`-(x^(3)cos3x)/3+(x^(2)sin3x)/3-(2xcos3x)/9-(2sin3x)/27+C` 4)`(x^(3)cos3x)/3+(x^(2)sin3x)/3-(2xcos3x)/9-(2sin3x)/27+C` Answer :A

Discussion

471.	If the two circles (x - 1)^(2) + (y - 3)^(2) = r^(2) and x^(2) + y^(2) - 8x+ 2y + 8 = 0 intersect at two distinct points, then
Answer» `(3sqrt(3),-5)` `(-1,-5)` `(5sqrt(3),-7)` `(7-sqrt(3))` Answer :C

Discussion

472.	Evaluate int_(a)^(b) e^(x) dx using the definition of a definite integral as the limit of a sum.
Answer» ANSWER :`E^(B)-e^(a)`

Discussion

473.	underset(x to pi//2+)"Lt" tanx
Answer» 0 `OO` `-oo` does not exist Answer :C

Discussion

474.	Express the following as trigonometric ratios of some acute angles.cot (-3888^@)
Answer» SOLUTION :`COT (-3888^@) = -cot 3888^@ = -cot (43 (pi)/2 + 18^@) = -(-tan 18^@) = TANT 18^@`

Discussion

475.	If thetain(0,pi/2) , then the value of : \|((sintheta+"cosec"theta)^2,(sintheta-"cosec"theta)^2,1),((costheta+sectheta)^2,(costheta-sectheta)^2,1),((tantheta+cottheta)^2,(tantheta-cottheta)^2,1)\|=
Answer» `SIN THETA +costheta+tantheta` 1 0 4 Answer :C

Discussion

476.	Range of the function f(x) = (x-1)^(5)/(x^(5)-1) is
Answer» (1,16] (0, 16] [0, 16] `(0, 0)CUP(1,16]` ANSWER :B

Discussion

477.	If the cube roots of unity are 1,omega,omega^(2) then the roots of the equation (x-1)^(3)+8=0 are
Answer» ANSWER :`-1,1,-omega,1,-2omega^2`

Discussion

478.	Let X and Y be sets containing m and n elements respectively.How many functions from X to Y are one-one according as m lt n, m gt n "and" m=n?
Answer» Solution :If\|x\|=m and \|y\|=N then If m lt n then NUMBER of one-one functions `=""^nP_m`. If `m GT n` then number of one-one functions =0 Ifm=n then number of one-one functions `=m!`

Discussion

479.	Find the value of t which satisfies (t-[\|sinx\|]!=3!5! Where [.] denotes the greatest integer function.
Answer» Solution :(t-[\|sin x \|])!=3! 5! 7! If `x=n pi+(pi)/(2) (n in I)` then `(t-1)!=(3xx2)XX(5xx4xx3xx2)xx7!` or` (t-1)!=10xx9xx8xx7!=10!` or t-1=10 or t=11 If `x NE n pi+(pi)/(2) (n in I)`, then (t-0)!=10! Or t=10

Discussion

480.	Match the following : {:("Column-I","Column -II"),(" (A) " \|z-6i\| + \|z-8\|=k " will represent an ellipse for k equals to ", "(p) 2"),("(B)" \|\|z-12i+3\|-\|z-2\|\|=k " will represent hyperbola if k equals to " , "(q) 8"),("(C)" \|z=ki\| + \|z-4\|=sqrt(10k) " will represent line segment if k equals to " , " (r) 12 "),("(D)" (z-k+2ki)/(\|z-2+4i\|)=k " will represent circle if k equals to " , "(s) 11"),(, "(t) 10"):}
Answer» <P> Answer :A(r,s), B(p,Q,r,s,t), C(p,q),D(q,r,s,t)

Discussion

481.	If A=[((1)/(2)(e^(ix)+e^(-ix)),(1)/(2)(e^(ix)-e^(-ix))),((1)/(2)(e^(ix)-e^(-ix)),(1)/(2)(e^(ix)+e^(-ix)))] then A^(-1) exists
Answer» for all real x for positive real x only for negative real x only NONE of these Answer :A

Discussion

482.	If the plane 7x+11y+13z = 3003, meets the coordinate axes in A,B,C the the centroid of the triangle ABCis
Answer» `(143,91,77)` `(143,77,91)` `(91,143,77)` `(143,66,91)` ANSWER :A

Discussion

483.	For a Binomial variate X with n = 6 , if P(X= 2) = 9P(X = 4), then its veriance is ,
Answer» `8/9` `1/4` `9/8` 4 Answer :C

Discussion

484.	The solution of (dy)/(dx) = (x^(2) + y^(2))/(xy) is
Answer» `e^((x^(2))/(y^(2)) = CX` `e^((y^(2))/(2x^(2)) = cx` `e^((y^(2))/(2x^(2)) = CY` `e^((y^(2))/(2x^(2)) = c` ANSWER :A

Discussion

485.	If plamda^(4)+qlamda^3+rlamda^2+slamda+t =\|(lamda^3+3lamda,lamda-1,lamda+3),(lamda+1,2-lamda,lamda-3),(lamda-3,lamda+4,3lamda)\| then t is equal to :
Answer» 24 23 22 21 Answer :D

Discussion

486.	If the angle between overline(a) and overline(b) is (P1)/(4) and overline(c)=3overline(a)-3overline(b), then c^(2)=
Answer» `9A^(2)+SQRT(2)ab+4b^(2)` `9a^(2)-6sqrt(2)ab+4b^(2)` `9a^(2)-6AB+4b^(2)` `9a^(2)+b^(2)+6ab` Answer :B

Discussion

487.	(1 + x)^(n) = p_(0) + p_(1) x + p_(2) x^(2) + … + p_(n) x^(n), then p_(0) + p_(3) + p_(6) + ….. =
Answer» `(1)/(3) [ 2^(n-1) + cos "" (n PI)/(3)]` `(2)/(3) [ 2^(n-1) + cos "" (NPI)/(3)]` ` (1)/(3) [2^(n-2) + SIN "" (npi)/(3)]` `(2)/(3) [2^(n-2) + sin"" (npi)/(6)]` Answer :B

Discussion

488.	Evaluate the following integrals (ii) int_(0)^(2)\|1-x\|dx
Answer» ANSWER :1

Discussion

489.	In what ratio should a given line be divided into a parts so that’s the rectangle contained by them is maximum ?
Answer» `1 : 1` `4 : 3` `3 : 2` `SQRT(5) + 1 : sqrt(5) - 1` Answer :A

Discussion

490.	Through any point (x, y) of a curve which passes through the origin, lines are drawn parallel to the coordinate axes. The curve, given that it divides the rectangle formed by the two lines and the axis into two areas, one of which is twice the other, represent a family of
Answer» circles parabolas hyperbolas straight lines Answer :B

Discussion

491.	int(dx)/(4 cos^(3)2x-3 cos2x)=....
Answer» `(1)/(3)LOG[sec6x+tan6x]+c` `(1)/(6)log[sec6x+tan6x]+c` `log[sec6x+tan6x]+c` None of these Answer :B

Discussion

492.	The points A(3,6,9),B(10,20,30) and C(25,-41,5)
Answer» A. are collinear B. form the vertices of a isosceles TRIANGLE C. equilateral triangle D. NONE of these

Discussion

493.	A space vector makes the angle 150^(@) and 60^(@) with the positive direction of x and y-axes. The angle made by the vector with the positive direction of z-axis is :
Answer» `60^(@)` `90^(@)` `120^(@)` `180^(@)` ANSWER :B

Discussion

494.	Let A=[{:(1,2),(-1,3):}],B=[{:(4,0),(1,5):}],C=[{:(2,0),(1,-2):}]and a=4, b =-2shows that : (i) A+(B+C)=(A+B)+C (ii)A(BC)=(AB)C (iii)(a+b)B=aB+bB (iv)a(C-A)=aC-aA (v)(A^(T))^(T)=A (vi) (bA)^(T)=B^(T)=bA^(T) (vii)(AB)^(T)=B^(T)A^(T) (viii)(A-B)*C=AC-BC (ix)(A-B)^(T)=A^(T)-B^(T)
Answer» ANSWER :(i) `=(A+B)+C` (ii)`=(AB)C` `=aB+bB` (iv) `=aC-aA` (v) `=A` (vi) `=bA^(T)` (vii) `=B^(T)A^(T)` (VIII) `=AC-BC` (IX) `=A^(T)-B^(T)`

Discussion

495.	If M and N are square matrices order 3, then which one of the following statements is not true?
Answer» For all symmetric matrices M and N, MN-NM is skew symmetric MN MN is symmetric or skew symmetric according as M is symmetric or skew symmetric For all symmetric matrices M and N, matrix MN is symmertic For any TWO matrices M and N, ADJ (MN) and adj (NM) NEED not be equal Answer :C

Discussion

496.	If the standard deviation of x_(1),x_(2),….,x_(n) is 3.5 then the standard deviation of -2x_(1)-3, -2x_(2)-3,….,-2x_(n)-3 is
Answer» `-7` `-4` 7 1.75 Answer :C

Discussion

497.	Find the modulus and principal argument of (1 + i) and hence express it in the polar form.
Answer» ANSWER :`SQRT(2) (COS pi/4 +ISIN pi/4)`

Discussion

498.	underset(0)overset(pi)int (cos^(4)x)/(cos^(4)x + sin^(4)x) dx=
Answer» `(PI)/(4)` `(pi)/(2)` `(pi)/(8)` `pi` ANSWER :B

Discussion

499.	A(4,3,5),B(0,-2,2)and C(3,2,1) are three points .The coordinates of the pointin whichthe bisector oftriangleBAC meets the sidebar(BC) is
Answer» `(15/8,4/8,11/8)` `(12/7,2/7,10/7)` `(9/5,2/5,7/5)` `(3/2,0,3/2)` ANSWER :A

Discussion

500.	If x+y=1 then sum_(r=0)^(n) r^2. ^(n) C_r x^r .y^(n-r)=
Answer» `N XY` `NX (x+yn)` `nx (nx+y)` none Answer :C

Discussion

Explore topic-wise InterviewSolutions in .

ABCD is a parallelogram . If L arid M and the middle points of BC and CD respec tively, then find lambda , if AM =lambda AD - LM

If I_(1)=int_(0)^(pi//4)(tanx)^(cosx)dx, I_(2)=int_(0)^(pi//4)(cotx)^(tanx)dx I_(3)=int_(0)^(pi//4)(tanx)^(tanx)dx, I_(4)=int_(0)^(pi//4)(cotx)^(cotx)dx then

dIiscuss the global maxima/minima of followingfunction in the given interval f(x) = |x^(2) - 4x +3| in [0.5]. (b) f(x) = 3x^(4) - 2x^(3)-6x^(2)+6x+1 in [0,2]. (c) f(x) = sqrt((1-x^(2))(1+2x^(2)) in [-1,1] (d) f(x)=sinxsin2x in (-infty, infty).

Compute the area of the region bounded by the straight lines x = 0, x = 2 and the curves y=2^(x) and y=2x-x^(2).

A class consistsof 80 students, 25 of them are girls. If 10 of the students are rich and 20 of the studentsare fair complexioned, then the probabilityof selecting a fair complexioned rich girl from the class (assuming three traits as independent) is

Find the area of the region {(x,y): x^(2)-x-1 le y le -1}

1+(w^2x)/(1!)+(wx^2)/(1!)+(x^3)/(3!) + (w^2x^4)/(4!) +(wx^5)/(5!) +(wx^5)/(5!) +(x^6)/(6!) + .... oo =

If x and y are connected parametrically by the equations without eliminating the parameter, find (dy)/(dx) x=a (theta- sin theta), y= a (1 + cos theta)

The point of intersection of the lines represented by r = (hat(i) + 2 hat(j)) + lambda[2 hat(i) + 3hat(j) + 4hat(k)] and r = (-hat(i) - 3hat(j) + 7 hat(k)) + mu(hat(i) + 2hat(j) - hat(k)) is

int(e^(-x))/(1+e^(x))dx=....

If the volume of a shpere increases at the rate of 2pi cm^3/s, then the rate of increase of its radius (in cm/s), when the volume is 288pi cm^3, is

If three events of a sample space are E, F and G, then P(Enn F nnG) is equal to

The products of lengths of perpendicuylars from anypoint of hyperbola x^(2)-y^(2)=8 to its asymptotes, is

Let f(x)=x^(2)-3x +4, the value of x which satisfiesf(1)+f(x)=f(1) f(x) is

Evaluate int(sin^(4)x)/(cos^(6)x)dx

If the plane ax + by = 0 is rotated about its line of intersection with the plane z = 0 through an angle α, then prove that the equation of the plane in its new position isax+by pm (sqrt(a^2+b^2)tan alpha)z=0

Prove that |{:(18,,40,,89),(40 ,,89,,198),( 89,, 198,,440):}| = 3 abc -a^(3) -b^(3)-c^(3)

int" x"^(3)sin3xdx=

If the two circles (x - 1)^(2) + (y - 3)^(2) = r^(2) and x^(2) + y^(2) - 8x+ 2y + 8 = 0 intersect at two distinct points, then

Evaluate int_(a)^(b) e^(x) dx using the definition of a definite integral as the limit of a sum.

underset(x to pi//2+)"Lt" tanx

Express the following as trigonometric ratios of some acute angles.cot (-3888^@)

If thetain(0,pi/2) , then the value of : |((sintheta+"cosec"theta)^2,(sintheta-"cosec"theta)^2,1),((costheta+sectheta)^2,(costheta-sectheta)^2,1),((tantheta+cottheta)^2,(tantheta-cottheta)^2,1)|=

Range of the function f(x) = (x-1)^(5)/(x^(5)-1) is

If the cube roots of unity are 1,omega,omega^(2) then the roots of the equation (x-1)^(3)+8=0 are

Let X and Y be sets containing m and n elements respectively.How many functions from X to Y are one-one according as m lt n, m gt n "and" m=n?

Find the value of t which satisfies (t-[|sinx|]!=3!5! Where [.] denotes the greatest integer function.

If A=[((1)/(2)(e^(ix)+e^(-ix)),(1)/(2)(e^(ix)-e^(-ix))),((1)/(2)(e^(ix)-e^(-ix)),(1)/(2)(e^(ix)+e^(-ix)))] then A^(-1) exists

If the plane 7x+11y+13z = 3003, meets the coordinate axes in A,B,C the the centroid of the triangle ABCis

For a Binomial variate X with n = 6 , if P(X= 2) = 9P(X = 4), then its veriance is ,

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

If plamda^(4)+qlamda^3+rlamda^2+slamda+t =|(lamda^3+3lamda,lamda-1,lamda+3),(lamda+1,2-lamda,lamda-3),(lamda-3,lamda+4,3lamda)| then t is equal to :

If the angle between overline(a) and overline(b) is (P1)/(4) and overline(c)=3overline(a)-3overline(b), then c^(2)=

(1 + x)^(n) = p_(0) + p_(1) x + p_(2) x^(2) + … + p_(n) x^(n), then p_(0) + p_(3) + p_(6) + ….. =

Evaluate the following integrals (ii) int_(0)^(2)|1-x|dx

In what ratio should a given line be divided into a parts so that’s the rectangle contained by them is maximum ?

Through any point (x, y) of a curve which passes through the origin, lines are drawn parallel to the coordinate axes. The curve, given that it divides the rectangle formed by the two lines and the axis into two areas, one of which is twice the other, represent a family of

int(dx)/(4 cos^(3)2x-3 cos2x)=....

The points A(3,6,9),B(10,20,30) and C(25,-41,5)

A space vector makes the angle 150^(@) and 60^(@) with the positive direction of x and y-axes. The angle made by the vector with the positive direction of z-axis is :

Let A=[{:(1,2),(-1,3):}],B=[{:(4,0),(1,5):}],C=[{:(2,0),(1,-2):}]and a=4, b =-2shows that : (i) A+(B+C)=(A+B)+C (ii)A*(BC)=(AB)*C (iii)(a+b)B=a*B+b*B (iv)a(C-A)=aC-aA (v)(A^(T))^(T)=A (vi) (b*A)^(T)=B^(T)=b*A^(T) (vii)(A*B)^(T)=B^(T)*A^(T) (viii)(A-B)*C=AC-BC (ix)(A-B)^(T)=A^(T)-B^(T)

If M and N are square matrices order 3, then which one of the following statements is not true?

If the standard deviation of x_(1),x_(2),….,x_(n) is 3.5 then the standard deviation of -2x_(1)-3, -2x_(2)-3,….,-2x_(n)-3 is

Find the modulus and principal argument of (1 + i) and hence express it in the polar form.

underset(0)overset(pi)int (cos^(4)x)/(cos^(4)x + sin^(4)x) dx=

A(4,3,5),B(0,-2,2)and C(3,2,1) are three points .The coordinates of the pointin whichthe bisector oftriangleBAC meets the sidebar(BC) is

If x+y=1 then sum_(r=0)^(n) r^2. ^(n) C_r x^r .y^(n-r)=

Let A=[{:(1,2),(-1,3):}],B=[{:(4,0),(1,5):}],C=[{:(2,0),(1,-2):}]and a=4, b =-2shows that : (i) A+(B+C)=(A+B)+C (ii)A(BC)=(AB)C (iii)(a+b)B=aB+bB (iv)a(C-A)=aC-aA (v)(A^(T))^(T)=A (vi) (bA)^(T)=B^(T)=bA^(T) (vii)(AB)^(T)=B^(T)A^(T) (viii)(A-B)*C=AC-BC (ix)(A-B)^(T)=A^(T)-B^(T)