28278 + Interview Questions in Maths in Class 12

1.	If the equation x^(3) -7x^(2) + 14x -8=0 is trasformed to y^(3) + py - (20)/(27) =0 when its roots are diminshed by k, then p=
Answer» Option1`(8)/(3)` Option2`(7)/(3)` OPTION3`(-7)/(3)` Option4`(-8)/(3)` ANSWER :C

Discussion

2.	If the lines 3x + 4y+ 1 = 0, 5x +lambday + 3 = 0 and 2x + y-1 = 0 are concurrent, then lambda=
Answer» -8 8 4 -4 Answer :B

Discussion

3.	R is circumradii of DeltaABC, H is orthocentre, R_(1), R_(2), R_(3) are circumradii of Delta AHB, Delta BHC. If AH produced meet the circumradii of ABC at M and intersect BC at L, angle AHB =180^(@)-C (c )/(sin (180^(@)-C))=2R_(1) (c)/(sin C) =2R_(1) R_(1)=R Ratio of area of Delta AHB to Delta BML, is
Answer» `COS B: 2 cos A` `2:1` `cos A : cos B cos C` NONE of these Answer :C

Discussion

4.	If the vector 19hati+22hatj+5hatk bisects an angle between the vectors a and 6hati+8hatj, then the unit vector in the direction of a is
Answer» `(1)/(5)(4hati+3hatj)` `(1)/(3)(2hati+2hatj+hatk)` `(1)/(3)(hati+2hatj+2hatk)` `(1)/(3)(2hati+2hatj-hatk)` ANSWER :B

Discussion

5.	R is circumradii of DeltaABC, H is orthocentre, R_(1), R_(2), R_(3) are circumradii of Delta AHB, Delta BHC. If AH produced meet the circumradii of ABC at M and intersect BC at L, angle AHB =180^(@)-C (c )/(sin (180^(@)-C))=2R_(1) (c)/(sin C) =2R_(1) R_(1)=RArea of Delta AHB
Answer» 2R COS A cos B cos C `R^(2)` cos A cos B cos C `2R^(2)` cos A cos B cos C None of the above Answer :C

Discussion

6.	Find (dy)/(dx) of y=sin(logx)
Answer» SOLUTION :`d/dxsin(LOGX)=(COS(logx))/X`

Discussion

7.	R is circumradii of DeltaABC, H is orthocentre, R_(1), R_(2), R_(3) are circumradii of Delta AHB, Delta BHC. If AH produced meet the circumradii of ABC at M and intersect BC at L, angle AHB =180^(@)-C (c )/(sin (180^(@)-C))=2R_(1) (c)/(sin C) =2R_(1) R_(1)=RR_(1)R_(2) +R_(2) R_(3) +R_(1)R_(3) is equal to
Answer» `2R^(2)` `3R^(2)` `5R^(2)` `R^(2)` ANSWER :B

Discussion

8.	A(2,3) and B(-3,4) be two given points. Find the equation of the locus of P so that the area of the triangle PAB is 8.5 sq.units.
Answer» ANSWER :`(x+5y-34)(x+5y)=0`

Discussion

9.	Statement 1 : If (3,4)is point on a hyperbola having focus (3,0 )and(lambda ,0)and length of the transverse axis being 1 units thenlambdacan take the value 0 or 3 Statement 2 : \| S' P -SP \|=2 a where S and S' are two foci 2a= length of the transverse axis and Pbe any points on the hyperbolaThen the correct statement is
Answer» Both the statement are TRUE and II is the CORRECT explanation of I Both the statement are True but Statement II is Not the correct explanation of Statement I. statement -I is True and Statement -II is False statement -I is False and statement -II is True ANSWER :D

Discussion

10.	Evalute the following integrals int (1)/(sqrt(1+5x)) dx
Answer» ANSWER :`(2)/(5)SQRT(1+5)+C`

Discussion

11.	int_(1//pi)^(2//pi)(sin(1//x))/(x^(2))dx=
Answer» 1 -1 `1/3` `pi/2` ANSWER :A

Discussion

12.	Find the probability of guessing atleast one out of 10 answers in multiple choice question with 4 possible answers.
Answer» ANSWER :`1-((3)/(4))^(10)`

Discussion

13.	Differentiate w.r.t x the function (log x)^(log x), x gt 1
Answer» ANSWER :`(dy)/(DX)= (LOG X)^(log x) [(1)/(x) + (log (log x))/(x)]`

Discussion

14.	For the circle x^(2)+y^(2)-6x+8y-1=0, points (2,3), (-2,-1) are
Answer» CONJUGATE POINTS end points of a DIAMETER INVERSE points none Answer :A

Discussion

15.	Coefficient of x^(10) in the expansion of (2+3x)e^(-x) is
Answer» `(-26)/((10)!)` `(-28)/((10)!)` `(-30)/((10)!)` `(-32)/((10)!)` Answer :B

Discussion

16.	If d is the distance between the parallel tangents with positive slope to y^2=4ax and
Answer» `10ltdlt20` `4ltdlt6` `dlt4` NONE of these ANSWER :C

Discussion

17.	Integrate the following function : int(x+3)/(sqrt(5-4x+x^(2)))
Answer» Answer :`SQRT(X^(2)-4x+5)+5log\|(x-2)+sqrt(x^(2)-4x+5)\|+C`

Discussion

18.	Equation of a common tangent to the circle x^(2) + y^(2) - 6x = 0 and the parabola, y^(2) = 4x, is
Answer» `sqrt(3) y = 3x + 1` `2 sqrt(3) y = 12X + 1` `sqrt(3) y = x + 3` `2 sqrt(3) y = - x - 12` Solution :We know that, equation of tangent to parabola `y^(2) = 4ax` `y = mx + (a)/(m)` `:.` Equation of tangent to the parabola `y^(2) = 4x` is `y = mx + (1)/(m)``( :' a = 1)` `implies m^(2) x - my + 1 = 0` Now, let line (i) is also a tangent to the circle. Equation of circle `x^(2) + y^(2) - 6X = 0` Clearly, centre of given circle is (3, 0) and radius = 3 [`:'` for the circle `x^(2) + y^(2) + 2 gx + fy + c = 0`, centre = (-g, -f) and radius `= sqrt(g^(2) + f^(2) -c]` `:.` The perpendicular distance of (3,0) from the line (i) is 3. [`:'` Radius is perpendicular to the tangent of cirlce] `implies (\|m^(2).3 - m.0 + 1\|)/(sqrt((m^(2))^(2) + (-m)^(2))) = 3` The LENGTH of perpendicular from a point `(x_(1), y_(1))` to the line `ax + by + c = 0` is `\|(ax_(1) + by_(1) + c)/(sqrt(a^(2) + B^(2)))\|` `implies (3m^(2) + 1)/(sqrt(m^(4) + m^(2))) = 3` `implies 9m^(4) + 6m^(2) + 1 = 9 (m^(4) + m^(2))` `implies m ~~ oo` or `m = +- (1)/(sqrt(3))` `[:' underset(m to oo)("lim") (3m^(2) + 1)/(sqrt(m^(4) + m^(2))) = underset(m to oo)("lim") (3 + (1)/(m^(2)))/(sqrt(1 + (1)/(m^(2))) = 3]` `:. ` Equation of common tangents are x = 0 `y = (x)/(sqrt(3)) + sqrt(3)` and `y = (-x)/(sqrt(3)) - sqrt(3)`

Discussion

19.	If n is a positive integer and C_(r )= ""^(n)C_(r ) then find the vlaue of sum_(r =1)^(n) r^(2)((C_(r ))/(C_(r -1))).
Answer» SOLUTION :N/A

Discussion

20.	If cosalpha+cosbeta+cosgamma=sinalpha+sinbeta+singamma=0, then
Answer» `cos2alpha+cos2beta+cos2gamma=0` `sin2alpha+sin2beta+sin2gamma=0` `cos(beta+gamma)+cos(gamma+alpha)+cos(alpha+beta)=0` `SIN(beta+gamma)+sin(gamma+alpha)+sin(alpha+beta)=0` Answer :A::B::C::D

Discussion

21.	The vertices of the triangle ABC are A(0, 0), B(3, 0) and C(3, 4), where A and C are foci of an ellipse and B lies on the ellipse. If the length of the latus rectum of the ellipse is (12)/(p) units, then the vlaue of p is
Answer» ANSWER :3.5

Discussion

22.	For each of the differential equations in Exercises 11 to 14, find a particular solution satisfying the given condition: 11. (x^(3) + x^(2) + x+ 1)(dy)/(dx) = 2x^(2) + x, y = 1 when x = 0.
Answer» ANSWER :`y = (1)/(4) LOG [ (X + 1)^(2)(x^(2) + 1)^(3)]- (1)/(2) tan^(-1) x+ 1`

Discussion

23.	For what value of n , (a ^(n +3) + b ^(n +3))/(a ^(n +2) + b ^(n +2)), a ne b in the A.M. of a and b.
Answer» ANSWER :`N =-2`

Discussion

24.	int_(0)^(pi) (tan x)/(sec x + cos x) dx=
Answer» `PI` `pi/4` `pi/2` `2PI` ANSWER :C

Discussion

25.	Find delta f and df when f(x) = 2x^2 - 1, x = 1, delta x = 0 cdot 02
Answer» SOLUTION : `f(x) = 2x^2 - 1, x = 1, delta x = 0 cdot 02` Then `delta f = f(x+ Delta x) - f(x)` =f(1.02) - f(1) = `2 (1 cdot 02)^2 - 1 - (2- 1)` =`2 cdot 0808 - 2 = 0 cdot 0808` Again `df= 4X DX = 4 xx 1 xx 0 cdot 02 = 0 cdot 08`

Discussion

26.	The range of a random variable X={1,2,3,…………..) and the probabilities are given by P(X=k)=(3^(ck))/(k!)(k=1,2,3,………..) and c is a constant . Then c=
Answer» `(1)/(2) log (log 2)` `log _(3) (log 2)` `(log _(E)(log 2))/(log _(3)e)` `log_(2) (log 3)` Answer :B

Discussion

27.	If f: R rarrR is defined by f(x) =x^(2)-3x+2 , find f(f(x)).
Answer» SOLUTION :N/A

Discussion

28.	The transformed equation of 2x^(2) + 4xy+ 5y^(2) - 4x - 22y+7=0 when the axes are translated to the point (-2,3) is
Answer» only 1 is TRUE only II is true both I and II are true neither I nor II are true ANSWER :C

Discussion

29.	Observe the following statements :Statement - I: The total number of terms in the expansion of (x+y)^100 + (x - y)^100 after simplification is 51 Statement - II : If ""^43C_(r-6) = ""^43C_(r + 1) then r = 12Statement - III : The coefficient of x^n in (1-x)^(-2) is (n+1) . Then the true statements are :
Answer» only I, II only II, III only III, I all the three Answer :C

Discussion

30.	Fivecardsare drawnsuccessivelywithreplacementfromawithreplacementfroma wellshuffleddeckof52cards . Whatisthe probabilitythat I. all fivecardsare spades ? II.Only3 cardsare spades? III.Noneis spade ?
Answer» ANSWER :`=(243 )/(1024)`

Discussion

31.	A straight line passing through O(0, 0) cuts the lines x = alpha , y = alphaand x + y = 8 at A, B and C respectively such that OA. OB. OC = 48sqrt 2and f(alpha ,beta ) tl=0 where f(x, y) = \|y/2 - 3/2 \| +(3x - 2y)^6+ sqrt(ex + 2y - 2e - 6) Find the equation of line OA.
Answer» `y - X =0` `y + x= 0 ` `y + SQRT(2) x = 0` `sqrt(2) y + x = 0` ANSWER :A

Discussion

32.	If sum_(r=1)^n I(r)=(3^n -1) , then sum_(r=1)^n 1/(I(r)) is equal to :
Answer» `2(1-(1/3)^N)` `(1-(1/3)^n)` `3/4(1-(1/3)^n)` `4/3(1-(1/3)^n)` ANSWER :C

Discussion

33.	A straight line passing through O(0, 0) cuts the lines x = alpha , y = alphaand x + y = 8 at A, B and C respectively such that OA. OB. OC = 48sqrt 2and f(alpha ,beta ) tl=0 where f(x, y) = \|y/2 - 3/2 \| +(3x - 2y)^6+ sqrt(ex + 2y - 2e - 6) Find the point of intersection of lines x = alpha and y = beta
Answer» (3, 2) (3, 2) (–2, –3) (–2, –3) ANSWER :B

Discussion

34.	A bag contains 4 red and 4 black balls, another bag contains 2 red and 6 black balls. One of the two bags is selected at random and a ball is drawn from the bag which is found to be red. Find the probability that the ball is drawn from the first bag.
Answer» ANSWER :`(2)/(3)`

Discussion

35.	Iff(x)= 2x^4 - 13 x^2 + ax +b isdivisiblebyx^2-3x +2then(a,b)=
Answer» `(-9 ,-2)` `(6,4)` `(9,2)` `(2,9)` ANSWER :C

Discussion

36.	A straight line passing through O(0, 0) cuts the lines x = alpha , y = alphaand x + y = 8 at A, B and C respectively such that OA. OB. OC = 48sqrt 2and f(alpha ,beta ) tl=0 where f(x, y) = \|y/2 - 3/2 \| +(3x - 2y)^6+ sqrt(ex + 2y - 2e - 6) Find the value of (OA + OB + OC)
Answer» `7sqrt2` `8 SQRT2` `9 sqrt2` none of these ANSWER :C

Discussion

37.	Evaluate int x sec^(-1) xdx
Answer» ANSWER :`(X^(2))/(2) SEC^(-1) x - (1)/(2) sqrt(x^(2) - 1) + c`

Discussion

38.	(1 - 1/2)/(3) =
Answer» 6 3 `1//3` `1//6` ANSWER :D

Discussion

39.	Evalute the following integrals int (2x + 3)/((x + 3)(x^(2)+ 4)) dx
Answer» Answer :`-(3)/(10)log\|x+3\|+(3)/(26)log\|x^(2)+4\|+(17)/(26)tan^(-1)((x)/(2))+C`

Discussion

40.	Verify Rolle's theorem for the function y= x^(2) + 2, a = - 2 and b= 2
Answer» ANSWER :F'(C ) = 0 and `c = 0 in (-2, 2)`

Discussion

41.	Match the following . {:("List - I ","List - II"),((1)(1.3)/(1)+(2.4)/(1.2)+(3.5)/(1.2.3)+(4.6)/(1.2.3.4)+....+oo,(a)2/3),((2)(1+(1)/(2!)+(1)/(4!)+(1)/(6!)+....)^2,(b)4e),((3)"coefficient "x^2" in " e^(2x+3),(c) 1),((4) "coefficient of " x^4 " in cosh " (2x),(d) 2e^3):}
Answer» `{:(1,2,3,4),(C,B,d,a):}` `{:(1,2,3,4),(c,b,d,a):}` `{:(1,2,3,4),(c,b,d,a):}` `{:(1,2,3,4),(c,b,d,a):}` ANSWER :B

Discussion

42.	A die is thrown twice and the sum of number appearing is observed to be 7. What is the conditional probabilitythat the number 2 has appeared at least once ?
Answer» ANSWER :`(1)/(3)`

Discussion

43.	If the 4 letter words formed by using the letters of the word EQUATION, a, b, c are respectively the number of words begin with an vowel, begin and end with vowels, end with a consonent then the descending order of a, b, c is
Answer» a,B,C b,c, a c, b, a a, c, b Answer :D

Discussion

44.	State the order of [[1,0,1,4], [2,1,3,0], [-3,2,1,3]]matrices.
Answer» SOLUTION :`(3xx4)`

Discussion

45.	If(x_i y_i) ,i = 1,2,3,4are concyclic points on xy=c^(2) and if y_1. y_2.y_3. y_4 =4then c^(2)=
Answer» 16 4 1 2 Answer :D

Discussion

46.	Let a, b, c, d in R. If the equations 2bx^(2) + 3c x - d = 0 and 2ax^(2) + 3bx + 4c = 0 have a common root and (4bc + ad)/(k(b^(2) - ac)) = (bd + 4c^(2))/(4bc + ad'), then k =
Answer» `(9)/(2)` `(2)/(9)` `(1)/(9)` `(1)/(3)` ANSWER :A

Discussion

47.	(p,q) is called a lattice point if p and q are both integers . How many lattice points lie in the area strictly between the two curves x^(2) + y^(2) = 9 and x^(2) + y^(2) - 6x + 5 = 0 ?
Answer» 0 1 2 3 Solution :Plot the graphs of `y = pm sqrt(9 - x^(2)) ` and `y = pm sqrt(-x^2 + 6x - 5)` in the STANDARD WINDOW , but with FORMAT set to Grid On. The "grid" CONSISTS exactly of the lattice points . ZOOM/Z Box around the area enclosed by the two graphs , and count the number of lattice points in that area to be 3 . The points (1,0) and (3,0) appear close to the boundary , but a mental check finds that (1,0) is on the boundary of the second curve , while (3,0) is on the boundary of the first .

Discussion

48.	Two natural numbers a and b are selected at random, find the probability that a^(2) + b^(2) is divisible by 7.
Answer» ANSWER :`(1)/(49)`

Discussion

49.	A firm manufactures two types of productsA and B and sells tehm at a profit of rs 5 per unit of type A and Rs 3 perunit to type B. One unti of type A requires oneminute ofprocess ign time on M_(1) and two minutes of processing time on M_(2)find out how many units of each type of procuctthe firmshould producve a day in order to maximizethe profitsolve the problemgraphically
Answer» ANSWER :A::B::D

Discussion

50.	Assertion (A): If the circle x^2+y^2+6x-2y+k=0bisects the circumference of the circle x^2+y^2-2x-6y-15=0 , then k is -35. Reason (R) : If a circle bisects the circum ference of another circle, then common chord passes through the centre of the second circle.
Answer» Both ASSERTION and REASON are true and Reason is the CORRECT EXPLANATION of Assertion Both Assertion and Reason are true but Reason is not the correct explanation of Assertion Assertion is true but Reason is false Assertion is false but REASONIS true Answer :A

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

If the equation x^(3) -7x^(2) + 14x -8=0 is trasformed to y^(3) + py - (20)/(27) =0 when its roots are diminshed by k, then p=

If the lines 3x + 4y+ 1 = 0, 5x +lambday + 3 = 0﻿ and 2x + y-1 = 0 are concurrent, then lambda=

If the vector 19hati+22hatj+5hatk bisects an angle between the vectors a and 6hati+8hatj, then the unit vector in the direction of a is

R is circumradii of DeltaABC, H is orthocentre, R_(1), R_(2), R_(3) are circumradii of Delta AHB, Delta BHC. If AH produced meet the circumradii of ABC at M and intersect BC at L, angle AHB =180^(@)-C (c )/(sin (180^(@)-C))=2R_(1) (c)/(sin C) =2R_(1) R_(1)=RArea of Delta AHB

Find (dy)/(dx) of y=sin(logx)

A(2,3) and B(-3,4) be two given points. Find the equation of the locus of P so that the area of the triangle PAB is 8.5 sq.units.

Evalute the following integrals int (1)/(sqrt(1+5x)) dx

int_(1//pi)^(2//pi)(sin(1//x))/(x^(2))dx=

Find the probability of guessing atleast one out of 10 answers in multiple choice question with 4 possible answers.

Differentiate w.r.t x the function (log x)^(log x), x gt 1

For the circle x^(2)+y^(2)-6x+8y-1=0, points (2,3), (-2,-1) are

Coefficient of x^(10) in the expansion of (2+3x)e^(-x) is

If d is the distance between the parallel tangents with positive slope to y^2=4ax and

Integrate the following function : int(x+3)/(sqrt(5-4x+x^(2)))

Equation of a common tangent to the circle x^(2) + y^(2) - 6x = 0 and the parabola, y^(2) = 4x, is

If n is a positive integer and C_(r )= ""^(n)C_(r ) then find the vlaue of sum_(r =1)^(n) r^(2)((C_(r ))/(C_(r -1))).

If cosalpha+cosbeta+cosgamma=sinalpha+sinbeta+singamma=0, then

The vertices of the triangle ABC are A(0, 0), B(3, 0) and C(3, 4), where A and C are foci of an ellipse and B lies on the ellipse. If the length of the latus rectum of the ellipse is (12)/(p) units, then the vlaue of p is

For each of the differential equations in Exercises 11 to 14, find a particular solution satisfying the given condition: 11. (x^(3) + x^(2) + x+ 1)(dy)/(dx) = 2x^(2) + x, y = 1 when x = 0.

For what value of n , (a ^(n +3) + b ^(n +3))/(a ^(n +2) + b ^(n +2)), a ne b in the A.M. of a and b.

int_(0)^(pi) (tan x)/(sec x + cos x) dx=

Find delta f and df when f(x) = 2x^2 - 1, x = 1, delta x = 0 cdot 02

The range of a random variable X={1,2,3,…………..) and the probabilities are given by P(X=k)=(3^(ck))/(k!)(k=1,2,3,………..) and c is a constant . Then c=

If f: R rarrR is defined by f(x) =x^(2)-3x+2 , find f(f(x)).

The transformed equation of 2x^(2) + 4xy+ 5y^(2) - 4x - 22y+7=0 when the axes are translated to the point (-2,3) is

Fivecardsare drawnsuccessivelywithreplacementfromawithreplacementfroma wellshuffleddeckof52cards . Whatisthe probabilitythat I. all fivecardsare spades ? II.Only3 cardsare spades? III.Noneis spade ?

A straight line passing through O(0, 0) cuts the lines x = alpha , y = alphaand x + y = 8 at A, B and C respectively such that OA. OB. OC = 48sqrt 2and f(alpha ,beta ) tl=0 where f(x, y) = |y/2 - 3/2 | +(3x - 2y)^6+ sqrt(ex + 2y - 2e - 6) Find the equation of line OA.

If sum_(r=1)^n I(r)=(3^n -1) , then sum_(r=1)^n 1/(I(r)) is equal to :

A bag contains 4 red and 4 black balls, another bag contains 2 red and 6 black balls. One of the two bags is selected at random and a ball is drawn from the bag which is found to be red. Find the probability that the ball is drawn from the first bag.

Iff(x)= 2x^4 - 13 x^2 + ax +b isdivisiblebyx^2-3x +2then(a,b)=

A straight line passing through O(0, 0) cuts the lines x = alpha , y = alphaand x + y = 8 at A, B and C respectively such that OA. OB. OC = 48sqrt 2and f(alpha ,beta ) tl=0 where f(x, y) = |y/2 - 3/2 | +(3x - 2y)^6+ sqrt(ex + 2y - 2e - 6) Find the value of (OA + OB + OC)

Evaluate int x sec^(-1) xdx

(1 - 1/2)/(3) =

Evalute the following integrals int (2x + 3)/((x + 3)(x^(2)+ 4)) dx

Verify Rolle's theorem for the function y= x^(2) + 2, a = - 2 and b= 2

Match the following . {:("List - I ","List - II"),((1)(1.3)/(1)+(2.4)/(1.2)+(3.5)/(1.2.3)+(4.6)/(1.2.3.4)+....+oo,(a)2/3),((2)(1+(1)/(2!)+(1)/(4!)+(1)/(6!)+....)^2,(b)4e),((3)"coefficient "x^2" in " e^(2x+3),(c) 1),((4) "coefficient of " x^4 " in cosh " (2x),(d) 2e^3):}

A die is thrown twice and the sum of number appearing is observed to be 7. What is the conditional probabilitythat the number 2 has appeared at least once ?

If the 4 letter words formed by using the letters of the word EQUATION, a, b, c are respectively the number of words begin with an vowel, begin and end with vowels, end with a consonent then the descending order of a, b, c is

State the order of [[1,0,1,4], [2,1,3,0], [-3,2,1,3]]matrices.

If(x_i y_i) ,i = 1,2,3,4are concyclic points on xy=c^(2) and if y_1. y_2.y_3. y_4 =4then c^(2)=

Let a, b, c, d in R. If the equations 2bx^(2) + 3c x - d = 0 and 2ax^(2) + 3bx + 4c = 0 have a common root and (4bc + ad)/(k(b^(2) - ac)) = (bd + 4c^(2))/(4bc + ad'), then k =

(p,q) is called a lattice point if p and q are both integers . How many lattice points lie in the area strictly between the two curves x^(2) + y^(2) = 9 and x^(2) + y^(2) - 6x + 5 = 0 ?

Two natural numbers a and b are selected at random, find the probability that a^(2) + b^(2) is divisible by 7.

Assertion (A): If the circle x^2+y^2+6x-2y+k=0bisects the circumference of the circle x^2+y^2-2x-6y-15=0 , then k is -35. Reason (R) : If a circle bisects the circum ference of another circle, then common chord passes through the centre of the second circle.

If the lines 3x + 4y+ 1 = 0, 5x +lambday + 3 = 0 and 2x + y-1 = 0 are concurrent, then lambda=