28278 + Interview Questions in Maths in Class 12

1.	Match the following {:(,"List-I",,"List-II",),((1),(x+2y^(3))(dy)/(dx)=y,(a),e^(tanx),),((2),cos^(2)x(dy)/(dx)+y = tanx,(b),(1)/(x),),((3),log x.(dy)/(dx)+(y)/(x) = sin 2x,(c),(1)/(y),),((4),ydx-xdy+log xdx = 0,(d),\|log x\|,),(,,(e),y,):}
Answer» 1-c, 2-a, 3-d, 4-b 1-a, 2-b, 3-d, 4-c 1-c, 2-d, 3-b, 4-a 1-a, 2-d, 3-b, 4-c Answer :A

Discussion

2.	5 coins are tossed whose faces are marked 2 and 3. If sum of these 5 numbers on the coins is even. Find the probabiltiy that the sum is not less than 12.
Answer» ANSWER :`(15)/(16)`

Discussion

3.	P is a variable point on the line L=0 . Tangents are drawn to the circles x^(2)+y^(2)=4 from P to touch it at Q and R. The parallelogram PQSR is completed. If P -=(3,4), then the coordinates of S are
Answer» `(-46//25,63//25)` `(-51//25,-68//25)` `(-46//25,68//25)` `(-68//25,51//25)` SOLUTION :As `P -=(3,4)` , the equationof QR is `3x+4y=4 `(1) Let ` S -= (x_(1),y_(1))`. S is the MIRROR image of Pw.r.t. (1). Then, `(x_(1)-3)/(3)=(y_(1)-4)/(4)= (-2(3xx3+4xx4-4))/(3^(2)+4^(2))=-(42)/(25)` `:. x_(1)=-(51)/(25),y_(1)=-(68)/(25)` or `S-=(-(51)/(25),-(68)/(25))`

Discussion

4.	P is a variable point on the line L=0 . Tangents are drawn to the circles x^(2)+y^(2)=4 from P to touch it at Q and R. The parallelogram PQSR is completed.If P-= (6,8), then the area of Delta QRS is
Answer» `(3sqrt(6))/(25)` sq. units `(3sqrt(24))/(25)` sq. units `(48sqrt(6))/(25)` sq. units `(192sqrt(6))/(25)` sq. units Solution :`P -= (6,8)` Thereforem the equation of QR (chord of contact ) is `6x+8y=4` or `3x+4y-2=0 ` `:. PM =(48)/(50` and `PQ =SQRT(96)` `QM =sqrt(96-(48^(2))/(25))=sqrt((96)/(25))` `:. QR = 2 sqrt((96)/(25))` `:. ` Area of `Delta PQR =(1)/(2) XX PM xx QR =(192 sqrt(6))/(25)` PQRS is a rhombus. Therefore, Area of `DeltaRS =` Area of `Delta PQR = (192sqrt(6))/(25)`

Discussion

5.	Check the injectivty and surjectiveity of the following functions : (i)f : N to Ngiven by f (x) = x ^(2) (ii) f :Z to Z given by f (x) = x ^(2)
Answer» ANSWER :(i) Injective but not SURJECTIVE (ii) Neither injective nor surjective (iii) Neither injective nor surjective (iv) Injective but not surjective (v) Injective but not surjective

Discussion

6.	Statement-1: If f(x)=int_(1)^(x)(log_(e )t)/(1+t+t^(2))dt, then f(x)=f((1)/(x))for all x gr 0. Statement-2:If f(x)=int_(1)^(x)(log_(e )t)/(1+t)dt, then f(x)+f((1)/(x))=((log_(e )x)^(2))/(2)
Answer» Statement-1 is true, Statement-2 is True,Statement-2 is a correct explanation for Statement-1. Statement-1 is True, Statement-2 is not a correct explanation for Statement-1. Statement-1 is True, Statement-2 is False. Statement-1 is False, Statement-2 is True. Solution :If F(X)`=underset(1)overset(x)int (log_(E )t)/(1+t+t^(2))dt`, then `f((1)/(x))=underset(1)overset(1//x)int (log_(e )t)/(1+t+t^(2))dt` `RARR f((1)/(x))=underset(1)overset(x)int (log_(e )u)/(1+u+u^(2))du`, where `t=(1)/(u)` `rArr f((1)/(x))=f(x)` So, statement-1 is true. If`f(x)=underset(1)overset(x)int (log_(e )t)/(2+t)dt`, then `((1)/(x))=underset(1)overset(1//x)int(log_(e )t)/(1+t)dt` `rArr f((1)/(x))=underset(1)overset(x)int(log_(e )u)/(u(1+u))du`, where `t=(1)/(u)` `rArr f((1)/(x))=underset(1)overset(x)int(log_(e ))/(t(l+t))dt` `:. f(x)+f((1)/(x))=underset(1)overset(x)int (log_(e )t)/(t+1)(1+(1)/(t))dt` `=underset(1)overset(x)int (logt)/(t)dt=[((log_(e )t)^(2))/(2)]_(1)^(x)=((log_(e )x)^(2))/(2)` So, statement-2 is also true.

Discussion

7.	Find the values of a and b such that the function defined by f(x)= {(5,"if" x le 2),(ax + b",","If " 2 lt x lt 10),(21,"If" x ge 10):} is a continuous function
Answer» ANSWER :1

Discussion

8.	The points (2, -1, 3), (-1, 2, -4), (-12, -1, -3), (6, 2, -1) are
Answer» COLLINEAR COPLANAR but not collinear noncoplanar none Answer :B

Discussion

9.	Show that the function given by f(x)=3x+17 is increasing on R.
Answer» ANSWER :`F'(X)GT 0`

Discussion

10.	Parametric form of the equation of the line 3x-6y-2z-15=2x+y-2z-5=0 is
Answer» `(x-5)/(14)=(y)/(2)=(z)/(15)` `(x-1)/(14)=(y-5)/(2)=(z-1)/(15)` `(x-3)/(14)=(y+1)/(2)=(z)/(15)` none of these Answer :C

Discussion

11.	Prove that b^2 + c^2 -a^2 = bc, then A = 60^@
Answer» SOLUTION :`b^2 + c^2 -a^2 = BC` or, `(b^2 + c^2 -a^2)/(ABC) = 1/2` or COSA = 1/2 or A = `60^@`

Discussion

12.	int_0^(pi/2) sin^(1/2x)/(sin^(1/2)x+cos^(1/2)x)dx is equal to :
Answer» 0 (PI)/2 (pi)/3 (pi)/4 Answer :D

Discussion

13.	Find the remainder when 2^(60) is divided with 7.
Answer» SOLUTION :N/A

Discussion

14.	Evaluate the following integrals int_(0)^((16pi)/(3)) \|sin x\|dx
Answer» ANSWER :`(21)/(2)`

Discussion

15.	The value of lim_(x to 0) (cos(sin x)-cos x)/(x^(4)) is equal to
Answer» `1//5` `1//6` `1//4` `1//2` Solution :`underset(x to 0)LIM (COS (sin x)-cos x)/(x^(4))` `underset(x to 0)lim (2sin((x+sinx)/(2))sin((x-sinx)/(2)))/(x^(4))` `2underset(x to 0)lim [(sin ((x+sinx)/(2)))/(((x+sin x)/(2)))xx(sin((x-sinx)/2))/(((x-sin x)/(2)))xx((x +sin x)/(2x))((x-sinx)/(2x^(3)))]` `2underset(x to 0)lim [(sin ((x+sinx)/(2)))/((x+sin x)/(2))xx(sin((x-sinx)/2))/((x-sin x)/(2))xx((1)/(2)+(sin x)/(2x))((x-sinx)/(2x^(3)))]` `=2xx1xx1xx((1)/(2)+(1)/(2)) underset(x to 0)lim (x-sinx)/(2x^(3))` `underset(x to 0)lim (x-sin x)/(x^(3))=underset(x to 0)lim (x-(x-(x^(3))/(3!)+(x^(5))/(5!)-.....))/(x^(3))` `=underset(x to 0)lim ((1)/(3!)-(x^(2))/(5!)+.....)=(1)/(6)`

Discussion

16.	If {{:(ax+b , if x le1),(ax^2+c, if 1 lt x le 2),((dx^2+1)/x,if x ge 2):} Is differentiable on R, then ad- bc =
Answer» 0 1 `-1` 2 Answer :C

Discussion

17.	Observe the following facts for a parabola. (i) Axis of the parabola is the only line which can be the perpendicular bisector of the two chords of the parabola. (ii) If AB and CD are two parallel chords of the parabola and the normals at A and B intersect at P and the normals at C and D intersect at Q, then PQ is a normal to the parabola. For the parabola y^(2)=4x, AB and CD are any two parallel chords having slope 1. C_(1) is a circle passing through O, A and B and C_(2) is a circle passing through O, C and D. C_(1)andC_(2) intersect at
Answer» (4, -4) (-4, 4) (4, 4) (-4, -4) ANSWER :A

Discussion

18.	Observe the following facts for a parabola. (i) Axis of the parabola is the only line which can be the perpendicular bisector of the two chords of the parabola. (ii) If AB and CD are two parallel chords of the parabola and the normals at A and B intersect at P and the normals at C and D intersect at Q, then PQ is a normal to the parabola. The vertex of the parabola passing through (0, 1), (-1, 3), (3, 3) and (2, 1) is
Answer» `(1,1/3)` `(1/3,1)` (1, 3) (3, 1) ANSWER :A

Discussion

19.	Ifalphaisa positiverootof theequationx^4+x^3 -4x^2 +x+1=0thenalpha+1/alpha
Answer» 2 `-2` `3` `4` ANSWER :A

Discussion

20.	Observe the following facts for a parabola. (i) Axis of the parabola is the only line which can be the perpendicular bisector of the two chords of the parabola. (ii) If AB and CD are two parallel chords of the parabola and the normals at A and B intersect at P and the normals at C and D intersect at Q, then PQ is a normal to the parabola. The directrix of the parabola is
Answer» `y-1/24=0` `y+1/24=0` `y+1/12=0` `y-1/12=0` ANSWER :B

Discussion

21.	Statement - I : If z_(1) and z_(2) are two nonzero complex numbers such that \|z_(1) + z_(2) \| = \|z_(1)\| + \|z_(2)\| then arg z_(1) - arg z_(2) is pi//2 Statement - II : z_(1) and z_(2) are two complex numbers such that \|z_(1) z_(2)\| = 1 and arg z_(1)- arg z_(2) is pi//2 then barz_(1) z_(2) = -i
Answer» Only I is TRUE Only II is true Both I and II are true NEITHER I nor II are true ANSWER :B

Discussion

22.	The minimum value of \|z - 1\| + \| z- 2\| + \|z -3\| + \|z - 4\|+ \|z - 5\| is
Answer» 3 5 7 6 Answer :D

Discussion

23.	int ( x^(2) -2x + 3) "In"xdx
Answer» Answer :`((X^(3) )/(3) - x^(2) + 3x) "In" x -(x^3)/( 9) + (x^2)/( 2) - 3x +C`.

Discussion

24.	Find(dy)/(dx) , wheny = e^(-x^(2)) sin (log x)
Answer» Solution : Let ` y = e ^(-X^(2)) sin ( log x ) ` `(dy)/(DX)= e^(-x^(2)) d/(dx) ( sin (log x)) + sin ( log x) d/(dx) (e^(-x^(2)))` ` = e^(-x^(2)) . Cos (LOGX ) . 1/x + sin ( log x) e^(-x^(2) (-2X)`

Discussion

25.	An unbiased coin is tossed to get 2 points for turning up a head and one point for the tail . If three unbiased conis are tossed simultaneously , then the probability of getting a total of odd number of points is ,
Answer» `1/2` `1/4` `1/8` `3/8` ANSWER :A

Discussion

26.	For the angle alpha shown below , which of the following statements is true ?
Answer» `sin ALPHA =-3/5` `cosalpha =4/5` `TAN alpha =-3/4` `COT alpha =-4/3` ANSWER :A

Discussion

27.	Let p in IR, then the differential equation of the family of curves y = (alpha + beta x) e^(px), where alpha, beta are arbitrary constant is
Answer» `y + 4py' + p^(2)= 0` `y" - 2py' + p^(2) y= 0` `Y" + 2 py' - p^(2) y = 0` `y" + 2py' + p^(2) y = 0` ANSWER :B

Discussion

28.	Form the differential equation representing thefamily of curves y = qx where, q is arbitrary constant.
Answer» ANSWER :`X(DY)/(DX) - y = 0`

Discussion

29.	int(log\|x\|)/(x sqrt(1+log\|x\|))dx=...+c.
Answer» `(2)/(3) SQRT(1+log\|x\|)(log\|x\|-5)` `(2)/(3) sqrt(1+log\|x\|)(log\|x\|-2)` `(1)/(3) sqrt(1+log\|x\|)(log\|x\|-2)` `2sqrt(1+log\|x\|)(log\|x\|-2)` Answer :B

Discussion

30.	If angle thetabertween the line (x+1)/1=(y-1)/2=(z-2)/2and the plane 2x-y+sqrt(lambda)z+4=0is such that sin theta=1//3,the value of lambdais a. -3/5 b. 5/3 c. -4/3 d. 3/4
Answer» `-(4)/(3)` `(3)/(4)` `(5)/(3)` `-(3)/(5)` ANSWER :C

Discussion

31.	Let a_(1), a_(2), a_(3) …. a_(n) be in G.P. If the area bounded by the curve y^(2) = 4a_(n) X and y^(2) = 4a_(n) (a_(n) - x) be A_(n), then the sequence A_(1), A_(2), A_(3)…….A_(n) are in
Answer» A.P G.P H.P none of these Answer :B

Discussion

32.	If f(x) = 1+ x/(1!) + x^(2)/(2!)+ x^(3)/(3!) + ------ + x^(n)/(n!) then f(x)=0 (n is odd, n ge 3)
Answer» can't have any REAL root can't have any repeated root has ONE POSITIVE root none of these Answer :B

Discussion

33.	On the parabola = y^(2)=8x. If one extrimity of focal chord is ((1)/(2),-2) then its other extrimity is
Answer» `(8,(1)/(2))` `((1)/(8), -8)` `(2,2)` (8,8) ANSWER :D

Discussion

34.	Integrate the following inte^(x/3)dx
Answer» SOLUTION :`INTE^(x/3)DX [PUT x/3=t then dx=3dt] `inte^tcdot3dt =3e^t+C=3e^(x/3)+C`

Discussion

35.	Find a particular solution of the differential equation (x - y)(dx + dy) = dx - dy given that y = -1, when x = 0.(Hint : put x - y = t)
Answer» ANSWER :`LOG \| X - y\| = x + y + 1`

Discussion

36.	Integrate the following functions : e^(x)((1+xlogx)/(x))
Answer» ANSWER :`E^(X)logx+c`

Discussion

37.	A lamppost stands in the centre of a circular garden and makes angle alpha at point A and B on the boundary where AB subtends an angle 2 beta at the foot of the lamppost. If gamma is the angle which the lamppost subtends at C, the middle point of the line joining A and B, then tan gamma =
Answer» `TAN alpha tan beta` `sec alpha tan beta` `tan alpha sec beta` NONE of these ANSWER :C

Discussion

38.	Solve 3^(1+x)+3^(1-x)=10.
Answer» ANSWER :X= 1, -1

Discussion

39.	If int_(0)^(1)x^(11)e^(-x^(24))dx=A, and int_(0)^(1)x^(3)e^(-x^(8))dx=B, then the relation between A and B is
Answer» `A = 3B` `B = 3A` `A+3B=0` `B+3A=0` ANSWER :B

Discussion

40.	If the roots of (b-c) x^(2)+(c-a)x +(a-b) =0 areequal, then a+c =
Answer» 2B `B^(2)` 3B b ANSWER :a

Discussion

41.	Consider a triangle ABC with vertex A(2, -4). The internal bisectors of the angle B and C are x+y=2 andx- 3y = 6respectively. Let the two bisectors meet at I.If(x_(1), y_(1)) and (x_(2), y_(2)) are the co-ordinates of the point B and C respectively, then the value of(x_(1)x_(2)+y_(1)y_(2)) is equal to :
Answer» 4 5 6 8 Answer :D

Discussion

42.	Insert 10 A.M. between 3 and 80 .
Answer» ANSWER :`10, 17, 24,……..,73.`

Discussion

43.	A contest consists of predicting the result (win, draw and loss) 5 foot ball matches. The probability that an entry contains at least 3 correct answers is
Answer» `17//243` `17//81` `17//27` `9//17` ANSWER :B

Discussion

44.	Evaluate the following lim_(xto1) (x^3 -1)/(x-1)
Answer» SOLUTION :`lim_(xto1) (x^3 -1)/(x-1)` `lim_(xto1)((x-1)(x^2+x+1))/(x-1)` `limto(xto1)(x^2+x+1)` 1+1+1=3

Discussion

45.	Consider f:N to N, g : N to N and h: N to R defined as f (x) =2x,g (h) = 3y + 4 and h (z= sin z, AA x, y and z in N. Show that h(gof) = (hog) of.
Answer» ANSWER :(HOG) o F

Discussion

46.	If z^(2) + z + 1 = 0, where z is a complex number , prove that( z + 1/z)^(2) + ( z^(2) + 1/z^(2)) + (z^(3) + 1/z^(3))^(2) + (z^(4) + 1/z^(4))^(2) + (z^(5) + 1/z^(5)) ^(2) + ( z^(6) + 1/z^(6)) = 12 .
Answer»

Discussion

47.	Let overset(to)(u) " and" overset(to)(v)beunitvectors. If overset(to)(w) is avector suchthatoverset(to)(w) +(overset(to)(w) xx overset(to)(u)) = overset(to)(v) Thenprovethat \|(overset(to)(u) xx overset(to)( v)) . overset(to)(w) \|le .(1)/(2)and that theequalityholdsif andonluy ifoverset(to)(u) is perpendicular to overset(to)(v).
Answer» Solution :Givenequationis `vec(w) +v(vec(w) xx vec(u)) = vec(v)` Takingcrossproductwith `vec(u) ` we get `vec(u) xx [vec(w) + (vec(w) xx vec(u))]=vec(u) xx vec(v)` `rArrvec(u) xx vec(w) + vec(u) (vec(w) xx vec(u)) = vec(u) xx vec(v)` `RARR vec(u) xx vec(w) + (vec(u) "." vec(u)) vec(w)- (vec(u)"." vec(w)) =vec(u) =vec(u) xx vec(v)` Nowtakigndotproductof EQ. (i) with `vec(u)` we get ` vec(u) "." vec(w) +vec(u) "."(vec(w) xx vec(u)) =vec(u) "." vec(v)` `rArr vec(u) ". " vec(w) = vec(u)". " vec(v)[ :' vec(u) . (vec(w) xx vec(u)) =vec(v) "." vec(v)` Nowtakingdot productof Eq. (i) with ` vec(u)` we get ` vec(v) ". " vec(w)+vec(v) ". " (vec(w) xx vec(u)) =vec(v) ". " vec(v)` `rArrvec(v) ". " vec(w) + [vec(v) vec(w) vec(u)]= 1 rArrvec(v)". " vec(w) + [ vec(v) vec(w) vec(u)] -1=0` `rArr-(vec(u) xx vec(u)) ". " vec(w) - vec(v) ". " vec(w) +1=0` `rArr 1-vec(v) ". " vec(w) = (vec(u) xx vec(v)) ". " vec(w)` Takingdotproductof Eq (ii) with`vec(w)` we get `(vec(u)xx vec(w)) ". " vec(w) + vec(w) ". " vec(w)-vec(u)"." vec(w)) (vec(u)"." vec(w)) =(vec(u)xxvec(v))" ."vec(w)` `rArr 0+ \|vec(w)\|^(2) -(vec(u)". " vec(w))^(2) =(vec(u) xx vec(v))"." vec(w)` `rArr (vec(u) xx vec(v)) ". " vec(w) =\|vec(w)\|^(2)-(vec(u) ". " vec(w))^(2)` takingdotproductof Eq. (i) with `vec(w)` we get `vec(w) ". " vec(w) + (vec(w) xx vec(u)) ". " vec(w) = vec(v) ". " vec(w)` `rArr \|vec(w)\|^(2) =1-(vec(u) xx vec(v))"." vec(w)` Again fromEq. (v)we get `(vec(u) xx vec(v)) "."vec(w)\|vec(w)\|^(2) - (vec(u)"." vec(w))^(2) =1- (vec(u) xx vec(v)) "." vec(w) - (vec(u)"."vec(w))^(2)` `rArr 2(vec(u) ". " vec(v)) "." vec(w) =1 - (vec(u)"." vec(v))^(2)` `rArr \|(vec(u) xx vec(w)) "." vec(w)\|=(1)/(2)\|1-(vec(u) "." vec(v))^(2) \|LE (1)/(2) [ :' (vec(u) "." vec(v))^(2) ge 0 ]` Theequality holdsif andonlyif `vec(u)". " vec(v) = 0 " Iff" vec(u)` is perpendicularto `vec(v)`

Discussion

48.	Let R be the relation in the set N given by R={(a,b):a=b -2,b gt 6} choose the correct answer
Answer» `(2,4) in R` `(3,8) in R` `(6,8) in R` `(8,7) in R` ANSWER :C

Discussion

49.	Find the vector and the Cartesian equations of the line through the point (5, 2, - 4) and which is parallel to the vector 3hati+2hatj-8hatk.vecr=(5+3lambda)hati+(2+2lambda)hatj+(-4-8lambda)hatk and certesian equations (x-5)/(3)=(y-2)/(2)=(z+4)/(-8)
Answer» ANSWER :VECTOR EQUATIONS

Discussion

50.	Two cards are drawn in succession from a standard well shuffled pack of 52 card. What is the probability that both the cards are aces if the cards are drawn without replacement ?
Answer» 0.0045 0.0385 0.045 0.0059 Answer :A

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Match the following {:(,"List-I",,"List-II",),((1),(x+2y^(3))(dy)/(dx)=y,(a),e^(tanx),),((2),cos^(2)x(dy)/(dx)+y = tanx,(b),(1)/(x),),((3),log x.(dy)/(dx)+(y)/(x) = sin 2x,(c),(1)/(y),),((4),ydx-xdy+log xdx = 0,(d),|log x|,),(,,(e),y,):}

5 coins are tossed whose faces are marked 2 and 3. If sum of these 5 numbers on the coins is even. Find the probabiltiy that the sum is not less than 12.

P is a variable point on the line L=0 . Tangents are drawn to the circles x^(2)+y^(2)=4 from P to touch it at Q and R. The parallelogram PQSR is completed. If P -=(3,4), then the coordinates of S are

P is a variable point on the line L=0 . Tangents are drawn to the circles x^(2)+y^(2)=4 from P to touch it at Q and R. The parallelogram PQSR is completed.If P-= (6,8), then the area of Delta QRS is

Check the injectivty and surjectiveity of the following functions : (i)f : N to Ngiven by f (x) = x ^(2) (ii) f :Z to Z given by f (x) = x ^(2)

Statement-1: If f(x)=int_(1)^(x)(log_(e )t)/(1+t+t^(2))dt, then f(x)=f((1)/(x))for all x gr 0. Statement-2:If f(x)=int_(1)^(x)(log_(e )t)/(1+t)dt, then f(x)+f((1)/(x))=((log_(e )x)^(2))/(2)

Find the values of a and b such that the function defined by f(x)= {(5,"if" x le 2),(ax + b",","If " 2 lt x lt 10),(21,"If" x ge 10):} is a continuous function

The points (2, -1, 3), (-1, 2, -4), (-12, -1, -3), (6, 2, -1) are

Show that the function given by f(x)=3x+17 is increasing on R.

Parametric form of the equation of the line 3x-6y-2z-15=2x+y-2z-5=0 is

Prove that b^2 + c^2 -a^2 = bc, then A = 60^@

int_0^(pi/2) sin^(1/2x)/(sin^(1/2)x+cos^(1/2)x)dx is equal to :

Find the remainder when 2^(60) is divided with 7.

Evaluate the following integrals int_(0)^((16pi)/(3)) |sin x|dx

The value of lim_(x to 0) (cos(sin x)-cos x)/(x^(4)) is equal to

If {{:(ax+b , if x le1),(ax^2+c, if 1 lt x le 2),((dx^2+1)/x,if x ge 2):} Is differentiable on R, then ad- bc =

Ifalphaisa positiverootof theequationx^4+x^3 -4x^2 +x+1=0thenalpha+1/alpha

Statement - I : If z_(1) and z_(2) are two nonzero complex numbers such that |z_(1) + z_(2) | = |z_(1)| + |z_(2)| then arg z_(1) - arg z_(2) is pi//2 Statement - II : z_(1) and z_(2) are two complex numbers such that |z_(1) z_(2)| = 1 and arg z_(1)- arg z_(2) is pi//2 then barz_(1) z_(2) = -i

The minimum value of |z - 1| + | z- 2| + |z -3| + |z - 4|+ |z - 5| is

int ( x^(2) -2x + 3) "In"xdx

Find(dy)/(dx) , wheny = e^(-x^(2)) sin (log x)

An unbiased coin is tossed to get 2 points for turning up a head and one point for the tail . If three unbiased conis are tossed simultaneously , then the probability of getting a total of odd number of points is ,

For the angle alpha shown below , which of the following statements is true ?

Let p in IR, then the differential equation of the family of curves y = (alpha + beta x) e^(px), where alpha, beta are arbitrary constant is

Form the differential equation representing thefamily of curves y = qx where, q is arbitrary constant.

int(log|x|)/(x sqrt(1+log|x|))dx=...+c.

If angle thetabertween the line (x+1)/1=(y-1)/2=(z-2)/2and the plane 2x-y+sqrt(lambda)z+4=0is such that sin theta=1//3,the value of lambdais a. -3/5 b. 5/3 c. -4/3 d. 3/4

Let a_(1), a_(2), a_(3) …. a_(n) be in G.P. If the area bounded by the curve y^(2) = 4a_(n) X and y^(2) = 4a_(n) (a_(n) - x) be A_(n), then the sequence A_(1), A_(2), A_(3)…….A_(n) are in

If f(x) = 1+ x/(1!) + x^(2)/(2!)+ x^(3)/(3!) + ------ + x^(n)/(n!) then f(x)=0 (n is odd, n ge 3)

On the parabola = y^(2)=8x. If one extrimity of focal chord is ((1)/(2),-2) then its other extrimity is

Integrate the following inte^(x/3)dx

Find a particular solution of the differential equation (x - y)(dx + dy) = dx - dy given that y = -1, when x = 0.(Hint : put x - y = t)

Integrate the following functions : e^(x)((1+xlogx)/(x))

A lamppost stands in the centre of a circular garden and makes angle alpha at point A and B on the boundary where AB subtends an angle 2 beta at the foot of the lamppost. If gamma is the angle which the lamppost subtends at C, the middle point of the line joining A and B, then tan gamma =

Solve 3^(1+x)+3^(1-x)=10.

If int_(0)^(1)x^(11)e^(-x^(24))dx=A, and int_(0)^(1)x^(3)e^(-x^(8))dx=B, then the relation between A and B is

If the roots of (b-c) x^(2)+(c-a)x +(a-b) =0 areequal, then a+c =

Insert 10 A.M. between 3 and 80 .

A contest consists of predicting the result (win, draw and loss) 5 foot ball matches. The probability that an entry contains at least 3 correct answers is

Evaluate the following lim_(xto1) (x^3 -1)/(x-1)

Consider f:N to N, g : N to N and h: N to R defined as f (x) =2x,g (h) = 3y + 4 and h (z= sin z, AA x, y and z in N. Show that h(gof) = (hog) of.

If z^(2) + z + 1 = 0, where z is a complex number , prove that( z + 1/z)^(2) + ( z^(2) + 1/z^(2)) + (z^(3) + 1/z^(3))^(2) + (z^(4) + 1/z^(4))^(2) + (z^(5) + 1/z^(5)) ^(2) + ( z^(6) + 1/z^(6)) = 12 .

Let R be the relation in the set N given by R={(a,b):a=b -2,b gt 6} choose the correct answer

Find the vector and the Cartesian equations of the line through the point (5, 2, - 4) and which is parallel to the vector 3hati+2hatj-8hatk.vecr=(5+3lambda)hati+(2+2lambda)hatj+(-4-8lambda)hatk and certesian equations (x-5)/(3)=(y-2)/(2)=(z+4)/(-8)

Two cards are drawn in succession from a standard well shuffled pack of 52 card. What is the probability that both the cards are aces if the cards are drawn without replacement ?