28278 + Interview Questions in Maths in Class 12

1.	If S is circumcentre and 'O' is orthocentre of Delta ABC, then match the following {:(I.,SA + SB + SC,(a),(1)/(2)OS),(II.,OA + OB + OC,(b),2 OS),(III.,AO + OB + OC,(c),2 AS),(IV.,OG,(d),(2)/(3)OS),(,,(e),SO):}
Answer» a, E, C, B e, b, d, c e, b, c, d b, d, c, e ANSWER :C

Discussion

2.	Find the value of the integral underset(0)overset(2pi)int sin^(2)x cos^(4)x dx
Answer» ANSWER :`(PI)/(8)`

Discussion

3.	Ifa, band care unitvectorssuchthata + b+c=0and(a,b)=(pi)/(3) , then\|a xx b \| +\|b xxc \|+\|c xx a\|=
Answer» `3/2` `0` `(3sqrt(3))/(2)` `3` ANSWER :C

Discussion

4.	The tangent to x^(2)//a^(2)+y^(2)//b^(2)=1 meets the major and minor axes in P and Q respectively, then a^(2)//CP^(2)+b^(2)//CQ^(2)=
Answer» ANSWER :1

Discussion

5.	After successfully infiltrating into the castle, Tintin has to send a word back to his island for his army to prepare, so he uses his secret cube technique. He made an hollow glassy rubik’s cube that can be unfolded in any fashion like any normal cube. He inscribed letters on the centre square of each face indicating the orientation of cube which she always keep the same( F-front , B-back, L-left, R-right, U-up , D-down) and also inscribed digits from 1-8 on rest of the squares.The unfolded image of the current configuration is shown in fig_1. He wrote one word on each face in the gaps and rotated left and right face clockwise and also makes an additional rotation. Unfolding the cube in some another way, which is shown in fig_2 , he sends it with his pigeon. How many letters are common on Front and Back face before making any rotations ?
Answer» 2 3 4 None of These Solution :To check which face is rotated check the orientation of CENTER letter of each face which has been changed after the two rotation have been made. Observe along the line UBDF . Wesee that the orientation of the U face is been changed CLOCKWISE. The moves that are made in order are : 1. LEFT face clockwise 2. RIGHT face clockwise 3. UP face clockwise We need to trace back the letters to get them in their ORIGINAL position. For this we have tosee the effect of following moves on the current CONFIGURATION. 1. UP face anticlockwise. 2. RIGHT face anticlockwise. 3. LEFT face anticlokwise. Trace the changes in the letters on each face. i.e. When Up face is rotated clockwise it will change letters in right , left , front , back face willchange. Postions of the letters in the Up face will change and no effect will be observe on the Down face. Similarly Left and Rightface rotation wont effect letters of the other one. Letters can be guessed even when they are rotated. But some letters can have different possiblities like W and M which can be found by OBSERVING the orientation of a nearbylettter. Hence after all the moves are made letters on the face are:: Front face :F D R E A M S Back face: B W O R K Hence the common letter is only R.

Discussion

6.	After successfully infiltrating into the castle, Tintin has to send a word back to his island for his army to prepare, so he uses his secret cube technique. He made an hollow glassy rubik’s cube that can be unfolded in any fashion like any normal cube. He inscribed letters on the centre square of each face indicating the orientation of cube which she always keep the same( F-front , B-back, L-left, R-right, U-up , D-down) and also inscribed digits from 1-8 on rest of the squares.The unfolded image of the current configuration is shown in fig_1. He wrote one word on each face in the gaps and rotated left and right face clockwise and also makes an additional rotation. Unfolding the cube in some another way, which is shown in fig_2 , he sends it with his pigeon. What was the additional rotation that Tintin made?
Answer» Down face CLOCKWISE Rotation Up face counter-clockwise rotation Down Face counter clockwise Rotation Up face clockwise rotation Solution :To check which face is rotated check the orientation of center letter of each face which has been changed after the two rotation have been made. Observe along the line UBDF . Wesee that the orientation of the U face is been changed clockwise. The moves that are made in order are : 1. LEFT face clockwise 2. RIGHT face clockwise 3. UP face clockwise We need to trace back the letters to get them in their original position. For this we have tosee the effect of FOLLOWING moves on the current configuration. 1. UP face ANTICLOCKWISE. 2. RIGHT face anticlockwise. 3. LEFT face anticlokwise. Trace the changes in the letters on each face. i.e. When Up face is rotated clockwise it will change letters in right , left , front , back face willchange. Postions of the letters in the Up face will change and no effect will be observe on the Down face. Similarly Left and Rightface rotation WONT effect letters of the other one. Letters can be guessed even when they are rotated. But some letters can have different possiblities LIKE W and M which can be found by observing the orientation of a nearbylettter. Hence after all the moves are made letters on the face are:: Front face :F D R E A M S Back face: B W O R K Hence the common letter is only R.

Discussion

7.	\|{:(1!,2!,3!),(2!,3!,4!),(3!,4!,5!):}\|=..........
Answer» 5 ! 4 ! 3 ! 2 ! ANSWER :B

Discussion

8.	Find the middle term (s) in the expansion of((3x)/(7) - 2y)^10
Answer» ANSWER :`T_6 = ""^(-10)C_5 (6/7)^5 x^5.y^5`

Discussion

9.	A scientistclaims to haveperfected a technique in which he can spontaneously convert an electroncompletely into energy in the laboratory without any other material required. What is the conclusion about this claim from our current understanding of physics ?
Answer» This is possible because Einstein's equation says that mass and energy are equivalent....it is just very difficult to achieve with electrons This is possible and it is DONE all the time in the high-energy physics labs. The scientist is almost CORRECT... Except that in convertingthe electron to energy, an electron's anti-particle is produced in the PROCESS as well This is not possible because charge conservation WOULD be violated. Solution :Charge is conserved. In ORDER to fully convert an electron into energy, a positron (the electron's antiparticle must be involved). That is, electron + position `- gt` energy, NOT electron `- gt` positron + energy.

Discussion

10.	Four natural numbers are selected at random and are multiplied. The probability that the product is divisible by 5 or 10 is
Answer» `49/625` `369/625` `64/625` `256/625` ANSWER :B

Discussion

11.	If veca and vecb are unit vectors represented by the adjacent sides of a regular hexagon, taken in order, what are the vectors represented by the other sides taken in order?
Answer» Solution :LET `vec(AB)` = `VECA, vec(BC)` = `VECB` `implies vec(AC)` = `veca+vecb` `vec(AD)` = `2vec(BC)`= `2vecb` (therefore `vec(AD)` is parallel to `vec(BC)` and twice of `vec(BC)`) therefore `vec(CD)` = `vec(AD)-vec(AC)` = `2vecb-(veca+vecb)` = `vecb-veca` `vec(DE)` = `-veca` `vec(EF)` = `-vecb` `vec(FA)` = `-vec(CD)` = `veca-vecb`.

Discussion

12.	Let a, b, c be sides of a triangle ABC and Delta denotes its area . Ifa=2, Delta=sqrt(3) and a cosC+sqrt(3) a sinC-b-c=0, then find the value of (b+c). (symbols used have usual meaning in DeltaABC).
Answer» ANSWER :4

Discussion

13.	Number of terms in the extension (9x -2/ (3x) )^11 is-
Answer» `10` `11` `12` `13`

Discussion

14.	has four statements (A,B,C andD) given in Coumn-I and five statements (P,Q,R,S and T) given in Column-II. Any given statement in Column-I can have correct matching with one or more statement(s) given in Column-II. {:(Column-I,Column-II),((A)"A rectangular box has volume 48,and the sum of",(P)1),("length of the twelve edges of the box is 48. The largest",),("integer that could be the length of an edge of the box,is",),((B)"The number of zeroes at the end in the product of first",(Q)2),("20 prime numbers, is"(p),),((C)"The number of solutions of" 2^(2x)-3^(2y)=55 "in which x and y",(R)3),("are integers,is"(0),(S)4),((D)"The number" (7+5sqrt(2))^(1//3)+(7-5sqrt(2))^(1//3)"is equal to",(T)6):}
Answer» <P> ANSWER :T,P,P,Q

Discussion

15.	Let A, B and C be three sets such that P(A) cup P(B) = P( C), then
Answer» `A CAP B = C` `A cup B =C` `A cup B SUBE C` `C sube A cap B` ANSWER :C

Discussion

16.	A point "P" is at the 9 unit distance from the centre of a circle of radius 15 units. The total number of different chords of the circle passing through point P and have integral length is
Answer» ANSWER :A

Discussion

17.	If z = x + iy then the equation of a straight line Ax + By + C = 0 where A, B, C inR, can be written on the complex plane in the form a_z +a_z 2C =0 where ‘a’ is equal to
Answer» `((A+iB))/2` `(A+iB)/2` `A+iB` NONE of these ANSWER :C

Discussion

18.	Let f(x)=lim_(nto oo) (2x^(2n) sin (1)/(x)+x)/(1+x^(2n)) , then which of the following alternative(s) is/ are correct?
Answer» `lim_(XTO OO) XF(x)=2` `lim_(xto1)f(x)` does not exist `lim_(xto0) f(x)` does not exist `lim_(XTOOO) f(x)` is euqal to zero Answer :A::D

Discussion

19.	Let vecalpha=hati+hatj+hatk,vecbeta=hati-hatj-hatk" and "vecgamma=-hati+hatj-hatk be three vectors. A vector vecdelta, in the plane of vecalpha and vecbeta, whose projection on vecgamma is (1)/(sqrt(3)), is given by
Answer» `-HAT(i)-3HAT(J)-3hat(K)` `hati-3hat(j)-3hat(k)` `-hati+3hat(j)+3hat(k)` `hati+3hat(j)-3hat(k)` Answer :B

Discussion

20.	Consider the system of linear equations a_1x+b_1y+c_1z+d_1=0 , a_2x + b_2y+c_2z+d_2=0and a_3x+b_3y+c_3z+d_3=0 . Let us denoteby Delta(a,b,c) the determinant \|(a_1,b_1,c_1),(a_2,b_2,c_2),(a_3,b_3,c_3)\| . IfDelta(a,b,c)ne0, thenthe value of x in the uniquesolutionof the aboveequationsis :
Answer» `(Delta(BCD))/(Delta(ABC))` `(Delta(-bcd))/(Delta(abc))` `(Delta(ACD))/(Delta(abc))` `-(Delta(abd))/(Delta(abc))` Answer :B

Discussion

21.	int (2x^2 - 4x^2 - x - 3 )/(x^2 - 2x - 3)dx =
Answer» `7/2 " log " \| x - 1\| + 3/2 log \| x + 3 \| + C ` `2 log \| x - 1\| + 7/2 log \| x + 3 \| + c` `2x + 1/2 log \| x+ 1\| + 3/4 log \| x - 3 \| + c ` `x^2 + 2 log \| x + 1 \| + 3 log \| x - 3 \| + c ` Answer :D

Discussion

22.	If sec theta" and "tan theta are the roots of ax^(2)+bx+c=0 (a,b ne 0), then the value of sec theta - tan theta is
Answer» `(-a)/(B)` `(-b)/(a)` `(a^2)/(b^2)` `1+(a^2)/(b^2)` ANSWER :A

Discussion

23.	Let a_(n) be the n^(th) term of a G.P of positive integers. Let sum_(n = 1)^(100) a _(2n) = alpha and sum_(n = 1)^(100) a_(2n +1) = beta such that alpha != beta. Then the common ratio is
Answer» `alpha/beta` `beta/alpha` `(alpha/beta)^(1//2)` `(beta/alpha)^(1//2)` ANSWER :B

Discussion

24.	OA, OB, OC are the sides of a rectangular parallelopiped whose diagonals are OO', AA' , BB' and CC' . D is the centre of the rectangle AC'O'B' and D' is the centre of the rectangle O'A'CB' . If the sides OA, OB , OC are in the ratio 1:2:3 , the angleangle DOD' is equal to
Answer» `COS^(-1) (24)/(sqrt697) ` `cos^(-1) (22)/(sqrt619)` `SIN^(-1) (24)/(sqrt697)` `sin^(-1) (22)/(sqrt619)` Answer :A

Discussion

25.	Supposeo ltt lt(pi)/(2) andsint + cost =1/5 thentan "" t/2isequalto
Answer» `2 secx ` ` 2 cosx ` ` sec x` ` COS x ` ANSWER :A

Discussion

26.	If x,y,z are nonzero real number , then the inverse of matrix A= {:[( x,0,0),( 0,y,0) ,( 0,0,z) ]:}is
Answer» `{:[(x^(-1), 0,0),( 0,y^(-1) , 0),( 0,0,Z^(-1))]:} ` `XYZ {:[( x^(-1) ,0,0),( 0,y^(-1) ,0),( 0,0,z^(-1)) ]:}` `(1)/(xyz) {:[( x ,0,0),( 0,y ,0),( 0,0,z) ]:}` `(1)/(xyz) {:[( 1 ,0,0),( 0,1 ,0),( 0,0,1) ]:}` Answer :A

Discussion

27.	The value of the integral int_(-10)^(0) (\|(2\|x\|)/([x]-3x)\|)/(((2\|x\|)/(3x-[x])))dx where [.] denotes the solutions of f(x)+x=0, is
Answer» `(28)/(3)` 0 10 -10 Answer :A

Discussion

28.	Discuss the maxima and minima of the function (x-a)^(p) (x-b )^(q) , where p and q are positive integers.
Answer»

Discussion

29.	Solution of the differential equation : (3tan x=4 cot y-7)sin^(2)ydx-(4 tanx+7 cot y-5)cos^(2)xdy=0 is
Answer» `(3)/(2)cot^(2)X-7 cotx+(7)/(2) TAN^(2)y-5 tany+4 cotx. tany=C` `(3)/(2)tan^(2)x-7 tanx+(7)/(2)cot^(2)y-5 cot y+4tanx. coty=c` `3 tan^(2)y-14cotx.tan^(2)y+7cot^(2)x-10tanycot^(2)x+8cotx. Tany+2c cot^(2)x tan^(2)y=0`. `3 cot^(2)y-14cotx.cot^(2)y+7cot^(2)x+10coty tan^(2)x+8 tan x. coty=0` Answer :B,C

Discussion

30.	Find the number of selections of 10 balls from unlimited of red, black, white and green balls so that the each selection must contains atleast one ball of each colour.
Answer» ANSWER :84

Discussion

31.	Evaluate underset(pi//6)overset(pi//3)int (sqrt(x))/(sqrt(sinx)+sqrt(cosx))dx
Answer» ANSWER :`(PI)/(12)`

Discussion

32.	Find the vector equation of a line passing\| through (2, -1, 1) and parallel to the line whose equations are (x-3)/(2)=(y+1)/(7)=(z-2)/(-3)
Answer» ANSWER :`vecr=2hati-hatj+hatk+lambda(2hati+7hatj-3hatk)`

Discussion

33.	Which one of the following exams has been marked as having the highest Stress Factor?
Answer» CET 1990 CET 1991 CET 1992 CET 1993 Answer :A

Discussion

34.	Find the surface area of the ellipsoid formed by revolving the ellipse (x^(2))/(a^(2)) + (y^(2))/(b^(2))=1 about the x-axis (a gt b)
Answer» <P> ANSWER :`P= 4PI a^(2)`

Discussion

35.	I=int(dx)/(2xsqrt(1-x)sqrt(2-x+sqrt(1-x)))=-(1)/(2sqrt(3))log\|u+(1)/(2)+sqrt(u^(2)+u+(1)/(3))\|+Klog\|v-(1)/(2)+sqrt(v^(2)-v+1)\|+C where u = (1)/(sqrt(1-x)-1)' v = (1)/(sqrt(1-x)+1) then K is equal to
Answer» ANSWER :0.5

Discussion

36.	Given four parallel lines L_1,L_2,L_3 and L_4 Let the distacnes between them be d_(12),d_(23),d_(34) respectively. Let P be a point sum of whose distances from four lines is K (d_(12) lt d_(23) gtd_(34)) . Then the locus of the point P
Answer» q r s p Answer :D

Discussion

37.	(1) Draw the rough sketch of the ellipse (x^(2))/(a^(2)) + (y^(2))/(b^(2)) = 1. Find the area enclosed by the ellipse (x^(2))/(a^(2)) + (y^(2))/(b^(2)) = 1.
Answer» ANSWER :`piab`

Discussion

38.	Let R = {(a,a^3) \| ais a prime number less than 10 } Find R.
Answer» Solution :R = {(a,a^3)\| a is a PRIME NUMBER less than 10 . R = {(2,8),(3,27),(5,125),(7,343)}

Discussion

39.	If 2 cards are drawn from a pack of cards then the probability of getting both red or both kings is
Answer» ANSWER :`(55)/(221)`

Discussion

40.	If the function f(x)=2x^(3)-9ax^(2)+12a^(2)x+1, where a gt 0, attains its maximum and minimum at p and q respectivelt such that p^(2)=q then a is ………..
Answer» `(1)/(2)` 3 1 2 Answer :D

Discussion

41.	The normal at any point P(x_1,y_1) of curve is a line perpendicular to tangent at the point P(x_1,y_1). In case of rectangular hyperbola xy=c^2, the equation of normal at (ct,(c )/(t)) is xt^3-yt-ct^4+c=0. The shortest distance between any two curves always along the common normal. The number of normals drawn from ((7)/(6),4) to parabola y^2=2x-1 is :
Answer» 1 2 3 4 Answer :A

Discussion

42.	The normal at any point P(x_1,y_1) of curve is a line perpendicular to tangent at the point P(x_1,y_1). In case of rectangular hyperbola xy=c^2, the equation of normal at (ct,(c )/(t)) is xt^3-yt-ct^4+c=0. The shortest distance between any two curves always along the common normal. The shortest distance between the parabola 2y^2=2x-1,2x^2=2y-1 is:
Answer» `2sqrt(2)` `(1)/(2sqrt(2))` 4 `SQRT((36)/(5))` ANSWER :B

Discussion

43.	The normal at any point P(x_1,y_1) of curve is a line perpendicular to tangent at the point P(x_1,y_1). In case of rectangular hyperbola xy=c^2, the equation of normal at (ct,(c )/(t)) is xt^3-yt-ct^4+c=0. The shortest distance between any two curves always along the common normal. If normal at (5, 3) of rectangular hyperbola xy-y-2x-2=0 intersect it again at a point:
Answer» `(-1,0)` `(-1,1)` `(0,-2)` `((3)/(4),-14)` ANSWER :D

Discussion

44.	The probability of an event that student gets I, II and III grade in exam is(1)/(10),(3)/(5) and (1)/(4)respectively. Then ......... is the probability that he fails in exam.
Answer» `(197)/(200)` `(27)/(100)` `(83)/(100)` `(127)/(100)` Answer :B

Discussion

45.	From a variable point P tangents are drawn to the ellipse 4x^(2) + 9y^(2) = 36. If the chord of contact is bisected by the line x + y = 1, find the locus of P.
Answer» ANSWER :x+y

Discussion

46.	int_(0)^((pi)/(2))(sin x dx)/(1-cos^(2)+cos^(4)x)
Answer» ANSWER :`(pi)/(4)-(1)/(2sqrt(3))log(2-sqrt(3))`

Discussion

47.	The reaction of 4 - bromobenzylchloride with sodium cyanide in ethanol leads to
Answer» 4-bromobenzylcyanide 4-cyanobenzlychloride 4-cyanbenzyl CYANIDE 4-bromo-2-cyanobenzyl CHLORIDE ANSWER :A

Discussion

48.	show that the given differential equation is homogeneous and solve it. (1 + x^(2))dy + 2xy dx = cot x dx (x ne 0)
Answer» Answer :`y = (1 + x)^(-1) LOG \|sin x\|+ C(1 + x^(2))^(-1)`

Discussion

49.	Integrate the functions 1/(cos^(2)x(1-tanx)^(2))
Answer» ANSWER :`(1)/(1-tanx)+C`

Discussion

50.	If R and S are two non-empty relations on set A, then incorrect statement is :
Answer» R and S are reflexive , then `R CAP S ` is ALSO reflexive . R and S are symmetric , then `R cup S ` is alsosymmetric R and S are transitive , then `R cap S ` is also transitive . R and S are transitive , then `R cup S ` is also transitive. ANSWER :B

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

If S is circumcentre and 'O' is orthocentre of Delta ABC, then match the following {:(I.,SA + SB + SC,(a),(1)/(2)OS),(II.,OA + OB + OC,(b),2 OS),(III.,AO + OB + OC,(c),2 AS),(IV.,OG,(d),(2)/(3)OS),(,,(e),SO):}

Find the value of the integral underset(0)overset(2pi)int sin^(2)x cos^(4)x dx

Ifa, band care unitvectorssuchthata + b+c=0and(a,b)=(pi)/(3) , then|a xx b | +|b xxc |+|c xx a|=

The tangent to x^(2)//a^(2)+y^(2)//b^(2)=1 meets the major and minor axes in P and Q respectively, then a^(2)//CP^(2)+b^(2)//CQ^(2)=

|{:(1!,2!,3!),(2!,3!,4!),(3!,4!,5!):}|=..........

Find the middle term (s) in the expansion of((3x)/(7) - 2y)^10

A scientistclaims to haveperfected a technique in which he can spontaneously convert an electroncompletely into energy in the laboratory without any other material required. What is the conclusion about this claim from our current understanding of physics ?

Four natural numbers are selected at random and are multiplied. The probability that the product is divisible by 5 or 10 is

If veca and vecb are unit vectors represented by the adjacent sides of a regular hexagon, taken in order, what are the vectors represented by the other sides taken in order?

Let a, b, c be sides of a triangle ABC and Delta denotes its area . Ifa=2, Delta=sqrt(3) and a cosC+sqrt(3) a sinC-b-c=0, then find the value of (b+c). (symbols used have usual meaning in DeltaABC).

Number of terms in the extension (9x -2/ (3x) )^11 is-

Let A, B and C be three sets such that P(A) cup P(B) = P( C), then

A point "P" is at the 9 unit distance from the centre of a circle of radius 15 units. The total number of different chords of the circle passing through point P and have integral length is

If z = x + iy then the equation of a straight line Ax + By + C = 0 where A, B, C inR, can be written on the complex plane in the form a_z +a_z 2C =0 where ‘a’ is equal to

Let f(x)=lim_(nto oo) (2x^(2n) sin (1)/(x)+x)/(1+x^(2n)) , then which of the following alternative(s) is/ are correct?

Let vecalpha=hati+hatj+hatk,vecbeta=hati-hatj-hatk" and "vecgamma=-hati+hatj-hatk be three vectors. A vector vecdelta, in the plane of vecalpha and vecbeta, whose projection on vecgamma is (1)/(sqrt(3)), is given by

Consider the system of linear equations a_1x+b_1y+c_1z+d_1=0 , a_2x + b_2y+c_2z+d_2=0and a_3x+b_3y+c_3z+d_3=0 . Let us denoteby Delta(a,b,c) the determinant |(a_1,b_1,c_1),(a_2,b_2,c_2),(a_3,b_3,c_3)| . IfDelta(a,b,c)ne0, thenthe value of x in the uniquesolutionof the aboveequationsis :

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

If sec theta" and "tan theta are the roots of ax^(2)+bx+c=0 (a,b ne 0), then the value of sec theta - tan theta is

Let a_(n) be the n^(th) term of a G.P of positive integers. Let sum_(n = 1)^(100) a _(2n) = alpha and sum_(n = 1)^(100) a_(2n +1) = beta such that alpha != beta. Then the common ratio is

OA, OB, OC are the sides of a rectangular parallelopiped whose diagonals are OO', AA' , BB' and CC' . D is the centre of the rectangle AC'O'B' and D' is the centre of the rectangle O'A'CB' . If the sides OA, OB , OC are in the ratio 1:2:3 , the angleangle DOD' is equal to

Supposeo ltt lt(pi)/(2) andsint + cost =1/5 thentan "" t/2isequalto

If x,y,z are nonzero real number , then the inverse of matrix A= {:[( x,0,0),( 0,y,0) ,( 0,0,z) ]:}is

The value of the integral int_(-10)^(0) (|(2|x|)/([x]-3x)|)/(((2|x|)/(3x-[x])))dx where [.] denotes the solutions of f(x)+x=0, is

Discuss the maxima and minima of the function (x-a)^(p) (x-b )^(q) , where p and q are positive integers.

Solution of the differential equation : (3tan x=4 cot y-7)sin^(2)ydx-(4 tanx+7 cot y-5)cos^(2)xdy=0 is

Find the number of selections of 10 balls from unlimited of red, black, white and green balls so that the each selection must contains atleast one ball of each colour.

Evaluate underset(pi//6)overset(pi//3)int (sqrt(x))/(sqrt(sinx)+sqrt(cosx))dx

Find the vector equation of a line passing| through (2, -1, 1) and parallel to the line whose equations are (x-3)/(2)=(y+1)/(7)=(z-2)/(-3)

Which one of the following exams has been marked as having the highest Stress Factor?

Find the surface area of the ellipsoid formed by revolving the ellipse (x^(2))/(a^(2)) + (y^(2))/(b^(2))=1 about the x-axis (a gt b)

I=int(dx)/(2xsqrt(1-x)sqrt(2-x+sqrt(1-x)))=-(1)/(2sqrt(3))log|u+(1)/(2)+sqrt(u^(2)+u+(1)/(3))|+Klog|v-(1)/(2)+sqrt(v^(2)-v+1)|+C where u = (1)/(sqrt(1-x)-1)' v = (1)/(sqrt(1-x)+1) then K is equal to

Given four parallel lines L_1,L_2,L_3 and L_4 Let the distacnes between them be d_(12),d_(23),d_(34) respectively. Let P be a point sum of whose distances from four lines is K (d_(12) lt d_(23) gtd_(34)) . Then the locus of the point P

(1) Draw the rough sketch of the ellipse (x^(2))/(a^(2)) + (y^(2))/(b^(2)) = 1. Find the area enclosed by the ellipse (x^(2))/(a^(2)) + (y^(2))/(b^(2)) = 1.

Let R = {(a,a^3) | ais a prime number less than 10 } Find R.

If 2 cards are drawn from a pack of cards then the probability of getting both red or both kings is

If the function f(x)=2x^(3)-9ax^(2)+12a^(2)x+1, where a gt 0, attains its maximum and minimum at p and q respectivelt such that p^(2)=q then a is ………..

The probability of an event that student gets I, II and III grade in exam is(1)/(10),(3)/(5) and (1)/(4)respectively. Then ......... is the probability that he fails in exam.

From a variable point P tangents are drawn to the ellipse 4x^(2) + 9y^(2) = 36. If the chord of contact is bisected by the line x + y = 1, find the locus of P.

int_(0)^((pi)/(2))(sin x dx)/(1-cos^(2)+cos^(4)x)

The reaction of 4 - bromobenzylchloride with sodium cyanide in ethanol leads to

show that the given differential equation is homogeneous and solve it. (1 + x^(2))dy + 2xy dx = cot x dx (x ne 0)

Integrate the functions 1/(cos^(2)x(1-tanx)^(2))

If R and S are two non-empty relations on set A, then incorrect statement is :