28278 + Interview Questions in Maths in Class 12

1.	If the equation of the plane bisecting the line segment joining the points P (3, 2, 4) and Q (-1, 0, -2) and perpendicular to PQ is ax + by + cz + d = 0, then ac + bd
Answer» A0 B12 C6 D1 Answer :A

Discussion

2.	(a.(b xx c))/(b.(c xx a))+(b.(a x b))/(a. (b xx c)) is equal to
Answer» 1 2 0 `oo` Solution :Now, `(a(bxxc))/(B(cxxa))+(b(AXXB))/(a(axxc))=([abc])/(["bca"])+([bab])/(["abc"])` `=1+0=1""[because[bab]=0]`

Discussion

3.	underset ( x to oo) (lim) underset(r=1)overset(n-1) (sum) sqrt((n+r)/(n^2 (n-r) )=
Answer» `pi/2` `(pi+1)/(2)` `(pi+2)/(2)` `(pi-2)/(2)` ANSWER :C

Discussion

4.	Determine for which values of x the function y = (x-2)/(x + 1), x ne -1 is strictly increasing or decreasing.
Answer» ANSWER :`R - (1)`

Discussion

5.	int_(-pi) ^(pi) (sin^(4) x) / (sin ^(4) x + cos^(4)x)dx=
Answer» `PI` `2PI` `pi/2` `(3PI)/2` ANSWER :A

Discussion

6.	Find the locus of the points of trisection of double ordinate of a parabola y^(2)=4ax (agt0)
Answer» ANSWER :`9Y^(2) = 4 AX`

Discussion

7.	When a blood vessels wall is injured, which one of the following phenomenas take place with thrombocyte ?
Answer» AGGLUTINATION Aggregration Activation Adhesion Answer :A

Discussion

8.	A person buys a lottery ticket in 50 lotteries, in each of which his chance of winning and prize is 1/100. What is the probability that he will win a prize. (a) at least once (b) exactly once
Answer» Answer :(a) `1-((99)/(100))^(50)` (b) `(1)/(2)((99)/(100))^(49)` (C) `1-(149)/(100)((99)/(100))^(49)`

Discussion

9.	When the origin is shifted to the point (2,3) and then the coordinate axes are rotated through and angle (pi)/(3) in the counter clockwise sense, then the transformed equation of 3x^(2)+2xy+3y^(2)-18x-22y+50=0 is
Answer» `3x^(2)+3Y^(2)-1=0` `(6+sqrt(3))X^(2)-2XY+(6-sqrt(3))y^(2)-2=0` `4X^(2)+2y^(2)-1=0` `(6-sqrt(3))x^(2)+(6+sqrt(3))y^2+2xy=0` Answer :B

Discussion

10.	A and B arenon-empty sets such that absA = m, absB = n. How many relations can be defined from A to B ? ( Remember that the number of relations is the number of subsets of A xx B) .
Answer» SOLUTION :`absA` = m, `absB` = N `rArr abs (A XX B)` = mn A RELATIONS is a from of A to B =NUMBER of subset of `A xx B` `2^mn (because abs(A xx B) = mn)

Discussion

11.	An instructor has a question bank consisting of 300 easy true /false questions, 200difficult true/ false question, 500 easy multiply choice questions and 400 difficult multiple choice questions. If a question isselected at random from the test bank , what is the probability that it will be an easy question given that it is a multiplechoice question ?
Answer» ANSWER :`(5)/(9)`

Discussion

12.	A: If origin is a limiting point of the coaxal system containing the circlex^(2) + y^(2) + 2gx + 2fy + c = 0then the other limiting point is ((-gc)/(g^(2) + f^(2)), (-fc)/(g^(2) + f^(2)))
Answer» Both A and R are TRUE and R is the correct explanation of A Both A and R are true but R is not CORRCET explanation of A A is true but R is FALSE A is false but R is true . Answer :A::D

Discussion

13.	What are the unit vectors parallel to xy-plane and perpendicular to the vector 4hat(i)-3hat(j)+hat(k)?
Answer» `pm(3HAT(i)+4hat(J))//5` `pm(4hat(i)+3hat(j))//5` `pm(3hat(i)-4hat(j))//5` `pm(4hat(i)-3hat(j))//5` Solution :A vector whose dot product with the vector `4hat(i)-3hat(j)+hat(k)` is zero and MAGNITUDE is 1, will be the required vectors. By TAKING option (a) `pm((3hat(i)+4hat(j)))/(5).(4hat(i)-3hat(j)+hat(k))=(1)/(5)(12-12)=0` Hence, the vector given in option 'a' is the required vector.

Discussion

14.	Let \|{:(y^(5)z^(6)(z^(3)-y^(3)),,x^(4)z^(6)(x^(3)-z^(3)),,x^(4)y^(5)(y^(3)-x^(3))),(y^(2)z^(3)(y^(6)-z^(6)),,xz^(3)(z^(6)-x^(6)) ,,xy^(2)(x^(6)-y^(6))),(y^(2)^(3)(z^(3)-y^(3)),,xz^(3)(x^(3)-z^(3)),,xy^(2)(y^(3)-x^(3))):}\| " and " Delta_(2)= \|{:(x,,y^(2),,z^(3)),(x^(4),,y^(5) ,,z^(6)),(x^(7),,y^(8),,z^(9)):}\| .Then Delta_(1)Delta_(2) is equal to
Answer» ANSWER :4

Discussion

15.	Choose the correct answer . Which of the following differential equation has y = x as one of its particular solution ?
Answer» `(d^2y)/(DX^2) - x^2(dy)/(dx) + XY = x` `(d^2y)/(dx^2) + x(dy)/(dx) + xy = x` `(d^2y)/(dx^2) - x^2(dy)/(dx) + xy = 0` `(d^2y)/(dx^2) + x(dy)/(dx) + xy = 0` ANSWER :C

Discussion

16.	If a = 2i + j - 3k, b = 1 - 2j + k then the vector of length 2 sqrt(3) and perpendicular to both a and b is
Answer» I + J + k I - j - k 2i - 2J + 2k 2i - 2j - 2k Answer :C

Discussion

17.	Ifsin4 A - cos2 A= cos4 A - sin2A(0 ltAlt (pi)/( 4)) then thevalueof tan4Ais
Answer» 1 `(1)/(SQRT(3))` `sqrt(3)` `(sqrt(3)-1)/(sqrt(3)+1)` ANSWER :C

Discussion

18.	Express the following relationson A to B in each case in tabular form : A = { n in N : n le 10 } , B = N f= {(x,y) in A xx B : y = x^2}
Answer» SOLUTION :A = `{N in N : n LE 10}` {1,2,3,…….10}, B = N `therefore` B = {1,2,3,……} `therefore f = {(X,y) in A xx B : y = x^2}` = {(1,1), (2,4), (3,9) ….(10,100)}

Discussion

19.	Consider a matrix A=[a_(ij)[_(3xx3) where, a_(ij)={{:(i+2j,ij="even"),(2i-3j,ij="odd"):}. If b_(ij) is the cafactor of a_(ij) in matrix A and C_(ij)=Sigma_(r=1)^(3)a_(ir)b_(jr), then [C_(ij)]_(3xx3) is
Answer» `[(1,0,0),(0,1,0),(0,0,1)]` `[(-1,5,-7),(4,6,8),(3,9,-3)]` `[(88,0,0),(0,88,0),(0,0,88)]` `[(2,3,1),(1,6,2),(-1,5,2)]` ANSWER :C

Discussion

20.	Assertion (A) : (sqrt3+i)^6+(sqrt3-i)^6=-128 Reason (R): If n is a positive integer then (sqrt3+i)^n+(sqrt3-i)^n=2^(n+1)cos(npi)/(6)
Answer» `2^(n+1)COS(npi)/(2)` `2^(n+1)cos(npi)/(3)` `2^(n+1)cos(npi)/(5)` `2^(n+1)cos(npi)/(6)` ANSWER :D

Discussion

21.	Using the property of determinants andd without expanding in following exercises 1 to 7 prove that \|{:(a-b-c,2a,2a),(2b,b-c-a,2b),(2c,2c,c-a-b):}\|=(a+b+c)^3
Answer» ANSWER :`(a+b+c)^3`

Discussion

22.	The value of int (sin alpha)/(sqrt(1+cos alpha)) dalpha is
Answer» `2sqrt(2) cos (alpha/2) + C` `-2 SQRT(2) cos (alpha//2) + C` `sqrt(2) cos (alpha//2) + C` `-sqrt(2) cos (alpha//2)+C` ANSWER :B

Discussion

23.	The locus of the point, whose chord of contact w.r.t the circlex^(2)+y^(2)=a^(2) makes an angle 2alpha at the centre of the circle is
Answer» `X^(2)+y^(2)=2R^(2)` `x^(2)+y^(2)=r^(2)cos^(2) theta` `x^(2)+y^(2)=(r^(2))/2` `x^(2)+y^(2)=r^(2)sec^(2)theta` Answer :D

Discussion

24.	To receive Grade A in a course , one must obtain an averager of 90 marks or more in five examinations (each 0f 100 marks).If sunita 's' marks in first four examinations are 87, 92,94 and 95, find minimum marks that sunita must obtain in fifthexamination to get Grade 'A' in the course.
Answer» Answer :Sunitha must OBTAIN a minimum of 82 marks to GET 'A' grade in the COURSE.

Discussion

25.	If the differential equation representing the family of all circles touching x-axis at the origin is (x^(2)-y^(2))(dy)/(dx)=g(x)y, then g(x) equals :
Answer» `(1)/(2)x` `2X^(2)` `2x` `(1)/(2)x^(2)` ANSWER :3

Discussion

26.	If y = cos^(-1)x then find (d^2 y)/(dx^2) in terms of y alone.
Answer» ANSWER :`-COT y "COSEC"^(2) y`

Discussion

27.	The value of int_(pi//4)^(pi//3) (dx)/( sinx + tanx) is
Answer» `3//4` `1//2` `2//3- SQRT(2) //2` NONE of these Answer :D

Discussion

28.	Evaluate the following integrals. int(1)/(sqrt(x^(2)+x-2))dx
Answer» ANSWER :`COSH^(-1)((2x+1)/(3))+C`

Discussion

29.	Let L: x-2y+4z=9 be a plane, P(2,1,-1) be a point and O, be the Origin. Q is the foot of the perpendicular from P on the plane L, then (OP)^(2)+(PQ)^(2) is equal to
Answer» `(190)/(21)` `(43)/(21)` `(295)/(21)` `(211)/(21)` ANSWER :C

Discussion

30.	int_(1//2)^(1) (1)/(sqrt(x-x^(2)))dx=
Answer» `PI` 0 `pi/4` `pi/2` ANSWER :D

Discussion

31.	Consider the system of equations ax+by+cz=2 bx+cy+az=2 cx+ay+bz=2 Where a,b,c are real number such that a+b+c=0 Then the system
Answer» has two solutions in INCONSISTANT has UNIQUE solutions has INFINITELY MANY solutions Answer :B

Discussion

32.	Vector bar(a)=6hati-3hatj,bar(b)=2hati-6hatj and bar( c )=-2hati+21hatj are such that bar(alpha)=bar(a)+bar(b)+bar( c ). The vector bar(alpha) is represented as …………….. A component of bar(a) and bar(b).
Answer» `3BAR(a)-2BAR(B)` `2bar(a)-3bar(b)` `3bar(b)-2bar(a)` NONE of these ANSWER :B

Discussion

33.	Evaluate int (a " tan " x - b " cot x " )^(2) dx
Answer» ANSWER :`a^(2) tanx + b^(2) ( - COT X) - (a + b)^(2) x + C`

Discussion

34.	Find the number of 7 letter Palindromes that can be formed using the letters of the word EQUATION
Answer» ANSWER :`8^4`

Discussion

35.	Which of the following has least tendency to form nitride with nitrogen gas?
Answer» Mg CA BA Al Solution :Due to the LESS ionisation energy of barium it is not capable to bread the tripple bond of `N_(2)` so it can't FORM nitrite with nitrogen gas.

Discussion

36.	(Street plan): A city has two main roads which cross each other at the centre of the city. These two roads are along the North-South direction and East_West direction. All the other streets of the city run parallel to these roads and are 200m apart. There are 5 streets in each direaction. Using 1 cm =200cm, draw a model of teh city on your note book. Represent the roads/streets by single lines. There are many cross-streets in your model. A particular cross-street is made by two streets, one running in the North-South directin and another in the East-West direction. Each cross street is rreferred to in the following manner, If the 2 ^(nd) steeet running in teh North-South direction 5 ^(th) in the East-West direction meet at some crossing, then we will call this cross-street (2,5). Using this convection, find: How many cross-streets can be referred at as (4,3)
Answer» ANSWER :There is only ONE cross-street, which can be REFERRED as (4,3)

Discussion

37.	Find the value of cos theta. cos 2theta. cos 2^(2)theta . cos 2^(3)theta"……." cos 2^(n-1) theta is
Answer» `(cos2^(N)theta)/(2^(n)SINTHETA)` `(sin2^(n)theta)/(2^(n)costheta)` `(cos2^(n)theta)/(2^(n)costheta)` `(sin2^(n)theta)/(2^(n)SIN theta)` ANSWER :A

Discussion

38.	Maximize : Z=5y+2x subject to constraints- x+2y le 4, 7x + 8y ge 56, x ge 0, y ge 0. The solution ofthe above LPP is-
Answer» 30 48 36 none of these Answer :D

Discussion

39.	(Street plan): A city has two main roads which cross each other at the centre of the city. These two roads are along the North-South direction and East_West direction. All the other streets of the city run parallel to these roads and are 200m apart. There are 5 streets in each direaction. Using 1 cm =200cm, draw a model of teh city on your note book. Represent the roads/streets by single lines. There are many cross-streets in your model. A particular cross-street is made by two streets, one running in the North-South directin and another in the East-West direction. Each cross street is rreferred to in the following manner, If the 2 ^(nd) steeet running in teh North-South direction 5 ^(th) in the East-West direction meet at some crossing, then we will call this cross-street (2,5). Using this convection, find: How many cross-streets can be referred to as (3,4)
Answer» ANSWER :There is only ONE cross-street, which can be REFERRED as (3,4)

Discussion

40.	write the value of d/dxunderset0overset(x^2)intsintdt
Answer» SOLUTION :`d/dxunderset0overset(x^2)intsintdt=sinx^2(2X)=2xsinx^2`

Discussion

41.	Find the coefficient ofx^(n) in ((1+2x)^(3))/((1-x)^(2))
Answer» SOLUTION :N/A

Discussion

42.	A small firm manufactures gold rings and chains. The combined number or rings and chains manufacured per day is at most 24. It takes 1 hour to make a ring and jalf an hour for a chain. The maximum number of hours available per day is 16. If the profit on a ring is Rs. 300 and that on a chain is rs. 190 how many of each should be manufactured daily so as to maximize the profit?
Answer» Answer :Nuber F rings =8, nuber of chains =16

Discussion

43.	(e^(x) + e^(-x))dy - (e^(x) - e^(-x)) dx = 0
Answer» ANSWER :`y = LOG (E^(X) + e^(-x)) + C`

Discussion

44.	n and r integers such that 1lerlen, then n. ""^(n-1)C_(r-1) is
Answer» `""^(N)C_(R)` `n.""^(n)C_(r)` `r.""^(n)C_(r)` `(n-1)""^(n)C_(r)` ANSWER :C

Discussion

45.	IfP = (tan(3^(n+1)theta - tantheta)
Answer» `P=2Q` `P=3Q` `2P=Q` `3P=Q` ANSWER :A

Discussion

46.	The table above shows some values of the linear function f. Which of the following defines f ?
Answer» F(N)=n-3 f(n) = 2n-4 f(n) = 3n-5 f(n) = 4n-6 ANSWER :C

Discussion

47.	Let p,q, r denote respectively the statements :" you are honest ", "you are laborious ", " you will receive a promotion " Translate ~~r rarr ~~pstatements into English language .
Answer» SOLUTION :If you will not RECEIVE a PROMOTION, then you are not HONEST.

Discussion

48.	If int_(0)^(x)f(z)dz=x+int_(x)^(1)zf(z), then int_(1)^(2)f(x)dx equals
Answer» `1+x` `LOG((2)/(3))` `LOG3` `log((3)/(2))` ANSWER :D

Discussion

49.	If alpha, beta, gamma are roots of the equationx^(3) + px^(2) + qx + r = 0, then (alpha + beta) (beta + gamma)(gamma + alpha) =
Answer» ANSWER :`-PQ +R`

Discussion

50.	If f(x) is continuous at x=pi/2, wheref(x)=(1-sin x)/((pi/2 -x)^(2)), for x!= pi/2, then f(pi/2)=
Answer» `1/2` `(-1)/(2)` `PI/2` `(-pi)/(2)` ANSWER :A

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

If the equation of the plane bisecting the line segment joining the points P (3, 2, 4) and Q (-1, 0, -2) and perpendicular to PQ is ax + by + cz + d = 0, then ac + bd

(a.(b xx c))/(b.(c xx a))+(b.(a x b))/(a. (b xx c)) is equal to

underset ( x to oo) (lim) underset(r=1)overset(n-1) (sum) sqrt((n+r)/(n^2 (n-r) )=

Determine for which values of x the function y = (x-2)/(x + 1), x ne -1 is strictly increasing or decreasing.

int_(-pi) ^(pi) (sin^(4) x) / (sin ^(4) x + cos^(4)x)dx=

Find the locus of the points of trisection of double ordinate of a parabola y^(2)=4ax (agt0)

When a blood vessels wall is injured, which one of the following phenomenas take place with thrombocyte ?

A person buys a lottery ticket in 50 lotteries, in each of which his chance of winning and prize is 1/100. What is the probability that he will win a prize. (a) at least once (b) exactly once

When the origin is shifted to the point (2,3) and then the coordinate axes are rotated through and angle (pi)/(3) in the counter clockwise sense, then the transformed equation of 3x^(2)+2xy+3y^(2)-18x-22y+50=0 is

A and B arenon-empty sets such that absA = m, absB = n. How many relations can be defined from A to B ? ( Remember that the number of relations is the number of subsets of A xx B) .

A: If origin is a limiting point of the coaxal system containing the circlex^(2) + y^(2) + 2gx + 2fy + c = 0then the other limiting point is ((-gc)/(g^(2) + f^(2)), (-fc)/(g^(2) + f^(2)))

What are the unit vectors parallel to xy-plane and perpendicular to the vector 4hat(i)-3hat(j)+hat(k)?

Choose the correct answer . Which of the following differential equation has y = x as one of its particular solution ?

If a = 2i + j - 3k, b = 1 - 2j + k then the vector of length 2 sqrt(3) and perpendicular to both a and b is

Ifsin4 A - cos2 A= cos4 A - sin2A(0 ltAlt (pi)/( 4)) then thevalueof tan4Ais

Express the following relationson A to B in each case in tabular form : A = { n in N : n le 10 } , B = N f= {(x,y) in A xx B : y = x^2}

Consider a matrix A=[a_(ij)[_(3xx3) where, a_(ij)={{:(i+2j,ij="even"),(2i-3j,ij="odd"):}. If b_(ij) is the cafactor of a_(ij) in matrix A and C_(ij)=Sigma_(r=1)^(3)a_(ir)b_(jr), then [C_(ij)]_(3xx3) is

Assertion (A) : (sqrt3+i)^6+(sqrt3-i)^6=-128 Reason (R): If n is a positive integer then (sqrt3+i)^n+(sqrt3-i)^n=2^(n+1)cos(npi)/(6)

Using the property of determinants andd without expanding in following exercises 1 to 7 prove that |{:(a-b-c,2a,2a),(2b,b-c-a,2b),(2c,2c,c-a-b):}|=(a+b+c)^3

The value of int (sin alpha)/(sqrt(1+cos alpha)) dalpha is

The locus of the point, whose chord of contact w.r.t the circlex^(2)+y^(2)=a^(2) makes an angle 2alpha at the centre of the circle is

To receive Grade A in a course , one must obtain an averager of 90 marks or more in five examinations (each 0f 100 marks).If sunita 's' marks in first four examinations are 87, 92,94 and 95, find minimum marks that sunita must obtain in fifthexamination to get Grade 'A' in the course.

If the differential equation representing the family of all circles touching x-axis at the origin is (x^(2)-y^(2))(dy)/(dx)=g(x)y, then g(x) equals :

If y = cos^(-1)x then find (d^2 y)/(dx^2) in terms of y alone.

The value of int_(pi//4)^(pi//3) (dx)/( sinx + tanx) is

Evaluate the following integrals. int(1)/(sqrt(x^(2)+x-2))dx

Let L: x-2y+4z=9 be a plane, P(2,1,-1) be a point and O, be the Origin. Q is the foot of the perpendicular from P on the plane L, then (OP)^(2)+(PQ)^(2) is equal to

int_(1//2)^(1) (1)/(sqrt(x-x^(2)))dx=

Consider the system of equations ax+by+cz=2 bx+cy+az=2 cx+ay+bz=2 Where a,b,c are real number such that a+b+c=0 Then the system

Vector bar(a)=6hati-3hatj,bar(b)=2hati-6hatj and bar( c )=-2hati+21hatj are such that bar(alpha)=bar(a)+bar(b)+bar( c ). The vector bar(alpha) is represented as …………….. A component of bar(a) and bar(b).

Evaluate int (a " tan " x - b " cot x " )^(2) dx

Find the number of 7 letter Palindromes that can be formed using the letters of the word EQUATION

Which of the following has least tendency to form nitride with nitrogen gas?

Find the value of cos theta. cos 2theta. cos 2^(2)theta . cos 2^(3)theta"……." cos 2^(n-1) theta is

Maximize : Z=5y+2x subject to constraints- x+2y le 4, 7x + 8y ge 56, x ge 0, y ge 0. The solution ofthe above LPP is-

write the value of d/dxunderset0overset(x^2)intsintdt

Find the coefficient ofx^(n) in ((1+2x)^(3))/((1-x)^(2))

(e^(x) + e^(-x))dy - (e^(x) - e^(-x)) dx = 0

n and r integers such that 1lerlen, then n. ""^(n-1)C_(r-1) is

IfP = (tan(3^(n+1)theta - tantheta)

The table above shows some values of the linear function f. Which of the following defines f ?

Let p,q, r denote respectively the statements :" you are honest ", "you are laborious ", " you will receive a promotion " Translate ~~r rarr ~~pstatements into English language .

If int_(0)^(x)f(z)dz=x+int_(x)^(1)zf(z), then int_(1)^(2)f(x)dx equals

If alpha, beta, gamma are roots of the equationx^(3) + px^(2) + qx + r = 0, then (alpha + beta) (beta + gamma)(gamma + alpha) =

If f(x) is continuous at x=pi/2, wheref(x)=(1-sin x)/((pi/2 -x)^(2)), for x!= pi/2, then f(pi/2)=

Let p,q, r denote respectively the statements :" you are honest ", "you are laborious ", " you will receive a promotion " Translate r rarr pstatements into English language .