28278 + Interview Questions in Maths in Class 12

1.	Find all points of dicontinuity of the function f(t)= (1)/(t^(2) + t-2), where t = (1)/(x-1)
Answer» ANSWER :`X = (1)/(2) and x= 2`

Discussion

2.	If A denotes the area bounded by f (x)= \|(sin x + cos x)/(x)\| x axis, x = pi and x = 3 pi then
Answer» 1 LT A lt 3 0 lt A lt 2 2 lt A lt 3 none of these Answer :B

Discussion

3.	Position vector of a point vec(P) is a vector whose initial point is origin.
Answer» ANSWER :TRUE STATEMENT

Discussion

4.	If int(cos^(7)x+cos^(5)x)/(sin^(2)x+sin^(4)x)=-Asin^(3)x+5sinx-(2)/(sinx)-12tan^(-1)+C then A is equal to
Answer» ANSWER :`0.33`

Discussion

5.	Find the coefficient of variation if the sum of squares of the deviations of 10 observations taken from the mean 50 is 250.
Answer» Answer :`=(sigma)/(X)xx100%=(5)/(50)xx100%=10%`

Discussion

6.	Sketch the graph of y = \|x+3\| and evaluate int_(-6)^(0)\|x+3\|dx .
Answer» ANSWER :9

Discussion

7.	int( dx )/( x ( x^(7) +1))is equal to
Answer» `log \| ( X^(7))/( x^(7) +1)\|+C` `(1)/( 7 ) log \| ( x^(7))/( x^(7) + 1) \| +C` `log \| ( x^(7) + 1)/( x^(7)) \| +C` `(1)/( 7) log \| (x^(7) + 1)/( x^(7)) \|+ C` Answer :B

Discussion

8.	Find (dy)/(dx): x=a sin 2t (1+ cos 2t) and y= b cos 2t (1-cos 2t) show that, ((dy)/(dx))_(t = (pi)/(4))= (b)/(a)
Answer» ANSWER :`(B)/(a)`

Discussion

9.	If t_(1) ne t_(2) ne t_(3) and the lines t_(1)x+y=2at_(1)+at_(1)^(3),t_(2)x+y=2at_(2)+at_(2)^(3), t_(3)x+y=2at_(3)+at_(3)^(3) are concurrent then t_(1)+t_(2)+t_(3) is
Answer» 0 -1 1 none ANSWER :A

Discussion

10.	The equation whose roots are reciprocals of the roots of 6x^(6) - 25x^(5) + 31x^(4) - 31x^(2) + 25x - 6 = 0is
Answer» `1,1, -2, - (1)/(2)` `1, (1 pm SQRT(3)i)/(2), (3 pm sqrt(5))/(2) ` 1, -1, -2, -` (1)/(2), 3, (1)/(3)` 2, `(1)/(2), 3 , (1)/(3)` Answer :3

Discussion

11.	In the parabola y^(2) = 4x, the length of the chord passing through the vertex and muking an angle (pi)/(4) with the axis is
Answer» `SQRT(2)` `2sqrt(2)` `4sqrt(2)` `8sqrt(2)` ANSWER :C

Discussion

12.	If the following informations is given about a parabola, then in whichaet parabola is not unique
Answer» FOCUS, EQUATION of TANGENT at vertex focus, vertex equation of directrix, vertex equation of directrix, equation of tangent at vertex ANSWER :D

Discussion

13.	Which of the following is inverse of the proposition :If a number is a prime then it is odd.
Answer» If a NUMBER is not PRIME then it is ODD. if a number is not a prime, then it is not odd. if a number is not odd, then it is not a prime. If a number is not odd, then it is a prime. Answer :B

Discussion

14.	A medical company has factories at two places, A and B.From these places, supply is made to each of its three agencies situated at P,Q, and R.The monthly requirements of the agencies are respectively 40,40 and 50 packets of the medicines, while the production capacity of the factories A and B, are 60 and 60 packets respectively.The transportation costper packet from the factories to the agencies are given below: How many packets from each factory be transported to each agency so that the cost of transportation is minimum? Also find the minimum cost.
Answer» Answer :From A: 10 packets, 0 packet and 50 packet to P,Q and R respectively. From B: 50 packets, 40 packets and 0 packets to P.Q and R respectively.

Discussion

15.	Evaluate the following integrals : int_(0)^(sqrt2)sqrt(2-x^(2))dx
Answer» ANSWER :`(PI)/(2)`

Discussion

16.	Find the angle between the planes 2x - y + z = 6 and x + y + 2 z = 7 .
Answer» ANSWER :D

Discussion

17.	Find adjoint of each of the matrices [{:(3,-2,3),(2,1,-1),(4,-3,2):}]
Answer» ANSWER :`[{:(-1,-5,-1),(-8-6,9),(-10,1,7):}]`

Discussion

18.	Which of the following Is equivalent to (12x^2+4x+5y)+(3x^2-2x+3y)?
Answer» `2x^2-2x+8y` `2x^2+15x+8y` `15x^2-2x+8y` `15x^2+2x+8y` ANSWER :D

Discussion

19.	If Q. 43, (d^(2)y)/(dx^(2)) is equal to
Answer» `sqrt(1+9y^(2))` `(1)/(sqrt(1+9y^(2)))` `9y` `(1)/(9)y` Answer :C

Discussion

20.	Find the condition on a, b and c so that the following system of linear equation has one parametric family of solutions.2x+y+z=ax+3y-2z=b9x+12y-3z=c
Answer» ANSWER :`C = 3a-4b`

Discussion

21.	If alpha,beta, gamma are non-zero vectors such that \|beta\|=\|gamma\|=1 and\| alpha\|= 10, then
Answer» 10 1 0 12 Answer :C

Discussion

22.	Three vectors a=hati+hatj-hatk, b=-hati+2hatj+hatk and c=-hati+2hatj-hatk, then the unit vector perpendicular to both a+b and b+c is
Answer» `(HATI)/(sqrt3)` `6hatk` `(HATK)/(sqrt3)` `(hati+hatj+hatk)/(sqrt3)` SOLUTION :`(a+b) xx (b+c)=3hatj xx (-2hati+4hatj)=6hatk` So, REQUIRED UNIT vector is `6hatk`.

Discussion

23.	A bag contains 17 tickets numbered from 1 to 17. A ticket is drawn at random, the another ticket is drawn without replacing the first one. The probability that both the tickets may show even number is
Answer» `7/34` `8/17` `7/16` `7/17` ANSWER :A

Discussion

24.	cos70^(@)+sin40^(@)=
Answer» `sin10^(@)` `cos10^(@)` `TAN10^(@)` `COT 10^(@)` ANSWER :B

Discussion

25.	Find the number of ways of arranging the letters of the word. SINGING
Answer» ANSWER :`(7!)/(2!2!2!)`

Discussion

26.	Show that P(m,1)+P (n,1)=P(M+n,1)for all positive integers m, n.
Answer» SOLUTION :`""^mP_1+""^(m+N)P_1 AA m,n in Z` `:.L.H.S,=""^mP_1+""^nP_1=m+n=""^(m+n)P_1=R.H.S.` `( :' ""^nP_1=n).`

Discussion

27.	The projection of vectors veca=2hati+3hatj+2hatk on vacb=hati+2hatj+hatk is :
Answer» sqrt5/6 2/3sqrt6 sqrt3/2 5/3sqrt6 Answer :D

Discussion

28.	Which of the following set of points are non-collinear?
Answer» `(1,-1,1),(-1,1,1),(0,0,1)` `(1,2,3),(3,2,1),(2,2,2)` `(-2,4,-3),(4,-3,-2),(-3,-2,4)` `(2,0,-1),(3,2,-2),(5,6,-4)` ANSWER :C

Discussion

29.	The values that can take so that straight line y=4x+n touches the curve x^(2)+4y^(2)=4 is
Answer» `PM 45` `pm sqrt60` `pm sqrt65` `pm sqrt72` ANSWER :C

Discussion

30.	Using elementary transformations, find the inverseof the matrices [(1,-1),(2,3)]
Answer» ANSWER :`[((3)/(5), (1)/(5)),((-2)/(5),(1)/(5))]`

Discussion

31.	Integrate the functions 1/(sqrt(x+a)+sqrt(x+b))
Answer» ANSWER :`2/(3(a-b))[(x+a)^(3/2)-(x+b)^(3/2)]+C`

Discussion

32.	Integrate the following intsinxcosxdx (sinx=v)
Answer» SOLUTION :`intsinxcosxdx` [put sinx=v then COSX DX =dv] `intvdv=(1/2)v^2+C=(1/2)sin^2x+C`

Discussion

33.	f: N rarr R , f(x) = 4x^(2) +12x +5. Show that f: N rarr R is invertible function . Find the inverse of f.
Answer» SOLUTION :N/A

Discussion

34.	If graph of xy = 1 is reflected in y = 2x to give the graph 12x^(2) +rxy +sy^(2) +t = 0, then
Answer» `r = 7` `s =- 12` `t = 25` `r +s =- 19` Solution :Let IMAGE of POINT `A(alpha,beta)` about `y = 2x` is `B (a,b)` `RARR` mid point of AB i.e. `M -= ((alpha +a)/(2),(beta+b)/(2))` lie on `y -2x =0` `rArr ((beta +b)/(2)) =2 ((alpha +a)/(2)) rArr beta +b = 2alpha +2a `(i) and slope of `AB =- (1)/(2)` `rArr (beta-b)/(alpha-a) = -(1)/(2) rArr beta -b =- (1)/(2) alpha +(a)/(2)`(ii) Subtracting (i) and (ii), `rArr 2b = (5)/(2) alpha +(3)/(2) alpha rArr a = (4b-3a)/(5)` `rArr beta=(8b -6a)/(5) +2a - b = (3b+4a)/(5)` `rArr (alpha, beta)` lies on `xy =1` `rArr ((4b-3a)/(5))((3b+4a)/(5)) =1` `rArr 12b^(2) +7ab -12 a^(2) =25` `rArr 12 x^(2) - 7xy =12y^(2) +25 =0`

Discussion

35.	If 0 lt x lt (pi)/(2) then int [ 1+ 2 cot x (cot x " cosecx" )]^(1//2) dx =
Answer» `SQRT("COT x cosec")+C ` `1 LOG \|sin x//2\| + C ` log \|cosecx + COTX \| + C 2 log \| cos x/2\| + C Answer :B

Discussion

36.	Find the mean and variance of the number obtainedon the throw of an unbaised die.
Answer» ANSWER :`(35)/(12)`

Discussion

37.	The solution of (dy)/(dx) = sec(x+y) is
Answer» `SEC(x+y) + TAN (x-y) = C.e^(2x+y)` `sec(x-y) + tan (x-y) = c.e^(2x+y)` `sec(x-y) + tan (x+y) = c.e^(2x+y)` `y = c + tan.(x+y)/(2)` ANSWER :D

Discussion

38.	Let f: N toN be defined by f (n) = {{:((n +1)/( 2 ), if n " is odd" ), ( (n)/(2), "if n is even "):} for all n in N. State whether the function f is bijective. Justify your answer.
Answer» ANSWER :NO

Discussion

39.	The total area of page is 150 cm^(2). The combined width of the margin at the top and bottom is 3 cm and the side 2 cm. What must be the dimensions of the page in order that the area of the printed matter may be maximum ?
Answer» ANSWER :`10 CM XX 15 cm`

Discussion

40.	Find (dy)/(dx) in the following : xy+y^(2)= tan x+y.
Answer» ANSWER :`(SEC^(2)x-y)/(x+2y-1)`

Discussion

41.	let f(x)=(sin4pi[x])/(1+[x]^(2)), where px] is the greatest integer less than or equal to x then
Answer» f(x) is not DIFFERENTIABLE at some points f'(x) exits but is DIFFERENT from zero f'(x) for all x f'(x)=0 but f is not a constant Answer :C

Discussion

42.	The order and degree of the differential equation (dy/dx)^4+3y(d^2y)/dx^2=0 are
Answer» order 1, DEGREE 2 order 2, degree 1 order 2, degree 4 order 4, degree 2 Answer :B

Discussion

43.	Let OA, OB, OC be coterminous edges of a cubboid. If l, m, n be the shortest distances between the sides OA, OB, OC and their respective skew body diagonals to them, respectively, then find(((1)/(l^(2))+(1)/(m^(2))+(1)/(n^(2))))/(((1)/(OA^(2))+(1)/(OB^(2))+(1)/(OC^(2)))).
Answer» ANSWER :2

Discussion

44.	Given four points A(2, 1, 0), B(1, 0, 1), C(3, 0, 1) and D(0, 0, 2). Point D lies on aline L orthogonal to the plane determined by the points A, B and C. The equation of the plane ABC is
Answer» `x+y+z-3=0` `y+z-1=0` `x+z-1=0` `2y+z-1=0` Solution : `""\|{:(x-2,,y-1,,z),(1-2,,0-1,,1-0),(3-2,,0-1,,1-0):}\|=0` `""(x-2)[(-1)-(-1)]-(y-1)[(-1)-1]+z[1+1]=0` or `""2(y-1)+2z=0` or `""y+z-1=0` The VECTOR normal to the PLANE is `vecr= 0hati+hatj+ hatk` The equation of the line through `(0, 0, 2)` and parallel to `vecn` is `vecr = 2hatk+lamda(hatj+hatk)` The perpendicular DISTANCE of `D(0, 0, 2)` from plane `ABC` is `\|(2-1)/(sqrt(1^(2)+1^(2))\|=(1)/(sqrt2)`

Discussion

45.	Evalute the following integrals int (1)/((x + 1) sqrt(2x^(2) + 3x + 1)) " dx, I " sub R - [ - 1, - (1)/(2)]
Answer» Answer :`2 SQRT((2x +1)/(x + 1)) + C `

Discussion

46.	{:(,"List - I",,"List - II"),((1),~(~p) harr "p is " ,(a),(~p vv ~q)),((2),(p ^^ q)^^ (~(p vv q))" is ",(b),"a tautology"),((3),~(p ^^ q)-=,(c ),(~p ^^ ~q)),(,,(d),"a contradiction"):} The correct match is :
Answer» 1-B, 2-a, 3-d 1-b, 2-d, 3-a 1-d, 2-b, 3-a 1-c, 2-a, 3-d Answer :B

Discussion

47.	Assertion (A) : There are three doors to a room. The number of ways in which a student can enter the room and leave it by a different door is 6. Reason (R) : If an operation can be performed in m ways and another operation can be performed in n ways, then the two operations in succession can be performed in mn ways. The correct answer is
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 correct explanation of A A is true but R is FALSE A is false but R is true Answer :A

Discussion

48.	Findthe areaof theregionboundedby they=x^2 -4 ,X- axisand thelinesx=-1 andx=2.
Answer» ANSWER :9 SP UNITS

Discussion

49.	Arathi took 3 examinations in a year. The marks obtained by her in the second and third examinations are more than 5 and 10 respectively than in the first examination. If her average mark is atleast 80, find the minimum mark that she should get in the first examination.
Answer» Answer :ARATHI should get ATLEAST 75 MARKS in the first EXAMINATION.

Discussion

50.	Find the number of ordered pairs of positive integers (a,b) such that a+b= 1000 and neither a nor b has a zero digit. Note that (2, 998) and (998,2) should be counted as two distinct solutions.
Answer» ANSWER :738

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Find all points of dicontinuity of the function f(t)= (1)/(t^(2) + t-2), where t = (1)/(x-1)

If A denotes the area bounded by f (x)= |(sin x + cos x)/(x)| x axis, x = pi and x = 3 pi then

Position vector of a point vec(P) is a vector whose initial point is origin.

If int(cos^(7)x+cos^(5)x)/(sin^(2)x+sin^(4)x)=-Asin^(3)x+5sinx-(2)/(sinx)-12tan^(-1)+C then A is equal to

Find the coefficient of variation if the sum of squares of the deviations of 10 observations taken from the mean 50 is 250.

Sketch the graph of y = |x+3| and evaluate int_(-6)^(0)|x+3|dx .

int( dx )/( x ( x^(7) +1))is equal to

Find (dy)/(dx): x=a sin 2t (1+ cos 2t) and y= b cos 2t (1-cos 2t) show that, ((dy)/(dx))_(t = (pi)/(4))= (b)/(a)

If t_(1) ne t_(2) ne t_(3) and the lines t_(1)x+y=2at_(1)+at_(1)^(3),t_(2)x+y=2at_(2)+at_(2)^(3), t_(3)x+y=2at_(3)+at_(3)^(3) are concurrent then t_(1)+t_(2)+t_(3) is

The equation whose roots are reciprocals of the roots of 6x^(6) - 25x^(5) + 31x^(4) - 31x^(2) + 25x - 6 = 0is

In the parabola y^(2) = 4x, the length of the chord passing through the vertex and muking an angle (pi)/(4) with the axis is

If the following informations is given about a parabola, then in whichaet parabola is not unique

Which of the following is inverse of the proposition :If a number is a prime then it is odd.

Evaluate the following integrals : int_(0)^(sqrt2)sqrt(2-x^(2))dx

Find the angle between the planes 2x - y + z = 6 and x + y + 2 z = 7 .

Find adjoint of each of the matrices [{:(3,-2,3),(2,1,-1),(4,-3,2):}]

Which of the following Is equivalent to (12x^2+4x+5y)+(3x^2-2x+3y)?

If Q. 43, (d^(2)y)/(dx^(2)) is equal to

Find the condition on a, b and c so that the following system of linear equation has one parametric family of solutions.2x+y+z=ax+3y-2z=b9x+12y-3z=c

If alpha,beta, gamma are non-zero vectors such that |beta|=|gamma|=1 and| alpha|= 10, then

Three vectors a=hati+hatj-hatk, b=-hati+2hatj+hatk and c=-hati+2hatj-hatk, then the unit vector perpendicular to both a+b and b+c is

A bag contains 17 tickets numbered from 1 to 17. A ticket is drawn at random, the another ticket is drawn without replacing the first one. The probability that both the tickets may show even number is

cos70^(@)+sin40^(@)=

Find the number of ways of arranging the letters of the word. SINGING

Show that P(m,1)+P (n,1)=P(M+n,1)for all positive integers m, n.

The projection of vectors veca=2hati+3hatj+2hatk on vacb=hati+2hatj+hatk is :

Which of the following set of points are non-collinear?

The values that can take so that straight line y=4x+n touches the curve x^(2)+4y^(2)=4 is

Using elementary transformations, find the inverseof the matrices [(1,-1),(2,3)]

Integrate the functions 1/(sqrt(x+a)+sqrt(x+b))

Integrate the following intsinxcosxdx (sinx=v)

f: N rarr R , f(x) = 4x^(2) +12x +5. Show that f: N rarr R is invertible function . Find the inverse of f.

If graph of xy = 1 is reflected in y = 2x to give the graph 12x^(2) +rxy +sy^(2) +t = 0, then

If 0 lt x lt (pi)/(2) then int [ 1+ 2 cot x (cot x " cosecx" )]^(1//2) dx =

Find the mean and variance of the number obtainedon the throw of an unbaised die.

The solution of (dy)/(dx) = sec(x+y) is

Let f: N toN be defined by f (n) = {{:((n +1)/( 2 ), if n " is odd" ), ( (n)/(2), "if n is even "):} for all n in N. State whether the function f is bijective. Justify your answer.

The total area of page is 150 cm^(2). The combined width of the margin at the top and bottom is 3 cm and the side 2 cm. What must be the dimensions of the page in order that the area of the printed matter may be maximum ?

Find (dy)/(dx) in the following : xy+y^(2)= tan x+y.

let f(x)=(sin4pi[x])/(1+[x]^(2)), where px] is the greatest integer less than or equal to x then

The order and degree of the differential equation (dy/dx)^4+3y(d^2y)/dx^2=0 are

Let OA, OB, OC be coterminous edges of a cubboid. If l, m, n be the shortest distances between the sides OA, OB, OC and their respective skew body diagonals to them, respectively, then find(((1)/(l^(2))+(1)/(m^(2))+(1)/(n^(2))))/(((1)/(OA^(2))+(1)/(OB^(2))+(1)/(OC^(2)))).

Given four points A(2, 1, 0), B(1, 0, 1), C(3, 0, 1) and D(0, 0, 2). Point D lies on aline L orthogonal to the plane determined by the points A, B and C. The equation of the plane ABC is

Evalute the following integrals int (1)/((x + 1) sqrt(2x^(2) + 3x + 1)) " dx, I " sub R - [ - 1, - (1)/(2)]

{:(,"List - I",,"List - II"),((1),~(~p) harr "p is " ,(a),(~p vv ~q)),((2),(p ^^ q)^^ (~(p vv q))" is ",(b),"a tautology"),((3),~(p ^^ q)-=,(c ),(~p ^^ ~q)),(,,(d),"a contradiction"):} The correct match is :

Findthe areaof theregionboundedby they=x^2 -4 ,X- axisand thelinesx=-1 andx=2.

Arathi took 3 examinations in a year. The marks obtained by her in the second and third examinations are more than 5 and 10 respectively than in the first examination. If her average mark is atleast 80, find the minimum mark that she should get in the first examination.

Find the number of ordered pairs of positive integers (a,b) such that a+b= 1000 and neither a nor b has a zero digit. Note that (2, 998) and (998,2) should be counted as two distinct solutions.