28278 + Interview Questions in Maths in Class 12

1.	Integrate the following functions: sin^2x/(1+cosx)
Answer» SOLUTION :`INT sin^2x/(1+cosx) = (1-cos^2x)/(1+cosx)` `=((1-cosx)(1+cosx))/(1+cosx) = 1-cosx` THEREFORE` int sin^2x/(1+cosx) DX = x-sinx+c`

Discussion

2.	The vectors from origin to the points A and B are bar(a)=2bar(i)-3bar(j)+2bar(k) and bar(b)=2bar(i)+3bar(j)+bar(k) respectively, then the area of DeltaOAB is equal to …….
Answer» 340 `2sqrt(5)` `SQRT(229)` `(1)/(2)(sqrt(229))` Answer :D

Discussion

3.	For any positive n, let f(n)=(4n+sqrt(4n^(2)-1))/(sqrt(2n+1)+sqrt(2n-1)). Then ((Sigma_(k=1)^(40)f(k))/(100)) is equal to
Answer» ANSWER :3.64

Discussion

4.	Differentiate the functions (x cos x)^(x) + (x sin x)^((1)/(x))
Answer» ANSWER :`(x COS x)^(x) [1- x TAN x + log (x cos x)] + (x sin x)^((1)/(x)) [(x COT x +1 - log (x sin x))/(x^(2))]`

Discussion

5.	In the given .....................
Answer» SOLUTION :At the instant of same energy, energy of CAPACITOR is half of maximum energy. So charge on capacitor is `q_("MAX")/sqrt(2)` so, time REQUIRED for this process is `T/8=1/8 (2pi)/omega=pi/4 sqrt(LC)`

Discussion

6.	If P(A) = 0.8, P(B) = 0.5 and P(B\|A) =0.4 then find P(A cap B).
Answer» <P> ANSWER :`P(A CAP B) = 0.32`

Discussion

7.	Find the equation of parabola whose Vertex is (-1,-2) latus rectum is 4 and axis is parallel toy axis
Answer» ANSWER :`(x+1)^(2)= PM4(y+2)`

Discussion

8.	Draw the region of relation [x][y]= 6, x, y ge 0. Here [*] denotes the greatest integer function.
Answer» Solution :We have `[x][y]= 6, x, y ge 0`. So we have the FOLLOWING CASES. The region satisfying the above conditions is as shown in the following figure.

Discussion

9.	Without expanding prove thatDelta ={:\|( x+y,y+z,z+x) ,( z,x,y),( 1,1,1) \|:} =0
Answer» ANSWER :`DELTA =0 `

Discussion

10.	If the angles of a triangleABC are (pi)/(7), (2pi)/(7)" and " (4pi)/(7) and R is the radius of the circumcircle then a^2 +b^2+ c^2 has the value equal to?
Answer» ANSWER :`7R^2`

Discussion

11.	A farmer has a supply of chemical fertilizer of type A, which contains 10% nitrogen and 5% phospheric acid and type B, which contains 6% nitrogen and 10% phospheric acid.After testing the soil conditions of the field, it was found that at least 14 kg of nitrogen and 14 kg of phospheric acod are required for producing a good crop.The fertilizer of type A costs ₹ 5 per kg and type B costs ₹ 3 per kg.How many kg of each type of the fertilizer should be used to meet the requirement at minimum cost? Using LPP, solve the above problem graphically.
Answer» ANSWER :MINIMUM COST is₹700

Discussion

12.	A circle cuts the parabola y^2=4ax at right angles and passes through the focus , show that its centre lies on the curve y^2(a+2x)=a(a+3x)^2.
Answer» ANSWER : `y^2(a+2x)=a(a+3x)^2`.

Discussion

13.	overline(a)is perpendicular to both overline(b) and overline( c). The angle between overline(b) and overline( c) is (2pi)/(3). If \|overline(a)\|=2, \|overline(b) \|=3, \|overline( c)\|=4, then overline( c) . ( overline( a) xxoverline(b))=
Answer» `18sqrt(3)` `12SQRT(3)` `8sqrt(3)` `6sqrt(3)` ANSWER :B

Discussion

14.	If xy = a, xz = b, yz = c and abc ne 0,find the value of x^2 + y^2 + z^2 in terms of a, b, c.
Answer» Answer :`(sqrt((AB)/C), sqrt((CA)/B), sqrt((bc)/a)) or (-sqrt((ab)/c), -sqrt((ac)/b), -sqrt((bc)/a))`

Discussion

15.	If A+B+C=pi, then prove the following. sin2A+sin2B-sin2C=4cosA cdot cosB cdot sinC
Answer» Solution :L.H.S. =sin2A+sin2B-SIN2C `2sinfrac{2A+2B}{2}cosfrac{2A-2B}{2}-sin2C` `=2SIN(A+B)COS(A-B)-2sinCcosC` `=2sinCcos(A-B)-2sinCcosC` `[becauseA+B=pi-C` or, sin(A+B)=sin(pi-C)=sinC]` `=2sinC[cos(A-B)-cosC]` `=2sinC[cos(A-B)-cos(A+B)]` `=2sinC cdot 2cosA cdot cosB` `=4cosA cosBsinC=R.H.S`

Discussion

16.	For what value fo x [[2x,0,0],[0,1,2],[-1,2,0]]=[[1,0,0],[2,3,4],[0,3,5]] ?
Answer» SOLUTION :`[[2X,0,0],[0,1,2],[-1,2,0]]=[[1,0,0],[2,3,4],[0,3,5]]` or, `2x[[1,2],[2,0]]=1[[3,4],[3,5]]` or, 2x(0-4)=15-12 -8x=3 or, x=-3/8

Discussion

17.	A hare sees a hound 100 m away from her and runs off in the opposite direction at a speed of 12 KM an hour. A minute later the hound perceives her and gives a chase at a speed of 16 KM an hour. The distance at which the hound catches the hare (in meters) is________
Answer» ANSWER :1200 METER

Discussion

18.	int_0^1(dx)/(sqrt(1-x^2)dx
Answer» Solution :`int_0^1(DX)/(SQRT(1-x^2)dx)=[sin^(-1)x]_0^1` sin^(-1)1-sin^(-1)0=pi/2`

Discussion

19.	If f(x) = 3x^(2) + 15x + 5, then the approximate value of f (3.02) is
Answer» 47.66 57.66 67.66 77.66 Answer :D

Discussion

20.	X is a poisson variate with parameter lambda. Then match the following. The correct matching is
Answer» `{:(A,B,C,D),(5,4,2,1):}` `{:(A,B,C,D),(4,5,2,1):}` `{:(A,B,C,D),(5,4,1,2):}` `{:(A,B,C,D),(2,5,1,2):}` ANSWER :C

Discussion

21.	If veca=hati+hatj+hatk,vecb=2hatj-hatj+3hatkandvecc=hati-2hatj+hatk,find a unit vector parallel to the vector 2veca-vecb+3vecc.
Answer» ANSWER :`(3)/(sqrt(22))HATI-(3)/(sqrt(22))HATJ+(2)/(sqrt(22))HATK`

Discussion

22.	From a heap containing 10 pairs of shoes 6 shoes are selected at random. Find the probability that (i) There is no complete pair in the selected shoes (ii) atleast one correct pair in the selected shoes (iii) 2 correct pairs in the selected shoes.
Answer» Answer :`(i) (.^(10)C_(6)xx2^(6))/(.^(20)C_(6))` `(II) (211)/(323)` `(III) (42)/(323)`

Discussion

23.	If O and O' denote respectively the circumcente and orthocentre of Delta ABC, then O' A + O' B + O' C is equal orthocentre of delta ABC, then O'A + O' B + O' C is equal to
Answer» O' O O O ' 20'0 O Solution :Let G be the CENTROID of Delta ABC. Then, O', G, O are collinear and G divides O' O in the ratio 2 : 1` I, e, (O' G)/ (OG)= 2/1 ` Now, we have `OA+OB + OC = 3OG` `implies OA+ OB + OC = 2OG + OG` `implies OA + OB + OC = GO + OG""[:'2OG=GO ]` `impliesOA +OB+OC=OO'`

Discussion

24.	In a box containing 15 bulbs, 5 are defective. If 5 bulbs are selected at random from the box, find the probability of the event, that (i) None of them is defective (ii) Only one of them is defective. (iii) Atleast one of them is defective.
Answer» Answer :(a) `(12)/(143)` (B) `(50)/(143)` (C) `(131)/(143)`

Discussion

25.	Find the graph of linear inequation in xy plane 4x+8 gt 0
Answer»

Discussion

26.	Find the area of the region bounded by the curve y = x^(2) and the line y = 4.
Answer» ANSWER :(32)/(3)`

Discussion

27.	Let f :R to R be a differentiable function satisfying: f (xy) =(f(x))/(x) AAx, y in R ^(+)also f (1)=0,f '(1) =1 find lim _(x to e) [(1)/(f (x))](where [.] denotes greatest integer function).
Answer» ANSWER :2

Discussion

28.	If vectors -3bar(i)+4bar(j)+lambdabar(k),mubar(i)+8bar(j)+6bar(k) are collinear vectors then find lambda & mu.
Answer» ANSWER :`lamda=3,mu=-6`

Discussion

29.	Orthocentre of the triangle formed by the lines 3x^(2)+8xy-y^(2)=0 and x+2y-3=0 is
Answer» `((3)/(5), (6)/(5))` `((6)/(5), (3)/(5))` `((-6)/(5), (-12)/(5))` `((12)/(5), (6)/(5))` ANSWER :C

Discussion

30.	If A and B be subsets of a set X. Then
Answer» `(A)/(B)=AUUB` `(A)/(B)=ANNB` `(A)/(B)=A'nnB` `(A)/(B)=AnnB'` ANSWER :D

Discussion

31.	The tangents of the angles subtended by a tower at four points A, B, C and D on the ground are in H.P. If O be the foot of the tower on the ground, then
Answer» OA + OC = OB + OD OA + OB = OC + OD OA + OD = OB + OC AB + CD = BC + CD Answer :C

Discussion

32.	Which of the following functions are decreasing on 0,(pi)/(2) ?
Answer» COS x cos 2x cos 3x tan x Answer :A::B

Discussion

33.	If omega , omega^(2) are cube root of unity then, omega/1+omega^(2) + omega/1+omega =
Answer» `-2OMEGA^(2)` `-2omega` 2 -2 Answer :D

Discussion

34.	Find the number of integral solutions of x_(1)+x_(2)+x_(3)+x_(4)=4 where each x_(i)ge-10
Answer» ANSWER :`=""^(47)C_(3)`

Discussion

35.	Find the principle value of the followingcosec^(-1)(2)
Answer» SOLUTION :We KNOW `SIN (pi/6)=1/2 RARR cosec (pi/6)=2` and `pi/6 in [-pi/2,pi/2]-{0}` `therefore` The principal value of `cosec^(-1)(2)=pi/6`

Discussion

36.	From the top of the hill h metres high the angles of depression of the topand the bottom of a pillar are alpha and beta respectively. The height ( in metres) of the pillar is
Answer» `(H (tanbeta-tanalpha))/(tanbeta)` `(h (tanalpha-tanbeta))/(tanalpha)` `(h (tanbeta+tanalpha))/(tan BETA)` `(h(tanbeta+tanalpha))/(tan ALPHA)` ANSWER :A

Discussion

37.	Thequotientobtainedwhenx^4 + 11 x^3-44 x^2 + 76x+ 48isdividedbyx^2 -2x+1 is
Answer» `x^2 -13 x +5` `x^2 +13 x-19` `x^2 -13x +19` `x^2 +13x +25` ANSWER :B

Discussion

38.	(dy)/(dx) = sin^(-1)x
Answer» Answer :`y = X SIN^(-1)x + sqrt(1 - x^(2)) + C`

Discussion

39.	If triangle ABC (Fig 10.18), which of the following is not true : (A) vec(AB)+vec(BC)+vec(CA)=vec(0) (B) vec(AB)+vec(BC)-vec(AC)=vec(0) ( C ) vec(AB)+vec(BC)-vec(CA)=vec(0) (D) vec(AB)-vec(CB)+vec(CA)=vec(0)
Answer» ANSWER :(A), (B) and (D) are TRUE and ( C ) is not true.

Discussion

40.	int x^(3) cos (x^(2)) dx =
Answer» `(1)/(2) [X^(2) sin(x^(2)) - cos (x^(2)) ] + c ` `(1)/(3) [x^(2) sin (x^(2)) + cos(x^(2)) ] + c` `(1)/(2) [ x^(2) sin(x^(2)) + cos (x^(2)) ] + c ` `(1)/(3) [x^(2) sin(x^(2)) - cos (x^(2)) ] + c` ANSWER :C

Discussion

41.	If three fair dice are thrown and the sum is an odd number, then the probability that all the three dice show an odd number is
Answer» `(3)/(4)` `(1)/(2)` `(5)/(6)` `(1)/(4)` ANSWER :D

Discussion

42.	A coin is tossed thrice. In which of the following cases events are independent ? (i) A = In first toss head is obtained. B = In last toss tail is obtained. (ii) A = Head obtained twice B = Last toss result is head. (iii) A = Head obtained in odd tossed. B = Tail obtained in odd tossed.
Answer» ANSWER :(i) Are INDEPENDENT

Discussion

43.	Let \|A\| be square matrix of order 3 and \|A\| = 6, then \|2A\| =
Answer» 12 72 24 48 Answer :D

Discussion

44.	int e^(x). "(cot x- cosec"^(2)" x) dx "
Answer» ANSWER :` E^(X). COT x+c`

Discussion

45.	If P(A)=(6)/(11), P(B)=(5)/(11) amd P(A cup B)=(7)/(11), find (i) P(A cap B) (ii) P(A\|B) (iii) P(B\|A)
Answer» ANSWER :(i) `(4)/(11)`, (ii) `(4)/(5)`, (iii) `(2)/(3)`

Discussion

46.	If 2 int_(0)^(1) tan^(-1) x dx = int_(0)^(1) cot^(-1) (1- x+x^(2))dx, then int_(0)^(1) tan^(-1) (1-x+x^(2))dx is equal to
Answer» `pi/2 + LOG 2` `log 2` `pi/4 + log 4` `log 4` ANSWER :B

Discussion

47.	For which of the following values of m, is the area of the region bounded by the curve y=x-x^(2) and the line y = mx equals (9)/(2) ?
Answer» `-4` `-2` 2 4 Answer :B::D

Discussion

48.	A straight line with slope 3 intersects a straight line with slope 6 at the point (30,40). Then the difference between the y-intercepts of the straight lines is
Answer» 60 70 80 90 Answer :D

Discussion

49.	If sin^(-1)(3/x)+sin^(-1)(4/x)=pi/2, thenx is equal to
Answer» 3 5 7 11 Answer :B

Discussion

50.	If [.] denotes the greatest integer functin, then the integral int _(0)^(x//2) (e^(sinx-(sinx))d(sin^(2) x- [sin^(2)x]))/(sin x- [sin x]) is lamda, then [lamda -1] is equal to:
Answer» 0 1 2 3 Answer :C

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Integrate the following functions: sin^2x/(1+cosx)

The vectors from origin to the points A and B are bar(a)=2bar(i)-3bar(j)+2bar(k) and bar(b)=2bar(i)+3bar(j)+bar(k) respectively, then the area of DeltaOAB is equal to …….

For any positive n, let f(n)=(4n+sqrt(4n^(2)-1))/(sqrt(2n+1)+sqrt(2n-1)). Then ((Sigma_(k=1)^(40)f(k))/(100)) is equal to

Differentiate the functions (x cos x)^(x) + (x sin x)^((1)/(x))

In the given .....................

If P(A) = 0.8, P(B) = 0.5 and P(B|A) =0.4 then find P(A cap B).

Find the equation of parabola whose Vertex is (-1,-2) latus rectum is 4 and axis is parallel toy axis

Draw the region of relation [x][y]= 6, x, y ge 0. Here [*] denotes the greatest integer function.

Without expanding prove thatDelta ={:|( x+y,y+z,z+x) ,( z,x,y),( 1,1,1) |:} =0

If the angles of a triangleABC are (pi)/(7), (2pi)/(7)" and " (4pi)/(7) and R is the radius of the circumcircle then a^2 +b^2+ c^2 has the value equal to?

A circle cuts the parabola y^2=4ax at right angles and passes through the focus , show that its centre lies on the curve y^2(a+2x)=a(a+3x)^2.

overline(a)is perpendicular to both overline(b) and overline( c). The angle between overline(b) and overline( c) is (2pi)/(3). If |overline(a)|=2, |overline(b) |=3, |overline( c)|=4, then overline( c) . ( overline( a) xxoverline(b))=

If xy = a, xz = b, yz = c and abc ne 0,find the value of x^2 + y^2 + z^2 in terms of a, b, c.

If A+B+C=pi, then prove the following. sin2A+sin2B-sin2C=4cosA cdot cosB cdot sinC

For what value fo x [[2x,0,0],[0,1,2],[-1,2,0]]=[[1,0,0],[2,3,4],[0,3,5]] ?

A hare sees a hound 100 m away from her and runs off in the opposite direction at a speed of 12 KM an hour. A minute later the hound perceives her and gives a chase at a speed of 16 KM an hour. The distance at which the hound catches the hare (in meters) is________

int_0^1(dx)/(sqrt(1-x^2)dx

If f(x) = 3x^(2) + 15x + 5, then the approximate value of f (3.02) is

X is a poisson variate with parameter lambda. Then match the following. The correct matching is

If veca=hati+hatj+hatk,vecb=2hatj-hatj+3hatkandvecc=hati-2hatj+hatk,find a unit vector parallel to the vector 2veca-vecb+3vecc.

From a heap containing 10 pairs of shoes 6 shoes are selected at random. Find the probability that (i) There is no complete pair in the selected shoes (ii) atleast one correct pair in the selected shoes (iii) 2 correct pairs in the selected shoes.

If O and O' denote respectively the circumcente and orthocentre of Delta ABC, then O' A + O' B + O' C is equal orthocentre of delta ABC, then O'A + O' B + O' C is equal to

In a box containing 15 bulbs, 5 are defective. If 5 bulbs are selected at random from the box, find the probability of the event, that (i) None of them is defective (ii) Only one of them is defective. (iii) Atleast one of them is defective.

Find the graph of linear inequation in xy plane 4x+8 gt 0

Find the area of the region bounded by the curve y = x^(2) and the line y = 4.

Let f :R to R be a differentiable function satisfying: f (xy) =(f(x))/(x) AAx, y in R ^(+)also f (1)=0,f '(1) =1 find lim _(x to e) [(1)/(f (x))](where [.] denotes greatest integer function).

If vectors -3bar(i)+4bar(j)+lambdabar(k),mubar(i)+8bar(j)+6bar(k) are collinear vectors then find lambda & mu.

Orthocentre of the triangle formed by the lines 3x^(2)+8xy-y^(2)=0 and x+2y-3=0 is

If A and B be subsets of a set X. Then

The tangents of the angles subtended by a tower at four points A, B, C and D on the ground are in H.P. If O be the foot of the tower on the ground, then

Which of the following functions are decreasing on 0,(pi)/(2) ?

If omega , omega^(2) are cube root of unity then, omega/1+omega^(2) + omega/1+omega =

Find the number of integral solutions of x_(1)+x_(2)+x_(3)+x_(4)=4 where each x_(i)ge-10

Find the principle value of the followingcosec^(-1)(2)

From the top of the hill h metres high the angles of depression of the topand the bottom of a pillar are alpha and beta respectively. The height ( in metres) of the pillar is

Thequotientobtainedwhenx^4 + 11 x^3-44 x^2 + 76x+ 48isdividedbyx^2 -2x+1 is

(dy)/(dx) = sin^(-1)x

If triangle ABC (Fig 10.18), which of the following is not true : (A) vec(AB)+vec(BC)+vec(CA)=vec(0) (B) vec(AB)+vec(BC)-vec(AC)=vec(0) ( C ) vec(AB)+vec(BC)-vec(CA)=vec(0) (D) vec(AB)-vec(CB)+vec(CA)=vec(0)

int x^(3) cos (x^(2)) dx =

If three fair dice are thrown and the sum is an odd number, then the probability that all the three dice show an odd number is

A coin is tossed thrice. In which of the following cases events are independent ? (i) A = In first toss head is obtained. B = In last toss tail is obtained. (ii) A = Head obtained twice B = Last toss result is head. (iii) A = Head obtained in odd tossed. B = Tail obtained in odd tossed.

Let |A| be square matrix of order 3 and |A| = 6, then |2A| =

int e^(x). "(cot x- cosec"^(2)" x) dx "

If P(A)=(6)/(11), P(B)=(5)/(11) amd P(A cup B)=(7)/(11), find (i) P(A cap B) (ii) P(A|B) (iii) P(B|A)

If 2 int_(0)^(1) tan^(-1) x dx = int_(0)^(1) cot^(-1) (1- x+x^(2))dx, then int_(0)^(1) tan^(-1) (1-x+x^(2))dx is equal to

For which of the following values of m, is the area of the region bounded by the curve y=x-x^(2) and the line y = mx equals (9)/(2) ?

A straight line with slope 3 intersects a﻿ straight line with slope 6 at the point﻿ (30,40). Then the difference between the﻿ y-intercepts of the straight lines is﻿

If sin^(-1)(3/x)+sin^(-1)(4/x)=pi/2, thenx is equal to

If [.] denotes the greatest integer functin, then the integral int _(0)^(x//2) (e^(sinx-(sinx))d(sin^(2) x- [sin^(2)x]))/(sin x- [sin x]) is lamda, then [lamda -1] is equal to:

A straight line with slope 3 intersects a straight line with slope 6 at the point (30,40). Then the difference between the y-intercepts of the straight lines is