28278 + Interview Questions in Maths in Class 12

1.	The sum of three numbers in A.P. is 27, and their product is 504, find them.
Answer» ANSWER :`4,9,14`

Discussion

2.	ABCD is a square of side l. A line parallel to the diagonal BD at a distance 'x' from the vertex A cuts two adjacentsides. Express the area of the segment of the square with A at a vertex, as a function of x. Find this area at x=1//sqrt(2) and at x=2, when l=2.
Answer» Solution :There are TWO CASES CASE -I : when `x=AP le OA, i.e., x le (l)/(sqrt(2))` `:. Ar(triangle AEF)=(1)/(2)x,2x=x^(2) "" ( :' PE =PF=AP=x)` Case-II : when` x=AP gt OA, i.e., x gt (l)/(sqrt(2)) " but " x le sqrt(2) l` `ar(ABEFDA)=ar(ABCD)-ar( triangle CFE)` `=l^(2)-(1)/(2)(sqrt(2)l-x)*2(sqrt(2)l-x) "" [ :' CP=sqrt(2)l-x]` `=l^(2)-(2L^(2)+x^(2)-2sqrt(2)lx)=2sqrt(2)lx-x^(2)-l^(2)` So, the required function s(x) is `s(x) ={(x^(2)","0le x le (l)/(sqrt(2))),(2sqrt(2)lx-x^(2)-l^(2)","(l)/(sqrt(2)) lt x le sqrt(2)l):}` ` :. s(x) ={((1)/(2)" at " x=(1)/(sqrt(2))),(8(sqrt(2)-l)" at " x=2):}`

Discussion

3.	underset(x to pi//2)"Lt" [sin x]=
Answer» 1 0 `-1` none Answer :B

Discussion

4.	Find the area enclosed between the curves y= 2-x^(2) and y= x^(2)
Answer» ANSWER :`((8)/(3))`

Discussion

5.	Find the equation of the circle for which the point given below are the end points of a diameter. (0,0) ,(8,5)
Answer» ANSWER :` X^(2)+ y ^(2)-8x -5Y =0`

Discussion

6.	If 7l^(2)-9m^(2) + 8l + 1 = 0and we have to find equation of circle having lx + my + 1 = 0 is a tangent and we can adjust given condition as16l^(2) + 8l + 1 = 9(l^(2) + m^(2)) or (4l + 1)^(2) = 9(l^(2) + m^(2)) rArr (\|1 4l+1\|)/(sqrt((l^(2) + m^(2)))) = 3 Centre of circle = (4, 0) and radius = 3 when any two non parallel lines touching a circle, then centre of circle lies on angle bisector of lines. On the basis of above information, answer the following questions : If 4l^(2) – 5m^(2) + 6l + 1 = 0, then the centre and radius of the circle which have lx + my + 1 = 0 is a tangent is
Answer» `(0, 4), SQRT(5)` `(4, 0), sqrt(5)` `(0, 3), sqrt(5)` `(3, 0), sqrt(5)` Answer :D

Discussion

7.	For the circle C with the equation x^(2)+y^(2)-16x-12y+64=0 match the list-I with the list-II given below:
Answer» I) d. ii). B, iii). a, iv). C I) d. ii). a, iii). b, iv). e I) c. ii). d, iii). a, iv). b I) c. ii). e, iii). b, iv). a Answer :C

Discussion

8.	If 7l^(2)-9m^(2) + 8l + 1 = 0and we have to find equation of circle having lx + my + 1 = 0 is a tangent and we can adjust given condition as16l^(2) + 8l + 1 = 9(l^(2) + m^(2)) or (4l + 1)^(2) = 9(l^(2) + m^(2)) rArr (\|1 4l+1\|)/(sqrt((l^(2) + m^(2)))) = 3 Centre of circle = (4, 0) and radius = 3 when any two non parallel lines touching a circle, then centre of circle lies on angle bisector of lines. On the basis of above information, answer the following questions : If 16l^(2) + 9m^(2) = 24lm + 6l + 8m + 1 and if S be the equation of the circle having lx + my + 1 = 0 is a tangent when the equation of director circle of S is
Answer» `X^(2) + y^(2) + 6X + 8y = 25` `x^(2) + y^(2) - 6x + 8y = 25` `x^(2) + y^(2) - 6x - 8y = 25` `x^(2) + y^(2) + 6x - 8y = 25` ANSWER :C

Discussion

9.	The sum of last ten coefficients in the expansion of(1+x)^(19) when expanded in ascending powers ofxis
Answer» `2^(18)` `2^(19)` `2^(18)-""^(19)C_(10)` NONE of these Answer :B

Discussion

10.	Whenf: R to Rand g: R to Rare two functions defined by f(x)= 8x^(3)and g(x) == x^((1)/(3)) respectivelyand (g of ) (x) = k (f o g ) (x) , then k is
Answer» `4` ` 2` ` (1)/(2)` NONE of these ANSWER :A

Discussion

11.	Using the letters of the word 'RAM' How many 6 letter words can be prepared so that all the 3 letters are to appear in the same word atleast once.
Answer» ANSWER :540

Discussion

12.	If 7l^(2)-9m^(2) + 8l + 1 = 0and we have to find equation of circle having lx + my + 1 = 0 is a tangent and we can adjust given condition as16l^(2) + 8l + 1 = 9(l^(2) + m^(2)) or (4l + 1)^(2) = 9(l^(2) + m^(2)) rArr (\|1 4l+1\|)/(sqrt((l^(2) + m^(2)))) = 3 Centre of circle = (4, 0) and radius = 3 when any two non parallel lines touching a circle, then centre of circle lies on angle bisector of lines. On the basis of above information, answer the following questions : If 16m^(2) – 8l– 1 = 0, then equation of the circle having lx + my + 1 = 0 is a tangent is
Answer» `X^(2) + y^(2) + 8x = 0` `x^(2) + y^(2) - 8x = 0` `x^(2) + y^(2) + 8y = 0` `x^(2) + y^(2) - 8y = 0` ANSWER :B

Discussion

13.	The normal at a point P on the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1(a gt b) meets the axis in M and N so that (PM)/(PN)=2/3. Then the value of eccentricity is
Answer» `1-E^(2)` `e^(2)-1` `1+e^(2)` `e^(2)` ANSWER :A

Discussion

14.	Consider a 2xx2 matrix A=[a_(ij)] , where a_(ij)=(i+2j)^2/2 Find A+A^T
Answer» SOLUTION :`a_11=(1+2xx1)^2/2=9/2,` `a_12=(1+2xx2)^2/2=25/2` `a_21=(2+2xx1)^2/2=16/2=8`. `a_22=(2+2xx2)^2/2=36/2=18`, HENCE, `A=[[9/2, 25/2],[8, 18]]`

Discussion

15.	I= int "arc" tan x dx.
Answer» ANSWER :`= x "ARC" tan x - (1)/(2) "In" (1+ x^2) + C`.

Discussion

16.	int((1+x^(2))(2+x^2))/((xco sx+sinx)^(4))dx equals
Answer» `tan(x+cot^(-1)x)+(tan^(3)(x+cot^(-1)x))/(3)+C` `tan(x-cot^(-1)x)+(tan^(3)(x-cot^(-1)x))/(3)+c` `-(1)/(3)((1-xtanx)/(x+tanx))^(3)-((1-xtanx)/(x+tanx))+c` `-(1)/(2)((1+xtanx)/(x-tanx))^(3)-((1+xtanx)/(x-tanx))+c` Answer :B::C

Discussion

17.	If f:R rarr [(pi)/(3),pi) defined by f(x)=cos^(-1)((lambda-x^(2))/(x^(2)+2)) is a surjective function, then the value of lambda is equal to
Answer» 0 3 2 1 Answer :D

Discussion

18.	For a > 0, let the curves C_(1) : y^(2) = ax and C_(2) : x^(2) = ayintersect at origin O and a point P. Let the linex = b(0 lt b lt a) intersect the chord OP and the x-axis at points Q and R, respectively. If the line x = b bisects the area bounded by the curves, C_(1)and C_2, and the area of triangleOQR = 1//2, then 'a' satisfies the equation:
Answer» `x^(6) - 12X^(3) + 4=0` `x^(6) - 12x^(3) - 4=0` `x^(6) + 6x^(3) -4=0` `x^(6) - 6x^(2) + 4=0` ANSWER :A

Discussion

19.	Locus of the point of intersection of the tangents at the points with eccentric angle theta and (pi)/(2)+thetais
Answer» `x^(2)+y^(2)=a^(2)` `x^(2)+y^(2)=b^(2)` `(x^(2))/(a^(2))+(y^(2))/(b^(2))=2` `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1` ANSWER :C

Discussion

20.	Integrate the following functions sinx sin(cosx).
Answer» SOLUTION :Let t = COSX. Then dt = -sinx dx therefore `int sinx SIN(cosx) dx = int sintxx-dt` =`-int sintt dt = -(-cost)+C` =`cost=c = cos(cosx)+c`

Discussion

21.	IFa = x hati+ y hatj+ z hatkthen( a xx hati) . ( hati+ hatj )+ ( a xxhatj) . ( hatj + hatk ) + ( axx hatk ) . ( hatk + hati ) =
Answer» `X-y+z` `x+y+z` `x+y-z` `-x +y+z` ANSWER :B

Discussion

22.	Using integration find the area of the triangular region whose sides have the equations y =2x+1, y =3x +1 and x= 4.
Answer» ANSWER :8

Discussion

23.	If f(x)=x+(1)/(x), then :
Answer» RELATIVE MINIMUM gt relative MAXIMUM relative maximum gt relative minimum relative maximum does not exist relative minimum does not exist. Answer :A

Discussion

24.	Integrate the following functions w.r.t. x: (i) sinmx (ii) 2xsin(x^(2)+1) (iii) (tan^(4)sqrtxsec^(2)sqrtx)/(sqrtx) (iv) (sin(tan^(-1)x))/(1+x^(2))
Answer» Answer :`-(1)/(m) cos (mx)+C, (II) -cos(x^(2)+1)+c` (III) `(2)/(5)TAN^(5)( sqrt(x))+c, (iv) -cos(tan^(-1)x)+c`

Discussion

25.	If ""^(n)P_(7)=42. ""^(n)P_(5). find n.
Answer» ANSWER :12

Discussion

26.	Find the point of contant of the tangent line 4x+y-7=0 with the ellipse x^(2)+3y^(2)=3
Answer» ANSWER :`((12)/(7),(1)/(7))`

Discussion

27.	From any point on the hyperbolax^(2) -y^(2) =a^(2) -b^(2)two tangents are drawn to the ellipsex^(2)//a^(2) +y^(2) //b^(2) =1Then they make anglesalpha and betasuch that
Answer» ` tan alpha -tan beta +1` ` tan alpha + tan beta =1` ` tan alpha tan beta =1` ` tan alpha tan beta =-1` Answer :C

Discussion

28.	If z_(0) is one of the roots of the equation z^(n)cos theta_(0)+z^(n-1)cos theta_(1)+…+z cos theta_(n-1)cos theta_(n)=2, where theta_(i) in R, then
Answer» `\|z_(0)\|lt (1)/(2)` `\|z_(0)\|GT (1)/(2)` `\|z_(0)\|=(1)/(2)` none of these Answer :B

Discussion

29.	The value of the determinant \|{:(x,x+y,x+2y),(x+2y,x,x+y),(x+y,x+2y,x):}\|" is "".........."
Answer» `9x^2(x+y)` `9y^2(x+2y)` `3y^2(x+y)` `7x^2(x+y)` ANSWER :B

Discussion

30.	For any three vectors bara,barb,barc prove that [barb+barc barc+bara bara+barb] = 2[bara barb barc].
Answer» ANSWER :`=2[BARA BARB BARC]`

Discussion

31.	Using the example from #27, what's the remainder when xy is divided by 9?
Answer» ANSWER :3

Discussion

32.	Two persons A and B toss a die. The person who first throws 6 wins. If A starts then find the probability of A winning the game.
Answer» ANSWER :`(6)/(11)`

Discussion

33.	A biased die is tossed and the respective probabilities for the face to turn up are given below : {:("Face",1,2,3,4,5,6),("Probability",0.1,0.24,0.19,0.18,0.14,0.15):} If an odd face has turned up, then the probability for the face turned up is 3 or 5 is
Answer» `(3)/(4)` `(30)/(43)` `(33)/(43)` `(10)/(43)` ANSWER :C

Discussion

34.	int (2x-sin 2x)/(1-cos 2x) dx
Answer» ANSWER :`-X COT x+c`

Discussion

35.	There are 5% defective items in a large bulk of items. What is the probability that a sample of 10 items will include not more than one defective item?
Answer» ANSWER :`((29)/(20))((19)/(20))^(9)`

Discussion

36.	int(sec^(4)x+tan^(4)x)dx=
Answer» `2/3tan^(3)x-2/3tanx+x+C` `1/3sec^(2)xtanx+5/3tanx+(tan^(3)x)/3+x+c` `2/3tan^(3)x+x+c` `1/3sec^(2)xtanx-5/3tanx+(tan^(3)x)/3+x+c` ANSWER :C

Discussion

37.	If P is a point on the parabola y^(2)=8x and A is the point (1,0) then the locus of the mid point of the line segment AP is
Answer» `y^(2)=4 (X-(1)/(2))` `y^(2)=2(2x+1)` `y^(2)=x-(1)/(2)` `y^(2)=2x+1` ANSWER :A

Discussion

38.	Find the approximate volume of metal in a hollow spherical shell whose internal and external radii are 3 cm and 3.0005 cm, respectively.
Answer» ANSWER :`=0.018 PI (CM)^(3)`

Discussion

39.	y=sinxcdotsin2xcdotsin4xcdotsin8x
Answer» ANSWER :`sinxcdot sin2xsin4xcdot sin8x[cotx+2cot2x+4cot4x+8cot8x]`

Discussion

40.	Find the coefficient of x^(7) in the expansion of (1-x-x^(2)+x^(3))^(6).
Answer» SOLUTION :N/A

Discussion

41.	Show that A(-3,0) lies on x^(2)+y^(2) + 8x+ 12 y + 15 = 0 and find the other end of diameter thorugh A.
Answer» ANSWER :` (-5,-12) `

Discussion

42.	If \|2x-3\| lt \|x+5\| , then x lies in the interval
Answer» `(-3,5)` `(5,9)` `(-2/3,8)` `(-8 , 2/3)` ANSWER :C

Discussion

43.	A man has 5 male and 4 female relatives. His wife has 4 male and 5 female relatives. The number of ways in which they can invite 5 male and 5 female relatives so that 5 of them are man's relatives and remaining 5 are his wife's relatives
Answer» A5426 B5226 C5526 D5626 Answer :D

Discussion

44.	Evaluate int_(0)^(pi)ln(1+bcosx) dx, 'b'being parameter.
Answer» SOLUTION :N//A

Discussion

45.	If A = {:[(4, 2),(-1,1)]:}, the (2I - A) (A -3I) is
Answer» 1 `-1` `O_2` `A^(-1)` ANSWER :C

Discussion

46.	(3 - omega) ( 3- omega^(2)) ( 3- omega^(4)) (3 - omega^(8)) =
Answer» 81 `13^(4)` `169` 0 Answer :C

Discussion

47.	Whichof thefollowingfunctionhas / havea reaovablediscontinuityattheindicated point ?
Answer» `F(x) =(x^(2)-2x-8)/(x+2)at x=-2` `f(x) =(x-7)/(\|x-7\|)at x=7` `f(x) =(x^(3)+64)/(\|x+4\|)at x=-4` `f(x) =(3-sqrt(x))/(9-x)at x=9` ANSWER :A::C::D

Discussion

48.	IF theequationk ( 6 x^2+ 3)+ rz+ 2x^2-1=0and6k( 2 x^2+1) + px + 4x ^2-2=0haveboththerootcommon, thenthe valueof2r-pis
Answer» 0 1 2 3 Answer :A

Discussion

49.	Computethe areaboundedby thelinesx+ 2y = 2 , y - x=1 and2x +y =7
Answer» ANSWER :`=6` SEQ . UNIT

Discussion

50.	Differentiate cosec 3x
Answer» SOLUTION :LET`y=COSEC 3X` Then `dy/dx=-3"cosec"3x CDOT cot3x`

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

The sum of three numbers in A.P. is 27, and their product is 504, find them.

ABCD is a square of side l. A line parallel to the diagonal BD at a distance 'x' from the vertex A cuts two adjacentsides. Express the area of the segment of the square with A at a vertex, as a function of x. Find this area at x=1//sqrt(2) and at x=2, when l=2.

underset(x to pi//2)"Lt" [sin x]=

Find the area enclosed between the curves y= 2-x^(2) and y= x^(2)

Find the equation of the circle for which the point given below are the end points of a diameter. (0,0) ,(8,5)

For the circle C with the equation x^(2)+y^(2)-16x-12y+64=0 match the list-I with the list-II given below:

The sum of last ten coefficients in the expansion of(1+x)^(19) when expanded in ascending powers ofxis

Whenf: R to Rand g: R to Rare two functions defined by f(x)= 8x^(3)and g(x) == x^((1)/(3)) respectivelyand (g of ) (x) = k (f o g ) (x) , then k is

Using the letters of the word 'RAM' How many 6 letter words can be prepared so that all the 3 letters are to appear in the same word atleast once.

The normal at a point P on the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1(a gt b) meets the axis in M and N so that (PM)/(PN)=2/3. Then the value of eccentricity is

Consider a 2xx2 matrix A=[a_(ij)] , where a_(ij)=(i+2j)^2/2 Find A+A^T

I= int "arc" tan x dx.

int((1+x^(2))(2+x^2))/((xco sx+sinx)^(4))dx equals

If f:R rarr [(pi)/(3),pi) defined by f(x)=cos^(-1)((lambda-x^(2))/(x^(2)+2)) is a surjective function, then the value of lambda is equal to

Locus of the point of intersection of the tangents at the points with eccentric angle theta and (pi)/(2)+thetais

Integrate the following functions sinx sin(cosx).

IFa = x hati+ y hatj+ z hatkthen( a xx hati) . ( hati+ hatj )+ ( a xxhatj) . ( hatj + hatk ) + ( axx hatk ) . ( hatk + hati ) =

Using integration find the area of the triangular region whose sides have the equations y =2x+1, y =3x +1 and x= 4.

If f(x)=x+(1)/(x), then :

Integrate the following functions w.r.t. x: (i) sinmx (ii) 2xsin(x^(2)+1) (iii) (tan^(4)sqrtxsec^(2)sqrtx)/(sqrtx) (iv) (sin(tan^(-1)x))/(1+x^(2))

If ""^(n)P_(7)=42. ""^(n)P_(5). find n.

Find the point of contant of the tangent line 4x+y-7=0 with the ellipse x^(2)+3y^(2)=3

From any point on the hyperbolax^(2) -y^(2) =a^(2) -b^(2)two tangents are drawn to the ellipsex^(2)//a^(2) +y^(2) //b^(2) =1Then they make anglesalpha and betasuch that

If z_(0) is one of the roots of the equation z^(n)cos theta_(0)+z^(n-1)cos theta_(1)+…+z cos theta_(n-1)cos theta_(n)=2, where theta_(i) in R, then

The value of the determinant |{:(x,x+y,x+2y),(x+2y,x,x+y),(x+y,x+2y,x):}|" is "".........."

For any three vectors bara,barb,barc prove that [barb+barc barc+bara bara+barb] = 2[bara barb barc].

Using the example from #27, what's the remainder when xy is divided by 9?

Two persons A and B toss a die. The person who first throws 6 wins. If A starts then find the probability of A winning the game.

A biased die is tossed and the respective probabilities for the face to turn up are given below : {:("Face",1,2,3,4,5,6),("Probability",0.1,0.24,0.19,0.18,0.14,0.15):} If an odd face has turned up, then the probability for the face turned up is 3 or 5 is

int (2x-sin 2x)/(1-cos 2x) dx

There are 5% defective items in a large bulk of items. What is the probability﻿ that a sample of 10 items will include not more than one defective item?﻿

int(sec^(4)x+tan^(4)x)dx=

If P is a point on the parabola y^(2)=8x and A is the point (1,0) then the locus of the mid point of the line segment AP is

Find the approximate volume of metal in a hollow spherical shell whose internal and external radii are 3 cm and 3.0005 cm, respectively.

y=sinxcdotsin2xcdotsin4xcdotsin8x

Find the coefficient of x^(7) in the expansion of (1-x-x^(2)+x^(3))^(6).

Show that A(-3,0) lies on x^(2)+y^(2) + 8x+ 12 y + 15 = 0 and find the other end of diameter thorugh A.

If |2x-3| lt |x+5| , then x lies in the interval

A man has 5 male and 4 female relatives. His wife has 4 male and 5 female relatives. The number of ways in which they can invite 5 male and 5 female relatives so that 5 of them are man's relatives and remaining 5 are his wife's relatives

Evaluate int_(0)^(pi)ln(1+bcosx) dx, 'b'being parameter.

If A = {:[(4, 2),(-1,1)]:}, the (2I - A) (A -3I) is

(3 - omega) ( 3- omega^(2)) ( 3- omega^(4)) (3 - omega^(8)) =

Whichof thefollowingfunctionhas / havea reaovablediscontinuityattheindicated point ?

IF theequationk ( 6 x^2+ 3)+ rz+ 2x^2-1=0and6k( 2 x^2+1) + px + 4x ^2-2=0haveboththerootcommon, thenthe valueof2r-pis

Computethe areaboundedby thelinesx+ 2y = 2 , y - x=1 and2x +y =7

Differentiate cosec 3x

There are 5% defective items in a large bulk of items. What is the probability that a sample of 10 items will include not more than one defective item?