28278 + Interview Questions in Maths in Class 12

1.	Assertion (A): The pair of asymtotes of x^(2)/(10)-y^(2)/4=1 and the pair of asymptotes of x^(2)/(10)-y^(2)/4=-1 coincide. Reason (R) : A hyperbola and its conjugate hyperbola posses the same pair of asymptotes. 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 and R is not the correct explanation of A A is true, R is FALSE A is false, R is true Answer :B

Discussion

2.	An unbiased cubical die is thrown 5 times. The probability that the maximum number appearing on the die is 4 is
Answer» `7//6^5` `1023//6^5` `3781//6^5` `1781//6^5` ANSWER :B

Discussion

3.	Let A = {1,2} ,B = {1,2 ,3,4 } ,c={5,6} andd={5,6,7,8 }verifythatA xx ( B nn C ) = (A xx B ) nn (A xx C )
Answer» ANSWER :hence ` A xx( B CAP C)= (AXX B) cap (a xx C)`

Discussion

4.	Integrate the following function : int(x)/(sqrt(16x^(4)+9))dx
Answer» Answer :`(1)/(8)log\|4x^(2)+SQRT(16X^(2)+9)\|+c`

Discussion

5.	A question paper is divided into 3 sections A, B and C containing 3, 4 and 5 questions respectively. Find the number of ways of attempting 6 questions choosing atleast one from each section
Answer» ANSWER :805

Discussion

6.	LetS = {x in R : 5^(2 x+1) + 20 x^(2) + 29x + 6 = (11) (5^(x)) + (x) (5^(x+2))} The number of integers lying is S is ______
Answer» ANSWER :3

Discussion

7.	Evaluate the following integrals inttan^(-1)sqrt(x)dx
Answer» ANSWER :`(x+1)TAN^(-1)SQRT(x)-sqrt(x)+C`

Discussion

8.	Functions f,g:RtoR are defined ,respectively, by f(x)=x^2+3x+1,g(x)=2x-3,findgof.
Answer» SOLUTION :N/A

Discussion

9.	Arrange the value of \|a + b + c\| in ascending order (A) If a,b,c are mutually perpendicular unit vectors (b) If a,b,c are vectors of lengths 2,3,4 respectively and if a,b,c are perpendicular to b + c, c + a , a+ b respectively. If a,b,c are vector of length 4,4,5 respectively and a,b,c are perpendicular to b + c, c + a, a + b respectively.
Answer» A,B,C C,B,A B,C,A B,A,C Answer :A

Discussion

10.	Solve [[x+a,b,c],[a,x+b,c],[a,b,x+c]]=0
Answer» Solution :`[[X+a,B,c],[a,x+b,c],[a,b,x+c]]=0` or, `[[x+a+b+c,b,c],[x+a+b+c,x+b,c],[x+a+b+c,b,x+c]]=0` `(C_1=C_1+C_2+C_3)` or, `(x+a+b+c)[[1,b,c],[1,x+b,c],[1,b,x+c]]=0` or, `(x+a+b+c)[[1,b,c],[0,x,0],[0,-x,x]]=0` `(R_2~~R_2-R_1,R_3~~R_3-R_2)` or, (x+a+b+c)[[x,0],[-x,x]]=0` or, `(x+a+b+c)x^2=0` or, x=0,x=-(a+b+c)

Discussion

11.	Find \|vec(a)\| and \|vec(b)\|, if (vec(a)+vec(b)).(vec(a)-vec(b))=8 and \|vec(a)\|=8\|vec(b)\|.
Answer» ANSWER :HENCE `\|VEC(a)\|=(16sqrt(2))/(3sqrt(7))` and `\|vec(b)\|=(2sqrt(2))/(3sqrt(7))`

Discussion

12.	If (5, 1) is a circumcentre and (7, 5) is the centroid of a triangle, then its orthocentre is
Answer» (3, -3) (-3, 3) (4, -4) (-2, 2). ANSWER :B

Discussion

13.	Angle made by double ordinate of length 24 of the parabola y^(2)= 12x at origin is
Answer» `(pi)/(6)` `(pi)/(4)` `(pi)/(3)` `(pi)/(2)` ANSWER :D

Discussion

14.	Prove that : If \|x\| is so small that x^(3) and higher powers or x can be neglected, find approximate value of ((4-7x)^(1//2))/((3+5x)^(3)).
Answer» SOLUTION :N/A

Discussion

15.	Using differentials, find the approximate value of each of the following upto 3 place of decimal. (ii) sqrt(49.5)
Answer» ANSWER :7.035

Discussion

16.	A class contains 4 boys and g girls. Every Sunday, five students with atleast 3 boys go for a pincnic. A different group is being sent every week. During the picnic, the class teacher gives each girls in the group a doll. If the total number of dolls distributed is 85, find g.
Answer» ANSWER :5

Discussion

17.	Find the equation of circle centred at (3,3) and touches the coordinate axes.
Answer» ANSWER :`x^2 + y^2 - 6X - 6Y + 9 = 0`

Discussion

18.	Find the distance between the following pairs of points. (-1,0) , (5,3) .
Answer» SOLUTION :DISTANCE between the points (-1,0) and (5,3) is `sqrt(3+2)^2+(4-1)^2 ` =`sqrt(36+9)`=`sqrt45`=`3SQRT5`

Discussion

19.	Perkyowl Designs operates its factory in two shifts. There are 65 workers in Shifts I and have mean wages of rupes 525 per day whereas there are 35 workers in the Shifts II. If the combined wagesof entire set of 100 workers is rupes 542, 50 then average wages (in rupes)of the workers in Shifts II, is ________________
Answer» ANSWER :`575.00`

Discussion

20.	The mean of a set observations is bar(x). If each observation if divided by alpha (!= 0) and it is increased by 10, then the mean of the new set is
Answer» `(BAR(X))/(ALPHA)` `(bar(x)+10)/(alpha)` `(bar(x)+10 alpha)/(alpha)` `alpha bar(x) + 10` Answer :C

Discussion

21.	If the greatest value of y=(x)/(logx) on [e,e^(3)] is u them (e^(3))/(u) is equal to -
Answer» ANSWER :3

Discussion

22.	From the point A (0,3) on the circle x^(2)+ 4x+(y-3)^(2) = 0 a chord AB is drawn and extended to a point M such that AM = 2 AB. Find the equation of the locus of M.
Answer» Answer :` THEREFORE ` LOCUS of M is ` X^(2) + y ^(2)+ 8X- 6Y + 9=0 `, which is a circle.

Discussion

23.	Find the second order derivative of the following functions xcosx
Answer» SOLUTION :`y=xcosx,dy/dx=-xsinx+cosx(d^2y)/(dx^2)=-[xcosx+sinx]-sinx=-xcosx-2sinx`

Discussion

24.	For a point (C,0) three normals are drawn to the parabola y^(2) = x. Then
Answer» `C LT (1)/(2)` `C = (1)/(2)` `C gt (1)/(2)` `(1)/(2) gt C gt (1)/(4)` ANSWER :c

Discussion

25.	""^(2n)P_(n) is equal to
Answer» `(N+1)!(""^(2N)C_(n))` `n!xx(""^(2n)C_(n))` `n!xx(""^(2n+1)C_(n))` `n!xx(""^(2n+1)C_(n+1))` ANSWER :B

Discussion

26.	Evaluation of definite integrals by subsitiution and properties of its : int_(0)^(2pi)cos^(99)xdx=............
Answer» 1 `-1` 99 0 Answer :D

Discussion

27.	Match the following {:(,"List-I",,"List-II",),((1),"The equation of family of curves for which",(a),y+e^(-x) = " c, y " - e^(x) = c,),(,"length of the normal = The radius vector.",,,),((2),"Solution of the differential equation " ((dy)/(dx))^(2) - (dy)/(dx)(e^(x)+e^(-x))+1=0 " is",(b),y = x cot (x+c),),((3),"The solution of " (xdy)/((x^(2)+y^(2))) = ((y)/(x^(2)+y^(2))-1)dx " is",(c),y^(2)+- x^(2) = k^(2),),(,,(d),e^(y)=e^(x)-1,):}
Answer» 1-a, 2-b, 3-d 1-c, 2-, 3-a 1-c, 2-a, 3-d 1-c, 2-a, 3-b Answer :D

Discussion

28.	Solve the following equation x : 2x + y = 5
Answer» ANSWER :`X = (5 - y)/(2)`

Discussion

29.	The order, degree of the differential equation x = 1 + ((dy)/(dx)) + (1)/(2!)((dy)/(dx))^(2) + (1)/(3!)((dy)/(dx))^(3) +… is
Answer» 3,1 4,2 1,1 not defined Answer :C

Discussion

30.	Definite integration as the limit of a sum : lim_(ntooo)sum_(K=1)^(n)(K)/(n^(2)+K^(2))=......
Answer» `(1)/(2)log2` `log2` `(pi)/(4)` `(pi)/(2)` Answer :A

Discussion

31.	In the group G = {1,3,7,9) under multiplication modulo 10, the inverse of 3 is...
Answer» 1 3 7 9 Answer :C

Discussion

32.	Find the number of ways of dividing 80 persons into 3 groups containing 35, 25, 20 persons.
Answer» ANSWER :`((80)!)/((20)!(35)!(25)!)`

Discussion

33.	The straight lines 3x + 4y - 5 = 0 and 4x -3y = 15 intersect at the point P. On these lines the points Q and R are chosen so that PQ = PR. The slopes of the lines QR passing through (1, 2) are
Answer» -7, `(1)/(7)` 7, `(1)/(7)` 7, `-(1)/(7)` 3, `-(1)/(3)` ANSWER :A

Discussion

34.	If the equations x^(2)+ax+bc=0 and x^(2)+bx+ca=0 have a common root and if a, b and c are non-zero distinct real numbers, then their other roots satisfy the equation
Answer» `X^(2)+x+abc=0` `x^(2)-(a+B)x+ab=0` `x^(2)+(a+b)x+ab=0` `x^(2)+x+ab=0` ANSWER :B

Discussion

35.	Evaluate the following integrals: int_-1^1 (x+1) dx
Answer» SOLUTION :`int_-1^1 (x+1) DX = [x^2/2+x]_-1^1` =`(1^2/2+1)-((-1)^2/2 +(-1))` `1/2 +1-(1/2-1) = 3/2 +1/2 = 2`

Discussion

36.	If f(x) = (1+ tanx) (1+ tan (pi//4 - x)) and g(x) is a function with domain R, then int_(0)^(1) x^(3) "g o"f(x) dx is
Answer» `1/2 g(pi//4)` `1/4 g(2)` `1/4 g(1)` NONE of these Answer :B

Discussion

37.	A : (1+i)^(6)+(1-i)^(6)=0 R : If n is a positive integer then (1+i)^(n)+(1-i)^(n)=2^((n//2)+1).cos""(npi)/(4)
Answer» Both A and R are true R is correct EXPLANATION to A Both A and R are true but R is not correct explanation to A A is true R is false A is false R is true Answer :A

Discussion

38.	The numberof valueof x inthe interval[0,3pi] satisfyingtheequation2sin^2+ 5 sin x-3 =0 is
Answer» 4 6 1 2 Answer :A

Discussion

39.	Compute P(X=k) for the binominal distribution, B(n,p) where n=9, p=1/2, k=7
Answer» ANSWER :`36(1/2)^(9)`

Discussion

40.	Find the total revenue function for the marginal revenue function given by M R = 20 e^(-(x)/(10))(1-(x)/(10)).
Answer» ANSWER :`R(x) = 20 x e^(-(x)/(10))`

Discussion

41.	int(x)/(1-sin2x)dx=
Answer» `(X)/(4)(tan2x+sec2x)-(1)/(2)log\|sec^2 2x+sec2xtan2x\|+C` `(x)/(4)(tan2x+sec2x)+(1)/(2)log\|sec^2 2x+sec2xtan2x\|+c` `(x)/(2)(tan2x+sec2x)-(1)/(4)log\|sec^2 2x+sec2xtan2x\|+c` `(x)/(2)(tan2x+sec2x)+(1)/(4)log\|sec^2 2x+sec2xtan2x\|+c` ANSWER :C

Discussion

42.	The point of intersaction of the line (x-1)/(2)=(y-2)/(-3)=(z+3)/(4) and the plane 2x=4y-z+1=0is
Answer» `(-(10)/(3),3/2, - 5/3)` `(-(10)/(3), -(3)/(2), (5)/(3))` `((10)/(3),(3)/(2),-(5)/(3))` `((10)/(3),-(3)/(2),(5)/(3))` ANSWER :D

Discussion

43.	Ife_(1) , e_(2)are eccentricities of the ellispex^(2)/a^(2) + y^(2)/b^(2) =1and the hyperbolax^(2)/a^(2) -y^(2)/b^(2) = 1then
Answer» `e_(1)^(2)- e_(2^(2) =1` `e_(1)^(2)+ e_(2)^(2) = 1 ` `e_(1)^(2) -e_(2)^(2) = 2` `e_(1)^(2)+e_(2)^(2) = 2` ANSWER :D

Discussion

44.	Construct Collection of all the days of a week in the form of set and describe it with the help of proposition.
Answer» Solution :D = {SUNDAY, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday } ={x:x is a DAY of week}

Discussion

45.	Evaluate the following determinates \|{:("3","-4","5"),(1,1,"-2"),(2,"3","1"):}\|
Answer» ANSWER :46

Discussion

46.	If the axes are rotated through an angle of45^(@)in the anticlockwise direction then the equation of rectangular hyperbolax^(2) -y^(2) =a^(2)changes to
Answer» ` xy=a^(2) ` ` xy=2a^(2) ` ` 2XY =a^(2) ` NONE ANSWER :D

Discussion

47.	Integrate the following functions (e^(2x) -e^(-2x))/(e^(2x) + e^(-2x)
Answer» Solution :Let t = `E^(2x)+e^(2x)`. Then DT = `(2e^(2x)-2e^(-2x))DX` =`2(e^(2x)-e^(-2x)) dx` `gt (e^(2x)-e^(-2x)) dx = (dt)/2` THEREFORE `INT (e^(2x)-e^(-2x))/(e^(2x)+e^(-2x)) dx = int 1/t (dt)/2 = 1/2 log\|t\|+c` =`1/2 log\|e^(2x)+e^(-2x)\|+c`

Discussion

48.	The value of prod_(k=1)^6((sin)(2pik)/(7)-(icos)(2pik)/(7)) is
Answer» -1 0 `-i` `i` ANSWER :A

Discussion

49.	If ABCD is a square then show that the points A, B, C and D are concyclic.
Answer» ANSWER : `rArr` C LIES on the circlepassing through A, B, D. `THEREFORE` A, B, C, D are concyclic.

Discussion

50.	Evaluate : int_(0)^(1) (sin^(-1) sx)/(sqrt(1-x^(2)))dx
Answer» Solution :`"LET sin"^(-1) x=t` `rArr ""(1)/(SQRT(1-x^(2)))dx =DT` `At x=0, ""t=sin^(-1) 0=0` `At x=1 ""t=sin^(-1) 1=PI//2` `:. int_(0)^(1) (sin^(-1)x)/(sqrt(1-x^(2))) dx =int_(0)^(pi//2) t dt = [(t^(2))/(2)]_(0)^(pi//2)` `=1/2 ((pi)/(2))^(2) -0=(pi^(2))/(8).`

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Assertion (A): The pair of asymtotes of x^(2)/(10)-y^(2)/4=1 and the pair of asymptotes of x^(2)/(10)-y^(2)/4=-1 coincide. Reason (R) : A hyperbola and its conjugate hyperbola posses the same pair of asymptotes. The correct answer is

An unbiased cubical die is thrown 5 times. The probability that the maximum number appearing on the die is 4 is

Let A = {1,2} ,B = {1,2 ,3,4 } ,c={5,6} andd={5,6,7,8 }verifythatA xx ( B nn C ) = (A xx B ) nn (A xx C )

Integrate the following function : int(x)/(sqrt(16x^(4)+9))dx

A question paper is divided into 3 sections A, B and C containing 3, 4 and 5 questions respectively. Find the number of ways of attempting 6 questions choosing atleast one from each section

LetS = {x in R : 5^(2 x+1) + 20 x^(2) + 29x + 6 = (11) (5^(x)) + (x) (5^(x+2))} The number of integers lying is S is ______

Evaluate the following integrals inttan^(-1)sqrt(x)dx

Functions f,g:RtoR are defined ,respectively, by f(x)=x^2+3x+1,g(x)=2x-3,findgof.

Solve [[x+a,b,c],[a,x+b,c],[a,b,x+c]]=0

Find |vec(a)| and |vec(b)|, if (vec(a)+vec(b)).(vec(a)-vec(b))=8 and |vec(a)|=8|vec(b)|.

If (5, 1) is a circumcentre and (7, 5) is the centroid of a triangle, then its orthocentre is

Angle made by double ordinate of length 24 of the parabola y^(2)= 12x at origin is

Prove that : If |x| is so small that x^(3) and higher powers or x can be neglected, find approximate value of ((4-7x)^(1//2))/((3+5x)^(3)).

Using differentials, find the approximate value of each of the following upto 3 place of decimal. (ii) sqrt(49.5)

A class contains 4 boys and g girls. Every Sunday, five students with atleast 3 boys go for a pincnic. A different group is being sent every week. During the picnic, the class teacher gives each girls in the group a doll. If the total number of dolls distributed is 85, find g.

Find the equation of circle centred at (3,3) and touches the coordinate axes.

Find the distance between the following pairs of points. (-1,0) , (5,3) .

The mean of a set observations is bar(x). If each observation if divided by alpha (!= 0) and it is increased by 10, then the mean of the new set is

If the greatest value of y=(x)/(logx) on [e,e^(3)] is u them (e^(3))/(u) is equal to -

From the point A (0,3) on the circle x^(2)+ 4x+(y-3)^(2) = 0 a chord AB is drawn and extended to a point M such that AM = 2 AB. Find the equation of the locus of M.

Find the second order derivative of the following functions xcosx

For a point (C,0) three normals are drawn to the parabola y^(2) = x. Then

""^(2n)P_(n) is equal to

Evaluation of definite integrals by subsitiution and properties of its : int_(0)^(2pi)cos^(99)xdx=............

Solve the following equation x : 2x + y = 5

The order, degree of the differential equation x = 1 + ((dy)/(dx)) + (1)/(2!)((dy)/(dx))^(2) + (1)/(3!)((dy)/(dx))^(3) +… is

Definite integration as the limit of a sum : lim_(ntooo)sum_(K=1)^(n)(K)/(n^(2)+K^(2))=......

In the group G = {1,3,7,9) under multiplication modulo 10, the inverse of 3 is...

Find the number of ways of dividing 80 persons into 3 groups containing 35, 25, 20 persons.

The straight lines 3x + 4y - 5 = 0 and﻿ 4x -3y = 15 intersect at the point P. On﻿ these lines the points Q and R are chosen﻿ so that PQ = PR. The slopes of the lines﻿ QR passing through (1, 2) are

If the equations x^(2)+ax+bc=0 and x^(2)+bx+ca=0 have a common root and if a, b and c are non-zero distinct real numbers, then their other roots satisfy the equation

Evaluate the following integrals: int_-1^1 (x+1) dx

If f(x) = (1+ tanx) (1+ tan (pi//4 - x)) and g(x) is a function with domain R, then int_(0)^(1) x^(3) "g o"f(x) dx is

A : (1+i)^(6)+(1-i)^(6)=0 R : If n is a positive integer then (1+i)^(n)+(1-i)^(n)=2^((n//2)+1).cos""(npi)/(4)

The numberof valueof x inthe interval[0,3pi] satisfyingtheequation2sin^2+ 5 sin x-3 =0 is

Compute P(X=k) for the binominal distribution, B(n,p) where n=9, p=1/2, k=7

Find the total revenue function for the marginal revenue function given by M R = 20 e^(-(x)/(10))(1-(x)/(10)).

int(x)/(1-sin2x)dx=

The point of intersaction of the line (x-1)/(2)=(y-2)/(-3)=(z+3)/(4) and the plane 2x=4y-z+1=0is

Ife_(1) , e_(2)are eccentricities of the ellispex^(2)/a^(2) + y^(2)/b^(2) =1and the hyperbolax^(2)/a^(2) -y^(2)/b^(2) = 1then

Construct Collection of all the days of a week in the form of set and describe it with the help of proposition.

Evaluate the following determinates |{:("3","-4","5"),(1,1,"-2"),(2,"3","1"):}|

If the axes are rotated through an angle of45^(@)in the anticlockwise direction then the equation of rectangular hyperbolax^(2) -y^(2) =a^(2)changes to

Integrate the following functions (e^(2x) -e^(-2x))/(e^(2x) + e^(-2x)

The value of prod_(k=1)^6((sin)(2pik)/(7)-(icos)(2pik)/(7)) is

If ABCD is a square then show that the points A, B, C and D are concyclic.

Evaluate : int_(0)^(1) (sin^(-1) sx)/(sqrt(1-x^(2)))dx

The straight lines 3x + 4y - 5 = 0 and 4x -3y = 15 intersect at the point P. On these lines the points Q and R are chosen so that PQ = PR. The slopes of the lines QR passing through (1, 2) are