28278 + Interview Questions in Maths in Class 12

1.	The vector i+j+k,i+2j+3k,2i+3j+k are
Answer» Collinear Non-coplanar Coplanar None Answer :B

Discussion

2.	Each side of DeltaABC is the polar of the opposite vertex with respect to a circle with centre P. Then P is ortho centre of DeltaABC.
Answer» ANSWER :the CIRCLE

Discussion

3.	A person gets dollars eqal to the square of the number which comes up when a balanced die, with faces marked 1, 2, 3, 4, 5, 6 is rooled one. If the game is repeated an indefinitely large number of times, how much money can be expect in the long run per game ?
Answer» ANSWER :15.17

Discussion

4.	Let x^2 - 2(a - 1)x + a - 1 = 0 (a in R) be a quadratic equation, then find the values of "a" for which (i) Exactly one root lies in (0,1) (ii) Both roots lies in (0, 1). (iii)Atleast one root lies in (0,1). (iv) One root is greater than 1 and other root is smaller than 0.
Answer» Answer :(i) `(-infty, 1) cup (2,infty)`, (II) `PHI`, (III) `(-infty, 1) cup (2, infty)`, (IV) `phi`

Discussion

5.	Isthe function f (x) = ( 3 x + 4 tan x)/( x)continuous at x = 0 ? If not, how many the function be defined to make it continuous at this point .
Answer» Answer :`f (x) = {{:((3x_4 TAN x)/(x)",",""x ne 0 ),(""7",",""x = 0 ):}`

Discussion

6.	Q. If a state is chosen at random, what is the probability that the minimum age for obtaining a driver's license in that state will be at least 16?
Answer» `(1)/(25)` `(2)/(25)` `(19)/(50)` `(31)/(50)` ANSWER :D

Discussion

7.	If c is the velocity of electromagneticradiation e is the charge of an electron m is the mass of an electron and h is the Planck's constant, then the combination of these universal constants that is dimensionless, is
Answer» `me^(2)//(hc)` `ch//(me)` `mc^(2)//H` none Solution : `h rarr ML^(2)T^(-1)` `C rarr LT^(-1)` `e rarr IT` `m rarr M`

Discussion

8.	Prove that the volume of the largest cone that can be inscribed in a sphere of radius R is (8)/(27) of the volume of the sphere.
Answer» ANSWER :`(8)/(27)`

Discussion

9.	If A=[{:(1,2,5),(5,1,1),(3,0,4):}]then find A-2A'.
Answer» ANSWER :`[{:(-1,-8,-1),(1,-1,1),(-7,-2,-4):}]`

Discussion

10.	lim_(xto-1) ((1+x)(1-x^2)(1+x^3) (1-x^4).......(1-x^4n))/([(1+x)(1-x^2)(1+x^3) (1-x^4) .....(1-x^2n)]^2) is equal to
Answer» `.^(4n)C_(2n)` `.^(2n)C_(N)` `2.^(4n)C_(2n)` `2.^(2n)C_(n)` Answer :A

Discussion

11.	Evaluate the following inegrals int((x^(3)-x)^(1//2))/(x^(4))dx
Answer» ANSWER :`(3)/(8)(1-(1)/(x^(2)))^(4//3)+C`

Discussion

12.	The point of intersection of the lines l_(1) : r(t)=(i-6j+2k) +t(i+2j+k) l_(2) : R(u)=(4j+k)+u (2i+j+2k) is
Answer» (4,4,5) (6,4,7) (8,8,9) (10,12,11) ANSWER :C

Discussion

13.	Which of the following set are finite and which are infinite ? The set of even integers.
Answer» SOLUTION :"The SET of EVEN INTEGERS " is an INFINITE set.

Discussion

14.	If the two coefficients of regression are - 0.6 and – 1.4, find the acute angle between theregression lines.
Answer» SOLUTION :N/A

Discussion

15.	A random variable X has the following probability distribution: Determine (i) K (ii) P(X lt 3) (iii) P(X gt 6) (iv) P(0 lt X lt 3)
Answer» Answer :(i) `k=(1)/(10)`, (II) `P(X lt 3)=(3)/(10)`, (iii) `P(X GT 6)=(17)/(100)`, (iv) `P(0 lt X lt 3)=(3)/(10)`

Discussion

16.	From the set S = {0, 1, 2, …., 53}, three distinct numbers are chosen. The probability that the sum of them is 54 is
Answer» `27/2756` `13/1378` `29/2756` `15/1378` ANSWER :A

Discussion

17.	From each of the three married couples one partner is selected at random. The probability of selecting two males and one female is
Answer» `(1)/(8)` `(1)/(4)` `(3)/(8)` `(1)/(2)` Answer :C

Discussion

18.	Solve the equation ""^(11)C_(1) x^(10) - ""^(11)C_(3) x^(8) + ""^(11)C_(5) x^(6) - ""^(11)C_(7) x^(4) + ""^(11)C_(9) x^(2) - ""^(11)C_(11) = 0
Answer» ANSWER :X = cot ` ((rpi)/(11)), r = pm 1 ,pm 2 ,…, pm 5 `

Discussion

19.	Solve the following differential equations. (dy)/(dx)+ysec x=tan x
Answer» ANSWER :`y(SEC X + TAN x) = (sec + tan x) - x +C`

Discussion

20.	Choose the correct answer intsqrt(1+x^(2))dx is equal to
Answer» `X/2sqrt(1+x^(2))+1/2logabs((x+sqrt(1+x^(2))))+C` `2/3(1+x^(2))^(3/2)+C` `2/3x(1+x^(2))^(3/2)+C` `(x^(2))/2sqrt(1+x^(2))+1/2x^(2)logabs(x+sqrt(1+x^(2)))+C` ANSWER :A

Discussion

21.	Let A be a2xx 2matrix with real entries and det (A)= d ne 0such that det (A+d(adj ) A)) =0 . Find the valued of det ( A-d(dj (A))
Answer» 8 7 4 none of these ANSWER :C

Discussion

22.	Therootsofx^3 - 13x^2 +39 x-27=0 are in
Answer» A.P G.P H.P A.G.P Answer :B

Discussion

23.	A balloon, which always remains spherical has a variable radius. Find the rate at which its volume is increasing with the radius when the later is 10 cm.
Answer» ANSWER :`400 PI CM^(3)//cm`

Discussion

24.	y^(2) = ax^(2) +bx + c then y^(3) (d^(2)y)/(dx^(2)) is a …….. function
Answer» constant only for X only for y for x and y Answer :A

Discussion

25.	Consider the following equations a) A-B=A-(A nn B) b) A=(A nn B)uu(A-B) c) A-(B uu C)=(A-B)uu(A-C) Which of these is / are correct
Answer» a and c b only b and c a and b Answer :D

Discussion

26.	Consider a pyramid OPQRS located in the first octant (xge0, yge0, zge0) with O as origin and OP and OR along the X-axis and the Y-axis , respectively. The base OPQRS of the pyramid is a square with OP=3. The point S is directly above the mid point T of diagonal OQ such that TS=3. Then,
Answer» <P>the acute angle between OQ and OS is `(pi)/(3)` the EQUATION of the plane containing ht `triangleOQS` is x-y=0 the length of perpendicular from P to the plane containing the `triangleOQS` is `(2)/(SQRT(3))` the perpendicular distance from O to the straight line containing RS is `sqrt((15)/(2))` Answer :`(b,c, d)`

Discussion

27.	Which of the following statement patten is a tautology ?
Answer» <P>`p vv(q to p)` `~q to ~p` `(q to p)vv(~p HARR q)` `p vv ~p` Answer :C

Discussion

28.	Find the coefficient of x^(3) in the power series expansion of (5x+6)/((x+2)(1-x)) specifying the region in which the expansion is valid.
Answer» ANSWER :`15/4`

Discussion

29.	int sin^(3) x.cos^(2)x dx =
Answer» `(1)/(5) COS^(5) x -(1)/(3) cos^(3)` x + C `(1)/(3) cos^(5) x -(1)/(3) cos^(3)` x + C `(1)/(5) cos^(5)x +(1)/(3) cos^(3) x + C` `(1)/(5) cos^(5)x -(1)/(3) cos^(5) x + C` ANSWER :A

Discussion

30.	Find all points of discontinuityof f, where f is defined by f(x)={{:(2x^(3)+4," if "x le2),(x^(2)+2," if "x gt 2):}
Answer» ANSWER :No POINT of DISCONTINUITY

Discussion

31.	If (1)/(3 - 4i) is a root of ax^(2) + bx + c = 0, (a,b, c in R, a ne 0)then
Answer» b + 6c =0 b = 6c a + 25 C = 0 `b^(2) = 6c` Answer :A

Discussion

32.	int_(0)^(2pi) x cos^(6) x dx=
Answer» `(3pi^(2))/(16)` `(3pi)/(8)` `(5PI^(2))/(8)` `(5pi^(2))/(16)` ANSWER :C

Discussion

33.	find the equation of line joining (1,2) and (3,6) using determinants
Answer» ANSWER :`y = 2X`

Discussion

34.	Find the point which provides the solution of linear programming problem: Maximise: Z=45x + 55y Subject to constraints: x, yge 0,6x + 4y le 120 and 3x + 10y le 180.
Answer» ANSWER :MAXIMUM VALUE of Z = 1275 at (10,15)

Discussion

35.	Find the number of ways of arranging 6 boys and 6 girls around a circle so that all the girls come together
Answer» ANSWER :`=lfloor6xxlfloor6`

Discussion

36.	Solve (1 + x^(2))dy + 2xy dx = cot x dx (x ne 0)
Answer»

Discussion

37.	If x=-(1)/(2) "sin h"^(-1)x +"cos ech"^(-1)x =
Answer» `"LOG"_(E)((7-3sqrt(5))/(2))` `"log"_(e)((3+sqrt(5))/(2))` `"log"_(e)[((sqrt(5)-1)(2+sqrt(3)))/(2)]` `"log"_(e)[((sqrt(5)+1)(2+sqrt(3)))/(2)]` Answer :A

Discussion

38.	Let I_(n)=int tan^(n)x dx, (n gt 1). If I_(4 ) +I_(6)=a tan^(5)x+bx^(5)+C, where C is a constant of integration, then the ordered pair (a, b) is equal to :
Answer» A) `(-(1)/(5), 1)` B) `((1)/(5),0)` C) `((1)/(5), -1)` D) `(-(1)/(5),0)` Answer :2

Discussion

39.	Given three arbitary vectors bara,barb,barc, then vectors baralpha=5bara+6barb+7barc,beta=7bara-8barb+9barc,bary=3bara+20barb+5barc are
Answer» collinear Coplanar Non-coplanar None of these Answer :B

Discussion

40.	If veca=hati+hatk, hatk, overset(-)b=hati-hatj+hatk, overset(-)c=hati+hatj-hatk and overset(-)d=hati-hatj-hatk, then match the following columns
Answer» `{:(,,A,B,C,D),(,a,3,1,2,6):}` `{:(,,A,B,C,D),(,b,3,1,6,5):}` `{:(,,A,B,C,D),(,c,1,3,2,6):}` `{:(,,A,B,C,D),(,d,1,3,6,4):}` ANSWER :B

Discussion

41.	If x = (-5 + isqrt3)/(2) then (x^(2) + 5x)^(2) + x ( x+ 5) =
Answer» 49 48 42 `-42` ANSWER :C

Discussion

42.	IF inDelta ABC , sinA/2sin C /2=sinB/2and 2sis theperimeterof thetriangle thens is
Answer» 2b b 3B 4b Answer :A

Discussion

43.	Find the shortest distance between the two given straight linesvecr=(2hati+3hatj+hatk)+t(-2hati+hatj+2hatk)and(x-3)/(2)=(y)/(-1)=(z+2)/(2).
Answer» ANSWER : ` SQRT((365))/(3) `

Discussion

44.	A vector coplanar with vectoreshati+ hatjandhatj + hatkand parallel to the vector2 hati- 2 hatj- 4hatk is
Answer» `HATI - hatk` `hati - hatj -2HATK ` `hati +hatj-hatk ` `3hati+3hatj-6hatk` Solution :Any vector COPLANAR with vectors ` hati+ hatj andhatj +hatk ` is `a=x (hati +hatj)+y (hatj +hatk)` `impliesa=xhati +(x+y)hatj +yhatk` Itis giventhata isparaallelto` 2 hati- 2 hatj- 4 hatk ` ` thereforea= LAMDA( 2 hati- 2hatj- 4 hatk )` for some SCALAR ` lamda `. `implies [ x hati +(x+y)hatj +yhatk ]= lamda (2 hati- 2hatj - 4 hatk)` `implies x= 2 lamda , x+y=- 2 lamdaandy=- 4 lamda ` `implies x=2lamdaandy=-4 lamda ` `thereforea= 2 lamda( hati - hatj- 2hatk )` , where`lamda inR.`

Discussion

45.	If c in R be such that the line 4x - y + c = 0touches the ellipse x^(2) + 4y^(2) = 4 , then an equation having all such values of c among its roots is
Answer» `x^(2) - (1 + sqrt(7) x + sqrt(17) = 0` `x^(2) - (1 - sqrt(17))x - sqrt(17) = 0` `x^(3) - x^(2) - 17X + 17 = 0` `x^(3) - x^(2) + 17x - 17 = 0 ` Answer :C

Discussion

46.	A circle touches the parabola y^(2)=2x" at "P(1/2,1) and cuts the parabola at its vertex V. If the centre of the circle is Q, then
Answer» The radius of the circle is `5//sqrt2` units The radius of the circle is the MAXIMUM value of `7/4sin3x+1/4cos3x` Area of `DeltaPVQ" is "15/16` sq. units Slope of PQ is -2 Answer :B::C

Discussion

47.	Show that int_(0)^(a)f(x)g(x)dx=2int_(0)^(a)f(x)dx, if f and g are defined as f (x) = f (a - x) and g(x) + g(a - x) = 4
Answer» ANSWER :`:. I=2 overset(a) underset(0)int F(X)DX`

Discussion

48.	If the bisectors of the angles of the lines represented by 3x^(2) - 4xy + 5y^(2) = 0 and 5x^(2) + 4xy + 3y^(2) = 0 are same , then the angle made by the lines represented by first with the second , is
Answer» `30^(@)` `60^(@)` `45^(@)` `90^(@)` ANSWER :D

Discussion

49.	For x epsilon Rlet f(x)=\|((x-4)^(2),(x-3)^(2),(x-2)^(2)),((x-3)^(2),(x-2)^(2),(x-1)^(2)),((x-2)^(2),(x-1)^(2),x^(2))\| then \|f(3.51)+f(4.49)\|=___________
Answer» ANSWER :16

Discussion

50.	Evaluate the following: int_(-pi/2)^(pi/2)sin^7xdx
Answer» Solution :`sin^7(-X) = (-sinx)^7 = -sin^7x` therefore`sin^7x` is an ODD FUNCTION therefore `int_(-pi/2)^(pi/2) sin^7 x dx` = 0

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

The vector i+j+k,i+2j+3k,2i+3j+k are

Each side of DeltaABC is the polar of the opposite vertex with respect to a circle with centre P. Then P is ortho centre of DeltaABC.

A person gets dollars eqal to the square of the number which comes up when a balanced die, with faces marked 1, 2, 3, 4, 5, 6 is rooled one. If the game is repeated an indefinitely large number of times, how much money can be expect in the long run per game ?

Let x^2 - 2(a - 1)x + a - 1 = 0 (a in R) be a quadratic equation, then find the values of "a" for which (i) Exactly one root lies in (0,1) (ii) Both roots lies in (0, 1). (iii)Atleast one root lies in (0,1). (iv) One root is greater than 1 and other root is smaller than 0.

Isthe function f (x) = ( 3 x + 4 tan x)/( x)continuous at x = 0 ? If not, how many the function be defined to make it continuous at this point .

Q. If a state is chosen at random, what is the probability that the minimum age for obtaining a driver's license in that state will be at least 16?

If c is the velocity of electromagneticradiation e is the charge of an electron m is the mass of an electron and h is the Planck's constant, then the combination of these universal constants that is dimensionless, is

Prove that the volume of the largest cone that can be inscribed in a sphere of radius R is (8)/(27) of the volume of the sphere.

If A=[{:(1,2,5),(5,1,1),(3,0,4):}]then find A-2A'.

lim_(xto-1) ((1+x)(1-x^2)(1+x^3) (1-x^4).......(1-x^4n))/([(1+x)(1-x^2)(1+x^3) (1-x^4) .....(1-x^2n)]^2) is equal to

Evaluate the following inegrals int((x^(3)-x)^(1//2))/(x^(4))dx

The point of intersection of the lines l_(1) : r(t)=(i-6j+2k) +t(i+2j+k) l_(2) : R(u)=(4j+k)+u (2i+j+2k) is

Which of the following set are finite and which are infinite ? The set of even integers.

If the two coefficients of regression are - 0.6 and – 1.4, find the acute angle between theregression lines.

A random variable X has the following probability distribution:﻿ ﻿ Determine﻿ (i) K﻿ (ii) P(X lt 3) ﻿ (iii) P(X gt 6)﻿ (iv) P(0 lt X lt 3)﻿

From the set S = {0, 1, 2, …., 53}, three distinct numbers are chosen. The probability that the sum of them is 54 is

From each of the three married couples one partner is selected at random. The probability of selecting two males and one female is

Solve the equation ""^(11)C_(1) x^(10) - ""^(11)C_(3) x^(8) + ""^(11)C_(5) x^(6) - ""^(11)C_(7) x^(4) + ""^(11)C_(9) x^(2) - ""^(11)C_(11) = 0

Solve the following differential equations. (dy)/(dx)+ysec x=tan x

Choose the correct answer intsqrt(1+x^(2))dx is equal to

Let A be a2xx 2matrix with real entries and det (A)= d ne 0such that det (A+d(adj ) A)) =0 . Find the valued of det ( A-d(dj (A))

Therootsofx^3 - 13x^2 +39 x-27=0 are in

A balloon, which always remains spherical has a variable radius. Find the rate at which its volume is increasing with the radius when the later is 10 cm.

y^(2) = ax^(2) +bx + c then y^(3) (d^(2)y)/(dx^(2)) is a …….. function

Consider the following equations a) A-B=A-(A nn B) b) A=(A nn B)uu(A-B) c) A-(B uu C)=(A-B)uu(A-C) Which of these is / are correct

Consider a pyramid OPQRS located in the first octant (xge0, yge0, zge0) with O as origin and OP and OR along the X-axis and the Y-axis , respectively. The base OPQRS of the pyramid is a square with OP=3. The point S is directly above the mid point T of diagonal OQ such that TS=3. Then,

Which of the following statement patten is a tautology ?

Find the coefficient of x^(3) in the power series expansion of (5x+6)/((x+2)(1-x)) specifying the region in which the expansion is valid.

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

Find all points of discontinuityof f, where f is defined by f(x)={{:(2x^(3)+4," if "x le2),(x^(2)+2," if "x gt 2):}

If (1)/(3 - 4i) is a root of ax^(2) + bx + c = 0, (a,b, c in R, a ne 0)then

int_(0)^(2pi) x cos^(6) x dx=

find the equation of line joining (1,2) and (3,6) using determinants

Find the point which provides the solution of linear programming problem: Maximise: Z=45x + 55y Subject to constraints: x, yge 0,6x + 4y le 120 and 3x + 10y le 180.

Find the number of ways of arranging 6 boys and 6 girls around a circle so that all the girls come together

Solve (1 + x^(2))dy + 2xy dx = cot x dx (x ne 0)

If x=-(1)/(2) "sin h"^(-1)x +"cos ech"^(-1)x =

Let I_(n)=int tan^(n)x dx, (n gt 1). If I_(4 ) +I_(6)=a tan^(5)x+bx^(5)+C, where C is a constant of integration, then the ordered pair (a, b) is equal to :

Given three arbitary vectors bara,barb,barc, then vectors baralpha=5bara+6barb+7barc,beta=7bara-8barb+9barc,bary=3bara+20barb+5barc are

If veca=hati+hatk, hatk, overset(-)b=hati-hatj+hatk, overset(-)c=hati+hatj-hatk and overset(-)d=hati-hatj-hatk, then match the following columns

If x = (-5 + isqrt3)/(2) then (x^(2) + 5x)^(2) + x ( x+ 5) =

IF inDelta ABC , sinA/2sin C /2=sinB/2and 2sis theperimeterof thetriangle thens is

Find the shortest distance between the two given straight linesvecr=(2hati+3hatj+hatk)+t(-2hati+hatj+2hatk)and(x-3)/(2)=(y)/(-1)=(z+2)/(2).

A vector coplanar with vectoreshati+ hatjandhatj + hatkand parallel to the vector2 hati- 2 hatj- 4hatk is

If c in R be such that the line 4x - y + c = 0touches the ellipse x^(2) + 4y^(2) = 4 , then an equation having all such values of c among its roots is

A circle touches the parabola y^(2)=2x" at "P(1/2,1) and cuts the parabola at its vertex V. If the centre of the circle is Q, then

Show that int_(0)^(a)f(x)g(x)dx=2int_(0)^(a)f(x)dx, if f and g are defined as f (x) = f (a - x) and g(x) + g(a - x) = 4

If the bisectors of the angles of the lines represented by 3x^(2) - 4xy + 5y^(2) = 0 and 5x^(2) + 4xy + 3y^(2) = 0 are same , then the angle made by the lines represented by first with the second , is

For x epsilon Rlet f(x)=|((x-4)^(2),(x-3)^(2),(x-2)^(2)),((x-3)^(2),(x-2)^(2),(x-1)^(2)),((x-2)^(2),(x-1)^(2),x^(2))| then |f(3.51)+f(4.49)|=___________

Evaluate the following: int_(-pi/2)^(pi/2)sin^7xdx

A random variable X has the following probability distribution: Determine (i) K (ii) P(X lt 3) (iii) P(X gt 6) (iv) P(0 lt X lt 3)