28278 + Interview Questions in Maths in Class 12

1.	Let mu, beta, gammaare the roots of the equation x^3 + 2x^2 + 3x + 1 = 0. If the value of (1/beta^(3) + 1/gamma^(3) -1/alpha^(3)) (1/alpha^(3)+1/gamma^(3) -1/beta^(3)) +(1/alpha^(3) + 1/beta^(3) -1/gamma^(3)) (1/alpha^(3) + 1/gamma^(3) -1/beta^(3)) + (1/alpha^(3) + 1/beta^(3) -1/gamma^(3)) (1/beta^(3) + 1/gamma^(3) - 1/alpha^(3)) is lambda. Then find the sum of digit of \|lambda\|
Answer» ANSWER :172

Discussion

2.	The range of the function f(x)=sqrt(9-x^(2)) is
Answer» 1.(0, 3) 2.[0, 3] 3.(0, 3] 4.[0, 3) ANSWER :B

Discussion

3.	IfA_(1)and A_(2)be areas of two regular polygons having the same perimeter and number of sides be n and 2n respectively, then :(A_(1))/(A_(2))is
Answer» `(2 sin((pi)/(N)))/(1+COS((pi)/(n)))` `(2 cos((pi)/(n)))/(1+sin((pi)/(n)))` `(2 cos((pi)/(n)))/(1+cos((pi)/(n)))` `(2 sin((pi)/(n)))/(1+sin((pi)/(n)))` Answer :C

Discussion

4.	A and B two points on the curve xy=a^2. Let N be the mid-point of AB. The line through A and B meets.x-axis at P and y-axis at Q, then:
Answer» N bisects PQ ON is perpendicular to AB (where O is ORIGIN) AP = BQ AQ = BP Answer :A::C::D

Discussion

5.	The negation of the statemen AA x in N, x + 1 gt 2is
Answer» `AA X cancel in N, x+ 1 LT 2` `EE x in N, ` such that x + 1 gt 2 `AA x in N, x + 1 lt= 2` `EE x in N,` such that ` x + 1 lt= 2 ` ANSWER :D

Discussion

6.	If inte^(x)(1+x) sec^(2)(xe^(x))dx = f(x) + constant, then f(x) is equal to
Answer» `cos(xe^(X))` `SIN(xe^(x))` `2tan^(-1)(x)` `TAN(xe^(x))` ANSWER :C

Discussion

7.	If the two circles x^(2)+y^(2)+2gz+2fy=0 and x^(2)+y^(2)+2g'x+2f'y=0 touch each other then show that f'g=fg'
Answer» `FG=F^(1)g^(1)` `fg^(1)=f^(1)g` `f+g=f^(1)+g^(1)` `f+f^(1)=g+g^(1)` ANSWER :B

Discussion

8.	Derive the equation of the line in space passing through a point and parallel to a vector both in vector and cartesian form.
Answer» ANSWER :`(x-x_1)/(a) =(y-y_1)/(B) =(z-z_1)/(C )`

Discussion

9.	If A=[(2,-3,5),(3,2,-4),(1,1,-2)], find A^(-1). UsingA^(-1) solve the system of equations. 2x-3y+5z=11 , 3x+2y-4z=-5 and x+y-2z=-3
Answer» Answer :`X = 1, y = 2, and Z = 3`

Discussion

10.	Find the circumcentre of the triangle whose sides are given byx+y+2=0,5x-y-2=0 and x-2y+5=0
Answer» ANSWER :`((-1)/(3).(2)/(3))`

Discussion

11.	The principal value of cot^(-1)(-sqrt3) is
Answer» `-pi/6` `pi/6` `(7pi)/6` `(5PI)/6` ANSWER :D

Discussion

12.	If therelationbetween A and B is known tobetothe form : B= k xx n^(4) , whatis the valueof ( k + n) ?The followingdata wasobservedbetweenthe variableA and B : {:(A,B),(3,24),(4,48),(5,96):}
Answer» ANSWER :5

Discussion

13.	Deficiency of red cells in the blood cells is determined by examining a specimen of blood under microscope. Suppose a small fixed volume on an average 20 red cells for normal persons. Using the poisson distribution find the probability that a specimen of blood taken from a normal person will contain less than 15 red cells.
Answer» ANSWER :`sum_(r-0)^(14) (e^(-20))/(lfloor r) (20)^(r)`

Discussion

14.	If two angles of a triangle are tan^(-1) ""(1)/(2) and tan^(-1)""(1)/(3) .Then the third angle is
Answer» `(PI)/(4)` `(5 pi)/(4)` `(pi)/(2)` `(3 pi)/(4)` Answer :D

Discussion

15.	Find the maximum value of the 5 sinx+12cosx
Answer» SOLUTION :LET `5=rcostheta, 12=rsintheta` `therefore5^2=r^2cos^2theta,12^2=r^2sin^2theta` `therefore5^2+12^2=r^2(cos^2theta+sin^2theta)=r^2` `thereforer=(sqrt25+144)=13` `therefore` themaximum value of `5 sinx+12cosx` is 13

Discussion

16.	Random variable X takes the integral values from 1 to 100 having equal probability. Then find E(X), E(X^(2)) and Var(X).
Answer» ANSWER :`(101)/(2),(6767)/(2), (3333)/(4)`

Discussion

17.	Let A be a 3xx3 matrix with entries from the set of numbers, If the system of equations A^(2) X=0 has a non - trivial solution then
Answer» AX =0 has a NON TRIVIAL SOLUTION AX= 0 does not have a non - trivial solution. A is a non -singular MATRIX none of these Answer :A

Discussion

18.	IF thesidesof a trianglearex^2 + x+1, x^2 -1and2x +1then thegreatestangleis
Answer» `90^@` `135^@` `115^@` `120^@` ANSWER :D

Discussion

19.	If A=[(cosalpha,-sinalpha),(sinalpha,cosalpha)], then A+A'=I, if the value of alpha is :
Answer» `PI/6` `pi/3` `pi` `(3PI)/(2)`. ANSWER :B

Discussion

20.	Evaluate the following integrals int (1-x) sqrtx dx
Answer» Solution :`INT(1-X) sqrtx DX = int (sqrtx-xsqrtx)dx` =`int (x^(1/2)-x^(3/2)dx = x^(1/2+1)/(1/2+1) -x^(3/2+1)/(3/2+1) +C = x^(3/2)/(3/2) - x^(5/2)/(5/2) +c = (2x^(3/2)/3 - (2x^(5/2)/5 +c`

Discussion

21.	Which of the following options is the only INCORRECT combination ?
Answer» (III) (iii) (R) (III) (IV) (S) (IV) (i) (R) (I) (II) (Q) Answer :B

Discussion

22.	If veca is any vector then the value of Sigma (veca xx veci)^(2) is :
Answer» `a^(2)` `2A^(2)` `3A^(2)` `4A^(2)` SOLUTION :N/A

Discussion

23.	What is the following sets has the larger standard deviation? A = {1,2,3,4,5} B = {1,4,15,21,27}
Answer» ANSWER :SET B is GREATER

Discussion

24.	The quadratic equation x^(2) + 7x = 14 (q^(2) + 1) , where q is an integer has
Answer» REAL and DISTINCT roots integral roots imaginary roots none of these Answer :A

Discussion

25.	int_(0)^(pi//3) \|tan x - 1\|dx=
Answer» `pi/2` `pi/4` `pi/6` `pi/2` ANSWER :C

Discussion

26.	Let m and n be two integers greater than 1. if lim_(alpha to 0) ((e^(cos (alpha^n))-e)/alpha^m)=-(e/2) then the value of n/m is
Answer» ANSWER :`0.50`

Discussion

27.	Thescalar product of the vector hat i + hat j + hat k with a unit vector along the sum of vectors 2 hat i + 4 hat j - 5 hat k and lambda hat i + 2 hat j + 3 hat k is equal to one. Find the value of lambda.
Answer» ANSWER :`lambda=1`

Discussion

28.	A system of circles is draen through two fixed points (-1,0) and (1,0), tangents are drawn to these circles parallel to the line y=x, the locus of the points of contact is
Answer» `x ^(2) - y ^(2) -2xy =1` `x ^(2) +y ^(2) =1` `x ^(2) +y ^(2) +2xy =0` `x ^(2) -y ^(2) +2xy +1=0` ANSWER :A

Discussion

29.	Find the domain and range of the function, f(x)= (1)/(3-sin 2x).
Answer» SOLUTION :N/A

Discussion

30.	Using elementary row transformations , find the inverse of [{:(2,-6),(1,-2):}]
Answer» ANSWER :`thereforeA^(-1)=[{:(-1,3),(-(1)/(2),1):}]`

Discussion

31.	If the common tangent to circle x^(2)+y^(2)= c^(2) and the parabola y^(2) = 4ax subtends an angle theta with X-axis then Tan^(2) theta =
Answer» `(sqrt(C^(2)+4A^(2))-c)/(2C)` `(sqrt(c^(2)+4a^(2))+c)/(2)` `(sqrt(c^(2)+4a^(2))+c)/(2c)` `(sqrt(c^(2)+4a^(2))-c)/(2)` Answer :A

Discussion

32.	(10x^(9) + 10^(x) log , 10)/(10^(x)+ x^(10))
Answer» `10^(X)-x^(10)+C` `10^(x)+x^(10)+C` `(10^(x)-x^(10))^(-1)+C` `log(10^(x)+x^(10))+C` ANSWER :D

Discussion

33.	Solve the following equations (where [] denotes greatest integer function and {} represent fractional part function and sgn represents signum function) (i) [x]+\|x-2\| le 0 and x in [-1,3] (ii) [2x]-2x=[x+1] (iii) [x^(2)]+2[x]=3x, 0 le x le 2
Answer» ANSWER :`(i)` no solution `(II)-1,-(1)/(2)` `(iii) 0,1`

Discussion

34.	If [(x+3,z+4,2y-7),(-6,a-1,0),(b-3,-21,0)]=[(0,6,3y-2),(-6,-3,2c+2),(2b+4,-21,0)] Find the values of a, b, c, x, y and z.
Answer» ANSWER :a=-2, b=-7, c=-1, x=-3, y=-5, z=2

Discussion

35.	The value of int1/(cos^(4)x+sin^(5)x)dx is equal to
Answer» `TAN^(-1)(tanx+cotx)+C` `-tan^(-1)(tanx+cotx)+C` `tan^(-1)(tanx-cotx)+C` `-tan^(-1)(tanx-cotx)+C` ANSWER :c

Discussion

36.	The normal unit vector of the plane x-3y + 2z = 6 is ............
Answer» `(1,-3,2)` `(1/6,1/2,1/3)` `((-1)/(sqrt(14)),(3)/(sqrt(14)),(-2)/(sqrt(14)))` `((1)/(sqrt(14)),(3)/(sqrt(14)),(2)/(sqrt(14))` ANSWER :C

Discussion

37.	If alpha_1 , alpha_2 ,……….,alpha_nare the roots of x^n + px + q = 0, then (alpha_n - alpha_1) (alpha_n - alpha_2) ………(alpha_n - alpha_(n-1) ) =
Answer» n 0 1 `-1` ANSWER :1

Discussion

38.	Find the asymptotes of the following curves : y = " arc tan " x
Answer» ANSWER :`y = PM (PIX)/2 - 1 `

Discussion

39.	If A = {0,1}and N be the set of natural numbers. Then , the mapping f: N rarr A defined by f(2n-1) = 0 , f(2n) = 1, AA n in N , is onto.
Answer» SOLUTION :N/A

Discussion

40.	If (1+x+2x^(2)+4x^(3))^(10)=a_(0)+a_(1)x+a_(2)x^(2)+….+a_(30)x^(30). Find the value ofa_(0) +a_(2)+a_(4) +…+ a_(30)
Answer» SOLUTION :N/A

Discussion

41.	Equation of a plane which passes through the point of intersection of lines (x-1)/(3)=(y-2)/(1)=(z-3)/(2) and (x-3)/(1)=(y-1)/(2)=(z-2)/(3) and at greatest distance from the origin is
Answer» 7x+2y+4z=54 4x+3y+5z= 50 3x+4y+5z=49 x+y+ z=12 Answer :B

Discussion

42.	A girl walks 4 km towards west, then she walks 3 km in a direction 30^(@) east ofnorth and stops. Determine the girl’s displacement from her initial point ofdeparture.
Answer» Answer :`(-5)/(2)hati+(3sqrt(3))/(2)HATJ`

Discussion

43.	Integrate the function in Exercise. x^(2)logx
Answer» Answer :`(X^(3))/(3)LOGX-(x^(3))/(9)+C`

Discussion

44.	Find the values of 1/x for the following values of x (2,5)(b ) [-5 ,-1]( c)( 3, oo)(d)(-3,oo)( e)(-oo , 4)
Answer» Solution :`-5 le x le -1` `rArr-2 lt x lt 0 or0 le x le 3` `For -2 lt x lt 0, x^2 in (0,4)` and for `0le x le 3, x^2 in [0,9] " "(1)` From (1) and (2) `x^2 in[0,9] " " (2)` Alternatively ,`x in (-2 ,3]` now least value of `x^2` is 0 which Greatest value of `x^2` is 9 for x =3 `rArrx^2 in [0,9]` (d) `(-3,OO)` Here least value of `x^2` is 0 for x=0 and when x goes up to `rArr x^2 in [0,oo)` ( e) `(-oo , 4)` Here least value of `x^2` is 0 for x =0 for x=0 and`x^2 rarr oo` when `xrarr -oo` Hence `x^2in [0,oo)`

Discussion

45.	Which is equivalent to (x-1/x)(1+1/(x-1)) ?
Answer» X+1 x-1 1 `x/(x+1)` ANSWER :A

Discussion

46.	The probability that atleast one of the two events A and B occurs is 0.6. If A and B occur simultaneously with probability 0.3, evaluate P(barA ) + P(barB).
Answer» ANSWER :1.1

Discussion

47.	Evaluate int_(-pi)^(199pi) sqrt((1- cos 2 x)/(2))dx
Answer» ANSWER :398

Discussion

48.	(d)/(dx ) " Tan ^(-1) (1)/(x ^(2) -1) }=
Answer» `(-1)/( X SQRT(x ^(2) -1))` `(1)/(x sqrt(x ^(2) -1))` `(-2)/(x sqrt(x ^(2) +1))` ` (-2)/(x sqrt(x ^(2) +1))` ANSWER :A

Discussion

49.	If the latus rectum of a hyperola forms an equilateral triangle with the centre of the hyperbola, then its eccentricity is
Answer» `(sqrt5+1)/(2)` `(sqrt11+1)/(2)` `(SQRT13+1)/(2SQRT3)` `(sqrt13*1)/(2sqrt3)` ANSWER :C

Discussion

50.	Using Rolle's theorem, find the point on the curve y= x (x-4), x in [0, 4], where the tangent is parallel to X-axis
Answer» ANSWER :`(2, -4)`

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

The range of the function f(x)=sqrt(9-x^(2)) is

IfA_(1)and A_(2)be areas of two regular polygons having the same perimeter and number of sides be n and 2n respectively, then :(A_(1))/(A_(2))is

A and B two points on the curve xy=a^2. Let N be the mid-point of AB. The line through A and B meets.x-axis at P and y-axis at Q, then:

The negation of the statemen AA x in N, x + 1 gt 2is

If inte^(x)(1+x) sec^(2)(xe^(x))dx = f(x) + constant, then f(x) is equal to

If the two circles x^(2)+y^(2)+2gz+2fy=0 and x^(2)+y^(2)+2g'x+2f'y=0 touch each other then show that f'g=fg'

Derive the equation of the line in space passing through a point and parallel to a vector both in vector and cartesian form.

If A=[(2,-3,5),(3,2,-4),(1,1,-2)], find A^(-1). UsingA^(-1) solve the system of equations. 2x-3y+5z=11 , 3x+2y-4z=-5 and x+y-2z=-3

Find the circumcentre of the triangle whose sides are given byx+y+2=0,5x-y-2=0 and x-2y+5=0

The principal value of cot^(-1)(-sqrt3) is

If therelationbetween A and B is known tobetothe form : B= k xx n^(4) , whatis the valueof ( k + n) ?The followingdata wasobservedbetweenthe variableA and B : {:(A,B),(3,24),(4,48),(5,96):}

If two angles of a triangle are tan^(-1) ""(1)/(2) and tan^(-1)""(1)/(3) .Then the third angle is

Find the maximum value of the 5 sinx+12cosx

Random variable X takes the integral values from 1 to 100 having equal probability. Then find E(X), E(X^(2)) and Var(X).

Let A be a 3xx3 matrix with entries from the set of numbers, If the system of equations A^(2) X=0 has a non - trivial solution then

IF thesidesof a trianglearex^2 + x+1, x^2 -1and2x +1then thegreatestangleis

If A=[(cosalpha,-sinalpha),(sinalpha,cosalpha)], then A+A'=I, if the value of alpha is :

Evaluate the following integrals int (1-x) sqrtx dx

Which of the following options is the only INCORRECT combination ?

If veca is any vector then the value of Sigma (veca xx veci)^(2) is :

What is the following sets has the larger standard deviation? A = {1,2,3,4,5} B = {1,4,15,21,27}

The quadratic equation x^(2) + 7x = 14 (q^(2) + 1) , where q is an integer has

int_(0)^(pi//3) |tan x - 1|dx=

Let m and n be two integers greater than 1. if lim_(alpha to 0) ((e^(cos (alpha^n))-e)/alpha^m)=-(e/2) then the value of n/m is

Thescalar product of the vector hat i + hat j + hat k with a unit vector along the sum of vectors 2 hat i + 4 hat j - 5 hat k and lambda hat i + 2 hat j + 3 hat k is equal to one. Find the value of lambda.

A system of circles is draen through two fixed points (-1,0) and (1,0), tangents are drawn to these circles parallel to the line y=x, the locus of the points of contact is

Find the domain and range of the function, f(x)= (1)/(3-sin 2x).

Using elementary row transformations , find the inverse of [{:(2,-6),(1,-2):}]

If the common tangent to circle x^(2)+y^(2)= c^(2) and the parabola y^(2) = 4ax subtends an angle theta with X-axis then Tan^(2) theta =

(10x^(9) + 10^(x) log , 10)/(10^(x)+ x^(10))

Solve the following equations (where [*] denotes greatest integer function and {*} represent fractional part function and sgn represents signum function) (i) [x]+|x-2| le 0 and x in [-1,3] (ii) [2x]-2x=[x+1] (iii) [x^(2)]+2[x]=3x, 0 le x le 2

If [(x+3,z+4,2y-7),(-6,a-1,0),(b-3,-21,0)]=[(0,6,3y-2),(-6,-3,2c+2),(2b+4,-21,0)] Find the values of a, b, c, x, y and z.

The value of int1/(cos^(4)x+sin^(5)x)dx is equal to

The normal unit vector of the plane x-3y + 2z = 6 is ............

If alpha_1 , alpha_2 ,……….,alpha_nare the roots of x^n + px + q = 0, then (alpha_n - alpha_1) (alpha_n - alpha_2) ………(alpha_n - alpha_(n-1) ) =

Find the asymptotes of the following curves : y = " arc tan " x

If A = {0,1}and N be the set of natural numbers. Then , the mapping f: N rarr A defined by f(2n-1) = 0 , f(2n) = 1, AA n in N , is onto.

If (1+x+2x^(2)+4x^(3))^(10)=a_(0)+a_(1)x+a_(2)x^(2)+….+a_(30)x^(30). Find the value ofa_(0) +a_(2)+a_(4) +…+ a_(30)

Equation of a plane which passes through the point of intersection of lines (x-1)/(3)=(y-2)/(1)=(z-3)/(2) and (x-3)/(1)=(y-1)/(2)=(z-2)/(3) and at greatest distance from the origin is

A girl walks 4 km towards west, then she walks 3 km in a direction 30^(@) east ofnorth and stops. Determine the girl’s displacement from her initial point ofdeparture.

Integrate the function in Exercise. x^(2)logx

Find the values of 1/x for the following values of x (2,5)(b ) [-5 ,-1]( c)( 3, oo)(d)(-3,oo)( e)(-oo , 4)

Which is equivalent to (x-1/x)(1+1/(x-1)) ?

The probability that atleast one of the two events A and B occurs is 0.6. If A and B occur simultaneously with probability 0.3, evaluate P(barA ) + P(barB).

Evaluate int_(-pi)^(199pi) sqrt((1- cos 2 x)/(2))dx

(d)/(dx ) " Tan ^(-1) (1)/(x ^(2) -1) }=

If the latus rectum of a hyperola forms an equilateral triangle with the centre of the hyperbola, then its eccentricity is

Using Rolle's theorem, find the point on the curve y= x (x-4), x in [0, 4], where the tangent is parallel to X-axis

Solve the following equations (where [] denotes greatest integer function and {} represent fractional part function and sgn represents signum function) (i) [x]+|x-2| le 0 and x in [-1,3] (ii) [2x]-2x=[x+1] (iii) [x^(2)]+2[x]=3x, 0 le x le 2