28278 + Interview Questions in Maths in Class 12 Page 18 InterviewSolution

851.	An ellipse whose distance between foci S and S is 4 units is incribed in the triangle ABC touching the sides AB, AN and BC at P, Q and R. If centre of ellipse is or origin and major axis along-axis, SP+SP=6, then answer the following questions. If angle BAC=90^(@) then locus of point A is
Answer» `x^(2)+y^(2)=12` `x^(2)+y^(2)=4` `x^(2)+y^(2)=14` NONE of these Answer :C

Discussion

852.	The numberof waysof dividing10booksinto3groupof 5,3,2, books respectivelyis
Answer» `(8!)/(6!5!4!)` `(9!)/(5!4!3!)` `(10!)/(5!3!2!)` `(12!)/(7!5!2!)` Answer :C

Discussion

853.	Find the centroid and the area of the triangle formed by the lines 2y^2-xy-6x^2=0,x+y+4=0
Answer» ANSWER :`56/3`sq.units

Discussion

854.	An ellipse whose distance between foci S and S is 4 units is incribed in the triangle ABC touching the sides AB, AN and BC at P, Q and R. If centre of ellipse is or origin and major axis along-axis, SP+SP=6, then answer the following questions. If chord PQ subtends 90^(@) angles of centre of ellipse, then locus of A is
Answer» `25X^(2)+81 y^(2)=620` `25x^(2)+81y^(2)=630` `9x^(2)+16y^(2)=25` NONE of these Answer :B

Discussion

855.	If f(x)=(sin(2pi[pi^(2)x]))/(5+[x]^(2)), ([*] denotes the greatestinteger function), Then the f(x) is
Answer» DISCONTINUOUS at some x continuous at all x, but the derivative F'(x) doesn't exist for some x f''(x) does not exist for all x none of these Answer :D

Discussion

856.	Show that the curves xy=a^(2) and x^(2)+y^(2)=2a^(2) touch each other.
Answer» ANSWER :`m_(2)=(-1)`

Discussion

857.	int_((-pi)/(2))^(pi/2) log((2-sin theta)/(2 + sin theta)) d theta is equal to
Answer» 0 1 2 `-1` ANSWER :A

Discussion

858.	If two vertices of an equilateral triangle are A ( -a,0) and B( a,0 ), a gt0and the third vertex C lies above x-axis , then the equation of the circumcircle of Delta ABCis
Answer» `3x^(2) +3y^(2) -2sqrt3ay =3A^(2) ` ` 3x^(2) +3y^(2) -2ay=3a^(2) ` ` X^(2) +y^(2) -2ay =a^(2) ` `x^(2) +y^(2) -sqrt3 ay = a^(2) ` ANSWER :A

Discussion

859.	A tea party is arranged for 16 people among two sides of a long table with 8 chairs on each side. Four men wish to sit on one particular side and two on the other side. The number of ways they can be seated is
Answer» `""^(6)C_(8).8!` `""^(10)C_(4).8!` `""^(16)C_(4).(8!)^(2)` `""^(10)C_(4).^(6)C_(6).(8!)^(2)` Answer :D

Discussion

860.	Calculate the magnitude of ring strain energy in (kJ/mol) of cyclopropane from the following data Delta_(f)H[C_(3)H_(6)(g)]=55,Delta_(f)H[C(g)]=715,Delta_(f)H[H(g)]=220, BE(C-C)=355,BE(C-H)=410 ( all in kJ/mol ) :
Answer» SOLUTION :[0115] Given `DeltaH_(4)=-B.E. (3C-C+6C-H)+`RING strain energy (RSE) `=DeltaH_(1)-DeltaH_(2)-DeltaH_(3)` `R.S.E=DeltaH_(1)=DeltaH_(1)-DeltaH_(2)-DeltaH_(3)`+B.E.(3C-C+6C-H) `=55-2145-1320+(3xx355+6xx410)` `=115kJ//mol`

Discussion

861.	A publisher sells a hardcover editin of a book for Rs. 72 and a paperback edition of the same for Rs.40. Costs to the publisher are Rs. 56 and Rs. 28 respectively in addition to weekly costs of Rs. 9600. Both types require 5 minutes of printing time although the hardcover edition requires 10 minutes of binding time and thre paperback editin requires only 2 minutes. Both the printing and binding operations have 4800 minutes available each week. How many of each type of books should be produced in order to maximize the profit? Also find the maximum profit per week.
Answer» Solution :LET X cpoies of the hardcover edition and y copies of the paperback edition be prepared. Then, `C=9600+56x+28yand S=72x+40y.` Profit function is `Z=(S-C),i.e., Z=16x+12y-9600.` MAXIMIZE Z subject to `x ge0,YGE0(5x+10x)+(5y+2y)le4800.`

Discussion

862.	In the matrix A=[[2,5,19,-7],[35,-2,5/2,12],[sqrt3,1,-5,17]] Write: Write the elements a_13, a_21, a_33, a_24, a_23
Answer» SOLUTION :`a_13=19, a_21=35, a_33=-5, a_24=12, a_23=5/2`

Discussion

863.	(1+1/(2!) + 1/(4!)+ .....)^2 - (1+1/(3!) + 1/(5!)+ .....)^2=
Answer» 2 `-2` 1 `-1` ANSWER :C

Discussion

864.	If tantheta.tan(120^(@)-theta)tan(120^(@)+theta)=(1)/(sqrt3),"then"theta is equal to
Answer» `(npi)/(3)+(PI)/(18),NINZ` `(npi)/(3)+(pi)/(12),ninZ` `(npi)/(12)+(pi)/(12),ninZ` `(npi)/(3)+(pi)/(6),ninZ` Answer :A

Discussion

865.	If y=[sin""(x)/(2)+cos ""(x)/(2)]^(2),find(dy)/(dx)"at"x (pi)/(6)
Answer» `(1)/(2)` `(sqrt(3))/(2)` 1 0 Answer :B

Discussion

866.	Solve using Cramer's rule:(4)/(x+5)+(3)/(y+7)=-1&(6)/(x+5)-(6)/(y+5)=-5
Answer» ANSWER :x=-7,y=4

Discussion

867.	for what value of lambda, the vectors veca=3hati-hatj+4hatk, b= lambdahati+3hatj+3hatk are perpendicular to each other
Answer» `3` `-3` `0` 0.05 Answer :B

Discussion

868.	If sin alpha+sinbeta=l, cos alpha cos beta= m and tan(alpha/2)tan(beta/2)=n(!= 1), then
Answer» `COS(alpha-beta)=(l^(2)+m^(2)-2)/(2)` `cos(alpha+beta)=(m^(2)-l^(2))/(m^(2)+l^(2))` `(1+n)/(1-n)=(l^(2)+m^(2))/(2N)` `alpha+beta=pi/2` if `l=m` Answer :A::B::C::D

Discussion

869.	IF lim_(x toinfty){(x^3+1)/(x^2+1)-(alphax+beta)} exist and equal to 2, then the ordered pair (alpha,beta) of real numbers is
Answer» `(1,-1)` (-2,1) (-1,1) (1,-2) ANSWER :D

Discussion

870.	Are the following sets relation ? A xx phi from A to phi.Determinethe domain range and inverse of each of the relations mentioned above.
Answer» SOLUTION : `A XX PHI` from A to `phi` is a RELATION.

Discussion

871.	The orthogona projection of overset(-)a" on overset(-)(b) is
Answer» `((VECA. VECB)veca)/(\|veca\|^(2))` `((veca.vecb)vecb)/(\|vecb\|^(2))` `(veca)/(\|veca\|^(2))` `(vecb)/(\|vecb\|)` ANSWER :B

Discussion

872.	The range of a random variable X is {1, 2, 3, ……..} and P(X=k)=(C^(k))/(lfloork) where k = 1, 2, 3,…. Find the value of C and P(0lt X lt 3).
Answer» ANSWER :`1n_(E) = 2 + ((ln_(e) 2)^(2))/(2)`

Discussion

873.	Assume that X,Y,Z,W and P are matrices of order 2xxn, 3xxk, 2xxp, nxx3 and pxxk respectively. Choose the correct answer in the following cases. The restriction on n,k and p so that PY+WY will be defined are:
Answer» k=3, p=n k is ARBITRARY, p=n p is arbitrary, k=3 k=2, p=3 Answer :A

Discussion

874.	Find points on the curve (x^(2))/(4)+(y^(2))/(25)=1 at which the tangents are(i) Parallel to X - axis(ii) Parallel to Y - axis.
Answer» Answer :(i) Tangents at POINTS (0, 5) and (0, -5) are parallel to X - AXIS and (II) Tangents at points (2, 0) and (-2, 0) are parallel to Y-axis.

Discussion

875.	LetS_n= cos ((n pi )/( 10)) , n = 1,2,3,…… thenthe valueof ( s_1 s_2 ……s_(10))/( s_1 + s_2 +…….. +s_(10)) isequal to
Answer» `(1)/( sqrt(2))` ` (sqrt(3))/(2)` `2 sqrt(2)` `0` ANSWER :D

Discussion

876.	Assume that X,Y,Z,W and P are matrices of order 2xxn, 3xxk, 2xxp, nxx3 and pxxk respectively. Choose the correct answer in the following cases.If n=p, then the order of the matrix 7X-5Z is:
Answer» `PXX2` `2XXN` `nxx3` `PXXN` ANSWER :B

Discussion

877.	{x in R: \|x-2\|= x^(2)}=
Answer» (-1, 2) (1, 2) (-1, -2) {1, -2} ANSWER :D

Discussion

878.	Let X_(n)={Z=x+iy:\|zA^(2)le(1)/(n)}for allintegers n le 1 then underset(n=1)overset(infty)cap x_(n) is
Answer» a SINGLETON SET not a FINITE set an empty set a finite set with more than one elements Answer :A

Discussion

879.	The meanof thenumbersobtainedonthrowinga diehavingwritten,1 onthreefaces , 2 ontwofacesand 5ononefaceis ….
Answer» 1 2 5 `8/3` ANSWER :B

Discussion

880.	If f(x)=sin(logx),(x gt 0) then find f'(x)
Answer» ANSWER :C

Discussion

881.	The shaded region in the given figure is a graph of ……………
Answer» `4x-2y LE 3` `4x-2y le -3` `2x-4y GE 3` `2x-4y le -3` ANSWER :B

Discussion

882.	If y = e^(sin^(-1)(t^(2)-1)) & x = e^(sec-1((1)/(t^(2-1))) then (dy)/(dx) is equal to
Answer» `(X)/(y)` `(-y)/(x)` `(y)/(x)` `(-x)/(y)` ANSWER :B

Discussion

883.	The equation of the line passing through the point of intersection of the lines 2x+y+1=0, x-y-7=0 and the point (3, -2) is
Answer» a, B, C c, a, b b, c, a c, b, a ANSWER :D

Discussion

884.	Find the shortest distance between the lines whose vector equations arevecr=(hati+2hatj+3hatk)+lambda(hati-3hatj+2hatk) and vecr=4hati+5hatj+6hatk+mu(2hati+3hatj+hatk)
Answer» ANSWER :`=(3)/(SQRT(19))`

Discussion

885.	Find the number of ordered pairs (x,y) such that L.C.M. of x and y is 2520.
Answer» ANSWER :315

Discussion

886.	Integration using rigonometric identities : int(sin theta)/(cos3 theta)+(sin 3 theta)/(cos9 theta)+( sin9 theta)/(cos 27theta)d theta=...+c
Answer» `(1)/(2)LOG\|(sec 27 THETA)/(sec theta)\|` `(1)/(2)log\|(sec theta)/(sec 27theta)\|` `(1)/(2)log\|sqrt((sec theta)/(sec 27theta))\|` None of these Answer :C

Discussion

887.	int(dx)/(x(x^(4)+1)) is equal to
Answer» `(1)/(4)log""(X^(4)+1)/(x^(4))+C` `(1)/(4)log""((x^(4))/(x^(4)+1))+C` `(1)/(4)log(x^(4)+1)+C` none of these Answer :B

Discussion

888.	If x=cosalpha+isinalpha,y=cosbeta+isinbeta," then "(x)/(y)+(y)/(x)
Answer» `2SIN(alpha+beta)` `2sin(alpha-beta)` `2COS (alpha+beta)` `2cos (alpha-beta)` ANSWER :D

Discussion

889.	If the points vectors of A,B and C are respectively 2hati-hatk+hatk, hati-3hatj-5hatk and 3hati-4hatj-4hatk", then "cos^(2) A is equal to
Answer» 0 `(6)/(41)` `(35)/(41)` 1 Answer :C

Discussion

890.	Sketch the graphs of the following functions: y = (x^(3))/(24) - log x
Answer» ANSWER :x=0

Discussion

891.	A binary operation is chosen at random from the set of all binary operations on a set A containing n elements. The probability that the binary operation is commutative is
Answer» `(N^(n))/(n^(n)^(2))` `(n^(n//2))/(n^(n)^(2))` `((n)^(n//2))/(n^((n^(2))//(2))` none Answer :C

Discussion

892.	Compute P(A\|B), if P(B) = 0.5 and P(AnnB) = 0.32
Answer» <P> ANSWER :`P(A\|B)=(16)/(25)`

Discussion

893.	Find the number of ways of arranging the letters of the word 'FATHER' so that no vowel occupies even place.
Answer» ANSWER :144

Discussion

894.	Find k so that the following equations are consistent: 2x-y+3=0, kx-y+1=0, 5x-y-3=0
Answer» 4 3 5 9 Answer :B

Discussion

895.	the order and degree of the differential equation (d^2y)/(dx^2) + ((dy)/(dx))^1/3 + x =0 are respectively
Answer» `2,3` `3,3` `2,2` `2,4` ANSWER :A

Discussion

896.	Let f(x)=x^(13)+2x^(12)+3x^(11)+...+13x+14 " and " alpha=cos""(2pi)/15+isin""(2pi)/15.If N=f(alpha)f(alpha^(2))...f(alpha^(14)), then
Answer» number of DIVISION of N is 144 number of DIVISORS of N is 196 number of divisors of N which are perfect squares of 49 number of divisors of N which are perfect SQUARE of 12 Answer :B

Discussion

897.	Coefficient of x^(6) in (1+x)(1+x^(2))^(2)(1+x^(3))^(3)…(1+x^(n))^(n) is
Answer» `26` `28` `30` `35` Solution :`(b)` The COEFFICIENT of `X^(6)` in the given expression `=` coefficient of `x^(6)` in `(1+^(6)C_(1)x^(6))(1+^(5)C_(1)x^(5))(1+^(4)C_(1)x^(4))(1+^(3)C_(1)x^(3)+^(3)C_(2)x^(6))(1+^(2)C_(1)x^(2)+^(2)C_(2)x^(4))(1+x)` `=` coefficient of `x^(6)` in `(1+6x^(6)+5x^(5)+4x^(4))(1+2x^(2)+3X^(3)+x^(4)+6x^(5)+3x^(6))(1+x)` `=` coefficient of `x^(6)` in `(11x^(5)+17x^(6))(1+x)=28`

Discussion

898.	Find (dy)/(dx) in the following: y= sin^(-1) (3x-4x^(3)), 0 lt x lt (1)/(2)
Answer» ANSWER :`(3)/(SQRT(1-x^(2)))`

Discussion

899.	Solve (1 + x^(2))(dy)/(dx) + 2xy = (1)/(1 + x^(2)), y = 0 whenx= 1
Answer» Answer :`y (1 + X^(2)) = tan^(-1)x - (pi)/(4)`

Discussion

900.	Which of the following functions is/are bounded?
Answer» `f(x)=(2X)/(1+x^(2)),[-2,2]` `f(x)=(x^(2))/(1-x),x in [0,2]-[1]` `f(x)=(x^(3)-8x+6)/(4x+1),[0,5]` none of these Solution :`f(x)=(2x)/(1+x^(2)),[-2,2]" has RANGE "[-1,1]," HENCE bounded."` `f(x)=(x^(2))/(1-x),x in [0,2]-{1}" is unbounded as"f(x)rarroo," when "xrarr1^(-)` `f(x)=(x^(3)-8x+6)/(4x+1),[0,5]" is bounded because domain does not contain"-1//4.`

Discussion

Explore topic-wise InterviewSolutions in .

An ellipse whose distance between foci S and S is 4 units is incribed in the triangle ABC touching the sides AB, AN and BC at P, Q and R. If centre of ellipse is or origin and major axis along-axis, SP+SP=6, then answer the following questions. If angle BAC=90^(@) then locus of point A is

The numberof waysof dividing10booksinto3groupof 5,3,2, books respectivelyis

Find the centroid and the area of the triangle formed by the lines 2y^2-xy-6x^2=0,x+y+4=0

If f(x)=(sin(2pi[pi^(2)x]))/(5+[x]^(2)), ([*] denotes the greatestinteger function), Then the f(x) is

Show that the curves xy=a^(2) and x^(2)+y^(2)=2a^(2) touch each other.

int_((-pi)/(2))^(pi/2) log((2-sin theta)/(2 + sin theta)) d theta is equal to

If two vertices of an equilateral triangle are A ( -a,0) and B( a,0 ), a gt0and the third vertex C lies above x-axis , then the equation of the circumcircle of Delta ABCis

A tea party is arranged for 16 people among two sides of a long table with 8 chairs on each side. Four men wish to sit on one particular side and two on the other side. The number of ways they can be seated is

Calculate the magnitude of ring strain energy in (kJ/mol) of cyclopropane from the following data Delta_(f)H[C_(3)H_(6)(g)]=55,Delta_(f)H[C(g)]=715,Delta_(f)H[H(g)]=220, BE(C-C)=355,BE(C-H)=410 ( all in kJ/mol ) :

In the matrix A=[[2,5,19,-7],[35,-2,5/2,12],[sqrt3,1,-5,17]] Write: Write the elements a_13, a_21, a_33, a_24, a_23

(1+1/(2!) + 1/(4!)+ .....)^2 - (1+1/(3!) + 1/(5!)+ .....)^2=

If tantheta.tan(120^(@)-theta)tan(120^(@)+theta)=(1)/(sqrt3),"then"theta is equal to

If y=[sin""(x)/(2)+cos ""(x)/(2)]^(2),find(dy)/(dx)"at"x (pi)/(6)

Solve using Cramer's rule:(4)/(x+5)+(3)/(y+7)=-1&(6)/(x+5)-(6)/(y+5)=-5

for what value of lambda, the vectors veca=3hati-hatj+4hatk, b= lambdahati+3hatj+3hatk are perpendicular to each other

If sin alpha+sinbeta=l, cos alpha cos beta= m and tan(alpha/2)tan(beta/2)=n(!= 1), then

IF lim_(x toinfty){(x^3+1)/(x^2+1)-(alphax+beta)} exist and equal to 2, then the ordered pair (alpha,beta) of real numbers is

Are the following sets relation ? A xx phi from A to phi.Determinethe domain range and inverse of each of the relations mentioned above.

The orthogona projection of overset(-)a" on overset(-)(b) is

The range of a random variable X is {1, 2, 3, ……..} and P(X=k)=(C^(k))/(lfloork) where k = 1, 2, 3,…. Find the value of C and P(0lt X lt 3).

Assume that X,Y,Z,W and P are matrices of order 2xxn, 3xxk, 2xxp, nxx3 and pxxk respectively. Choose the correct answer in the following cases. The restriction on n,k and p so that PY+WY will be defined are:

Find points on the curve (x^(2))/(4)+(y^(2))/(25)=1 at which the tangents are(i) Parallel to X - axis(ii) Parallel to Y - axis.

LetS_n= cos ((n pi )/( 10)) , n = 1,2,3,…… thenthe valueof ( s_1 s_2 ……s_(10))/( s_1 + s_2 +…….. +s_(10)) isequal to

Assume that X,Y,Z,W and P are matrices of order 2xxn, 3xxk, 2xxp, nxx3 and pxxk respectively. Choose the correct answer in the following cases.If n=p, then the order of the matrix 7X-5Z is:

{x in R: |x-2|= x^(2)}=

Let X_(n)={Z=x+iy:|zA^(2)le(1)/(n)}for allintegers n le 1 then underset(n=1)overset(infty)cap x_(n) is

The meanof thenumbersobtainedonthrowinga diehavingwritten,1 onthreefaces , 2 ontwofacesand 5ononefaceis ….

If f(x)=sin(logx),(x gt 0) then find f'(x)

The shaded region in the given figure is a graph of ……………

If y = e^(sin^(-1)(t^(2)-1)) & x = e^(sec-1((1)/(t^(2-1))) then (dy)/(dx) is equal to

The equation of the line passing through the point of intersection of the lines 2x+y+1=0, x-y-7=0 and the point (3, -2) is

Find the shortest distance between the lines whose vector equations arevecr=(hati+2hatj+3hatk)+lambda(hati-3hatj+2hatk) and vecr=4hati+5hatj+6hatk+mu(2hati+3hatj+hatk)

Find the number of ordered pairs (x,y) such that L.C.M. of x and y is 2520.

Integration using rigonometric identities : int(sin theta)/(cos3 theta)+(sin 3 theta)/(cos9 theta)+( sin9 theta)/(cos 27theta)d theta=...+c

int(dx)/(x(x^(4)+1)) is equal to

If x=cosalpha+isinalpha,y=cosbeta+isinbeta," then "(x)/(y)+(y)/(x)

If the points vectors of A,B and C are respectively 2hati-hatk+hatk, hati-3hatj-5hatk and 3hati-4hatj-4hatk", then "cos^(2) A is equal to

Sketch the graphs of the following functions: y = (x^(3))/(24) - log x

A binary operation is chosen at random from the set of all binary operations on a set A containing n elements. The probability that the binary operation is commutative is

Compute P(A|B), if P(B) = 0.5 and P(AnnB) = 0.32

Find the number of ways of arranging the letters of the word 'FATHER' so that no vowel occupies even place.

Find k so that the following equations are consistent: 2x-y+3=0, kx-y+1=0, 5x-y-3=0

the order and degree of the differential equation (d^2y)/(dx^2) + ((dy)/(dx))^1/3 + x =0 are respectively

Let f(x)=x^(13)+2x^(12)+3x^(11)+...+13x+14 " and " alpha=cos""(2pi)/15+isin""(2pi)/15.If N=f(alpha)f(alpha^(2))...f(alpha^(14)), then

Coefficient of x^(6) in (1+x)(1+x^(2))^(2)(1+x^(3))^(3)…(1+x^(n))^(n) is

Find (dy)/(dx) in the following: y= sin^(-1) (3x-4x^(3)), 0 lt x lt (1)/(2)

Solve (1 + x^(2))(dy)/(dx) + 2xy = (1)/(1 + x^(2)), y = 0 whenx= 1

Which of the following functions is/are bounded?