14949 + Interview Questions in Maths in Class 11 Page 181 InterviewSolution

9001.	Find the coordinate of the foci, coordinate of the vertices, eccentricity and the length of the latus rectum of the hyperbola 16x ^(2) - 9y ^(2) =576
Answer» Answer :FOCI `(PM 10, 0),` Vertices `(pm 6,0), E = 5/3,Latus rectum `= (64)/(3).`

Discussion

9002.	A die is thrown once . Find P(a number ge4),
Answer» ANSWER :`(3)/(6),i.e,(1)/(2)`

Discussion

9003.	cos^(2) (60^(@) - x) + cos^(2) (60^(@) +x) in
Answer» `[-(1)/(2), (1)/(2)]` `[(1)/(2), 1]` `[(1)/(2), (3)/(2)]` `[(3)/(2), 2]` ANSWER :C

Discussion

9004.	Find the general solution for each of the following equations : tantheta+tan(theta+(pi)/(3))+tan(theta+(2pi)/(3))=3
Answer» `theta=(4n _1)(PI)/3, n in Z` `theta=(4n+1)(pi)/2, n in Z` `theta=(4n+1)(pi)/4, n in Z` `theta=(4 n+1)(pi)/12, NIN Z` Answer :D

Discussion

9005.	If slope of line (cos theta+sin theta)x+(sin 2 theta)y=1 when theta=(pi)/6 is k then [k]=, when [.] is greatest integer function
Answer» -1 -2 1 2 Answer :B

Discussion

9006.	Solve each of the following equations for real x and y : 2x+yi=1 + (2 + 3i)
Answer» ANSWER :`X= (3)/(2), y= 3`

Discussion

9007.	(cos3A+sin3A)/(cosA-sinA)=
Answer» 1-2 SIN 2A 1+2 COS 2A 1-2 cos 2A 1+2 sin 2A Answer :D

Discussion

9008.	If alpha,beta are roots of x^(2)-px+q=0, find the value of (i) alpha^(2)+beta^(2) (ii) alpha^(3)+beta^(3) (iii) alpha-beta, (iv) alpha^(4)+beta^(4).
Answer» Answer :(i) `p^(2)-2p` (ii) `p^(3)-3pq`. (iii) `-sqrt(p^(2)-4Q)`, if `ALPHA lt BETA`. (iv) `p^(4)-4p^(2)q+2q^(2)`.

Discussion

9009.	Three straight lines 2x+11y-5=0, 24x+7y-20=0, and 4x-3y-2=1,
Answer» form a triangle are only CONCURRENT are concurrent with ONE line bisecting the angle between the other TWO NONE of the above Answer :C

Discussion

9010.	sqrt(2+sqrt(2(1+cos4A)))=
Answer» COS A cos 2A 2 cosA 2 cos2A Answer :C

Discussion

9011.	A rectangle ABCD has its side AB parallel to line y=x, and vertices A,Band D lie on y=1, x=2 and x=-2 respectively. The locus of vertex C is
Answer» x=5 x-y=5 y=5 x+y=5 Answer :C

Discussion

9012.	If tanx = b//a , then sqrt((a+b)//(a-b))+sqrt((a-b)//(a+b)) is equal to
Answer» `2 SIN x//sqrt(sin 2X)` `2 cos x//sqrt(cos 2 x)` `2 cos x//sqrt(sin 2x)` `2 sin x//sqrt(cos 2x)` ANSWER :B

Discussion

9013.	A commitree of 5 principals is to be selected from a group of 6 gent principals and 8 lady principals. If the selection is made randomly , find the probability that there are 3 lady principals and 2 gent principals .
Answer» Answer :`(""^(6)C_(2)XX""^(8)C_(3))/(""^(14)C_(5))=(60)/(143)`

Discussion

9014.	Find the derivative of the w.r.t.x log [(sin (log x ) + x log x log (log x)]
Answer» ANSWER :`((1)/(X) cos ( LOG x ) + log x. log ( log x) + log (log x ) +1)/( [SIN (log x)+ x log x. log ( log x) ])`

Discussion

9015.	Determine the angle between the lines whose equation are 3x+y-7=0 and x+2y+9=0,
Answer» ANSWER : `45^(@)`

Discussion

9016.	Period of cosec (x+(x)/(2) + (x)/(4)+…) is
Answer» `PI` `2PI` `(pi)/(2)` `(pi)/(4)` ANSWER :A

Discussion

9017.	Find the number of different words that can be formed from 12 consonants and 5 vowels by taking 4 consonants and 3 vowels in each words.
Answer» ANSWER :` ""^(12)C_(4)XX ""^(5)C_3 xx 7! = 24948000`

Discussion

9018.	If xy+yz+zx=1 , then sum(x+y)/(1-xy)=
Answer» `1/(XYZ)` `xyz` `-1/(xyz)` `-xyz` ANSWER :A

Discussion

9019.	The solution of costheta.cos2theta.cos3theta=1/4,0 lt theta lt pi/4 is:
Answer» `pi/8` `pi/6` `pi/9` `pi/12` SOLUTION :N//A

Discussion

9020.	Solve cos theta * cos 2 theta * cos 3 theta = (1)/( 4), 0 le theta le pi
Answer» ANSWER :`{(PI)/(8),(pi)/(3),(3PI)/(8),(5PI)/(8),(2pi)/(3),(7pi)/(8)}`

Discussion

9021.	For the smallest positive values of x and y, the eqation 2 (sin x + sin y) - 2 cos ( x - y) = 3 has a solution, then which of the following is/are true ?
Answer» `"SIN"(X+y)/2=1` `cos((x-h)/2)=1/2` NUMBER of ordered pairs (x,y) is 2 number of ordered pairs (x,y) is 3 Answer :A::B::C

Discussion

9022.	Find unit vector orthogonal to the vector 3bari + 2barj + 6bark and coplanar with the vectors 2bari + barj+bark and bari - barj + bark.
Answer» `1/(sqrt(41))(2bari-6barj+bark)` `1/(sqrt(13))(2bari-3barj)` `1/(sqrt(10))(3barj-bark)` `1/(sqrt(10))(3bari+barj)` Answer :A

Discussion

9023.	If A= {1, 3, 5, 7, 9, 11, 13, 15, 17}, B= {2, 4, 6, 8,……….18} and N the set of natural numbers is the universal set, then {A' cup (A cup B) cap B'} is
Answer» `PHI` `N` `A` `B` ANSWER :B

Discussion

9024.	The two supporting pillars of a suspension bridge in the shape of parabola are 30 met. High and both are 20 met. Appart from each other. The height of the bridge above the is centre is 5 met. There is a pillare of height 11.25 met. Fiind its distance from centre.
Answer» ANSWER :50 MET.

Discussion

9025.	Let p be " I will marry her," and let q be " she is beautiful." Translate into symbolic form. She is beautiful if and only if I will marry her.
Answer» <P> ANSWER :Q <=> p

Discussion

9026.	Useinductionto provethatn^(3) - 7n +3is divisibleby 3,for all naturalnumbers n ,.
Answer» ANSWER :3

Discussion

9027.	Find (7!)/(5!).
Answer» ANSWER :42

Discussion

9028.	If \|(z-2)/(z-3)\|=2 express a circle, then its radius is ......
Answer» 1 `(1)/(3)` `(3)/(4)` `(2)/(3)` ANSWER :D

Discussion

9029.	If vec(a).vec(i)=4, then (vec(a) . vec(j))xx (2vec(j)-3vec(k))=
Answer» 12 10 `-10` `-12` ANSWER :D

Discussion

9030.	If n is a positive integer and r is a non - negative integer, prove that the coefficients of x^(r ) and x^(n-r) in the expansion of (1+x)^(n) are equal.
Answer» ANSWER :`=""^(N)C_(n-r)`

Discussion

9031.	f(x) = (tan x)/(x) , x ne , f(0 ) = 1 , f(x)at x = 0 is
Answer» continuous discontinuous not DETERMINED NONE ANSWER :A

Discussion

9032.	A bag contains 5 black and 6 red balls. Determine the number of ways in which 2 black and 3 red balls can be selected.
Answer» ANSWER :200

Discussion

9033.	Distance between the parallel lines 16x^(2)+24xy+ ly^(2)+kx-12y-21=0 represents a pair of parallel lines is
Answer» `+-3` `+-4` `-16` `+-25` Answer :C

Discussion

9034.	Let S = [ a in N,a le 100] . If the equation [Tan^(2)x] - Tan x = a = 0has real roots then number of elements in S is(where [] is G.I function )
Answer» 10 1 9 0 Answer :C

Discussion

9035.	A differentiable function f(x) has a relative minimum at x=0 Then the funictiony=f(x)+ax+b has a relative minimum at x=0 for
Answer» all a and all B . all b if a =0 all `BGT0` all `AGT0` ANSWER :B

Discussion

9036.	If xy+x+y+1=0,x+ay-3=0 are concur rent then a =
Answer» 4 `-4` 3 `-3` ANSWER :B

Discussion

9037.	The upper 3/4th portion of a vertical pole subtends an angle tan^(-1)(3/5) at the point in the horizont plane through its foot. The tangent of the angle subtended by the pole at the same points is
Answer» 1 or 2 2 or 3 3 or 4 4 or 1 Answer :D

Discussion

9038.	If the pair of linesa^(2)(x^(2)+y^(2))=(ax-by)^(2) are perpendicular to each other, then
Answer» `a=b` `a=-b` `a=+-b` `a=2b` ANSWER :C

Discussion

9039.	A committee of 5 is to be formed from a group of 12 students consisting of 8 boys and 4 girls in how many ways can the committee be formed it contains at least 3 girls ?
Answer» ANSWER :` 120 `

Discussion

9040.	Let PS be the median of the triangle with vertices P(2, 2), Q(6, -1) and R(7, 3). The equation of the line passing through (1, -1) and parallel to PS is
Answer» `4x-7y-11=0` `2x+9y+7=0` `4x+7y+3=0` `2x-9y-11=0` ANSWER :B

Discussion

9041.	A,B in P(cup)" if " AsubB" then "A'cupB = .....
Answer» ANSWER :U

Discussion

9042.	A committee of 5 is to be formed from a group of 12 students consisting of 8 boys and 4 girls in how many ways can the committee be formed it consists of exactly 3 boys and 2 girls ,
Answer» ANSWER :` 336`

Discussion

9043.	x=npi-Tan^(-1)3 is a solution of the equation 12tan2x+sqrt(10)/(cosx)+1=0 if
Answer» N is any integer n is an EVEN integer n is a POSITIVE integer n is an ODD integer Answer :D

Discussion

9044.	lim_(ktooo)(1^(3)+2^(3)+……….+k^(3))/(k^(4)) is equal to
Answer» A. 0 B. 2 C. `1/3` D. `1/4` ANSWER :D

Discussion

9045.	A coin is tossed twice, what is the probability that etleast one tail occurs?
Answer» ANSWER :`3/4`

Discussion

9046.	For what values of x, the number (x+ 9), (x-6) and 4 are in G.P.?
Answer» ANSWER :`+-1`

Discussion

9047.	In triangle ABC ifDelta = 96, r_1=8,r_2 = 12 r_3= 24then the greatest side is
Answer» ` 10 ` ` 15` ` 20 ` ` 25` ANSWER :C

Discussion

9048.	If the pair of lines given by lamda(lamda-3)x^(2)+16xy+(lamda+1)y^(2)=0 perpendicular to each other, then lamda=
Answer» 1 2 3 4 Answer :A

Discussion

9049.	Are the following pairs of statements negations of each other: The number x is not a rational number. The number x is not an irrational number.
Answer» Answer :The negation of the FIRST statement is ''the number x is a rational number.'' which is the same as the second statement” This is because when a number is not irrational, it is a rational. Therefore, the GIVEN pairs are NEGATIONS of each other.

Discussion

9050.	(1+x)^(10)=a_(0)+a_(1)x+a_(2)x^(2)+……..+a_(10)x^(10) then the value of (a_(0)-a_(2)+a_(4)-a_(6)+a_(8)-a_(10))^(2)+(a_(1)-a_(3)+a_(5)-a_(7)+a_(9))^(2) is ……
Answer» `3^(10)` `2^(10)` `2^(9)` 0 Answer :B

Discussion

Explore topic-wise InterviewSolutions in .

Find the coordinate of the foci, coordinate of the vertices, eccentricity and the length of the latus rectum of the hyperbola 16x ^(2) - 9y ^(2) =576

A die is thrown once . Find P(a number ge4),

cos^(2) (60^(@) - x) + cos^(2) (60^(@) +x) in

Find the general solution for each of the following equations : tantheta+tan(theta+(pi)/(3))+tan(theta+(2pi)/(3))=3

If slope of line (cos theta+sin theta)x+(sin 2 theta)y=1 when theta=(pi)/6 is k then [k]=, when [.] is greatest integer function

Solve each of the following equations for real x and y : 2x+yi=1 + (2 + 3i)

(cos3A+sin3A)/(cosA-sinA)=

If alpha,beta are roots of x^(2)-px+q=0, find the value of (i) alpha^(2)+beta^(2) (ii) alpha^(3)+beta^(3) (iii) alpha-beta, (iv) alpha^(4)+beta^(4).

Three straight lines 2x+11y-5=0, 24x+7y-20=0, and 4x-3y-2=1,

sqrt(2+sqrt(2(1+cos4A)))=

A rectangle ABCD has its side AB parallel to line y=x, and vertices A,Band D lie on y=1, x=2 and x=-2 respectively. The locus of vertex C is

If tanx = b//a , then sqrt((a+b)//(a-b))+sqrt((a-b)//(a+b)) is equal to

A commitree of 5 principals is to be selected from a group of 6 gent principals and 8 lady principals. If the selection is made randomly , find the probability that there are 3 lady principals and 2 gent principals .

Find the derivative of the w.r.t.x log [(sin (log x ) + x log x log (log x)]

Determine the angle between the lines whose equation are 3x+y-7=0 and x+2y+9=0,

Period of cosec (x+(x)/(2) + (x)/(4)+…) is

Find the number of different words that can be formed from 12 consonants and 5 vowels by taking 4 consonants and 3 vowels in each words.

If xy+yz+zx=1 , then sum(x+y)/(1-xy)=

The solution of costheta.cos2theta.cos3theta=1/4,0 lt theta lt pi/4 is:

Solve cos theta * cos 2 theta * cos 3 theta = (1)/( 4), 0 le theta le pi

For the smallest positive values of x and y, the eqation 2 (sin x + sin y) - 2 cos ( x - y) = 3 has a solution, then which of the following is/are true ?

Find unit vector orthogonal to the vector 3bari + 2barj + 6bark and coplanar with the vectors 2bari + barj+bark and bari - barj + bark.

If A= {1, 3, 5, 7, 9, 11, 13, 15, 17}, B= {2, 4, 6, 8,……….18} and N the set of natural numbers is the universal set, then {A' cup (A cup B) cap B'} is

The two supporting pillars of a suspension bridge in the shape of parabola are 30 met. High and both are 20 met. Appart from each other. The height of the bridge above the is centre is 5 met. There is a pillare of height 11.25 met. Fiind its distance from centre.

Let p be " I will marry her," and let q be " she is beautiful." Translate into symbolic form. She is beautiful if and only if I will marry her.

Useinductionto provethatn^(3) - 7n +3is divisibleby 3,for all naturalnumbers n ,.

Find (7!)/(5!).

If |(z-2)/(z-3)|=2 express a circle, then its radius is ......

If vec(a).vec(i)=4, then (vec(a) . vec(j))xx (2vec(j)-3vec(k))=

If n is a positive integer and r is a non - negative integer, prove that the coefficients of x^(r ) and x^(n-r) in the expansion of (1+x)^(n) are equal.

f(x) = (tan x)/(x) , x ne , f(0 ) = 1 , f(x)at x = 0 is

A bag contains 5 black and 6 red balls. Determine the number of ways in which 2 black and 3 red balls can be selected.

Distance between the parallel lines 16x^(2)+24xy+ ly^(2)+kx-12y-21=0 represents a pair of parallel lines is

Let S = [ a in N,a le 100] . If the equation [Tan^(2)x] - Tan x = a = 0has real roots then number of elements in S is(where [] is G.I function )

A differentiable function f(x) has a relative minimum at x=0 Then the funictiony=f(x)+ax+b has a relative minimum at x=0 for

If xy+x+y+1=0,x+ay-3=0 are concur rent then a =

The upper 3/4th portion of a vertical pole subtends an angle tan^(-1)(3/5) at the point in the horizont plane through its foot. The tangent of the angle subtended by the pole at the same points is

If the pair of linesa^(2)(x^(2)+y^(2))=(ax-by)^(2) are perpendicular to each other, then

A committee of 5 is to be formed from a group of 12 students consisting of 8 boys and 4 girls in how many ways can the committee be formed it contains at least 3 girls ?

Let PS be the median of the triangle with vertices P(2, 2), Q(6, -1) and R(7, 3). The equation of the line passing through (1, -1) and parallel to PS is

A,B in P(cup)" if " AsubB" then "A'cupB = .....

A committee of 5 is to be formed from a group of 12 students consisting of 8 boys and 4 girls in how many ways can the committee be formed it consists of exactly 3 boys and 2 girls ,

x=npi-Tan^(-1)3 is a solution of the equation 12tan2x+sqrt(10)/(cosx)+1=0 if

lim_(ktooo)(1^(3)+2^(3)+……….+k^(3))/(k^(4)) is equal to

A coin is tossed twice, what is the probability that etleast one tail occurs?

For what values of x, the number (x+ 9), (x-6) and 4 are in G.P.?

In triangle ABC ifDelta = 96, r_1=8,r_2 = 12 r_3= 24then the greatest side is

If the pair of lines given by lamda(lamda-3)x^(2)+16xy+(lamda+1)y^(2)=0 perpendicular to each other, then lamda=

Are the following pairs of statements negations of each other: The number x is not a rational number. The number x is not an irrational number.

(1+x)^(10)=a_(0)+a_(1)x+a_(2)x^(2)+……..+a_(10)x^(10) then the value of (a_(0)-a_(2)+a_(4)-a_(6)+a_(8)-a_(10))^(2)+(a_(1)-a_(3)+a_(5)-a_(7)+a_(9))^(2) is ……