14949 + Interview Questions in Maths in Class 11 Page 121 InterviewSolution

6001.	If the binomial coefficients of three consecutive terms in the expansion of (a+x)^(n) are in the ratio 1:7:42, then find n.
Answer» ANSWER :55

Discussion

6002.	(i) Find the equation of a circle passes through the point (4,3) and whose centre is (-3,2). Find the equation of a circle in which the equations of its two diameters are 2x+y=5 and x-y=1 and its radius is 5 units.
Answer» ANSWER :`X^(2)+y^(2)+6x-4y-37=0`

Discussion

6003.	In triangleABC, angle B = pi//3. " and " angle C = pi//4 . Let D divide BC inernally in the ratio 1 : 3 . Then (sin angle BAD)/(sin angle CAD) equals
Answer» `1/sqrt6` `1/3` `1/sqrt3` `SQRT(2/3)` ANSWER :A

Discussion

6004.	If "2 tan" (alpha)/(2) = "tan" (beta)/(2) "then" (3 + 5 cos beta)/(5 + 3 cos beta)=
Answer» `cos ALPHA` `SIN alpha` `TAN alpha` `cot alpha` ANSWER :A

Discussion

6005.	What is the geometric property possessed by the straight lines of each system given by y +4 = m (x - 5)
Answer» SOLUTION :A FAMILY of lines PASSING through (5,-4)

Discussion

6006.	Statement. 1: The incenter of triangle ABC is the orthocenter of the triangle l_(1) l_(2) l_(3) where l_(1) l_(2) l_(3) are excenters of triangle ABC Statement - 2: The incenter of the triangle formed by the feet of altitudes from the vertices of triangle ABC to the opposite sides is the orthocenter of the triangle ABC
Answer» Statement-1 is TRUE, Statement-2 is True, Statement-2 is a CORRECT EXPLANATION for Statement-1 Statement-1 is True, Statement-2 is True, Statement-2 NOT a correct explanation for Statement-1 Statement-1 is True, Statement-2 is FALSE Statement -1 is False, Statement-2 is True Answer :A

Discussion

6007.	Given the vertices A(10, 4), B(-4, 9) and C(-2, -1) of DeltaABC, find the equation of the perpendicular bisector of the side AB.
Answer» ANSWER : `28x-10y=19`

Discussion

6008.	Compute : (12!)/((10!)(2!))
Answer» ANSWER :66

Discussion

6009.	Which of the following sets are empty sets ? {x : x^(2) -2=0, x " is a rational number "}
Answer» ANSWER :it is an emply SET

Discussion

6010.	If a_(1), a_(2), a_(3),……,a_(n) are in AP, where a_(i) gt 0 for all i, show that (1)/(sqrt(a_(1)) + sqrt(a_(2))) + (1)/(sqrt(a_(2)) + sqrt(a_(3))) + …..+ (1)/(sqrt(a_(n-1))+ sqrt(a_(n)))= (n-1)/(sqrt(a_(1)) + sqrt(a_(n)))
Answer» ANSWER :`((N-1)d)/(d(SQRT(a_(n))+ sqrt(a_(1))))`

Discussion

6011.	Iftan beta = 2 sin alpha sin gamma " cosec "(alpha + gamma) , thencot alpha , cot beta and cot gammaare in
Answer» A.P. G.P. H.P. A.G.P. Answer :A

Discussion

6012.	If (1, 2, 3) is the foot of the perpendicular from the origin to a plane, then find its equation.
Answer» ANSWER :14

Discussion

6013.	A straight line through P(3,4) makes an angle of 60^(@) with the positive direction of the X-axis. Find the coordinates of the points with the line whre are 5 units away from P.
Answer» ANSWER :`(1/2,(8-5sqrt(3))/2)`

Discussion

6014.	If A = { 3, 5, 7, 9, 11 }, B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}, find ( A ∪ D) ∩ ( B ∪ C)
Answer» ANSWER :`{ 7, 9, 11, 15 }`

Discussion

6015.	Find the absolute maximum value and the absolute minimum value of thefunctions in the given intervals: f(x) = (x-1)^(2) +3, x in[-3 ,1]
Answer» Answer :absolute MINIMUM = 3, absolute maximum= 19

Discussion

6016.	Find the absolute maximum value and the absolute minimum value of thefunctions in the given intervals: f(x) = x^(3), x in [– 2, 2]
Answer» ANSWER :ABSOLUTE MINIMUM = -8, absolute MAXIMUM= 8

Discussion

6017.	Find the absolute maximum value and absolute minimum value of the following functions on the domain specified against the function. f(x) = x + sin2x on [0, pi]
Answer» ANSWER :ABSOLUTE MINIMUM = 0, absolute maximum= `PI`

Discussion

6018.	Find the absolute maximum value and the absolute minimum value of thefunctions in the given intervals: f (x) = sin x + cos x , x in [0,pi]
Answer» ANSWER :ABSOLUTE MINIMUM = -1, absolute MAXIMUM= `sqrt(2)`

Discussion

6019.	Find the absolute maximum value and absolute minimum value of the following functions on the domain specified against the function. f(x) = 2\|x\| on [-1, 6]
Answer» Answer :ABSOLUTE MINIMUM = 0, absolute maximum= 12

Discussion

6020.	Find the ratio of division in the point of division lies on the line in
Answer» SOLUTION :1 :2 EXTERNALLY

Discussion

6021.	Let R be the relation on Z defined by R= {(a,b): a, b in Z, a-b is an integer}. Find the domain and range of R.
Answer» ANSWER :DOMAIN of R=Z RANGE of R=Z

Discussion

6022.	If vec(a), vec(b) are not perpendicular to each other and vec(r ) xx vec(b) = vec(c ) xx vec(b), vec(r ). vec(a)= 0, then vec(r )=
Answer» `VEC(C )- (vec(c ).vec(a))/(vec(a).vec(B))` `vec(c )+ (vec(a).vec(b))/(vec(c ).vec(a))` `vec(c )- (vec(c ).vec(a))/(vec(a).vec(b)) vec(b)` `vec(c )-(vec(a).vec(b))/(vec(c ).vec(a)) vec(b)` ANSWER :C

Discussion

6023.	The value of k such that (x-4)/(1)=(y-2)/(1)=(z-k)/(2) lies in the plane 2x-4y+z+7=0 is
Answer» 7 `-7` no REAL VALUE 4 Answer :A

Discussion

6024.	Find the vertex, focus, axis , latus rectum and directrix of the parabola y^(2)+4x+6y+17=0
Answer» Solution :Equation of parabola `y^(2)+4x+6y+17=0` `RARR""y^(2)+6y+9=-4x-17+9` `rArr""(y+3)^(2)=-4(x+2)` `rArr""Y^(2)=-4X` Comparing with `Y^(2)=-4AX` 4a=4 `rArr""a=1` Vertex A = (0,0) `rArr""X=0,Y=0` `rArr""x+2=0,y+3=0` `rArr""x=-2,y=-3` `:.` Co-ordinates of vertex = (-2,-3). Focus X = -a,Y=0 `rArr""x+2=-1,y+3=0` `rArr""x=-3,y=-3` `:.` Co-ordinates of focus = (-3, -3). Equation of axis Y=0 `rArr""y+3=0`. Equation of directrix X=a `rArr""x+2=1` `rArr""x+1=0` Length of latus RECTUM = 4a = 4.

Discussion

6025.	Match the planes given in List I with their perpendicular coordinate plane given in List II. {:(,ul"List - I",ul"List - II"),("A)",2x+3y+4=0,"I) YZ"),("B)",2y+3z+4=0,"II) ZX"),("C)",2z+3x+4=0,"III) XY"):} The correct match form list I to list II is
Answer» a - II, b - I, C - III a - I, b - II, c - III a - III, b - I, c - II a - III, b - II, c - I ANSWER :C

Discussion

6026.	What is the resulting sample space if one coins is tossed ,
Answer» ANSWER :S={H,T}

Discussion

6027.	lim_(x to 2)( ( sqrt(1-cos(2(x-2))))/((x-2)))
Answer» equals `-sqrt(2)` equals `(1)/(sqrt(2))` does not exist equls `sqrt(2)` ANSWER :C

Discussion

6028.	Let f(x) bea polnomial of degree four having extreme values at x=1 and at x=2 if underset(x to o) (Lt)[1+(f(x))/(x^(2))]=3then f(2) is equal to
Answer» `-8` `-4` 0 4 Answer :C

Discussion

6029.	Let \|{:(x^(2)+x+1,x+1,2x-3),(3x^(2)-1,x+2,x-1),(x^(2)+5x+1,2x+3,x+4):}\|=ax^(4)+bx^(3)+cx^(2)+dx+e be an identity in x. If a,b,c,d are known, then the value of e is
Answer» 29 24 16 9 Answer :B

Discussion

6030.	If ars of the same lengths in two circles subtend angles 65^(@) and 110^(@) at the centre, find the ratio of their radii.
Answer» ANSWER :`22:13`

Discussion

6031.	The period of sin((2pix)/(a))+3 cos ((2pix)/(b)) where a=12, b=9 is
Answer» 18 36 108 54 Answer :B

Discussion

6032.	Find the coordinates of the foci, the vertices, the eccentricity and the length of the latus rectum of the Hyperbola (x^(2))/(16)-(y^(2))/(9)=1
Answer» Solution :`(x^(2))/(16)-(y^(2))/(9)=1` Here,`a^(2)=16,b^(2)=9rArra=4,b=3` `:."Vertices"-=(pma,0)-=(pm4,0)` ECCENTRICITY `e=SQRT(1+(b^(2))/(a^(2)))=sqrt(1+(9)/(16))=(5)/(4)` Coordinates of foci `-=(pmae,0)-=(pm5,0)` Latus rectum `=(2b^(2))/(a)=(2xx9)/(4)=(9)/(2)`

Discussion

6033.	If a = 18 , b= 24 , c= 30 " then"r_2 r_1is
Answer» ` 6` ` 3` ` 1` ` 4`

Discussion

6034.	Find the derivative with respect to x of the following: (1+x^2)/( x^3)
Answer» ANSWER :`(3)/(x^4) - (1)/( x^2)`

Discussion

6035.	Find the mean deviation about the mean of the distribution:
Answer» ANSWER :1.25

Discussion

6036.	If cosec A = 4x + (1)/(16x) then cosec A + cot A =
Answer» `8X` (or) `- (1)/(8x)` `-8x` (or)` (1)/(8x)` `8x` (or) `(1)/(8x)` `-8x` (or) `- (1)/(8x)` ANSWER :C

Discussion

6037.	Evalute Lt_(x to oo)(11x^3-3x+4)/(13x^3-5x^2-7).
Answer» ANSWER :`11//3`

Discussion

6038.	Distance between the parallel line (x+2y)^2+13sqrt5(x+2y)+180=0 is
Answer» `SQRT(5)` `4sqrt(5)` 5 4 Answer :C

Discussion

6039.	The period of the function f(x)=x[x] is
Answer» 1 2 Non periodie 4 Answer :C

Discussion

6040.	sum (b^(2) -c^(2))/( a^(2)) sin ^(2) A =
Answer» ` -1` ` (1)/(2) ` `1` `0` ANSWER :D

Discussion

6041.	If A is a non zero column matrix of order mxx1 and B is a non zero row matrix of order 1xxn then the rank of AB is
Answer» 0 1 `-m` n Answer :B

Discussion

6042.	Consider the function f (x) = sqrtx, x ge 0. Does lim _(x to 0) f (x) exist ?
Answer» Answer :`lim _(X to 0) SQRTX` is does not exist

Discussion

6043.	Let : R rarr Rbe a function defined f(x+1) = (f(x)-5)/(f(x)-3) AA x in R. Thenwhich of the following statement(s) is/are true ?
Answer» `F(2008)=f(2004)` `f(2006)=f(2010)` `f(2006)=f(2002)` `f(2006)=f(2018)` Answer :A::B::C::D

Discussion

6044.	Range of f(x)= (x^(2)-x)/(x^(2)+ 2x) is …….
Answer» R `R-{1}` `R-{-(1)/(2), 1}` None of these Answer :B

Discussion

6045.	The sides of a Delta ^("le') ABCbe 8, 7, 6 and smallest angle is C then Length of median through vertex C is
Answer» `SQRT(95)` `sqrt(95/2)` `sqrt(95)/2` `sqrt(95)/4` ANSWER :b

Discussion

6046.	Let g: R rarr Rbe given by g(x)=3+4x. If g^(n)(x)=gogo.....og(x), and g^(n)(x)=A + Bx then A and B are
Answer» `2^(n+1)-1, 2^(n+1)` `4^(n)-1, 4^(n)` `3^(n), 3^(n)+1` `5^(n)-1, 5^(n)` ANSWER :B

Discussion

6047.	If A and B are any two events, then the probability that exactly one of them occur is:
Answer» <P>`P(AcupbarB)+P(barAcupB)` `P(AcapbarB)+P(barAcapB)` `P(A)+P(B)-2P(ACAPB)` `P(A)+P(B)+2P(AcapB)` ANSWER :B

Discussion

6048.	The values of 'theta' satisfying sin7 theta = sin 4theta - sin theta in 0 lt theta lt pi//2 are
Answer» `pi//9, pi//4` `pi//3, pi//9` `pi//6, pi//4` `pi//3, pi//4` ANSWER :A

Discussion

6049.	Statement-I If alpha=(pi)/(18) then cos alpha+ cos 2 alpha+..... +cos18 alpha=0 Statement- II If (a+2) sin theta(2a-1) cos theta=2a+1 then tan theta=(4)/(3) Which of the above statements is correct
Answer» Only I Only II Btoh I & II Neither I nor II Answer :B

Discussion

6050.	For which Domain, the functions f(x)=2x^(2)-1 and g(x)=1-3x are equal to
Answer» R `1/2, -2}` `(1/2, 2)` `[1/2, 2]` ANSWER :B

Discussion

Explore topic-wise InterviewSolutions in .

If the binomial coefficients of three consecutive terms in the expansion of (a+x)^(n) are in the ratio 1:7:42, then find n.

(i) Find the equation of a circle passes through the point (4,3) and whose centre is (-3,2). Find the equation of a circle in which the equations of its two diameters are 2x+y=5 and x-y=1 and its radius is 5 units.

In triangleABC, angle B = pi//3. " and " angle C = pi//4 . Let D divide BC inernally in the ratio 1 : 3 . Then (sin angle BAD)/(sin angle CAD) equals

If "2 tan" (alpha)/(2) = "tan" (beta)/(2) "then" (3 + 5 cos beta)/(5 + 3 cos beta)=

What is the geometric property possessed by the straight lines of each system given by y +4 = m (x - 5)

Given the vertices A(10, 4), B(-4, 9) and C(-2, -1) of DeltaABC, find the equation of the perpendicular bisector of the side AB.

Compute : (12!)/((10!)(2!))

Which of the following sets are empty sets ? {x : x^(2) -2=0, x " is a rational number "}

If a_(1), a_(2), a_(3),……,a_(n) are in AP, where a_(i) gt 0 for all i, show that (1)/(sqrt(a_(1)) + sqrt(a_(2))) + (1)/(sqrt(a_(2)) + sqrt(a_(3))) + …..+ (1)/(sqrt(a_(n-1))+ sqrt(a_(n)))= (n-1)/(sqrt(a_(1)) + sqrt(a_(n)))

Iftan beta = 2 sin alpha sin gamma " cosec "(alpha + gamma) , thencot alpha , cot beta and cot gammaare in

If (1, 2, 3) is the foot of the perpendicular from the origin to a plane, then find its equation.

A straight line through P(3,4) makes an angle of 60^(@) with the positive direction of the X-axis. Find the coordinates of the points with the line whre are 5 units away from P.

If A = { 3, 5, 7, 9, 11 }, B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}, find ( A ∪ D) ∩ ( B ∪ C)

Find the absolute maximum value and the absolute minimum value of thefunctions in the given intervals: f(x) = (x-1)^(2) +3, x in[-3 ,1]

Find the absolute maximum value and the absolute minimum value of thefunctions in the given intervals: f(x) = x^(3), x in [– 2, 2]

Find the absolute maximum value and absolute minimum value of the following functions on the domain specified against the function. f(x) = x + sin2x on [0, pi]

Find the absolute maximum value and the absolute minimum value of thefunctions in the given intervals: f (x) = sin x + cos x , x in [0,pi]

Find the absolute maximum value and absolute minimum value of the following functions on the domain specified against the function. f(x) = 2|x| on [-1, 6]

Find the ratio of division in the point of division lies on the line in

Let R be the relation on Z defined by R= {(a,b): a, b in Z, a-b is an integer}. Find the domain and range of R.

If vec(a), vec(b) are not perpendicular to each other and vec(r ) xx vec(b) = vec(c ) xx vec(b), vec(r ). vec(a)= 0, then vec(r )=

The value of k such that (x-4)/(1)=(y-2)/(1)=(z-k)/(2) lies in the plane 2x-4y+z+7=0 is

Find the vertex, focus, axis , latus rectum and directrix of the parabola y^(2)+4x+6y+17=0

Match the planes given in List I with their perpendicular coordinate plane given in List II. {:(,ul"List - I",ul"List - II"),("A)",2x+3y+4=0,"I) YZ"),("B)",2y+3z+4=0,"II) ZX"),("C)",2z+3x+4=0,"III) XY"):} The correct match form list I to list II is

What is the resulting sample space if one coins is tossed ,

lim_(x to 2)( ( sqrt(1-cos(2(x-2))))/((x-2)))

Let f(x) bea polnomial of degree four having extreme values at x=1 and at x=2 if underset(x to o) (Lt)[1+(f(x))/(x^(2))]=3then f(2) is equal to

Let |{:(x^(2)+x+1,x+1,2x-3),(3x^(2)-1,x+2,x-1),(x^(2)+5x+1,2x+3,x+4):}|=ax^(4)+bx^(3)+cx^(2)+dx+e be an identity in x. If a,b,c,d are known, then the value of e is

If ars of the same lengths in two circles subtend angles 65^(@) and 110^(@) at the centre, find the ratio of their radii.

The period of sin((2pix)/(a))+3 cos ((2pix)/(b)) where a=12, b=9 is

Find the coordinates of the foci, the vertices, the eccentricity and the length of the latus rectum of the Hyperbola (x^(2))/(16)-(y^(2))/(9)=1

If a = 18 , b= 24 , c= 30 " then"r_2 r_1is

Find the derivative with respect to x of the following: (1+x^2)/( x^3)

Find the mean deviation about the mean of the distribution:

If cosec A = 4x + (1)/(16x) then cosec A + cot A =

Evalute Lt_(x to oo)(11x^3-3x+4)/(13x^3-5x^2-7).

Distance between the parallel line (x+2y)^2+13sqrt5(x+2y)+180=0 is

The period of the function f(x)=x[x] is

sum (b^(2) -c^(2))/( a^(2)) sin ^(2) A =

If A is a non zero column matrix of order mxx1 and B is a non zero row matrix of order 1xxn then the rank of AB is

Consider the function f (x) = sqrtx, x ge 0. Does lim _(x to 0) f (x) exist ?

Let : R rarr Rbe a function defined f(x+1) = (f(x)-5)/(f(x)-3) AA x in R. Thenwhich of the following statement(s) is/are true ?

Range of f(x)= (x^(2)-x)/(x^(2)+ 2x) is …….

The sides of a Delta ^("le') ABCbe 8, 7, 6 and smallest angle is C then Length of median through vertex C is

Let g: R rarr Rbe given by g(x)=3+4x. If g^(n)(x)=gogo.....og(x), and g^(n)(x)=A + Bx then A and B are

If A and B are any two events, then the probability that exactly one of them occur is:

The values of 'theta' satisfying sin7 theta = sin 4theta - sin theta in 0 lt theta lt pi//2 are

Statement-I If alpha=(pi)/(18) then cos alpha+ cos 2 alpha+..... +cos18 alpha=0 Statement- II If (a+2) sin theta(2a-1) cos theta=2a+1 then tan theta=(4)/(3) Which of the above statements is correct

For which Domain, the functions f(x)=2x^(2)-1 and g(x)=1-3x are equal to