14949 + Interview Questions in Maths in Class 11 Page 115 InterviewSolution

5701.	Find a unit vector perpendicular to the plane determined by the points P(1, -1, 2), Q(2,0, -1) and R(0, 2, 1).
Answer» Answer :`+- (1)/(SQRT6) (2vec(i) + vec(j) + vec(K))`

Discussion

5702.	Solve the equations: Q. 2^(2x-1)-9xx2^(x-2)+1=0.
Answer» ANSWER :2 or -1.

Discussion

5703.	O(0,0) A(6,0)and B(0,4)are three points .If P is a point such that the area of DeltaPOB is twice the area of DeltaPOA, then find the locus of P.
Answer» ANSWER :`X^(2)-9Y^(2)=0`

Discussion

5704.	Let S be the sum, P the product and R the sum of reciprocals of n terms in a G.P. Prove that P^(2)R^(n) = S^n .
Answer» ANSWER :`S^(N)`

Discussion

5705.	The system of equations tan x =acot x, tan 2x=b cos y
Answer» cannot have a SOLUTION of a = 0 cannot have a solution if a = 1 cannot have a solution if `2 sqrt(a) lt \|b ( 1 - a)\|` has a solution for all a and b ANSWER :B::C

Discussion

5706.	A light ray emerging from the point source placed at P(1,3) is reflected at a pont Q in the axis of x. If the reflected ray passes through the point R(6,7), then the abscissa of Q is
Answer» `1` `3` `7/2` `5/2` ANSWER :D

Discussion

5707.	If g(x)=x^(2)+x-2 and 1/2 gof (x)=2x^(2)-5x+2, then which is f(x)
Answer» `2x-3` `-2x-3` `x-3` `x+3` ANSWER :C

Discussion

5708.	If the transformed equation of curve is 3x^(2) + xy - y^(2) - 7x + y + 7 = 0 when the axes are translated to the point (1,2) thenthe original equation of curve is
Answer» `3x^(2) + xy - y^(2) + 15 x + 4y + 13 = 0` `3x^(2) + xy - y^(2) - 15 x + 4y + 13 = 0` `3x^(2) + xy + y^(2) - 15 x + 4y + 13 = 0` `3x^(2) + xy - y^(2) - 15 x - 4y + 13 = 0` Answer :B

Discussion

5709.	If y=sqrt(x+sqrt(y+sqrt(x+sqrt(y+...oo)))), then (dy)/(dx)=
Answer» `(y^2 + X)/(2y^3 - 2XY - 1)` `(y^2 - x)/(2y^3 - 2xy - 1)` `(y^2 -x)/(2y^3 - 2xy + 1)` `(y^2)/(2y^3 - 2xy + 1)` ANSWER :B

Discussion

5710.	Find the range of 2Cos^(-1)x if x in [-1,0]
Answer» ANSWER :`[pi,2pi]`

Discussion

5711.	Find the sum of: 101 + 99 +97+ .... 47.
Answer» ANSWER :2072

Discussion

5712.	Prove the following ("sin"x-"sin"3x)/("sin"^(2)x-cos3x)=2"sin"x
Answer» ANSWER :RHS

Discussion

5713.	If cos h(3 theta) = 99 then cos h theta =
Answer» 3 9 11 27 Answer :A

Discussion

5714.	cos 2 thetain terms ofcos 4 theta,
Answer» Answer :`pm SQRT ((1 + cos 4 theta)/( 2 ))`

Discussion

5715.	If the conjugate complex number of (x+yi)(1-2i) is 1+i then......
Answer» `X=(3)/(5)` `y=(3)/(5)` `x+yi=(1+i)/(1-2i)` `x-yi=(1-i)/(1+2i)` ANSWER :A

Discussion

5716.	If (-2 + sqrt-3) (-3 + 2 sqrt-3)=a +bi, find the real numbers a and b with values of a and b, also find the modulus of a+bi
Answer» ANSWER :`a=0, B= -7 SQRT3`, MODULUS `=7sqrt3`

Discussion

5717.	(baraxxbarb)xx(barbxxbarc)=
Answer» `[vecavecbvecc]VECA` `[vecavecbvecc]VECB` `[vecavecbvecc]VECC` `[vecavecbvecc]` ANSWER :B

Discussion

5718.	Draw the graph of the following quadratic functions. y=x^(2)-4x+4""-1lexle5.
Answer» ANSWER :`(##SCH_OPM_ISC_MAT_XI_C10_E05_003_A01##)` `(##SCH_OPM_ISC_MAT_XI_C10_E05_003_A02##)`

Discussion

5719.	If bara is a unit vector then baraxx{baraxx(baraxxbarb)}=
Answer» `BARAXXBARB` `barbxxbara` `2(baraxxbarb)` `2(barbxxbara)` ANSWER :B

Discussion

5720.	Three vertices of a parallelogram ABCD are A (3,-1,2), B (1, 2, 4) and C(-1,1,2). Find the coordinates of the fourth vertex D.
Answer» ANSWER :`(1, -2,8)`

Discussion

5721.	Find the values oftheta between 0^(@) and 360^(@) that satisfy the equation sin ( theta + 30^(@)) = 2 cos (45^(@) + theta )
Answer» ANSWER :`THETA = 21 ^(@) ,51, 201 ^(@) 51`

Discussion

5722.	If (cos^(2) theta - 4) x^(2) + (cot theta + sqrt(3)) + cos^(2) ""(3 pi)/(2) = 0 " hold " AA x in R" then " theta =
Answer» `(5pi)/2,(11pi)/2` `(5pi)/6, (11p)/6` `(5pi)/3, (11pi)/3` `(5pi)/4,(11pi)/4` Answer :B

Discussion

5723.	If f(x) =(ax-b)/(bx-a), x ne a/b, a gt 0, b gt 0 and if g(x) = f(f(x) + f(f(1/x))) and g: [1,inft) to [2,infty), then find g^(-1)(x)
Answer» ANSWER :`g^(-1)(x) =(x+sqrt(x^(2)-4))/2, x GE 2`

Discussion

5724.	If 1+ 5+ 12+ 22 + 35+ ….. +to n terms = ( n^(2) (n+1) )/(2)then n^( th) term of L.H.S is
Answer» `(N ( 4n-1))/( 3) ` `(n(3n-1))/(2)` `(n (3n+1))/(2)` `(n (4n+1) )/(3)` ANSWER :B

Discussion

5725.	The shortest distance from the point (2,-7) to the circle x^(2) + y^(2) - 14x - 10y - 151 = 0 is equal to 5.
Answer» ANSWER :FALSE

Discussion

5726.	Find the orthocentre of the triangle formed by 4x-7y+10=0, x+y-5=0, 7x+4y-15=0.
Answer» ANSWER :(1,2)

Discussion

5727.	The vertices A, B, C of a triangle ABC have co-ordinates (4,4), (5,3) and (6,0) respectively. Find the equations of the perpendicular bisectors of AB and BC, the coordinates of the circumcentre and the radius of the circumcircle of the triangle ABC.
Answer» ANSWER :5

Discussion

5728.	Let S be the set of all triangles and R^(+) be the set of positive real numbers. Then the function f: S rarr R, f(Delta)= area of Delta, where Delta in S, is
Answer» INJECTIVE but not sujective surjective but not injective injective as WELL as surjective neither injective nor surjective Answer :B

Discussion

5729.	Value of ( 3 + cot 80^(@) cot 20^(@))/(cot 80^(@) cot 20 ^(@))is equal to
Answer» `COT 20^(@)` `TAN 50 ^(@)` `cot 50^(@)` `cot sqrt20` ANSWER :B

Discussion

5730.	Find the modulus and amplitude of (2+i)/(4i+(1+i)^(2)).
Answer» ANSWER :`- TAN^(-1)2`

Discussion

5731.	Evaluate the following limits : Lim_(theta to pi/2 ) ((2theta-pi)/cos theta )
Answer» ANSWER :`-2`

Discussion

5732.	f(x) = ( x^(2))/(\|x\|) , x ne 0 f (0) = 0at x = 0 , f is
Answer» LEFT CONTINUOUS RIGHT continuous continuous discontinuous Answer :C

Discussion

5733.	There is an error of pm0.04 cm in the measurment of the diameter of a sphre. When the radius is 10cm, the percntage error in the volumeof the sphere is
Answer» `pm1.2` `pm1.0` `pm10.8` `pm0.6` ANSWER :D

Discussion

5734.	(c- b cos A )/(b - c cos A ) =
Answer» `(COS C ) /(cos B) ` ` (cos B) /(cos C) ` ` (cos A ) /(cos B) ` ` (cos B)/(cos A) ` ANSWER :B

Discussion

5735.	If the lines 2x - 3y = 5 and 3x - 4y = 7 are the diameters of a circle of area 154 square units, then obtain the equation of the circle.
Answer» Answer :`X^(2) + y^(2) - 2X + 2Y = 47`, is required EQUATION of he CIRCLE.

Discussion

5736.	Differentiate sqrt(((x-3)(x^(2)+4))/((3x^(2)+4x+5))).
Answer» Answer :`y/2 ((1)/( x -3) + (2x)/(x ^(2) + 4) - ( 6X + 4)/( 3x ^(2) + 4X + 5))`

Discussion

5737.	Find the derivative of (x^(n)-a^(n))/(x-a)for some constant a.
Answer» ANSWER :`(NX^(n)-ANX^(n-1)-X^(n)+a^(n))/((x-a)^(2))`

Discussion

5738.	Number of solution (s) of the equation (sin x)/( cos 3 x) +( sin 3 x )/( co 9 x) + ( sin 9 x )/( cos 27 x) = 0in the interval (0, (pi)/( 4)) is
Answer» ANSWER :6

Discussion

5739.	Differentiate from first principles: 7. (1)/( sqrt (x+1))
Answer» ANSWER :`(-1)/( 2 (x+a)^(3//2))`

Discussion

5740.	Two pillars are 120 ft a part and the height of one in double that of the other. From the middle point of the line joining their feet an observer finds that the angular elevations of their tops are complementary. The height of the longer tower is ……….. feet.
Answer» `35sqrt(2)` `60sqrt(2)` `50sqrt(2)` `40sqrt(2)` ANSWER :B

Discussion

5741.	Find point on Y -axis which is at the equidistance from the given points A(-4, 3) and B(5, 2).
Answer» ANSWER :`(0,-2)`

Discussion

5742.	In the hexagon PQRSTU, RS\|\|PU\|\|QT. Which sides or diagonals have zero slope
Answer» ANSWER :PU, QT, RS

Discussion

5743.	Evaluate the following limits : Lim_(xto1) (x-1)/(2x^(2)-7x+5)
Answer» ANSWER :`(-1)/3`

Discussion

5744.	Vertex of parabola (y-3)^2=2(x+1)is ..........
Answer» ANSWER :`(-1,3)`

Discussion

5745.	If b = 20 , c = 21 ," and " sin A = 3/5then a =
Answer» 13 14 15 16 Answer :A

Discussion

5746.	(2,3) is a point on the side AB of DeltaABC. The third vertex C moves such that the sides AC, BC are bisected by x^2-y^2=0 at right angles. Then C lies one
Answer» `2x-3y=0` `3x-2y=0` `2x+3y=0` `3x-2y=0` ANSWER :C

Discussion

5747.	Find the union of each of the following pairs of sets : A = {1, 2, 3}, B = φ
Answer» ANSWER :`A ∪ B = {1, 2, 3 }`

Discussion

5748.	If f(x)=(1-x)^(1//2) and g(x)=ln(x) then the domain of (gof)(x) is
Answer» `(-OO, 2)` `(-1, 1)` `(-oo, 1]` `(-oo, 1)` ANSWER :D

Discussion

5749.	Check the continuity of function defined by f(x)={{:(4-x^(2),if, x le0),(x-5,if, 0 lt x le1),(4x^(2)-9, if,1 lt x lt 2),(3x+4,if,x ge 2):} at the points x=0, and 2.
Answer» ANSWER :DISCONTINUOUS at x=0,1,2

Discussion

5750.	Evaluate the following limits : Lim_(x to 0 ) (sqrt(1+x)-sqrt(1+x^(2)))/(sqrt(1-x^(2))-sqrt(1-x))
Answer» ANSWER :1

Discussion

Explore topic-wise InterviewSolutions in .

Find a unit vector perpendicular to the plane determined by the points P(1, -1, 2), Q(2,0, -1) and R(0, 2, 1).

Solve the equations: Q. 2^(2x-1)-9xx2^(x-2)+1=0.

O(0,0) A(6,0)and B(0,4)are three points .If P is a point such that the area of DeltaPOB is twice the area of DeltaPOA, then find the locus of P.

Let S be the sum, P the product and R the sum of reciprocals of n terms in a G.P. Prove that P^(2)R^(n) = S^n .

The system of equations tan x =acot x, tan 2x=b cos y

A light ray emerging from the point source placed at P(1,3) is reflected at a pont Q in the axis of x. If the reflected ray passes through the point R(6,7), then the abscissa of Q is

If g(x)=x^(2)+x-2 and 1/2 gof (x)=2x^(2)-5x+2, then which is f(x)

If the transformed equation of curve is 3x^(2) + xy - y^(2) - 7x + y + 7 = 0 when the axes are translated to the point (1,2) thenthe original equation of curve is

If y=sqrt(x+sqrt(y+sqrt(x+sqrt(y+...oo)))), then (dy)/(dx)=

Find the range of 2Cos^(-1)x if x in [-1,0]

Find the sum of: 101 + 99 +97+ .... 47.

Prove the following ("sin"x-"sin"3x)/("sin"^(2)x-cos3x)=2"sin"x

If cos h(3 theta) = 99 then cos h theta =

cos 2 thetain terms ofcos 4 theta,

If the conjugate complex number of (x+yi)(1-2i) is 1+i then......

If (-2 + sqrt-3) (-3 + 2 sqrt-3)=a +bi, find the real numbers a and b with values of a and b, also find the modulus of a+bi

(baraxxbarb)xx(barbxxbarc)=

Draw the graph of the following quadratic functions. y=x^(2)-4x+4""-1lexle5.

If bara is a unit vector then baraxx{baraxx(baraxxbarb)}=

Three vertices of a parallelogram ABCD are A (3,-1,2), B (1, 2, 4) and C(-1,1,2). Find the coordinates of the fourth vertex D.

Find the values oftheta between 0^(@) and 360^(@) that satisfy the equation sin ( theta + 30^(@)) = 2 cos (45^(@) + theta )

If (cos^(2) theta - 4) x^(2) + (cot theta + sqrt(3)) + cos^(2) ""(3 pi)/(2) = 0 " hold " AA x in R" then " theta =

If f(x) =(ax-b)/(bx-a), x ne a/b, a gt 0, b gt 0 and if g(x) = f(f(x) + f(f(1/x))) and g: [1,inft) to [2,infty), then find g^(-1)(x)

If 1+ 5+ 12+ 22 + 35+ ….. +to n terms = ( n^(2) (n+1) )/(2)then n^( th) term of L.H.S is

The shortest distance from the point (2,-7) to the circle x^(2) + y^(2) - 14x - 10y - 151 = 0 is equal to 5.

Find the orthocentre of the triangle formed by 4x-7y+10=0, x+y-5=0, 7x+4y-15=0.

The vertices A, B, C of a triangle ABC have co-ordinates (4,4), (5,3) and (6,0) respectively. Find the equations of the perpendicular bisectors of AB and BC, the coordinates of the circumcentre and the radius of the circumcircle of the triangle ABC.

Let S be the set of all triangles and R^(+) be the set of positive real numbers. Then the function f: S rarr R, f(Delta)= area of Delta, where Delta in S, is

Value of ( 3 + cot 80^(@) cot 20^(@))/(cot 80^(@) cot 20 ^(@))is equal to

Find the modulus and amplitude of (2+i)/(4i+(1+i)^(2)).

Evaluate the following limits : Lim_(theta to pi/2 ) ((2theta-pi)/cos theta )

f(x) = ( x^(2))/(|x|) , x ne 0 f (0) = 0at x = 0 , f is

There is an error of pm0.04 cm in the measurment of the diameter of a sphre. When the radius is 10cm, the percntage error in the volumeof the sphere is

(c- b cos A )/(b - c cos A ) =

If the lines 2x - 3y = 5 and 3x - 4y = 7 are the diameters of a circle of area 154 square units, then obtain the equation of the circle.

Differentiate sqrt(((x-3)(x^(2)+4))/((3x^(2)+4x+5))).

Find the derivative of (x^(n)-a^(n))/(x-a)for some constant a.

Number of solution (s) of the equation (sin x)/( cos 3 x) +( sin 3 x )/( co 9 x) + ( sin 9 x )/( cos 27 x) = 0in the interval (0, (pi)/( 4)) is

Differentiate from first principles: 7. (1)/( sqrt (x+1))

Two pillars are 120 ft a part and the height of one in double that of the other. From the middle point of the line joining their feet an observer finds that the angular elevations of their tops are complementary. The height of the longer tower is ……….. feet.

Find point on Y -axis which is at the equidistance from the given points A(-4, 3) and B(5, 2).

In the hexagon PQRSTU, RS||PU||QT. Which sides or diagonals have zero slope

Evaluate the following limits : Lim_(xto1) (x-1)/(2x^(2)-7x+5)

Vertex of parabola (y-3)^2=2(x+1)is ..........

If b = 20 , c = 21 ," and " sin A = 3/5then a =

(2,3) is a point on the side AB of DeltaABC. The third vertex C moves such that the sides AC, BC are bisected by x^2-y^2=0 at right angles. Then C lies one

Find the union of each of the following pairs of sets : A = {1, 2, 3}, B = φ

If f(x)=(1-x)^(1//2) and g(x)=ln(x) then the domain of (gof)(x) is

Check the continuity of function defined by f(x)={{:(4-x^(2),if, x le0),(x-5,if, 0 lt x le1),(4x^(2)-9, if,1 lt x lt 2),(3x+4,if,x ge 2):} at the points x=0, and 2.

Evaluate the following limits : Lim_(x to 0 ) (sqrt(1+x)-sqrt(1+x^(2)))/(sqrt(1-x^(2))-sqrt(1-x))