14949 + Interview Questions in Maths in Class 11 Page 227 InterviewSolution

11301.	Consider a variable line L which passes through the point of intersection P of the line 3x+4y-12=0 and x+2y-5=0 meetingt the coordinate axes at point A and B. Locus of the centroid of the variable triangle OAB has the equation (where O is origin )
Answer» `3x+4y+6xy=0` `3x-4y-6xy=0` `3x+4y-6xy=0` `4x+3y+6xy=0` ANSWER :C

Discussion

11302.	Consider a variable line L which passes through the point of intersection P of the line 3x+4y-12=0 and x+2y-5=0 meetingt the coordinate axes at point A and B. Locus of the middle point of the segment AB has the eqution
Answer» `3x+4y=4xy` `3x+4y=3xy` `4x+3y=4xy` `4x+3y=3xy` ANSWER :A

Discussion

11303.	If (3 sin h 2 theta)/(5 + 4 cos h 2 theta) = 1 then tan h^(2) theta + 6 tan h theta is equal to
Answer» 3 4 5 9 Answer :D

Discussion

11304.	Expand(x^(2)+sqrt(1-x^(2)))^(5)+(x^(2)-sqrt(1-x^(2)))^(5).
Answer» Answer :`=2[x^(10)-10X^(8)+15X^(6)-10x^(4)+5x^(2)]`

Discussion

11305.	(i) "sin"(A+B)=…......... (ii) cos(A+B)…........ (iii) "sin"(A-B)…...........
Answer» ANSWER :(i) SIN A COS B+cos A sin B (II) `cos A cos B-"sin" A sin `B sin A cos B-cos A sin B

Discussion

11306.	Probability of impossible events is zero.
Answer» ANSWER :TRUE STATEMENT

Discussion

11307.	Is g= {(1, 1), (2,3), (3,5), (4,7)} a function, justify. If this is described by the relation, g(x) = alpha x + beta, then what values should be assigned to alpha and beta ?
Answer» ANSWER :`alpha=2 and BETA= -1`

Discussion

11308.	Each side of a square is of length4 units. The centre of the square is at (3,7) and one of the diagonals is parallel to the line y=x. If the vertices of the square be (x_1,y_1),(x_2,x_2),(y_2,y_3) and (x_4,y_4), "then max " (y_1,y_2,y_3,y_4)-min(x_1,x_2,x_3,x_4) is
Answer» ANSWER :8

Discussion

11309.	Evalute Lt_(xto pi/2)(1+cos2x)/((pi-2x)^(2))
Answer» ANSWER :`1/2`

Discussion

11310.	Find the distance of the point (-1, 1)from the line 12 (x + 6) = 5 (y - 2).
Answer» ANSWER :5 UNITS

Discussion

11311.	A straight line L is drawn through the point A(2,1) is such that its point of intersection with x+y=9 at distance of 3sqrt(2) from A. Then angle made by L with positive direction of x-axis is
Answer» ANSWER :`pi//4`

Discussion

11312.	( cos 6 theta +6 cos 4 theta + 15 cos 2 theta + 10)/( cos 5 theta + 5 cos 3 theta + 10 cos theta)=
Answer» `SIN THETA ` `COS theta ` `2 sin theta ` `2 cos theta` ANSWER :D

Discussion

11313.	You have a single deck of well shuffled cards. Then, What is the probability that it is a face card?
Answer» ANSWER :`3/13`

Discussion

11314.	A line makes the same angle theta, with each of the x and z axis. If the angle beta, which it makes with y - axis, is such that sin^(2)beta' =3sin^(2) theta then cos^(2) theta=
Answer» `2//3` `1//5` `3//5` `2//5` ANSWER :C

Discussion

11315.	Find the mean and variance for the following data 2,4,5,6,8,17
Answer» ANSWER :0.30555555555556

Discussion

11316.	The value of cot((pi)/(4)+theta)cot((pi)/(4)-theta) is
Answer» `-1` 0 1 Not defined Answer :C

Discussion

11317.	Differentiate the following functions w.r.t. x. sin^2 (3x -2)
Answer» ANSWER :`6 SIN (3x -2) cos (3x -2) =3 sin (6x -4)`

Discussion

11318.	If \|{:(a,a^(2),1+a^(3)),(b,b^(2),1+b^(3)),(c,c^(2),1+c^(3)):}\| and \|{:(a,a^(2),1),(b,b^(2),1),(c,c^(2),1):}\|!=0 then show that abc=-1.
Answer» ANSWER :`-1`

Discussion

11319.	If area of DeltaABC(Delta) and angle C are given and if the side c opposite to given angle is minimum, then
Answer» `a= SQRT((2DELTA)/(sinC))` `b= sqrt((2Delta)/(sinC))` `b= sqrt((4Delta)/(sinC))` `b= sqrt((4Delta)/(sin^(2)C))` Answer :A::B

Discussion

11320.	Find the derivative of w.r.to x log _(7) (log x)
Answer» ANSWER :`(1)/( X LOG x. log 7)`

Discussion

11321.	The upper 3//4^(th) portion of a vertical pole subtends an angle "Tan"^(-1)(3//5) at a point in the horizontal plane through its foot and at a distance 40 m from the foot . Given that the vertical pole is at a height less than 100m from the gound ,find its height .
Answer» 20m 40m 60m 80m Answer :B

Discussion

11322.	The smallest positivevalue of x (in radians )log_(5) tan theta = log_(5)^(4), log _(4) ( e sin theta ) and [ 0, 8 pi] is
Answer» 0 2 4 3 Answer :C

Discussion

11323.	Write the first five terms of each of the sequenceswhose n^(th)terms are: a_(n) = (2n-3)/6
Answer» Answer :`-(1)/(6), (1)/(6), (1)/(2), (5)/(6) and (7)/(6)`

Discussion

11324.	What are the points on the y-axis whose distance from the linex/3 + y/4 = 1 is 4 units.
Answer» ANSWER :`(-2, 0) " and " (8, 0)`

Discussion

11325.	Find the sample space associated with the experiment of rolling a pair of dice (one is blue and the other red) once. Also, find the number of elements of this sample space.
Answer» Answer :`S = {(1, 1),(1, 2), (1, 3), (1, 4), (1,5), (1,6),(2, 1), (2, 2), (2, 3), (2, 4), (2,5), (2,6), (3, 1), (3, 2), (3, 3), (3, 4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (5, 1), (5,2), (5,3), (5, 4), (5,5), (5, 6), (6, 1), (6,2), (6,3), (6,4), (6,5), (6, 6)},`

Discussion

11326.	Find what the following equation becomes when origin is shifted of the point (1,1). (i) x^(2) + xy-3y^(2) - y+2=0
Answer» ANSWER :`X^(2) - 3Y^(2) +xy+3x-6y=0`

Discussion

11327.	In /_\ABC prove that (r_1)/(bc) + (r_2)/(ca) + (r_3)/(ab) = 1/r - 1/(2R).
Answer» ` (1)/ (R ) +(1)/ ( R) ` ` ( 1)/(r ) - ( 1)/( R ) ` ` ( 1)/(r ) + I(1) /(2R)` ` ( 1) /( r ) - (1)/( 2 R ) ` ANSWER :D

Discussion

11328.	If a convex polygon has 44 diagonals, than find the number of its sides. Remember : Numbers of diagonal of the polygon having n sides = ((n),(2))-n.
Answer» ANSWER :N = 11

Discussion

11329.	Findlimit of the following if it exists: lim_(xto0)(e^(2+x)-e^(2))/(x)
Answer» ANSWER :`E^(2)`

Discussion

11330.	Change the following complex numbers into polar form (1+ 3i)/(1-2i)
Answer» ANSWER :`SQRT2 ("cos" (3PI)/(4) + i "SIN" (3pi)/(4))`

Discussion

11331.	Find the derivative of the following functions (ax+b)^(n)
Answer» ANSWER :`NA(ax+b)^(n-1)`

Discussion

11332.	Prove that the distance from the origin to the orthocentre of the triangle formed by the lines (x)/(alpha)+(y)/(beta)=1 and ax^(2)+2hxy+by^(2)=0 is (alpha^(2)+beta^(2))^(1//2)\|((a+b) alpha)/(a alpha^(2)-2 halpha beta+b beta^(2))\|
Answer» ANSWER :`(ALPHA^(2)+BETA^(2))^(1//2)\|((a+b) alpha)/(a alpha^(2)-2 HALPHA beta+b beta^(2))\|`

Discussion

11333.	If f (x) = ax ^(2) + bx + cthen find Lt _(x to 5) (f (x) - f (5))/(x-5)
Answer» ANSWER :`10 a + B`

Discussion

11334.	If the sides of a trianglesare in the ratio2 : sqrt6 : sqrt3 + 1then itsangles are
Answer» ` 45 ^(@) , 60 ^(@) , 75 ^(@) ` ` 45 ^(@) , 60^(@) , 90 ^(@) ` ` 45 ^(@) , 30 ^(@) , 90 ^(@)` ` 30 ^(@) , 45^(@) , 60 ^(@) ` ANSWER :A

Discussion

11335.	If f (x+ y ) = f (x). F(y)for all real x,y and f(0 )ne 0then the funtions g (x) = ( f(x) )/(1+ { f(x) }^(2))is
Answer» EVEN function odd function odd if `F(X) gt 0` NEITHER even nor odd Answer :A

Discussion

11336.	What are the coefficients of (2r+1)^(th) and (r+2)^(th) terms in the expansion of (1+x)^43?
Answer» SOLUTION :`"^43C_(2R)`

Discussion

11337.	Find the mean deviation about the mean for the data :
Answer» ANSWER :11.28

Discussion

11338.	Find the equation of the line intersecting the y-axis at a distance of 2 units above the origin and making an angle of 30^(@) with positive direction of the x-axis.
Answer» ANSWER :`X - SQRT3 y + 2 sqrt3 = 0 `

Discussion

11339.	Find the mean deviation about the mean for the data :
Answer» ANSWER :157.92

Discussion

11340.	Find the mean deviation about the mean for the data :
Answer» ANSWER :16

Discussion

11341.	Find the mean deviation about the mean for the data :
Answer» ANSWER :6.32

Discussion

11342.	Construct index number for price for the year 2007 with 2005 as the base year from the following data by taking quantities in the base year as weights:
Answer» ANSWER :`=125`.

Discussion

11343.	The mean of 5 observations is 4.4 and their variance is 8.24. If three of the observations are 1, 2 and 6, find the other two observations.
Answer» ANSWER :4 and 9

Discussion

11344.	Three distinct balls are placed in two drawers. Write the sample space for this experiment.
Answer» Answer :`S={(-,ABC) (abc-) (AB,c) (AC,B) (bc,a) (a,bc) (b,ac) (c,ab)}`

Discussion

11345.	Let P(x,y) be a point which moves such that [x] = [y] where [] is greatest integer function, 0 le x le (7)/2, 0 le y le (7)/2 . If the locus of P constitutes a region , then find its area.
Answer» ANSWER :`13/4` SQUARE UNITS

Discussion

11346.	One of the lines of -3x^(2)+2xy+y^(2)=0 is parallel to lx+y+1=0 then l=
Answer» 0 1 2 `-1` ANSWER :D

Discussion

11347.	The minors of 1 and 7 in the matrix [(1,4,2),(2,-1,4),(-3,7,6)] are
Answer» 34, 0 `34,-1` `-34,1` `-34,0` ANSWER :D

Discussion

11348.	If 2x+3y+4=0, lamda x +ky+2=0 are identical lines then 3lamda-2k=
Answer» 1 `0` `-1` `2` ANSWER :B

Discussion

11349.	The volume of parallelopiped with vectors bara+2barb-barc,bara-barb,bara-barb-barc as coterminous edges is K[bara barb barc] then abs(K) =
Answer» `-2` 2 `-3` 3 Answer :D

Discussion

11350.	If bar(a^(1)),bar(b^(1)),bar(c^(1)) represents the reciprocal system of vectors bara,barb,barc then bara,bar(a^(1))+barb.bar(b^(1))+barc.bar(c^(1))=
Answer» 0 1 2 3 Answer :D

Discussion

Explore topic-wise InterviewSolutions in .

Consider a variable line L which passes through the point of intersection P of the line 3x+4y-12=0 and x+2y-5=0 meetingt the coordinate axes at point A and B. Locus of the centroid of the variable triangle OAB has the equation (where O is origin )

Consider a variable line L which passes through the point of intersection P of the line 3x+4y-12=0 and x+2y-5=0 meetingt the coordinate axes at point A and B. Locus of the middle point of the segment AB has the eqution

If (3 sin h 2 theta)/(5 + 4 cos h 2 theta) = 1 then tan h^(2) theta + 6 tan h theta is equal to

Expand(x^(2)+sqrt(1-x^(2)))^(5)+(x^(2)-sqrt(1-x^(2)))^(5).

(i) "sin"(A+B)=…......... (ii) cos(A+B)…........ (iii) "sin"(A-B)…...........

Probability of impossible events is zero.

Is g= {(1, 1), (2,3), (3,5), (4,7)} a function, justify. If this is described by the relation, g(x) = alpha x + beta, then what values should be assigned to alpha and beta ?

Each side of a square is of length4 units. The centre of the square is at (3,7) and one of the diagonals is parallel to the line y=x. If the vertices of the square be (x_1,y_1),(x_2,x_2),(y_2,y_3) and (x_4,y_4), "then max " (y_1,y_2,y_3,y_4)-min(x_1,x_2,x_3,x_4) is

Evalute Lt_(xto pi/2)(1+cos2x)/((pi-2x)^(2))

Find the distance of the point (-1, 1)from the line 12 (x + 6) = 5 (y - 2).

A straight line L is drawn through the point A(2,1) is such that its point of intersection with x+y=9 at distance of 3sqrt(2) from A. Then angle made by L with positive direction of x-axis is

( cos 6 theta +6 cos 4 theta + 15 cos 2 theta + 10)/( cos 5 theta + 5 cos 3 theta + 10 cos theta)=

You have a single deck of well shuffled cards. Then, What is the probability that it is a face card?

A line makes the same angle theta, with each of the x and z axis. If the angle beta, which it makes with y - axis, is such that sin^(2)beta' =3sin^(2) theta then cos^(2) theta=

Find the mean and variance for the following data 2,4,5,6,8,17

The value of cot((pi)/(4)+theta)cot((pi)/(4)-theta) is

Differentiate the following functions w.r.t. x. sin^2 (3x -2)

If |{:(a,a^(2),1+a^(3)),(b,b^(2),1+b^(3)),(c,c^(2),1+c^(3)):}| and |{:(a,a^(2),1),(b,b^(2),1),(c,c^(2),1):}|!=0 then show that abc=-1.

If area of DeltaABC(Delta) and angle C are given and if the side c opposite to given angle is minimum, then

Find the derivative of w.r.to x log _(7) (log x)

The upper 3//4^(th) portion of a vertical pole subtends an angle "Tan"^(-1)(3//5) at a point in the horizontal plane through its foot and at a distance 40 m from the foot . Given that the vertical pole is at a height less than 100m from the gound ,find its height .

The smallest positivevalue of x (in radians )log_(5) tan theta = log_(5)^(4), log _(4) ( e sin theta ) and [ 0, 8 pi] is

Write the first five terms of each of the sequenceswhose n^(th)terms are: a_(n) = (2n-3)/6

What are the points on the y-axis whose distance from the linex/3 + y/4 = 1 is 4 units.

Find the sample space associated with the experiment of rolling a pair of dice (one is blue and the other red) once. Also, find the number of elements of this sample space.

Find what the following equation becomes when origin is shifted of the point (1,1). (i) x^(2) + xy-3y^(2) - y+2=0

In /_\ABC prove that (r_1)/(bc) + (r_2)/(ca) + (r_3)/(ab) = 1/r - 1/(2R).

If a convex polygon has 44 diagonals, than find the number of its sides. Remember : Numbers of diagonal of the polygon having n sides = ((n),(2))-n.

Findlimit of the following if it exists: lim_(xto0)(e^(2+x)-e^(2))/(x)

Change the following complex numbers into polar form (1+ 3i)/(1-2i)

Find the derivative of the following functions (ax+b)^(n)

Prove that the distance from the origin to the orthocentre of the triangle formed by the lines (x)/(alpha)+(y)/(beta)=1 and ax^(2)+2hxy+by^(2)=0 is (alpha^(2)+beta^(2))^(1//2)|((a+b) alpha)/(a alpha^(2)-2 halpha beta+b beta^(2))|

If f (x) = ax ^(2) + bx + cthen find Lt _(x to 5) (f (x) - f (5))/(x-5)

If the sides of a trianglesare in the ratio2 : sqrt6 : sqrt3 + 1then itsangles are

If f (x+ y ) = f (x). F(y)for all real x,y and f(0 )ne 0then the funtions g (x) = ( f(x) )/(1+ { f(x) }^(2))is

What are the coefficients of (2r+1)^(th) and (r+2)^(th) terms in the expansion of (1+x)^43?

Find the mean deviation about the mean for the data :

Find the equation of the line intersecting the y-axis at a distance of 2 units above the origin and making an angle of 30^(@) with positive direction of the x-axis.

Find the mean deviation about the mean for the data :

Find the mean deviation about the mean for the data :

Find the mean deviation about the mean for the data :

Construct index number for price for the year 2007 with 2005 as the base year from the following data by taking quantities in the base year as weights:

The mean of 5 observations is 4.4 and their variance is 8.24. If three of the observations are 1, 2 and 6, find the other two observations.

Three distinct balls are placed in two drawers. Write the sample space for this experiment.

Let P(x,y) be a point which moves such that [x] = [y] where [] is greatest integer function, 0 le x le (7)/2, 0 le y le (7)/2 . If the locus of P constitutes a region , then find its area.

One of the lines of -3x^(2)+2xy+y^(2)=0 is parallel to lx+y+1=0 then l=

The minors of 1 and 7 in the matrix [(1,4,2),(2,-1,4),(-3,7,6)] are

If 2x+3y+4=0, lamda x +ky+2=0 are identical lines then 3lamda-2k=

The volume of parallelopiped with vectors bara+2barb-barc,bara-barb,bara-barb-barc as coterminous edges is K[bara barb barc] then abs(K) =

If bar(a^(1)),bar(b^(1)),bar(c^(1)) represents the reciprocal system of vectors bara,barb,barc then bara,bar(a^(1))+barb.bar(b^(1))+barc.bar(c^(1))=