14949 + Interview Questions in Maths in Class 11 Page 277 InterviewSolution

13801.	Let an object be placed at some height h cm and let p and Q be two points of oberservation which are at a distance 10 cm apart on a line inclined at angle15 ^(@) to the horizontal . If the angles of elevation of the object from P and Q are30^(@) and 60 ^(@)respectively then find h.
Answer» ANSWER :` 5SQRT3`

Discussion

13802.	Find the value of n so that (a^(n+1)+b^(n+1))/(a^(n)+b^n)may be the geometric mean between a and b.
Answer» ANSWER :`N=(-1)/2`

Discussion

13803.	If f(x) is an odd periodic function with period 2, then f(4)=
Answer» `0` `2` `4` `-4` ANSWER :A

Discussion

13804.	Let f(x)=(arc tanx)^(3)+(arc cotx)^(3). If the range of f(x) is [a,b) then the value of b/(7a) is
Answer» ANSWER :4

Discussion

13805.	A die I thrown, find the probability of following events: (i) A prime number will appear, (ii) A number les than or equal to 3 will appear, (iii) A number les than or equal to one will appear, (iv) A number more than 6 will appear, (v) A number les than 6 will appear.
Answer» ANSWER :(i) `1/2` (II) `2/3` (ii) `1/6` (IV) 0 (V) `5/6`

Discussion

13806.	Evaluate : lim_(xto 0 ) ((x+2)/(x+1))^(x+3)
Answer» ANSWER :`E^(Lim_(XTOOO)(x+3)/(x+1))=e^(1)=e`

Discussion

13807.	If G is the centroid of Delta ABC, G' is the centroid of Delta A' B' C' then vec(A)A' + vec(B)B' + vec(C)C' =
Answer» `BAR(0)` `bar(GG^(1))` `2bar(GG^(1))` `3BAR(GG^(1))` Answer :D

Discussion

13808.	Let A be a set of n distinct elements. Then the total number of distinct functions from A to A is
Answer» `N^(2)` `n^(n)` `2N` `n!` ANSWER :B

Discussion

13809.	Find the eccentricity of the hyperbola whose equation is 2x ^(2) - 3y ^(2) = 15.
Answer» ANSWER :`5/sqrt (15)`

Discussion

13810.	check whether it is statement or not .Do you like mathematics ?
Answer» ANSWER :Not a STATEMENT

Discussion

13811.	If sinA=sinBandcoA=cosB then A =
Answer» `2npi+B` `2npi-B` `NPI+B` `npi+(-1)^(N)B` ANSWER :A

Discussion

13812.	The shortest distance between the line vecr = (1-t) veci + (t-2) vecj + (3-2t) veck and vecr = (s + 1) vect + (2s -1) vecj - (2s + 1) veck is
Answer» `8//sqrt17` `8//sqrt(493)` `8//sqrt29` `16sqrt29` ANSWER :C

Discussion

13813.	If m_1,m_2 " are the roots of the equation " x^2-ax-a-1=0, then the area of the triangle formed by the three straight line y=m_1,x,y=m_2x and y=a(ane -1) is
Answer» `(a^2(a+2))/(2(a+1)), ifagt-1` `-(a^2(a+2))/(2(a+1)), ifagt-1` `-(a^2(a+2))/(2(a+1)), if -2ltalt-1` `-(a^2(a+2))/(29(a+1)), if alt-2` ANSWER :A::C::D

Discussion

13814.	Find the values of x and y, lying between 0 and 360 which satisfy the equations, cos((1)/(2)y^(@)+71^(@))=-0.3420.
Answer» ANSWER :`:.y=78^(@)` or `358^(@)`.

Discussion

13815.	Simplify the following sqrt(-9) + sqrt(-16)
Answer» ANSWER :7I

Discussion

13816.	Find the equation of the circle with centre at (0,0) and radius r.
Answer» ANSWER :`X^(2)+y^(2)=R^(2)

Discussion

13817.	Evaluate the following limits : Lim_( x to 5) (x^(4) - 625 )/(x^(3) - 125)
Answer» ANSWER :`20/3`

Discussion

13818.	Evaluate the following limits : Lim_( x to 1) (x-1)/(log_(e)x)
Answer» ANSWER :1

Discussion

13819.	There are three mathematics teachers in a college in which there are 6 classes. In how many different ways can they choose the classes provided one teaches one class only
Answer» ANSWER :` 120 `

Discussion

13820.	If a sin^(2) theta+bcos^(2) theta = c, then tan^(2) theta =
Answer» `(B-c)/(a-c)` `(c-b)/(a-c)` `(a-c)/(b-c)` `(a-c)/(c-b)` ANSWER :B

Discussion

13821.	Evaluate the following limits in lim_(xrarr0)(ax+x cosx)/(b sinx)
Answer» ANSWER :`(a+1)/(B)`

Discussion

13822.	(Cos^(-1)(41//49))/(Sin^(-1)(2//7))=
Answer» 4 3 2 1 Answer :C

Discussion

13823.	Find the sum to n terms of the series inwhose n^(th)terms is given by n^2+2^n
Answer» ANSWER :`n/6(n+1)(2n+1)+2(2^n-1)`

Discussion

13824.	Find the mean and variance for each of the data in First 10 multiples of 3
Answer» ANSWER :16.5, 74.25

Discussion

13825.	If 4-digit numbers greater than 5,000 are randomly formed from the digits 0, 1,3, 5, and 7, what is the probability of forming a number divided by 5 when, (i) the digits are repeated? (ii) the repeition of digits is not allowed?
Answer» ANSWER :(I) `33/83` (II) `3/8`

Discussion

13826.	The orthocentre of thetriangle formed by the lines x-2y+9=0,x+y-9=0,2x-y-9=0 is
Answer» (5,5) (5,-5) (-5,5) (-5,-5) ANSWER :A

Discussion

13827.	A tower of height 30 metres casts a shadow of length 40 meters at a certain instant. When the sun's elevation increases by Tan^(-1)"1/7, the length of the shadow cast by the tower, in meters is
Answer» `20` `25` `30` `45` ANSWER :C

Discussion

13828.	Find the 13t^th term in the expansion of ( 9x-1/3sqrtx)^18, x !=0.
Answer» ANSWER :`18564`

Discussion

13829.	Find the sum to n terms of each of the series in 1xx 2 xx 3 + 2 xx 3 xx 4 + 3 xx 4 xx 5 + ...
Answer» ANSWER :`(N(n+1)(n+2)(n+3))/4`

Discussion

13830.	sin (A - 45 ^(@) ) = (1)/( sqrt2) (sin A - cos A)
Answer» ANSWER :`45 ^(@) or 135 ^(@)`

Discussion

13831.	Converse of the statement if x^(2)=y^(2) then x=y is ……
Answer» If `X^(2)=y^(2)` then `x!=y` If `x=y` then `x^(2)=y^(2)` If `x!=y` then `x^(2)=y^(2)` If `x^(2)!=y^(2)` then `x=y` ANSWER :B

Discussion

13832.	The roots of the equation 4x^2-2sqrt5x+1=0 are
Answer» `sin 36^(@), sin 18^(@)` `sin 18^(@), COS 36^(@)` `sin 36^(@), cos 18^(@)` `cos 18^(@), cos 36^(@)` ANSWER :B

Discussion

13833.	Given P(A)=0.4 and P(AcupB)=0.7. Find P(B)if(i)A and B are mutually exclusive,(ii)A and B are independent events,(iii)P(A//B)=0.4,(iv)P(A//B)=0.5.P(A)=0.4,P(AcupB)=0.7,P(B)=?
Answer» ANSWER :(i)`0.3` (II)`=.5 (III)`=.5` (IV)`=0.5`

Discussion

13834.	If A= {3, 5, 7, 9, 11}, B= {7, 9, 11, 13}, C= {11, 13, 15}" and "D= {15, 17}, findA cup D, B cup C, (A cup D)cap (B cup C)
Answer» ANSWER :`{7, 9, 11, 13, 15}`

Discussion

13835.	P is a point on the segment joining the feet to vertical poles of heights a and b, The angles of elevation of the tops of the poles from P are 45^@ each. Then the square of the distance between the tops of the poles is:
Answer» `(a^(2)+B^(2))/(2)` `a^(2)+b^(2)` `2(a^(2)+b^(2))` `4(a^(2)+b^(2))` ANSWER :C

Discussion

13836.	Area of the triangle formed by the lines 3x^(2)-4xy+y^(2)=0, 2x-y=6 is
Answer» 16 25 36 49 Answer :C

Discussion

13837.	If the expansion of (x^2+1/x)^n has a term independent of x, then which of the following can be the value of n?
Answer» 18 16 22 13 Answer :A

Discussion

13838.	Write down the equation of the pair of straight lines joining the origin to the points of intersection of the 6x-y+8=0 with the pair of straight lines 3x^2+4xy-4y^2-11x+2y+6=0. Show that the lines so obtained make equal angles with the coordinates axes.
Answer» Answer :`COS^(-1)((13)/(sqrt(193)))`

Discussion

13839.	If a/(sqrtbc)-2=sqrt(b/c)+sqrt(c/b) " where a,b,c" gt "0 then family of lines " sqrtax+sqrtby+sqrtc=0 passes through the point
Answer» (1,1) (1,-2) (-1,2) (-1,1) ANSWER :B

Discussion

13840.	2 boys and 2 girls are in Room X, and 1 boy and 3 girls are in Room Y. Specify the sample space for the experiment in which a room is selected and then a person.
Answer» Answer :`{XB_(1), XB_(2), XG_(1), XG_(2), YB_(3), YG_(3), YG_(4), YG_(5)}`

Discussion

13841.	If f : R to R be a function defined by f (x) = max {x,x^(3)}, find the set of all points where f (x) is not differentiable.
Answer» ANSWER :`[-1,0,1]`

Discussion

13842.	The mean and variance of 7 observations are 8 and 16, respectively. If five of the observations are 2, 4, 10, 12, 14. Find the remaining two observations.
Answer» ANSWER :6, 8

Discussion

13843.	If sin(theta+alpha)=aandsin(theta+beta)=b, then prove that cos2(alpha-beta)-4abcos(alpha-beta)=1-2a^(2)-2b^(2).
Answer» ANSWER :`1-2a^(2)-2B^(2)`

Discussion

13844.	If [veca vecb vecc]=1 then (bara.(barbxxbarc))/((barcxxbara).barb)+(barb.(barcxxbara))/((baraxxbarb).barc)+(barc.(baraxxbarb))/((barbxxbarc).bara)=
Answer» 3 1 `-1` 0 Answer :A

Discussion

13845.	If H, G, S and I respectively denote orthocentre, centroid, circumcentre and in-centre of a triangle formed by the points (1, 2, 3), (2, 3, 1) and (3, 1, 2), then find H, G, S, I
Answer» ANSWER :`H=S=I=(2,2, 2)`

Discussion

13846.	Statement-I : Let A(0,0),B(cosalpha,sinalpha),C(sinalpha-cosalpha) are vertices of a trianlge then the locus of the centroid of triangle is 9x^(2)+9y^(2)=4 Statement-II : The locus of the point (acostheta,bsintheta) is (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 The correct statement is
Answer» only I only II both I and II neither I nor II Answer :2

Discussion

13847.	x^(2)-x + 2=0
Answer» ANSWER :`(1+-sqrt(7)i)/2`

Discussion

13848.	cos(sin^(-1)63//65)=
Answer» `16//63` `63//16` `11//63` `63//11` ANSWER :A

Discussion

13849.	If the lengths of the sides of a triangle are 3 , 4,5 find the circumradius of the triangle .
Answer» ANSWER :`( 5)/(2) ` UNITS

Discussion

13850.	If tanx=(3)/(4),piltxlt(3pi)/(2), find the value of sin""(x)/(2),cos""(x)/(2) and tan((x)/(2)).
Answer» ANSWER :`-3`

Discussion

Explore topic-wise InterviewSolutions in .

Let an object be placed at some height h cm and let p and Q be two points of oberservation which are at a distance 10 cm apart on a line inclined at angle15 ^(@) to the horizontal . If the angles of elevation of the object from P and Q are30^(@) and 60 ^(@)respectively then find h.

Find the value of n so that (a^(n+1)+b^(n+1))/(a^(n)+b^n)may be the geometric mean between a and b.

If f(x) is an odd periodic function with period 2, then f(4)=

Let f(x)=(arc tanx)^(3)+(arc cotx)^(3). If the range of f(x) is [a,b) then the value of b/(7a) is

A die I thrown, find the probability of following events: (i) A prime number will appear, (ii) A number les than or equal to 3 will appear, (iii) A number les than or equal to one will appear, (iv) A number more than 6 will appear, (v) A number les than 6 will appear.

Evaluate : lim_(xto 0 ) ((x+2)/(x+1))^(x+3)

If G is the centroid of Delta ABC, G' is the centroid of Delta A' B' C' then vec(A)A' + vec(B)B' + vec(C)C' =

Let A be a set of n distinct elements. Then the total number of distinct functions from A to A is

Find the eccentricity of the hyperbola whose equation is 2x ^(2) - 3y ^(2) = 15.

check whether it is statement or not .Do you like mathematics ?

If sinA=sinBandcoA=cosB then A =

The shortest distance between the line vecr = (1-t) veci + (t-2) vecj + (3-2t) veck and vecr = (s + 1) vect + (2s -1) vecj - (2s + 1) veck is

If m_1,m_2 " are the roots of the equation " x^2-ax-a-1=0, then the area of the triangle formed by the three straight line y=m_1,x,y=m_2x and y=a(ane -1) is

Find the values of x and y, lying between 0 and 360 which satisfy the equations, cos((1)/(2)y^(@)+71^(@))=-0.3420.

Simplify the following sqrt(-9) + sqrt(-16)

Find the equation of the circle with centre at (0,0) and radius r.

Evaluate the following limits : Lim_( x to 5) (x^(4) - 625 )/(x^(3) - 125)

Evaluate the following limits : Lim_( x to 1) (x-1)/(log_(e)x)

There are three mathematics teachers in a college in which there are 6 classes. In how many different ways can they choose the classes provided one teaches one class only

If a sin^(2) theta+bcos^(2) theta = c, then tan^(2) theta =

Evaluate the following limits in lim_(xrarr0)(ax+x cosx)/(b sinx)

(Cos^(-1)(41//49))/(Sin^(-1)(2//7))=

Find the sum to n terms of the series inwhose n^(th)terms is given by n^2+2^n

Find the mean and variance for each of the data in First 10 multiples of 3

If 4-digit numbers greater than 5,000 are randomly formed from the digits 0, 1,3, 5, and 7, what is the probability of forming a number divided by 5 when, (i) the digits are repeated? (ii) the repeition of digits is not allowed?

The orthocentre of thetriangle formed by the lines x-2y+9=0,x+y-9=0,2x-y-9=0 is

A tower of height 30 metres casts a shadow of length 40 meters at a certain instant. When the sun's elevation increases by Tan^(-1)"1/7, the length of the shadow cast by the tower, in meters is

Find the 13t^th term in the expansion of ( 9x-1/3sqrtx)^18, x !=0.

Find the sum to n terms of each of the series in 1xx 2 xx 3 + 2 xx 3 xx 4 + 3 xx 4 xx 5 + ...

sin (A - 45 ^(@) ) = (1)/( sqrt2) (sin A - cos A)

Converse of the statement if x^(2)=y^(2) then x=y is ……

The roots of the equation 4x^2-2sqrt5x+1=0 are

Given P(A)=0.4 and P(AcupB)=0.7. Find P(B)if(i)A and B are mutually exclusive,(ii)A and B are independent events,(iii)P(A//B)=0.4,(iv)P(A//B)=0.5.P(A)=0.4,P(AcupB)=0.7,P(B)=?

If A= {3, 5, 7, 9, 11}, B= {7, 9, 11, 13}, C= {11, 13, 15}" and "D= {15, 17}, findA cup D, B cup C, (A cup D)cap (B cup C)

P is a point on the segment joining the feet to vertical poles of heights a and b, The angles of elevation of the tops of the poles from P are 45^@ each. Then the square of the distance between the tops of the poles is:

Area of the triangle formed by the lines 3x^(2)-4xy+y^(2)=0, 2x-y=6 is

If the expansion of (x^2+1/x)^n has a term independent of x, then which of the following can be the value of n?

Write down the equation of the pair of straight lines joining the origin to the points of intersection of the 6x-y+8=0 with the pair of straight lines 3x^2+4xy-4y^2-11x+2y+6=0. Show that the lines so obtained make equal angles with the coordinates axes.

If a/(sqrtbc)-2=sqrt(b/c)+sqrt(c/b) " where a,b,c" gt "0 then family of lines " sqrtax+sqrtby+sqrtc=0 passes through the point

2 boys and 2 girls are in Room X, and 1 boy and 3 girls are in Room Y. Specify the sample space for the experiment in which a room is selected and then a person.

If f : R to R be a function defined by f (x) = max {x,x^(3)}, find the set of all points where f (x) is not differentiable.

The mean and variance of 7 observations are 8 and 16, respectively. If five of the observations are 2, 4, 10, 12, 14. Find the remaining two observations.

If sin(theta+alpha)=aandsin(theta+beta)=b, then prove that cos2(alpha-beta)-4abcos(alpha-beta)=1-2a^(2)-2b^(2).

If [veca vecb vecc]=1 then (bara.(barbxxbarc))/((barcxxbara).barb)+(barb.(barcxxbara))/((baraxxbarb).barc)+(barc.(baraxxbarb))/((barbxxbarc).bara)=

If H, G, S and I respectively denote orthocentre, centroid, circumcentre and in-centre of a triangle formed by the points (1, 2, 3), (2, 3, 1) and (3, 1, 2), then find H, G, S, I

Statement-I : Let A(0,0),B(cosalpha,sinalpha),C(sinalpha-cosalpha) are vertices of a trianlge then the locus of the centroid of triangle is 9x^(2)+9y^(2)=4 Statement-II : The locus of the point (acostheta,bsintheta) is (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 The correct statement is

x^(2)-x + 2=0

cos(sin^(-1)63//65)=

If the lengths of the sides of a triangle are 3 , 4,5 find the circumradius of the triangle .

If tanx=(3)/(4),piltxlt(3pi)/(2), find the value of sin""(x)/(2),cos""(x)/(2) and tan((x)/(2)).