14949 + Interview Questions in Maths in Class 11 Page 291 InterviewSolution

14501.	The minute hand of a big clock in 36 cms long how many cms does the extremity of the minute hand move in 20 minutes time. (use pi=22/7)
Answer» SOLUTION :`24pi`CMS

Discussion

14502.	Write the contrapositive and converse of the following statements. If the two lines are parallel, then they do not intersect in the same plane.
Answer» ANSWER :The CONTRAPOSITIVE is If two LINES intersect in the same PLANE, then they are not PARALLEL The converse is If two lines do not interesect in the same plane, then they are parallel

Discussion

14503.	sin x = 2/5, x lies in second quadrant. find trignometric ratio
Answer» ANSWER :`cosec X = 5/3, cos x =-4/5 , sec x =- 5/4 , TAN x=- 3/4, COT x =- 4/3`

Discussion

14504.	Three coin are tossed once. Find the probability of getting (i) 3 heads, (ii) 2 heads, (iii) atleast 2 heads, (iv) atmost 2 heads, (v) no heads, (vi) 3 tails, (vii) exactly two tail, (viii) no tail, (ix) atmost two tails.
Answer» Answer :(i) `1/8`, (ii) `3/8`, (iii) `1/2`, (IV) `7/8`, (v) `1/8`, (VI) `1/8`, (vii) `3/8`, (VIII) `1/8`, (IX) `7/8`,

Discussion

14505.	Find the value of sin""(31pi)/(3)
Answer» ANSWER :`(SQRT3)/(2)`

Discussion

14506.	Sin^(-1)(4/5)-Sin^(-1)(5/13)=
Answer» `SIN^(-1)(56/65)` `sin^(-1)(63/65)` `sin^(-1)(77/85)` `sin^(-1)(33/65)` ANSWER :D

Discussion

14507.	From a point on the level ground, the angle of elevation of the top of a pole is 30^@. On moving 20 metres nearer, the angle of elevation is 45^@. Then the height of the pole, in metres , is
Answer» `10(sqrt(3)-1)` `10(sqrt(3)+1)` `15` `20` ANSWER :B

Discussion

14508.	[barbbarcbarbxxbarc]+{barb.barc}^(2)=
Answer» `(BARB+BARC)^(2)` `ABS(barb)^(2)+abs(barc)^(2)` `abs(barb)+abs(barc)` `abs(barb)^(2)abs(barc)^(2)` ANSWER :D

Discussion

14509.	i) Express (sin 4theta)/(sin theta) interms of cos^(3) theta and costheta ii) Express cos^(6)A+sin^(6)A interms of sin 2A iii) Express (1-costheta+sintheta)/(1+cos theta+sin theta) interms of tantheta/2
Answer» ANSWER :i) `8Cos^(3)theta-4Costheta` ii) `1-3/4 SIN^(2)2A` iii)`"TAN"theta/2`

Discussion

14510.	Which of the following sets are finite or infinite : The set of odd natural numbers.
Answer» ANSWER :it is an INFINITE SET

Discussion

14511.	If the point (1, 2, 3) is changed to the point (2, 3, 1) through translation of axes, find the new origin.
Answer» ANSWER :(-1,-1,2)

Discussion

14512.	If y = e^(x) sin ax and (d^(2)y/(dx^(2))-2dy/dx + 5y = 0 find a:
Answer» 4 2 -1 0 Answer :B

Discussion

14513.	Find x if the median of the observation 33,28,20,25,34 and x is 29.
Answer» ANSWER :30

Discussion

14514.	If 2 sin ^(2) x + 3 sin x - 2 gt 0 and x^(2) - x - 2 lt 0 (x is measured in radians) then x lies in
Answer» `((PI)/6, (5PI)/6)` `(-(5pi)/6)` `(-1,2)` `((pi)/6,2)` ANSWER :D

Discussion

14515.	Point of intersection of the graph of sine function with X - axis has value zero.
Answer» ANSWER :TRUE STATEMENT

Discussion

14516.	A rod of length 12 cm moves with its ends always touching the coordinate axes. Determine the equation of the locus of a point P on the rod, which is 3 cm from the end in contact with the x-axis.
Answer» ANSWER :`(X^(2))/(81)+(y^(2))/(9)=1`

Discussion

14517.	sin[(pi)/6+cos^(-1)(-(sqrt(3))/2)]=
Answer» `-1` `0` `pi` `(SQRT(3))/2` Answer :B

Discussion

14518.	Evaluate : lim_(x to 0 ) ((1+6x^(2))/(1+4x^(2)))^(1/(x^(2)))
Answer» ANSWER :`E^(Lim_(e^(xto0)2)2/(1+4x^(2)))=e^(2)`

Discussion

14519.	If x,y,inR satisfies (x+5) ^(2) + (y-12) ^(2) = (14)^(2), then the minimum vlaue ofsqrt (x ^(2) + y ^(2)) is "______"
Answer» ANSWER :1

Discussion

14520.	Prove that C_(0)^(2)+C_(1)^(2)+C_(2)^(2)+….+C_(n)^(2)=(2n!)/((n!)^(2)).
Answer» ANSWER :`=(2N!)/((N!)^(2))`

Discussion

14521.	If theta=pi/(2^n+1)then cos theta cos 2 theta cos 2^(2) theta...... Cos2^(n-1) theta is equal to
Answer» `(1)/(2^(N))` `COS theta` 2 `2^(n)` ANSWER :A

Discussion

14522.	Prove that (1+cos""pi/10)(1+cos""(3pi)/10)(1+cos""(7pi)/10)(1+cos""(9pi)/10)=1/16
Answer» `1/8` `1/16` `1/4` 1 Answer :B

Discussion

14523.	Find the middle term in the expansion of((x)/(3)+9y)^(10)
Answer» ANSWER :61236 `x^5` `y^5`

Discussion

14524.	Find perpendicular distance from the origin to the line joining the points ( cos theta, sin theta) " and " ( cos phi , sin phi).
Answer» ANSWER :`\|COS ((PHI - THETA)/2)\|`

Discussion

14525.	Find the equation of locus of point which lies on bisectors of angles between the co-ordinate axes.
Answer» ANSWER :`X^(2)-y^(2)=0`

Discussion

14526.	If lim_(xto 1)(x^(2019)-1)/(x^(n)-1)=-(2019)/(2018) then n=……..
Answer» -2017 2018 2017 -2018 Answer :C

Discussion

14527.	x + y ge 4, 2x - y lt 0
Answer» Solution :First inequation :`x + y GE 4` CORRESPONDING equation : `x + y =4` It cuts the X-axis at A(4, 0) and Y-axis at B (0, 4). Join AB. At point (0, 0) from the inequation, 0`ge`4 (False) `:.`The solution of this inequation is that REGION of XY-plane divided by line AB in which (0, 0) does not lie. Second inequation : `2X - y lt 0 ` Corresponding equation : `2x - y = 0` This line passes through the pointsO(0, 0) and C(2, 4). Join OC by dotted line. At point (1, 0) , from the inequation, 2 lt 0 (False) `:.` The solution of this inequation is that region of XY-plane divided by line OC in which (1, 0) does not lie. The common solution of two inequation is shown by the shaded part.

Discussion

14528.	Length of latus rectum of ellipse 2x^(2)+81y^(2)=162
Answer» ANSWER :`(##KPK_AIO_MAT_XI_C11_E01_037_S01##)` `(##KPK_AIO_MAT_XI_C11_E01_037_S02##)`

Discussion

14529.	A line perpendicular to the line5x-y=0 form a triangle with the coordinate axes if the area of the triangle is 5 sq.units,then its equation is:
Answer» `x+5ypm5sqrt(2)=0` `x-5ypm5sqrt(2)=0` `5x+ypm5sqrt(2)=0` `5x-ypm5sqrt(2)=0` ANSWER :A

Discussion

14530.	Find equation of the line which is equidistant from parallel lines 9x + 6y - 7 = 0 " and " 3x + 2y + 6 = 0 .
Answer» ANSWER :`18X + 12Y + 11 = 0 `

Discussion

14531.	If the sides of trinangles arex^(2) + x+ 1,2 x + 1 , x^(-2) -1where,x>1,then the gratest angle is
Answer» `pi//3` `pi//4` `pi//6` `2pi//3` ANSWER :D

Discussion

14532.	If the vectors bara =bari - barj + 2bark, barb =2bari+4barj+bark and barc = gammabari - barj +mubark are mutually orthogonal, then (gamma,mu)=
Answer» (-3,2) (2,-3) (-2,3) (3,-2) ANSWER :D

Discussion

14533.	Which of the following is the nth term of an AP?
Answer» `3-2n` `n^2-3` `3^n-2` `2-3n^2` ANSWER :A

Discussion

14534.	If 'theta' is an acute angle and the vector (sin theta)bari +(cos theta)bari " is perpendicular to the vector " bari -sqrt3barj, " then " theta =
Answer» `pi/6` `pi/5` `pi/4` `pi/3` ANSWER :D

Discussion

14535.	Let f:(-1,1) rarr R be such that f(cos 4 theta) = (2)/(2-sec^(2) theta) for theta in (0, pi/4) uu (pi/4, pi/2). Then the value of f(1/3) is (are)
Answer» `1- SQRT(3/2)` `1+sqrt(3/2)` `1-sqrt(2/3)` `1+sqrt(2/3)` ANSWER :A::B

Discussion

14536.	Numbers of improper subsets of the given set A = {1,5,9} are 8 .
Answer» ANSWER :FALSE STATEMENT

Discussion

14537.	A =(1, 2, 3, 5) and B= {4, 6, 9). Define a relation R from A to B by R= {(x, y): the difference between x and y is odd, x in A, y in B}. Write R in roster form.
Answer» ANSWER :R={(1,4),(1,6),(2,9),(3,4),(3,6),(5,4),(5,6)}

Discussion

14538.	Find the equation of an ellipse whose latus rectum is 8 and eccentricity is 1/3
Answer» ANSWER :`8X^(2)+9Y^(2)=162`

Discussion

14539.	If theta in (-(pi)/(4), (pi)/(4)) and x=log_(e ) [cot((pi)/(4)+theta)] Find Tanhx when theta=(pi)/(6)
Answer» ANSWER :`-(SQRT(3))/(2)`

Discussion

14540.	Let U = { 1, 2, 3, 4, 5, 6, 7, 8, 9 }, A= { 1, 2, 3, 4}, B = { 2,4, 6, 8 } and C = { 3, 4, 5, 6 }. Find (A′)′
Answer» ANSWER :`{ 1, 2, 3, 4 }`

Discussion

14541.	Let U = { 1, 2, 3, 4, 5, 6, 7, 8, 9 }, A= { 1, 2, 3, 4}, B = { 2,4, 6, 8 } and C = { 3, 4, 5, 6 }. Find A'
Answer» ANSWER :`{ 5, 6, 7, 8, 9}`

Discussion

14542.	Range of f(x)= (1)/(1- 2 cos x) is
Answer» `[(1)/(3), 1]` `[-1, (1)/(3)]` `(-OO, -1) UU [(1)/(3), oo)` `[-(1)/(3), 1]` ANSWER :B

Discussion

14543.	A line points (a,2a) and (-2,3) is perpendicular to the line 4x + 3y + 5 = 0 , find the value of a .
Answer» ANSWER :`18//5`

Discussion

14544.	What is the coefficient of the (r+1)^(th) term in the expansion of (1+x)^n?
Answer» SOLUTION :`"^nC_r`

Discussion

14545.	Consider the line given by L_1=X+3Y-5=0, L_2=3x-ky-1=0 , match thestatements/expressions " in Column-I with the " statements /expression in Column-II.
Answer» ANSWER :A-p,Q;B-p,R;C-p;D-p

Discussion

14546.	If two tangents are drawn from a point to the circle x^(2)+y^(2)=32 to the circle x^(2)+y^(2)=16, then the angle between the tangents is :
Answer» `(PI)/(4)` `(pi)/(3)` `(pi)/(2)` `(pi)/(6)` SOLUTION :`S_(1):x^(2)+y^(2)=32` `S_(2):x^(2)+y^(2)=16` `rArr""S_(1)=0" is the director circle of "S_(2)=0` `rArr"Director circle is the LOCUS of two PERPENDICULAR tangents"` `"Angle is "(pi)/(2)`

Discussion

14547.	Determine n if ""^(2n)C_(3):""^(n)C_(3)=12:1 .
Answer» ANSWER :5

Discussion

14548.	Find the value of n such that (""^(n)P_(4))/(""^(n-1)P_(4))=(5)/(3), n gt 4
Answer» ANSWER :10

Discussion

14549.	If a = 26, b = 30 , cos C =( 63 )/( 65)then C=
Answer» ANSWER :`8`

Discussion

14550.	Find the sixth term of the expansion of (y^(1//2) + x^(1//3) )^(n), if the binomial coefficient of the third term from the end is 45.
Answer» ANSWER :`252 y^(5//2) X^(5//3)`

Discussion

Explore topic-wise InterviewSolutions in .

The minute hand of a big clock in 36 cms long how many cms does the extremity of the minute hand move in 20 minutes time. (use pi=22/7)

Write the contrapositive and converse of the following statements. If the two lines are parallel, then they do not intersect in the same plane.

sin x = 2/5, x lies in second quadrant. find trignometric ratio

Three coin are tossed once. Find the probability of getting (i) 3 heads, (ii) 2 heads, (iii) atleast 2 heads, (iv) atmost 2 heads, (v) no heads, (vi) 3 tails, (vii) exactly two tail, (viii) no tail, (ix) atmost two tails.

Find the value of sin""(31pi)/(3)

Sin^(-1)(4/5)-Sin^(-1)(5/13)=

From a point on the level ground, the angle of elevation of the top of a pole is 30^@. On moving 20 metres nearer, the angle of elevation is 45^@. Then the height of the pole, in metres , is

[barbbarcbarbxxbarc]+{barb.barc}^(2)=

i) Express (sin 4theta)/(sin theta) interms of cos^(3) theta and costheta ii) Express cos^(6)A+sin^(6)A interms of sin 2A iii) Express (1-costheta+sintheta)/(1+cos theta+sin theta) interms of tantheta/2

Which of the following sets are finite or infinite : The set of odd natural numbers.

If the point (1, 2, 3) is changed to the point (2, 3, 1) through translation of axes, find the new origin.

If y = e^(x) sin ax and (d^(2)y/(dx^(2))-2dy/dx + 5y = 0 find a:

Find x if the median of the observation 33,28,20,25,34 and x is 29.

If 2 sin ^(2) x + 3 sin x - 2 gt 0 and x^(2) - x - 2 lt 0 (x is measured in radians) then x lies in

Point of intersection of the graph of sine function with X - axis has value zero.

A rod of length 12 cm moves with its ends always touching the coordinate axes. Determine the equation of the locus of a point P on the rod, which is 3 cm from the end in contact with the x-axis.

sin[(pi)/6+cos^(-1)(-(sqrt(3))/2)]=

Evaluate : lim_(x to 0 ) ((1+6x^(2))/(1+4x^(2)))^(1/(x^(2)))

If x,y,inR satisfies (x+5) ^(2) + (y-12) ^(2) = (14)^(2), then the minimum vlaue ofsqrt (x ^(2) + y ^(2)) is "______"

Prove that C_(0)^(2)+C_(1)^(2)+C_(2)^(2)+….+C_(n)^(2)=(2n!)/((n!)^(2)).

If theta=pi/(2^n+1)then cos theta cos 2 theta cos 2^(2) theta...... Cos2^(n-1) theta is equal to

Prove that (1+cos""pi/10)(1+cos""(3pi)/10)(1+cos""(7pi)/10)(1+cos""(9pi)/10)=1/16

Find the middle term in the expansion of((x)/(3)+9y)^(10)

Find perpendicular distance from the origin to the line joining the points ( cos theta, sin theta) " and " ( cos phi , sin phi).

Find the equation of locus of point which lies on bisectors of angles between the co-ordinate axes.

If lim_(xto 1)(x^(2019)-1)/(x^(n)-1)=-(2019)/(2018) then n=……..

x + y ge 4, 2x - y lt 0

Length of latus rectum of ellipse 2x^(2)+81y^(2)=162

A line perpendicular to the line5x-y=0 form a triangle with the coordinate axes if the area of the triangle is 5 sq.units,then its equation is:

Find equation of the line which is equidistant from parallel lines 9x + 6y - 7 = 0 " and " 3x + 2y + 6 = 0 .

If the sides of trinangles arex^(2) + x+ 1,2 x + 1 , x^(-2) -1where,x>1,then the gratest angle is

If the vectors bara =bari - barj + 2bark, barb =2bari+4barj+bark and barc = gammabari - barj +mubark are mutually orthogonal, then (gamma,mu)=

Which of the following is the nth term of an AP?

If 'theta' is an acute angle and the vector (sin theta)bari +(cos theta)bari " is perpendicular to the vector " bari -sqrt3barj, " then " theta =

Let f:(-1,1) rarr R be such that f(cos 4 theta) = (2)/(2-sec^(2) theta) for theta in (0, pi/4) uu (pi/4, pi/2). Then the value of f(1/3) is (are)

Numbers of improper subsets of the given set A = {1,5,9} are 8 .

A =(1, 2, 3, 5) and B= {4, 6, 9). Define a relation R from A to B by R= {(x, y): the difference between x and y is odd, x in A, y in B}. Write R in roster form.

Find the equation of an ellipse whose latus rectum is 8 and eccentricity is 1/3

If theta in (-(pi)/(4), (pi)/(4)) and x=log_(e ) [cot((pi)/(4)+theta)] Find Tanhx when theta=(pi)/(6)

Let U = { 1, 2, 3, 4, 5, 6, 7, 8, 9 }, A= { 1, 2, 3, 4}, B = { 2,4, 6, 8 } and C = { 3, 4, 5, 6 }. Find (A′)′

Let U = { 1, 2, 3, 4, 5, 6, 7, 8, 9 }, A= { 1, 2, 3, 4}, B = { 2,4, 6, 8 } and C = { 3, 4, 5, 6 }. Find A'

Range of f(x)= (1)/(1- 2 cos x) is

A line points (a,2a) and (-2,3) is perpendicular to the line 4x + 3y + 5 = 0 , find the value of a .

What is the coefficient of the (r+1)^(th) term in the expansion of (1+x)^n?

Consider the line given by L_1=X+3Y-5=0, L_2=3x-ky-1=0 , match thestatements/expressions " in Column-I with the " statements /expression in Column-II.

If two tangents are drawn from a point to the circle x^(2)+y^(2)=32 to the circle x^(2)+y^(2)=16, then the angle between the tangents is :

Determine n if ""^(2n)C_(3):""^(n)C_(3)=12:1 .

Find the value of n such that (""^(n)P_(4))/(""^(n-1)P_(4))=(5)/(3), n gt 4

If a = 26, b = 30 , cos C =( 63 )/( 65)then C=

Find the sixth term of the expansion of (y^(1//2) + x^(1//3) )^(n), if the binomial coefficient of the third term from the end is 45.