14949 + Interview Questions in Maths in Class 11 Page 216 InterviewSolution

10751.	Write the component statementsof the following compound statement and check whether compound statement is true or false . Two lines intersect at a point or they are parallel"
Answer» Answer :p: TWO lines intersect ar a POINT or THEYARE parallel . Component STATEMENTS q: Two limes intersect at a point. r: Two lines are parallel. The statements q and r are false `RARR` compound statement p is false.

Discussion

10752.	If barA=baraxxbarb,barB=barbxxbarc,barC=barcxxbara then barAxx(barBxxbarC), barB(barCxxbarA),barCxx(barAxxbarB) are
Answer» collinear coplanar non-collinear non-coplanar Answer :B

Discussion

10753.	For problems Let cos^(-1)(4x^(3)-3x)=a+bcos^(-1)x If x in [-1/2, 1/2], then the principal value of sin^(-1)(sin""a/b)
Answer» `-pi/3` `pi/3` `-pi/6` 0 Answer :A

Discussion

10754.	If f(x)=sin^(6) x + cos^(6) xforx in R , then f(x) lies in the interval
Answer» `[(7)/(8) ,(5)/(4)]` `[(1)/(2),(5)/(8)]` `[(1)/(4),1]` `[(1)/(4),(1)/(2)]` Answer :3

Discussion

10755.	An experiment consists of rolling a die and then tossing a coin once if the number on die is even. If the number on die is odd, the coin is tossed twice. Write the sample space for this experiment.
Answer» ANSWER :{1HH, 1HT, 1TH, 1TT, 2H, 2T, 3HH, 3HT, 3TH, 3TT, 4H, 4T, 5HH, 5HT, 5TH, 5TT, 6H, 6T}

Discussion

10756.	If A=[(1,0,2),(-1,1,-2),(0,2,1)] and AdjA=[(5,x,-2),(1,1,0),(-2,-2,y)] then (x,y) =
Answer» `(-4,1)` `(4,1)` `(-4,-1)` `(4,-1)` ANSWER :B

Discussion

10757.	Find the coordinates of the point on the parabola y^(2)=8x whose focal distance is 8.
Answer» ANSWER :`(16,+4sqrt(3))`

Discussion

10758.	Find the derivate of x^(-4)(3-4x^(-5))
Answer» ANSWER :`(-12)/(x^(5))+(36)/(x^(10))`

Discussion

10759.	Let baru,barv,barw " be such that " absbaru =1, absbarv=2, absbarw=3 " if the projection of " barv " along " baru "is equal to that of " barw " along " baru and barv,barw are perpendicular to each other, then abs(baru-barv+barw) =
Answer» 2 14 `SQRT14` `SQRT7` ANSWER :C

Discussion

10760.	Find the area of the triangle having (3bar(i)+4bar(j)),(-5bar(i)+7bar(j)) as adjacent sides.
Answer» ANSWER :`(41)/(2)` SQ. UNITS

Discussion

10761.	For an A.P a = 20 and l = 97 then S_(20)= ..........
Answer» ANSWER :1170

Discussion

10762.	If vec(a), vec(b), vec(c ) are unit vectors such that vec(a).vec(b)= vec(a).vec(c )=0 and (vec(b), vec(c ))= (pi)/(6), then vec(a)=
Answer» `+- (VEC(a) xx vec(c ))` `+- 2(vec(a) xx vec(c ))` `+- (vec(B) xx vec( c))` `+- 2(vec(b) xx vec(c ))` ANSWER :D

Discussion

10763.	Show that 9^(n+1) - 8n - 9 is divisible by 64, whenever n is a positive interger.
Answer» Answer :`= 64 [.^((n+1))C_(2)+.^((n+1))C_(3).(8)+...+.^((n+1))C_((n+1))(8)^(n-1)]`

Discussion

10764.	Which of the following sentences are statement? Give reason for your answer: Sum of two positive numbers is positive numbers.
Answer» ANSWER :It is a STATEMENT.

Discussion

10765.	Is the given relation a function? Give reason for your answer. h= {(4, 6), (3,9), (-11, 6), (3,11)}
Answer» ANSWER :it is not a FUNCTION

Discussion

10766.	The sum of three numbers in G.P. is 56. If we subtract 1, 7, 21 from these numbersin that order, we obtain an arithmetic progression. Find the numbers.
Answer» ANSWER :`8, 16, 32`

Discussion

10767.	If there is an error of 1 % is made in the side of a cube then the percentage error in its volume is
Answer» 1 2 3 `1//2` ANSWER :C

Discussion

10768.	If S_(1), S_(2), S_(3) be respectively the sums of n, 2n, 3n, terms of a G.P., then prove that S_(1)(S_(3)-S_(2))=(S_(2)-S_(1))^(2).
Answer» ANSWER :`=(S_(2)-S_(1))^(2)`

Discussion

10769.	The point of intersction of barr xx bara= barbxx bara andbarr xx barb = bara xx barb where bara = bari + barj and barb = 2 bari - bark is
Answer» `3bari+barj-bark` `3bari-bark` `3bari+2barj-4bark` NONE of these Answer :A

Discussion

10770.	..............is the value of omega to represent line sqrt(3)x +y =10 in normal form.
Answer» ANSWER :`pi/6`

Discussion

10771.	A plane is 1km from one landmark and 2km from another. From the planes point of view the land between them subtends an angle 60^(@). How far apart are the landmarks?
Answer» ANSWER :`c-sqrt(5-2sqrt2)KM`

Discussion

10772.	If the straight lines y=4-3x, ay=x+10, 2y+bx+9=0 represent the three consecutive sides of a rectangle then ab =
Answer» 18 `-3` `1//2` `-1//3` ANSWER :A

Discussion

10773.	Let cos^(-1)(x)+cos^(-1)(2x)+cos^(-1)(3x)" be "pi. If x satisfies the equation ax^(3)+bx^(2)+cx-1=0 then the value of (b-a-c) is
Answer» ANSWER :2

Discussion

10774.	The minimum value of 3e^x+4e^(-x) is
Answer» `4sqrt3` `2SQRT3` `3sqrt2` 5 Answer :A

Discussion

10775.	Show that the lines x^(2)+16xy-11y^(2)=0 form an equilateral triangle with the line 2x+y+1=0 and find its area.
Answer» ANSWER :`(1)/(5sqrt(3))` SQ. UNITS

Discussion

10776.	sintheta = (3)/5 , (pi)/2 lt theta lt pi sin2theta = (-12)/25
Answer» ANSWER :FALSE STATEMENT

Discussion

10777.	The sets A and B are following, A= {(a, b) in R xx R : [a-5] lt 1" and "\|b-5\| lt 1}, B= {(a, b) in R xx R : 4(a-6)^(2) +9(b-5)^(2) le 36}. Then
Answer» `B SUB A` `A sub B` `A CAP B = PHI` `A cancelsub B" and "B cancelsub A` ANSWER :B

Discussion

10778.	If f(x)={:{(x^(2)",","for",x ge 0),(x",","for",x lt 0):}, then fof(x) is given by
Answer» `X^(2)` for `x ge 0, x ` for `x LT 0` `x^(4)` for `x ge 0, x^(2)` for `x lt 0` `x^(4)` for `x ge 0, -x^(2)` for `x lt 0` `x^(4)` for `x ge 0, - x ` for `x lt0` ANSWER :D

Discussion

10779.	Find the values of theta between 0^(@) and 360^(@) which satisfy the equations sin^(2)theta=(3)/(4)
Answer» ANSWER :`60^(@),120^(@),240^(@),300^(@)`

Discussion

10780.	Construct a composite index number from the following index numbers and weights:
Answer» ANSWER :`143`

Discussion

10781.	Which of the following sentences are statements? Give reasons for your answer All real numbers are complex numbers.
Answer» Answer :This is a TRUE STATEMENT because all real numbers can be written in the FORM `a + i xx 0.`

Discussion

10782.	If g is the inverse of f and f'(x) = 1/(2+x^n) , then g^(1)(x) is equal to
Answer» `2+x^N` `2+(F(x))^(n)` `2+(G(x)^(n))` 0 Answer :C

Discussion

10783.	The locus of the point which is at a distance of '3' unit from zx-plane is
Answer» `absx=3` `absz=3` `absy=3` `x+y=3` ANSWER :B

Discussion

10784.	The radius of the circle passing through the centre of incircle of Delta^("le") ABC and through the end points B, C is
Answer» `a//2` `(a)/(2)"SEC"(A)/(2)` `(a)/(2)SINA` `a secA//2` ANSWER :B

Discussion

10785.	An analysis of monthly wages paid to workers in two firms A and B , belonging to the same industry , gives the following results: (i) Which firm A or B pays larger amount as monthly wages? (ii) Which firm , A or B, shows greater variability in individual wages?
Answer» ANSWER :(i) B, (II) B

Discussion

10786.	Perpendiculars are drawn from points on the line (x + 2 )/(2) = (y+1)/(-1) = z/3 to the plane x + y + z =3. The feet of perpendiculars lie on the line
Answer» `x/5 = (y-1)/(8) = (z-2)/(-13)` `x/2 =(y-1)/(3) = (z-2)/(-5)` `x/4 = (y-1)/(3) = (z-2)/(-7)` `x/2 = (y-1)/(-7) = (z-2)/(5)` Answer :D

Discussion

10787.	Find n if : ""^(n)P_2 = 30
Answer» ANSWER :` 6`

Discussion

10788.	For a positive integer n , find the value of (1-i)^(n)(1-(1)/(i))^(n)
Answer» ANSWER :`2^(N)`

Discussion

10789.	When a cartakes a sudden left turn in the curved roadpassendgersare pushed towards the right due to
Answer» INERTIA of DIRECTION inertia of motion inertia of rest absence of inertia Solution :inertia of direction

Discussion

10790.	If u = f(x^2) , v = g(x^3), f^(1)(x) = sinx , g^(1)(x) = cos x then find (du)/(dv)
Answer» 1 `2/3` `(2 sinx^2)/(3x.cosx^3)` `(2x^2)/(3x^3)` ANSWER :C

Discussion

10791.	Find the condition that the ratio between the roots of the equation ax^(2)+bx+c=0 may be m:n.
Answer» ANSWER :`(m+n)^(2)ac=mnb(2)`.

Discussion

10792.	If (1+x+x^(2))^(n)=1 +a_(1)x+a_(2)x^(2)+a_(3)x^(3) +â€¦â€¦..+a_(2n).x^(2n) then prove that: (i) a_(1)+a_(3)+a_(5)+â€¦..+a_(2n-1) =(3^(n)-1)/(2) (ii) a_(2)+a_(4)+a_(6)+â€¦â€¦+a_(2n)=(3^(n)-1)/(2)
Answer» SOLUTION :N/a

Discussion

10793.	Find the slope of a line parallel to the which passes through the following points: (-5, -8) and (3, 0)
Answer» ANSWER : `1`

Discussion

10794.	The point represented by the complex nuber (2-i) is rotated about origin through an angle (pi)/(2) in the clockwise direction, the new position of point is
Answer» `1+2i` `-1-2i` `2+i` `-1+2i` ANSWER :B

Discussion

10795.	A sum of Rs. 10,000 is invested at 8% p.a. compound interest? What is the total sum of the money at the end of 3 years?
Answer» SOLUTION :`10,000(1.08)^3`

Discussion

10796.	x + 4y gt 8
Answer» SOLUTION :

Discussion

10797.	Length of y-intercept made by pair of lines 2x^(2)+lambda xy+3y^(2)+8x+14y+8=0 is
Answer» 10 `5//3` `10//3` `1//3` ANSWER :C

Discussion

10798.	If the functions f(x) and g(x) are defined on R rarr R such thatf(x)={:{(0, x in " rational "),(x, x in " irrational ") :}g(x)={:{(0, x in " irrational ") ,(x, xin" rational "):} then (f-g)(x) is
Answer» one-one and onto neither one-one nor onto one-one but not onto onto but not one-one Answer :A

Discussion

10799.	Convert(1-i)/( cos ""( pi)/( 3) +i sin ""(pi)/(3))into polar form
Answer» ANSWER :polar form is `SQRT(2) (cos (5pi)/12 + I SIN (5pi)/12)`

Discussion

10800.	Check the continuity of function defined b y f(x)={{:(1/2(x^(2)-4),if 0lt x lt2),(0,if x=2),(2-(8)/(x^(3)),if x gt2):} at x=2
Answer» ANSWER :DISCONTINUOUS

Discussion

Explore topic-wise InterviewSolutions in .

Write the component statementsof the following compound statement and check whether compound statement is true or false . Two lines intersect at a point or they are parallel"

If barA=baraxxbarb,barB=barbxxbarc,barC=barcxxbara then barAxx(barBxxbarC), barB(barCxxbarA),barCxx(barAxxbarB) are

For problems Let cos^(-1)(4x^(3)-3x)=a+bcos^(-1)x If x in [-1/2, 1/2], then the principal value of sin^(-1)(sin""a/b)

If f(x)=sin^(6) x + cos^(6) xforx in R , then f(x) lies in the interval

An experiment consists of rolling a die and then tossing a coin once if the number on die is even. If the number on die is odd, the coin is tossed twice. Write the sample space for this experiment.

If A=[(1,0,2),(-1,1,-2),(0,2,1)] and AdjA=[(5,x,-2),(1,1,0),(-2,-2,y)] then (x,y) =

Find the coordinates of the point on the parabola y^(2)=8x whose focal distance is 8.

Find the derivate of x^(-4)(3-4x^(-5))

Let baru,barv,barw " be such that " absbaru =1, absbarv=2, absbarw=3 " if the projection of " barv " along " baru "is equal to that of " barw " along " baru and barv,barw are perpendicular to each other, then abs(baru-barv+barw) =

Find the area of the triangle having (3bar(i)+4bar(j)),(-5bar(i)+7bar(j)) as adjacent sides.

For an A.P a = 20 and l = 97 then S_(20)= ..........

If vec(a), vec(b), vec(c ) are unit vectors such that vec(a).vec(b)= vec(a).vec(c )=0 and (vec(b), vec(c ))= (pi)/(6), then vec(a)=

Show that 9^(n+1) - 8n - 9 is divisible by 64, whenever n is a positive interger.

Which of the following sentences are statement? Give reason for your answer: Sum of two positive numbers is positive numbers.

Is the given relation a function? Give reason for your answer. h= {(4, 6), (3,9), (-11, 6), (3,11)}

The sum of three numbers in G.P. is 56. If we subtract 1, 7, 21 from these numbersin that order, we obtain an arithmetic progression. Find the numbers.

If there is an error of 1 % is made in the side of a cube then the percentage error in its volume is

If S_(1), S_(2), S_(3) be respectively the sums of n, 2n, 3n, terms of a G.P., then prove that S_(1)(S_(3)-S_(2))=(S_(2)-S_(1))^(2).

The point of intersction of barr xx bara= barbxx bara andbarr xx barb = bara xx barb where bara = bari + barj and barb = 2 bari - bark is

..............is the value of omega to represent line sqrt(3)x +y =10 in normal form.

A plane is 1km from one landmark and 2km from another. From the planes point of view the land between them subtends an angle 60^(@). How far apart are the landmarks?

If the straight lines y=4-3x, ay=x+10, 2y+bx+9=0 represent the three consecutive sides of a rectangle then ab =

Let cos^(-1)(x)+cos^(-1)(2x)+cos^(-1)(3x)" be "pi. If x satisfies the equation ax^(3)+bx^(2)+cx-1=0 then the value of (b-a-c) is

The minimum value of 3e^x+4e^(-x) is

Show that the lines x^(2)+16xy-11y^(2)=0 form an equilateral triangle with the line 2x+y+1=0 and find its area.

sintheta = (3)/5 , (pi)/2 lt theta lt pi sin2theta = (-12)/25

The sets A and B are following, A= {(a, b) in R xx R : [a-5] lt 1" and "|b-5| lt 1}, B= {(a, b) in R xx R : 4(a-6)^(2) +9(b-5)^(2) le 36}. Then

If f(x)={:{(x^(2)",","for",x ge 0),(x",","for",x lt 0):}, then fof(x) is given by

Find the values of theta between 0^(@) and 360^(@) which satisfy the equations sin^(2)theta=(3)/(4)

Construct a composite index number from the following index numbers and weights:

Which of the following sentences are statements? Give reasons for your answer All real numbers are complex numbers.

If g is the inverse of f and f'(x) = 1/(2+x^n) , then g^(1)(x) is equal to

The locus of the point which is at a distance of '3' unit from zx-plane is

The radius of the circle passing through the centre of incircle of Delta^("le") ABC and through the end points B, C is

An analysis of monthly wages paid to workers in two firms A and B , belonging to the same industry , gives the following results: (i) Which firm A or B pays larger amount as monthly wages? (ii) Which firm , A or B, shows greater variability in individual wages?

Perpendiculars are drawn from points on the line (x + 2 )/(2) = (y+1)/(-1) = z/3 to the plane x + y + z =3. The feet of perpendiculars lie on the line

Find n if : ""^(n)P_2 = 30

For a positive integer n , find the value of (1-i)^(n)(1-(1)/(i))^(n)

When a cartakes a sudden left turn in the curved roadpassendgersare pushed towards the right due to

If u = f(x^2) , v = g(x^3), f^(1)(x) = sinx , g^(1)(x) = cos x then find (du)/(dv)

Find the condition that the ratio between the roots of the equation ax^(2)+bx+c=0 may be m:n.

If (1+x+x^(2))^(n)=1 +a_(1)x+a_(2)x^(2)+a_(3)x^(3) +â€¦â€¦..+a_(2n).x^(2n) then prove that: (i) a_(1)+a_(3)+a_(5)+â€¦..+a_(2n-1) =(3^(n)-1)/(2) (ii) a_(2)+a_(4)+a_(6)+â€¦â€¦+a_(2n)=(3^(n)-1)/(2)

Find the slope of a line parallel to the which passes through the following points: (-5, -8) and (3, 0)

The point represented by the complex nuber (2-i) is rotated about origin through an angle (pi)/(2) in the clockwise direction, the new position of point is

A sum of Rs. 10,000 is invested at 8% p.a. compound interest? What is the total sum of the money at the end of 3 years?

x + 4y gt 8

Length of y-intercept made by pair of lines 2x^(2)+lambda xy+3y^(2)+8x+14y+8=0 is

If the functions f(x) and g(x) are defined on R rarr R such thatf(x)={:{(0, x in " rational "),(x, x in " irrational ") :}g(x)={:{(0, x in " irrational ") ,(x, xin" rational "):} then (f-g)(x) is

Convert(1-i)/( cos ""( pi)/( 3) +i sin ""(pi)/(3))into polar form

Check the continuity of function defined b y f(x)={{:(1/2(x^(2)-4),if 0lt x lt2),(0,if x=2),(2-(8)/(x^(3)),if x gt2):} at x=2