14949 + Interview Questions in Maths in Class 11 Page 102 InterviewSolution

5051.	If (tan3A)/(tanA) = k (k ne 1) then
Answer» `(COSA)/(cos3A) =(k^2-1)/(2K)` `(SIN3A)/(sinA) = (2k)/(k-1)` `k lt 1/(3)` `k gt 3` Answer :B::C::D

Discussion

5052.	Abag contains 20 balls . These are of three different colours : greenred and blue.A ball is chosen at random from the bag . The probability of a green ballis (1)/(4). The probability of a red ballis (2)/(5) .How many balls are green ?
Answer» ANSWER :5

Discussion

5053.	Abag contains 20 balls . These are of three different colours : greenred and blue.A ball is chosen at random from the bag . The probability of a green ballis (1)/(4). The probability of a red ballis (2)/(5) .How many balls are red ?
Answer» ANSWER :8

Discussion

5054.	Abag contains 20 balls . These are of three different colours : greenred and blue.A ball is chosen at random from the bag . The probability of a green ballis (1)/(4). The probability of a red ballis (2)/(5) .What is the probability of a blue ball ?
Answer» ANSWER :`(7)/(20)`

Discussion

5055.	Abag contains 20 balls . These are of three different colours : greenred and blue.A ball is chosen at random from the bag . The probability of a green ballis (1)/(4). The probability of a red ballis (2)/(5) .How many balls are blue ?
Answer» ANSWER :7

Discussion

5056.	find the derivative of f(x)=10x
Answer» ANSWER :10

Discussion

5057.	Find the eccentricity, distance between the foci, equation of the directrices, and the length and coordinates of the ends of the latusrectum of the ellipse 25x^(2)+16y^(2)=400.
Answer» ANSWER :Eccentricity = `3/5` Distance between the foci = 6 Equation of the directrices are `y=pma/e=pm 25/3" or "3y pm 25=0` LENGTH of the latus RECTUM `=32/5` The coordinates of the ENDS of the latera recta are `(16/5, 3), (-16/5, 3), (16/5, -3), ((-16)/5, -3)`.

Discussion

5058.	A line through the point (3, 0) meets the variable line y=tx at right angle at the point P. Find, in terms of t, the co-ordinates of P. Find the value of k for which Plies on the curve x^(2)+y^(2)=kx.
Answer» <P> ANSWER :`P((3)/(1+r^(2)),(3T)/(1+t^(2))),k=3`

Discussion

5059.	The maximum valueof 3 cos theta + 4 sin thetais
Answer» 3 4 5 `SQRT(5 )` ANSWER :3

Discussion

5060.	Find the modulus of ((3+2i) (1+i) (2+3i))/((3+4i) (4+5i))
Answer» ANSWER :`(13 SQRT2)/(5 sqrt41)`

Discussion

5061.	IfA = 60 ^(@)" then " ( 1)/(a+b) + (1) /( a+ c)=
Answer» `(3)/( a+ B+ C) ` `(3)/( a+ b- c) ` `(3)/( a- b- c) ` `(3)/( -a+ b- c) ` ANSWER :A

Discussion

5062.	If y = ax^(n+1)+bx^(n+1)then x^2(d^2y)/(dx^2) is equal to
Answer» `N(n-1)y` `n(n+1)y` `NY` `n^2y` ANSWER :B

Discussion

5063.	Which of the following funcitons is/are periodie ?
Answer» `{:{(1",","x is RATIONAL"),(0",","x is irrational"):}` `f(x)={:{(x-[x]",",2n le x lt 2n +1),(1/2,2n+1 le x lt 2n +2):}`, where[.] DENOTES the greatest INTEGER function, `n in Z` `f(x)= (-1)^([(2x)/(pi)])` where [.] denotes the greatest integer integer function `f(x)=x-[x+3]+tan ((pi x)/(2))`, where [.] denotes the greatest integer function, and a is a rational NUMBER ANSWER :A::B::C::D

Discussion

5064.	Let f:RtoR:f(x)=x^(2)" for all "x""inR.
Answer» Solution :Here, `F:RtoR:f(x)=x^(2)" for all "x""INR` Dom (f)=R and range `(f)={x""inR:ge0}=[0,OO)`. Now, we have: On a graph paper, we draw X' OX and YOY' as the x-axis and the y-axis respectively. Now, we plot the points A(-2,4), B(-1.5), C(-1.1), O(0,0), D(1,1), E(1.5,2.25) and F(2,4). Join these points freehand successively to obtain the required curve. Scale: 10 small divisions = 1 unit

Discussion

5065.	Find the equation of the parabola whose focus is (1,-1)and whose vertex is 2,1. Also, find its axis and latus-rectum.
Answer» ANSWER :`(x+2y-9)^(2)`

Discussion

5066.	Find the derivative of f (x) w.r.t. g(x) for the f (x) = Tan ^(-1) ((sqrt (1 + x ^(2)) -1)/( x )), g (x) = Tan ^(-1) x
Answer» ANSWER :`1/2`

Discussion

5067.	f(x) = (cos x - sinx)/(cos (2x)) , x ne (pi)/(4) is continuous on[ 0, (pi)/(2)] " then " f((pi)/(4)) =
Answer» `(1)/(SQRT(2))` `(-1)/(sqrt(2))` `(1)/(sqrt(3))` `(-1)/(sqrt(3))` ANSWER :A

Discussion

5068.	d/(dx)(log(e^x((x-2)/(x+2))^(3//4))) equal to
Answer» `(x^2-1)/(x^2-4)` 1 `(x^2+1)/(x^2-4)` `e^x((x^2-1)/(x^2-4))` ANSWER :A

Discussion

5069.	(a) Show that the functionf(x)=cos 2x is periodic and find its period. Show that the function f(x) =cos((x)/(2)+(pi)/(4)) isperiodic and find its period.
Answer» ANSWER :(a) `PI`(B) `4PI`

Discussion

5070.	Given that P(3,2,-4),Q(5,4,-6) and R(9,8,-10) are collinear. Find the ratio in which Q divides PR.
Answer» ANSWER :`1:2`

Discussion

5071.	n(A)= m, n (B) = n. The total number of non empty relation from A to B is……..
Answer» `m^(N)` `n^(m)-1` `MN-1` `2^(mn)-1` ANSWER :D

Discussion

5072.	Prove that the product of the lengths of the perpendiculars drawn from the points ( sqrt(a^(2) - b^(2) ), 0) and ( - sqrt(a^(2) - b^(2) ), 0) to the line (x)/( a) cos theta + (y)/( b) sin theta =1 is b^2.
Answer» ANSWER :`=b^2`

Discussion

5073.	Evaluate the following limits : Lim_(x to 0) (x(e^(x)-1))/(1-cos 2x)
Answer» ANSWER :`1/2`

Discussion

5074.	If x= -2 - sqrt3i, where i= sqrt(-1, find the value of 2x^(4) + 5x^(3) + 7x^(2)-x+ 41
Answer» ANSWER :6

Discussion

5075.	Assertion (A) : If A gt 0, B gt 0 and A+B=(pi)/(3) then the maximum value of Tan A tan B is (1)/(3) Reason (R) : If a_(1)+a_(2)+a_(3)+....a_(n)=k (constant) then value of a_(1)a_(2)....a_(n) is greatest when a_(1)=a_(2).....a_(n)
Answer» A is TURE and R is true, `R RARR A` A is true, and R is true, `R cancel rArrA` A is true, R is FALSE A is false, R is true Answer :B

Discussion

5076.	Which of the following sentences are statements? Justify y+9=7
Answer» ANSWER :It is not STATEMENT.

Discussion

5077.	Define f:Z rarrZ by f(x)={{:(x//2,"(x is even)"),(0,"(x is odd)"):} then f is
Answer» ONTO but not one-one many-one and into one-one and onto neither one-one nor onto Answer :A

Discussion

5078.	If B sub A , B sub Cand x in Athen x inC
Answer» ANSWER :FALSE STATEMENT

Discussion

5079.	If A(1, 2), B(-4, 2). Number of point P in the plane such that angleAPB=(pi)/(2) and area of DeltaAPB is 6.25 sq. units is
Answer» 0 2 3 4 Answer :D

Discussion

5080.	A plane is parallel to YZ-plane so it is perpendicular to
Answer» X-axis Y-axis Z-axis None of these Answer :A

Discussion

5081.	If z and we are two complex numbers such that \|zw\|=1 and arg(z)-arg(w)=(pi)/(2) then show that barzw=-i
Answer» ANSWER :`-i=RHS`

Discussion

5082.	If p:7 is not greater than 4 q : Paris is in France. Write ~(pvvq) in words.
Answer» ANSWER :7 is greater than 4 and PARIS is not in FRANCE.

Discussion

5083.	If alpha,beta,gamma are the lengths of the altitudes of Delta ABC, then cosA/alpha+cosB/beta+cosC/gamma=
Answer» ` DELTA ` ` (1)/( Delta ) ` ` R` ` (1) /( R ) ` ANSWER :A

Discussion

5084.	If (x_(1), y_(1)), (x_(2), y_(2)), (x_(3), y_(3)) are the verticesof an equilateral triangle such that (x_(1)-2)^(2)+(y_(1)-3)^(2)=(x_(2)-2)^(2)+(y_(2)-3)^(2)=(x_(3)-2)^(2)+(y_(3)-3)^(2)then x_(1)+x_(2)+x_(3)+2(y_(1)+y_(2)+y_(3))=
Answer» 18 24 6 8 Answer :B

Discussion

5085.	If the angles A, B and C of a triangle are in an arithmetic progression and if a, b and c denote the lengths of the sides opposite to A, B and C respectively, then the value of the expressin a/c sin 2C + c/a sin 2Ais
Answer» `1/2` `SQRT3/2` 1 `sqrt3` ANSWER :D

Discussion

5086.	U= {h, i, j, k, l, m, n, o, p} then find the complement of the following sets :C= {i, j, l, m, n}
Answer» <P> ANSWER :`= {H, K, o, p}`

Discussion

5087.	If bara+barb+barc =bar0 , " then " bara.bara+barb.barb+2(bara.barb)-barc.barc =
Answer» `BAR0` 0 `ABSBARA` `absbarb` Answer :B

Discussion

5088.	Find the derivative of e ^(sqrtx) w.r.t log x.
Answer» ANSWER :`SQRT XE ^( SQRTX)`

Discussion

5089.	Consider the line passing through the points (3,4) and (x,5) Find the slope of the line
Answer» SOLUTION :`1/(X - 3)`

Discussion

5090.	If f (x) has a derivative at x =a then find Lt _(x to a) (x f (a) - a f(x))/(x -a)
Answer» ANSWER :`F (a) - AF ^(1) (a)`

Discussion

5091.	A circle centered at O has radius 1 and contains point A. Segment AB is tangent to the ciecle at A and angleAOB= theta. If point C lies on OA, and BC bisects the angle ABO, then OC equals
Answer» `SECTHETA(sectheta-tan theta)` `(cos^(2)theta)/(1+sintheta)` `(1)/(1+sintheta)` `(1-sintheta)/(cos^(2)theta)` ANSWER :A::C

Discussion

5092.	Find the square root of the following complex numbers -40-42i
Answer» ANSWER :`+- (3-7i)`

Discussion

5093.	There are two childrens in a family. Theprobability that both of them are boys 1s
Answer» `(1)/(2)` `(1)/(3)` `(1)/(4)` `(2)/(3)` ANSWER :C

Discussion

5094.	Statement 1:f (x)sqrt(ax^(2)+bx+ c)" has range "[0, infty ) if b^(2)- 4ac gt 0 Statement 2:ax^(2)+bx+ c=0 " has real roots if "b^(2)- 4ac =0
Answer» Statement1 is true, statement 2 is true, statement 2 is a CORRECT explanation for statement 1. Statement1 is true, statement 2 is true, statement 2 is not a correct explanation for statement 1. Statement 1 is true, statement 2 is FALSE Statement 1 is false, statement 2 is true Answer :D

Discussion

5095.	f(x) = sqrt(x)at x = 0 then is
Answer» discontinuous continuous not DETERMINED NONE ANSWER :B

Discussion

5096.	Illustrate in the complex plane the following set of points and explain your answer arg (Z)= (pi)/(6)
Answer» ANSWER :`30^(@)`

Discussion

5097.	If f(x) is a function such that f(xy) = f(x)+f(y) and f(x)=
Answer» `X^(2)` `2^(x)` `log_(2)x` `log_(x)2` ANSWER :C

Discussion

5098.	The points (0,0,0) and (2,5,7) lies on the same side of the plane 2x+ay+3z+1=0 if
Answer» `alt0` `AGT0` `alt(-26)/(5)` `AGT(-26)/(5)` Answer :D

Discussion

5099.	Find the tenth term in the expansion (2x-y)^(11).
Answer» ANSWER :`=-220x^(2) y^(9)`.

Discussion

5100.	If Sin^(-1)x + Sin^(-1)y + Sin^(-1)z = pi, then prove that x^(4) + y^(4) + z^(4) + 4x^(2)y^(2)z^(2) = 2(x^(2)y^(2)+y^(2)z^(2)+z^(2)x^(2)).
Answer» ANSWER :2

Discussion

Explore topic-wise InterviewSolutions in .

If (tan3A)/(tanA) = k (k ne 1) then

Abag contains 20 balls . These are of three different colours : greenred and blue.A ball is chosen at random from the bag . The probability of a green ballis (1)/(4). The probability of a red ballis (2)/(5) .How many balls are green ?

Abag contains 20 balls . These are of three different colours : greenred and blue.A ball is chosen at random from the bag . The probability of a green ballis (1)/(4). The probability of a red ballis (2)/(5) .How many balls are red ?

Abag contains 20 balls . These are of three different colours : greenred and blue.A ball is chosen at random from the bag . The probability of a green ballis (1)/(4). The probability of a red ballis (2)/(5) .What is the probability of a blue ball ?

Abag contains 20 balls . These are of three different colours : greenred and blue.A ball is chosen at random from the bag . The probability of a green ballis (1)/(4). The probability of a red ballis (2)/(5) .How many balls are blue ?

find the derivative of f(x)=10x

Find the eccentricity, distance between the foci, equation of the directrices, and the length and coordinates of the ends of the latusrectum of the ellipse 25x^(2)+16y^(2)=400.

A line through the point (3, 0) meets the variable line y=tx at right angle at the point P. Find, in terms of t, the co-ordinates of P. Find the value of k for which Plies on the curve x^(2)+y^(2)=kx.

The maximum valueof 3 cos theta + 4 sin thetais

Find the modulus of ((3+2i) (1+i) (2+3i))/((3+4i) (4+5i))

IfA = 60 ^(@)" then " ( 1)/(a+b) + (1) /( a+ c)=

If y = ax^(n+1)+bx^(n+1)then x^2(d^2y)/(dx^2) is equal to

Which of the following funcitons is/are periodie ?

Let f:RtoR:f(x)=x^(2)" for all "x""inR.

Find the equation of the parabola whose focus is (1,-1)and whose vertex is 2,1. Also, find its axis and latus-rectum.

Find the derivative of f (x) w.r.t. g(x) for the f (x) = Tan ^(-1) ((sqrt (1 + x ^(2)) -1)/( x )), g (x) = Tan ^(-1) x

f(x) = (cos x - sinx)/(cos (2x)) , x ne (pi)/(4) is continuous on[ 0, (pi)/(2)] " then " f((pi)/(4)) =

d/(dx)(log(e^x((x-2)/(x+2))^(3//4))) equal to

(a) Show that the functionf(x)=cos 2x is periodic and find its period. Show that the function f(x) =cos((x)/(2)+(pi)/(4)) isperiodic and find its period.

Given that P(3,2,-4),Q(5,4,-6) and R(9,8,-10) are collinear. Find the ratio in which Q divides PR.

n(A)= m, n (B) = n. The total number of non empty relation from A to B is……..

Prove that the product of the lengths of the perpendiculars drawn from the points ( sqrt(a^(2) - b^(2) ), 0) and ( - sqrt(a^(2) - b^(2) ), 0) to the line (x)/( a) cos theta + (y)/( b) sin theta =1 is b^2.

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

If x= -2 - sqrt3i, where i= sqrt(-1, find the value of 2x^(4) + 5x^(3) + 7x^(2)-x+ 41

Assertion (A) : If A gt 0, B gt 0 and A+B=(pi)/(3) then the maximum value of Tan A tan B is (1)/(3) Reason (R) : If a_(1)+a_(2)+a_(3)+....a_(n)=k (constant) then value of a_(1)a_(2)....a_(n) is greatest when a_(1)=a_(2).....a_(n)

Which of the following sentences are statements? Justify y+9=7

Define f:Z rarrZ by f(x)={{:(x//2,"(x is even)"),(0,"(x is odd)"):} then f is

If B sub A , B sub Cand x in Athen x inC

If A(1, 2), B(-4, 2). Number of point P in the plane such that angleAPB=(pi)/(2) and area of DeltaAPB is 6.25 sq. units is

A plane is parallel to YZ-plane so it is perpendicular to

If z and we are two complex numbers such that |zw|=1 and arg(z)-arg(w)=(pi)/(2) then show that barzw=-i

If p:7 is not greater than 4 q : Paris is in France. Write ~(pvvq) in words.

If alpha,beta,gamma are the lengths of the altitudes of Delta ABC, then cosA/alpha+cosB/beta+cosC/gamma=

If (x_(1), y_(1)), (x_(2), y_(2)), (x_(3), y_(3)) are the verticesof an equilateral triangle such that (x_(1)-2)^(2)+(y_(1)-3)^(2)=(x_(2)-2)^(2)+(y_(2)-3)^(2)=(x_(3)-2)^(2)+(y_(3)-3)^(2)then x_(1)+x_(2)+x_(3)+2(y_(1)+y_(2)+y_(3))=

If the angles A, B and C of a triangle are in an arithmetic progression and if a, b and c denote the lengths of the sides opposite to A, B and C respectively, then the value of the expressin a/c sin 2C + c/a sin 2Ais

U= {h, i, j, k, l, m, n, o, p} then find the complement of the following sets :C= {i, j, l, m, n}

If bara+barb+barc =bar0 , " then " bara.bara+barb.barb+2(bara.barb)-barc.barc =

Find the derivative of e ^(sqrtx) w.r.t log x.

Consider the line passing through the points (3,4) and (x,5) Find the slope of the line

If f (x) has a derivative at x =a then find Lt _(x to a) (x f (a) - a f(x))/(x -a)

A circle centered at O has radius 1 and contains point A. Segment AB is tangent to the ciecle at A and angleAOB= theta. If point C lies on OA, and BC bisects the angle ABO, then OC equals

Find the square root of the following complex numbers -40-42i

There are two childrens in a family. Theprobability that both of them are boys 1s

Statement 1:f (x)sqrt(ax^(2)+bx+ c)" has range "[0, infty ) if b^(2)- 4ac gt 0 Statement 2:ax^(2)+bx+ c=0 " has real roots if "b^(2)- 4ac =0

f(x) = sqrt(x)at x = 0 then is

Illustrate in the complex plane the following set of points and explain your answer arg (Z)= (pi)/(6)

If f(x) is a function such that f(xy) = f(x)+f(y) and f(x)=

The points (0,0,0) and (2,5,7) lies on the same side of the plane 2x+ay+3z+1=0 if

Find the tenth term in the expansion (2x-y)^(11).

If Sin^(-1)x + Sin^(-1)y + Sin^(-1)z = pi, then prove that x^(4) + y^(4) + z^(4) + 4x^(2)y^(2)z^(2) = 2(x^(2)y^(2)+y^(2)z^(2)+z^(2)x^(2)).