14949 + Interview Questions in Maths in Class 11 Page 185 InterviewSolution

9201.	Find the domain and range of the relation R = { (x,y) :y=x^3,x is a positive prime number lt 8}
Answer» SOLUTION :DOM (R ) = {2,3,5,7}, RANGE of R = {8,27,125,343}

Discussion

9202.	A circle is inscribed in a trianlge ABC touching the side AB at D such that AD = 5, BD=3 . If lfloorA=60^(@) ten length BC equals
Answer» 9 `(120)/(13)` 13 12 Answer :C

Discussion

9203.	Lt_(x to 0)(cosx+sinx)^(1//x)=
Answer» ANSWER :E

Discussion

9204.	Find the derivative of the function 5 ^(x) + log x + x ^(3) e ^(x)
Answer» Answer :`5 ^(X) log 5 + (1)/(x) + e ^(x) (x^(3) + 2x ^(2)) `

Discussion

9205.	A die is loaded in such a way that each odd number is twice as likely to occur as each even number. Find P(G), where G is the event that a number greater than 3 occurs on a single roll of the die.
Answer» ANSWER :`=(4)/(9)`

Discussion

9206.	There are two urns. Urm A has 3 distinct red balls and urn B has 9 distinct blue balls . Fromeach urn two balls are taken out at random and then transferred to the other. The number of ways in which . This can be done is.
Answer» 3 36 66 108 Answer :D

Discussion

9207.	Differentiate w.r.t. 'x' : f(x) = log((a+b sin x)/(a - b sin x))
Answer» Answer :`(2 AB COS X)/(a^(2) - b^(2) SIN^(2) x)`

Discussion

9208.	A tower 51 m height has a mark at height of 25 m from the ground. At what distance the two parts subtend equal angle to an eye at theheight of5 m from the ground.
Answer» 20m 30m 15m 160m Answer :A

Discussion

9209.	cos x =- 1/3, x in quadrant III
Answer» ANSWER :`(SQRT6)/( 3),-(SQRT3)/(3), -SQRT2`

Discussion

9210.	Ifx^(2)+4y ^(2)= 4 and range off(x,y)" is "[L,M] " where"f(x,y)= x^(2) +y^(2)- xythen LM is
Answer» ANSWER :3

Discussion

9211.	x+y lt 5
Answer» ANSWER :`{(1,1),(1,2),(1,3),(2,1),(2,2),(3,1)}`

Discussion

9212.	If 2 sin ^(2) x + sin ^(2) 2 x = 2 then x = ____
Answer» ` n PI + (pi)/( 2) ,n in Z` `2n pi pm (pi)/(3) , n in Z` `n pi + (-1) ^(n) (pi)/(6), n in Z` `2n pi pm (pi)/(6) , n in Z` Answer :A

Discussion

9213.	cos^(-1)((3+5cosx)/(5+3cosx)) is equal to
Answer» `TAN^(-1)(1/2"tan"x/2)` `2TAN^(-1)(2"tan"x/2)` `1/2tan^(-1)(2"tan"x/2)` `2tan^(-1)(1/2"tan"x/2)` ANSWER :D

Discussion

9214.	Find deltay and dy for the following functions y=cosx,x=60^(@) and deltax=1^(@)
Answer» ANSWER :`-0.0152, -0.01516`

Discussion

9215.	Find the distance of the point P from the lines ABin the following cases : P(4, 2),AB is 5x-12y-9=0
Answer» ANSWER :1

Discussion

9216.	Let y = (x^8 + x^4 + 1)/(x^4 + x^2 + 1). If (dy)/(dx) = ax^3 + bx . Then
Answer» `a = 4, B = 2` `a = 4, b = -2` `a = -2, b = 4` `a = 2, b = -4` ANSWER :D

Discussion

9217.	If ends of a diagonal of a square are (2,-3,4) and (4,1,-2) then the length of one side is
Answer» `sqrt56` `sqrt28` `SQRT14` `SQRT7` ANSWER :B

Discussion

9218.	Solve: sqrt5x^2+x+sqrt5=0
Answer» ANSWER :`X=(-1pmisqrt19)/2SQRT5`

Discussion

9219.	If y=(logx)^3 then (dy)/(dx)=
Answer» `(3(LOGX)^2)/X` `3(logx)^2` `((logx)^2)/x` `(logx)^2` ANSWER :A

Discussion

9220.	State whether the points (3,2) and (-4,3) lie on the same side or opposite sides of the line 2x-3y+4=0.
Answer» ANSWER :SIDE of the LINE

Discussion

9221.	Period of tan((3pix)/(4) ) - 2 sec ((pix)/( 3)) + 5 sin((2pix)/( 5)) is
Answer» 20 30 60 80 Answer :C

Discussion

9222.	If (barbxxbarc)xx(barcxxbara)=3barc, then find [barbxxbarcbarcxxbarabaraxxbarb]
Answer» ANSWER :9

Discussion

9223.	Show that the statement For any real numbers a and b a^(2)=b^(2) implies that a=b" is not true by giving a counter example.
Answer» ANSWER :FALS

Discussion

9224.	Convert the following into simplest form (v) cot (theta- (13 pi)/(2))
Answer» ANSWER :`-TAN THETA`

Discussion

9225.	Find the distance of the point P(1, 2, 3) from the coordinates axes.
Answer» ANSWER :`SQRT(13),sqrt(10),sqrt(5)`

Discussion

9226.	From a well shuffled deck of 52 cards, 4 cards aredrawn at random. What is the probability that all the drawn cars are of thesame colour.
Answer» ANSWER :`(92)/(833)`

Discussion

9227.	The value of cot 70^(@) + 4 cos 70^(@) is
Answer» `(1)/(SQRT3)` `sqrt3` `2SQRT3` `1/2` ANSWER :B

Discussion

9228.	12 balls are keeped in three bags. The probability that there are 3 balls in first bag is:
Answer» `110/9(2/3)^(10)` `110/9(3/2)^(10)` `(.^(12)C_(3))/(3^(12))` `(.^(12)C_(3))/(12^(3))` SOLUTION :N/a

Discussion

9229.	Sketch roughly the lines satisfyingthe givenconditions and write their equations: inclination theta=150^(@), and distance from the origin = 3.
Answer» ANSWER : `x+sqrt(3)y=6 and x+sqrt(3)y+6=0`

Discussion

9230.	If ma and M respectively denote the minimum and maximum of f(x) =(x-1)^2+3 for xin [-3,1] then the ordered pair (m,M)=
Answer» `(-3,19)` `(3,19)` `(-19,3)` `(-19,-3)` ANSWER :B

Discussion

9231.	IF tan^2 theta=2 tan^2 phi +1 then find the value of cos 2 theta+sin^2 phi.
Answer» `-1` 1 0 2 Answer :C

Discussion

9232.	To find the sum sin^(2)""(2pi)/7 + sin^(2)""(4pi)/7 + sin^(2)""(8pi)/7 , we follow the following method . Put 7 theta = 2npi, where n is any integer . Then sin 4theta = sin (2npi - 3 theta)=-sin3 theta .......(i) This means that sin theta that takes the values 0,pm sin(2pi//7),pmsin(4pi//7), and pm sin(8pi//7) From Eq . (i) we now get 2 sin 2theta cos 2 theta = 4sin^(3) theta" or " 4 sin theta sin theta cos theta (1-2 sin^(2) theta)=(4sin^2theta - 3) sin theta Rejecting the value sin theta = 0we get 4 cos theta(1-2sin^2 theta)=4 sin^2 theta-3 or 16 cos^2 theta (1 - 2 sin^(2) theta)^(2) = (4 sin^(2) theta -3)^(2) " or " 16 ( 1- sin^(2) theta) (1-4sin^(2) theta+4sin^(4)theta)= 16 sin^(4) theta- 24 sin^(2) theta + 9 or 64 sin^(6) theta - 112 sin^(4) theta - 56 sin^(2) theta - 7 =0 , and this is cubic in sin^2 theta with the roots sin^(2)((2pi)/7) , sin^(2)((4pi)/7) and sin^(2)((8pi)/7) The sum of these roots in sin^(2)""(2pi)/7 + sin^(2)""(4pi)/7 + sin^(2)""(8pi)/7 = 112/64 = 7/4 . The value of (tan^(2)""(pi)/7+ tan^(2)""(2pi)/7+tan^(2)""(3pi)/7)xx(cot^2""(pi)/7+cot^2""(2pi)/7+cot^2""(3pi)/7) is
Answer» 105 35 210 none of these Answer :A

Discussion

9233.	f: [0, oo) rarr [4, oo) is defined by f(x)=I^(2)+4 then f^(-1)(13)=
Answer» 3 2 1 4 Answer :A

Discussion

9234.	If sin^(-1)(a-(a^(2))/3+(a^(3))/9+…..)+cos^(-1)(1+b+b^(2)=……..)=(pi)/2 then
Answer» `B=(2A-3)/(3A)` `b=(3a-2)/(2a)` `a=3/(2-3b)` `a=2/(3-2b)` ANSWER :A::C::D

Discussion

9235.	A survey shows that 63% of the Americans like cheese whereas 76% like apples , If x% of the Americans like both cheese and apples , then find value of x .
Answer» ANSWER :`39lexle63`

Discussion

9236.	Solve inequality3x-7 gt 2 (x-6), 6-x gt 11 -2x and represent solution graphically on number line.
Answer» ANSWER :`(5,OO)` `(##NCERT_TEL_MAT_XI_C06_E04_009_A01##)`

Discussion

9237.	Compare the following statements : p implies q
Answer» <P> Answer :All FIVE STATEMENTS are equivalents, i.e.,all are different WAYS of SAYING. "If p, then q."

Discussion

9238.	Assertion (A) : For a cone, if r=6 cm, h=12 cm and deltar=deltah=0.06 cm, then approximate error in volume is 3.6pi c.c Reason (R ) : cone valume v=pir^(2)h and error approximately, is dv=pi.(2r.deltar).deltah Choose the correct answer
Answer» A, R are true and `RimpliesA` A, R are ture `RnegtA` A is true, R is FALSE Both A, R are false ANSWER :C

Discussion

9239.	Find lim_(xto0)f(x) and lim_(xto1)f(x), where f(x)={{:(2x+3","xle0),(3(x+1)","xgt0):}
Answer» ANSWER :3, 6

Discussion

9240.	Look at the following figures. By observing the figures write down their cartesian equations
Answer» Solution :`x/2 + y/4 = 1,y = 1/sqrt 3 x, 2x - 3Y + 8 = 0,x -y + 1 = 0`

Discussion

9241.	Let f(x)=2/pi(sin^(-1)[x]+tan^(-1)[x]+cot^(-1)[x]) where [x] denotes greatest less than or equal to x. If A and B denote the domain and range of f(x) respectively, then the number of integers in (A cup B), is
Answer» 1 2 3 4 Answer :D

Discussion

9242.	Converse of prArrq is …… .
Answer» <P> ANSWER :`~Q => ~p`

Discussion

9243.	\|(3, a+b+c, a^(2)+b^(2)+c^(2)),(a+b+c, a^(2)+b^(2)+c^(2), a^(3)+b^(3)+c^(3)), (a^(2)+b^(2)+c^(2),a^(3)+b^(3)+c^(3), a^(4)+b^(4) +c^(4))\| =K(a-b)^(2)(b-c)^(2)(c-a)^(2) then k =
Answer» 4 3 1 0 Answer :C

Discussion

9244.	The work done by the Variable force is defined by_____
Answer» `int_(f)^(i) F xx VEC(dv)` `int_(f)^(i) vec(F) xx vec(DR)` `int_(i)^(f) vec(F) . vec(dr)` ` int_(i)^(f) vec(dr) xx VECF` SOLUTION :`int_(i)^(f) vec(F) . vec(dr)`

Discussion

9245.	Observe the following lists and matching from List - I to List - II is {:("List-I","List-II"),((A)[(0,1),(1,0)],"(1) skew symmetric matrix"),((B)[(2,-5),(-5,2)],"(2) Symmetric matrix"),((S)[(0,x),(-x,0)],"(3) Hermitian matrix "),((D)[(1,2+3i),(2-3i,5)],"(4) Involutory matrix"),(,"(5) Idempotent matrix"):}
Answer» `{:(A,B,C,D),(4,1,2,3):}` `{:(A,B,C,D),(4,2,1,3):}` `{:(A,B,C,D),(4,2,3,1):}` `{:(A,B,C,D),(4,3,1,2):}` ANSWER :B

Discussion

9246.	Write down the converse of following statements: If today is Monday then tomorrow is Tuesday.
Answer» ANSWER :If TOMORROW is TUESDAY then TODAY is MONDAY.

Discussion

9247.	Make correct statements by filling in the symbols ⊂ or ⊄ in the blank spaces : {x : x is a triangle in a plane} . . . {x : x is a rectangle in the plane}
Answer» ANSWER :`⊄`

Discussion

9248.	Differentiate the following functions: ( sqrt(x) + (1)/( sqrt( x) ) )^(2) , x ne 0
Answer» ANSWER :`1- (1)/(x^2)`

Discussion

9249.	If(2)/(11)is the probability of an event.What is the probability the event 'not A '
Answer» ANSWER :`9/11`

Discussion

9250.	Without using tables, give the value of each of the following : cos855^(@)
Answer» ANSWER :`-(1)/(SQRT(2))`

Discussion

Explore topic-wise InterviewSolutions in .

Find the domain and range of the relation R = { (x,y) :y=x^3,x is a positive prime number lt 8}

A circle is inscribed in a trianlge ABC touching the side AB at D such that AD = 5, BD=3 . If lfloorA=60^(@) ten length BC equals

Lt_(x to 0)(cosx+sinx)^(1//x)=

Find the derivative of the function 5 ^(x) + log x + x ^(3) e ^(x)

A die is loaded in such a way that each odd number is twice as likely to occur as each even number. Find P(G), where G is the event that a number greater than 3 occurs on a single roll of the die.

There are two urns. Urm A has 3 distinct red balls and urn B has 9 distinct blue balls . Fromeach urn two balls are taken out at random and then transferred to the other. The number of ways in which . This can be done is.

Differentiate w.r.t. 'x' : f(x) = log((a+b sin x)/(a - b sin x))

A tower 51 m height has a mark at height of 25 m from the ground. At what distance the two parts subtend equal angle to an eye at theheight of5 m from the ground.

cos x =- 1/3, x in quadrant III

Ifx^(2)+4y ^(2)= 4 and range off(x,y)" is "[L,M] " where"f(x,y)= x^(2) +y^(2)- xythen LM is

x+y lt 5

If 2 sin ^(2) x + sin ^(2) 2 x = 2 then x = ____

cos^(-1)((3+5cosx)/(5+3cosx)) is equal to

Find deltay and dy for the following functions y=cosx,x=60^(@) and deltax=1^(@)

Find the distance of the point P from the lines ABin the following cases : P(4, 2),AB is 5x-12y-9=0

Let y = (x^8 + x^4 + 1)/(x^4 + x^2 + 1). If (dy)/(dx) = ax^3 + bx . Then

If ends of a diagonal of a square are (2,-3,4) and (4,1,-2) then the length of one side is

Solve: sqrt5x^2+x+sqrt5=0

If y=(logx)^3 then (dy)/(dx)=

State whether the points (3,2) and (-4,3) lie on the same side or opposite sides of the line 2x-3y+4=0.

Period of tan((3pix)/(4) ) - 2 sec ((pix)/( 3)) + 5 sin((2pix)/( 5)) is

If (barbxxbarc)xx(barcxxbara)=3barc, then find [barbxxbarcbarcxxbarabaraxxbarb]

Show that the statement For any real numbers a and b a^(2)=b^(2) implies that a=b" is not true by giving a counter example.

Convert the following into simplest form (v) cot (theta- (13 pi)/(2))

Find the distance of the point P(1, 2, 3) from the coordinates axes.

From a well shuffled deck of 52 cards, 4 cards aredrawn at random. What is the probability that all the drawn cars are of thesame colour.

The value of cot 70^(@) + 4 cos 70^(@) is

12 balls are keeped in three bags. The probability that there are 3 balls in first bag is:

Sketch roughly the lines satisfyingthe givenconditions and write their equations: inclination theta=150^(@), and distance from the origin = 3.

If ma and M respectively denote the minimum and maximum of f(x) =(x-1)^2+3 for xin [-3,1] then the ordered pair (m,M)=

IF tan^2 theta=2 tan^2 phi +1 then find the value of cos 2 theta+sin^2 phi.

f: [0, oo) rarr [4, oo) is defined by f(x)=I^(2)+4 then f^(-1)(13)=

If sin^(-1)(a-(a^(2))/3+(a^(3))/9+…..)+cos^(-1)(1+b+b^(2)=……..)=(pi)/2 then

A survey shows that 63% of the Americans like cheese whereas 76% like apples , If x% of the Americans like both cheese and apples , then find value of x .

Solve inequality3x-7 gt 2 (x-6), 6-x gt 11 -2x and represent solution graphically on number line.

Compare the following statements : p implies q

Assertion (A) : For a cone, if r=6 cm, h=12 cm and deltar=deltah=0.06 cm, then approximate error in volume is 3.6pi c.c Reason (R ) : cone valume v=pir^(2)h and error approximately, is dv=pi.(2r.deltar).deltah Choose the correct answer

Find lim_(xto0)f(x) and lim_(xto1)f(x), where f(x)={{:(2x+3","xle0),(3(x+1)","xgt0):}

Look at the following figures. By observing the figures write down their cartesian equations

Let f(x)=2/pi(sin^(-1)[x]+tan^(-1)[x]+cot^(-1)[x]) where [x] denotes greatest less than or equal to x. If A and B denote the domain and range of f(x) respectively, then the number of integers in (A cup B), is

Converse of prArrq is …… .

|(3, a+b+c, a^(2)+b^(2)+c^(2)),(a+b+c, a^(2)+b^(2)+c^(2), a^(3)+b^(3)+c^(3)), (a^(2)+b^(2)+c^(2),a^(3)+b^(3)+c^(3), a^(4)+b^(4) +c^(4))| =K(a-b)^(2)(b-c)^(2)(c-a)^(2) then k =

The work done by the Variable force is defined by_____

Write down the converse of following statements: If today is Monday then tomorrow is Tuesday.

Make correct statements by filling in the symbols ⊂ or ⊄ in the blank spaces : {x : x is a triangle in a plane} . . . {x : x is a rectangle in the plane}

Differentiate the following functions: ( sqrt(x) + (1)/( sqrt( x) ) )^(2) , x ne 0

If(2)/(11)is the probability of an event.What is the probability the event 'not A '

Without using tables, give the value of each of the following : cos855^(@)