14949 + Interview Questions in Maths in Class 11 Page 237 InterviewSolution

11801.	From the top of a chiff 30 metres high, the angle of elevation of the top of a tower is found to be equal to the angle of depression of thefoot of the tower. The height of the tower is
Answer» 30 MTS `15sqrt2 mts` 60 mts `30sqrt2 mts` ANSWER :C

Discussion

11802.	Find the derivative of the function wrt x. sin ^(-1) (2x sqrt (1- x ^(2)))
Answer» ANSWER :`(2)/(SQRT(1- X ^(2)))`

Discussion

11803.	Let f: R rarr R and g:R rarr R be two one-one and onto functions such that they are the mirror images of each other about the line y=a. If h(x)=f(x)+g(x) then h(x) is
Answer» one-one onto one-one into many-one into many-one onto Answer :C

Discussion

11804.	Write the first five terms of each of the sequences whose n^(th) terms are as following a_(n)= cos ((n pi)/(2))
Answer» ANSWER :`-0, -1, 0, 1, 0`

Discussion

11805.	Evaluate(ii)cos^-1 [-(1/sqrt2)].
Answer» ANSWER :`(3PI)/4`

Discussion

11806.	A vector vec( c) perpendicular to the vectors 2vec(i) + 3vec(j)-vec(k) and vec(i)-2vec(j)+3vec(k) satisfying vec(c ).(2vec(i)-vec(j) +vec(k))=-6 is
Answer» `-3vec(i) + 3vec(J) + 3vec(K)` `-3vec(i) -3vec(j) + 3vec(k)` `3vec(i) -3vec(j)-3vec(k)` `3vec(i) +3vec(j)+ 3vec(k)` ANSWER :A

Discussion

11807.	If the line joining the circumcentre 'O' and the incentre I is parallel to BC, then cosB + cosC =
Answer» `3//2` 1 `3//4` 2 Answer :B

Discussion

11808.	A committee of 11 persons is to be made from 8 male and 5 female where m is number of ways of selecting at least 6 male and n is the number of ways of selecting at least 3 female, than :
Answer» `m=n=78` `m=n=68` `m+n=68` `m-n=8` ANSWER :A

Discussion

11809.	A bag contain 9 discs of which 4 are red , 3 are blue and 2 are yellow . The discs are similar in shape and size . A disc is drawn at random from the bag . Calculate the probability that it will be (i) red (ii) yellow (iii) blue ?
Answer» <P> ANSWER :(i) P (red ball)`= (4/9)` (II) P( yellow) `=(2/9)` (III)P( BLUE)`= (1/3)`

Discussion

11810.	cos ^(3) x sin 2x= sum _(x=0) ^(n) a _(r) sin (rx) AA x in R, then
Answer» `n=5 , a_(1) = 1//2` `n=5 , a_(1) = 1//4` `n=5 , a_(2) = 1//8` `n=5 , a_(2) = 1//4` ANSWER :B

Discussion

11811.	For non null sets A and B, Acap(AcapB )'=…. .
Answer» ANSWER :`A CAP B'`

Discussion

11812.	The maximum value of f(x)=100-\|45-x\| is
Answer» 100 145 55 45 Answer :A

Discussion

11813.	Write the first five terms of the sequence using the given rule. In each case, the initial value of the index is 1. a_(n)= 2n
Answer» ANSWER :2,4,6,8,10

Discussion

11814.	Prove that 16 cos ^(5) theta - 20 cos ^(3) theta+ 5 cos theta = cos 5 theta.
Answer» ANSWER :`COS THETA `

Discussion

11815.	If origin is the orthocentre of a triangle formed bythe points (cos alpha, sin alpha,0), (cos beta, sin beta,0), (cos gamma, sin gamma,0)then sumcos(2alpha-beta-gamma)=-
Answer» 0 1 2 3 Answer :D

Discussion

11816.	Find theperiodof cos^(2) x+ cos^(4) x
Answer» ANSWER :`pi//2`

Discussion

11817.	State the converse and contrapositive of each of the following statements: r: If it is hot outside, then you feel thirsty.
Answer» ANSWER :there is not HOT out SIDE.

Discussion

11818.	Assertion (A) : Approximate value of (1.0002)^(3000) is 1.6 Reason (R ) : For the differentiable function f(x+deltax)~~f(x)+f^(1)(x).deltax where deltax is change in x The correct answer is
Answer» A,R are TRUE and `RrArrA` A,R are true `RcancelrArrA` A is true R is FALSE A is false r is true ANSWER :A

Discussion

11819.	Write the first five terms of the sequence using the given rule. In each case, the initial value of the index is 1. a_(n) =((-1)^(n-1))/(n^(3))
Answer» ANSWER :`1, (-1)/(8) , (1)/(27) , (-1)/(64) , (1)/(125)`

Discussion

11820.	A man on a wharf 20 mt above the water level, pulls in a rope to which a boat is attached, at the rate of 4 mt per second. At what rate is the boat approaching the shore, when there is still 25 mt of rope out.
Answer» ANSWER :2/3 m/sec

Discussion

11821.	Write the first five terms of the sequence using the given rule. In each case, the initial value of the index is 1. a_(n) = nth prime number for all natural numbers n .
Answer» ANSWER :2,3,5,7,11

Discussion

11822.	An urn contains 8 white and 5 black balls while another urn contains 5 white and 6 black balls.One urn is chosen at random and two balls are drawn from it. Find the probability that the balls are white.
Answer» ANSWER :`(116)/(429)`

Discussion

11823.	Write the first five terms of the sequence using the given rule. In each case, the initial value of the index is 1. a_(n)=3n-2
Answer» ANSWER :1,4,7,10,13

Discussion

11824.	The straight line L-=X+Y+1=0and L_1-=X+2Y+3=0 " are intersectiong, m is the slope of the straight line " L_2 " such that L is the bisector of the angle between " L_1 and L_2 " The value of " m^2 is .
Answer» ANSWER :1

Discussion

11825.	Write the first five terms of the sequence using the given rule. In each case, the initial value of the index is 1. a_(n) = n^(2) +5
Answer» ANSWER :6,9,14,21,30

Discussion

11826.	If 2"sinh"^(-1)((a)/(sqrt(1-a^(2))))=log((1+x)/(1-x)) then x =
Answer» 2a 3a 4a a Answer :D

Discussion

11827.	If p gt q gt r gt 0 then sum Cot^(-1)((pq+1)/(p-q))=
Answer» 0 `pi` `2pi` `(pi)/(2)` ANSWER :C

Discussion

11828.	If the radius of a sphere is raised from 10 cm to 11 cm when heated then the percentage increase in volume is
Answer» 33.1% 34% 30% `33/(10)` ANSWER :B

Discussion

11829.	cos A =(3)/4 implies 32 sin""((A)/(2)) sin""((5A)/(2))=
Answer» 7 8 3 11 Answer :D

Discussion

11830.	Solve 3x-6≥0 graphically in two dimensional plane.
Answer» ANSWER :the solution region is the SHADED region on the right HAND side of the line `X = 2`.

Discussion

11831.	The vlaue ofsin ^(2) 12^(@) + sin ^(@) 21^(@) + sin ^(2) 39^(@) + sin ^(2) 48^(@) - sin ^(2) 9^(@) - sin ^(2) 18^(@) is "______"
Answer» ANSWER :1

Discussion

11832.	If 1lrf(x)x^(2)+2x+2,Aax in R then lim_(xto-1)f(x)=…………
Answer» 2 0 -1 1 Answer :D

Discussion

11833.	It is not true that 'Ram is claver OR Ram is bold. Then logical from of these statement is ……. .
Answer» ANSWER :`~(PVVQ)`

Discussion

11834.	Let alpha and beta be any two positive values of x for which 2 cos x,\|cos x\|, and 1-3cos^(2)x are in G.P. The minimum value of \|alpha-beta\| is
Answer» `(PI)/3` `(pi)/4` `(pi)/2` `(pi)/6` Answer :D

Discussion

11835.	One Indinaand fourAmericanmenand theirwivesare to beseated randomly around acirculartable . Theconditionalprobabiltiy that thegiventhat eachAmericanman isseated adjecent to his wife is ,
Answer» `(1)/(2)` `(1)/(3)` `(2)/(5)` `(1)/(5)` ANSWER :C

Discussion

11836.	If the point (a,a) is placed in between the lines abs(x+y)=4, then sum of integral values of a is
Answer» 0 1 4 3 Answer :A

Discussion

11837.	If H is the orthocentre of Delta ABC, then : cos(angle AHB)=
Answer» `- COS A` `- cos B` `- cos C` `-cos D` ANSWER :C

Discussion

11838.	Write Negation of the following statements: Each rectangle is a parallelogram.
Answer» ANSWER :Each rectagle is not a PARALLOGRAM.

Discussion

11839.	y = f(x), Where f satisfies the relation f(x + y) = 2f(x) + xf(y) + ysqrt(f(x)) AA x, y in R and f'(0) = 0. Then f(6) is equal to ………
Answer»

Discussion

11840.	"cosec" theta =1/2
Answer» ANSWER :FALSE STATEMENT

Discussion

11841.	Find the coordinates of the focus , axis, the question of the directrix and latus rectum of the parabola y^(2)=8x.
Answer» ANSWER :(i) `(2, PM 4)` (II) `(pm 4, -2)`

Discussion

11842.	If A, B, C, D be the angle of a quadrilateral, then (tan A + tan B + tan C + tan D)/( cot A + cot B + cot C + cot D) =
Answer» `tan A tan B tan C tan D` `0` `1` `cot A cot B cot C cot D` ANSWER :A

Discussion

11843.	If Negation of p then q has symbolic from
Answer» <P> ANSWER :`~p=>Q`

Discussion

11844.	Differentiate the following functions: (3)/(x^5)
Answer» ANSWER :`(-15)/( x^6)`

Discussion

11845.	Let f(x) = x^(2) and g(x) = sin xfor all x in R. Then the set of all x satisfying (fogogog)(x) = (gogof)(x), where (fog)(x) = f(g(x)), is
Answer» `PM SQRT(n pi), n in {0,1,2, . . . }` `pm sqrt(n pi), n in {1, 2, . . . }` `(pi)/(2)+ 2 n pi, n in {. . . . , -2, -1, 0, 1, 2, . . . }` `2 n pi , n in {. . . , -2, -1, 0, 1, 2. . . . }` Answer :A

Discussion

11846.	If f(x)= x^(2 )+ 2x + 3 then find f(1), f(2), f(3)
Answer» ANSWER :`6, 11, 18`

Discussion

11847.	sum a^(3)cos (B-C)=
Answer» ` 3ABC ` ` ABC ` ` 2ABC ` ` 0 ` ANSWER :A

Discussion

11848.	If (a + b)^(2) = c^(2) + ab " in a " Delta ABC " andif " sqrt2 (sin A + cos A) = sqrt3 then ascending order of angles A, B, C is
Answer» A, B, C A, C, B B, A, C C, B, A ANSWER :A

Discussion

11849.	If A+B+C=pi prove that "tan"A/2"tan"B/2+"tan"B/2"tan"C/2+"tan"C/2"tan"A/2=1
Answer» SOLUTION :NA

Discussion

11850.	If the lines 2x+y-3=0,5k+ky-3=0 and3x-y-2=0 areconcurrent ,find the value of K ?
Answer» ANSWER :`= -2`

Discussion

Explore topic-wise InterviewSolutions in .

From the top of a chiff 30 metres high, the angle of elevation of the top of a tower is found to be equal to the angle of depression of thefoot of the tower. The height of the tower is

Find the derivative of the function wrt x. sin ^(-1) (2x sqrt (1- x ^(2)))

Let f: R rarr R and g:R rarr R be two one-one and onto functions such that they are the mirror images of each other about the line y=a. If h(x)=f(x)+g(x) then h(x) is

Write the first five terms of each of the sequences whose n^(th) terms are as following a_(n)= cos ((n pi)/(2))

Evaluate(ii)cos^-1 [-(1/sqrt2)].

A vector vec( c) perpendicular to the vectors 2vec(i) + 3vec(j)-vec(k) and vec(i)-2vec(j)+3vec(k) satisfying vec(c ).(2vec(i)-vec(j) +vec(k))=-6 is

If the line joining the circumcentre 'O' and the incentre I is parallel to BC, then cosB + cosC =

A committee of 11 persons is to be made from 8 male and 5 female where m is number of ways of selecting at least 6 male and n is the number of ways of selecting at least 3 female, than :

A bag contain 9 discs of which 4 are red , 3 are blue and 2 are yellow . The discs are similar in shape and size . A disc is drawn at random from the bag . Calculate the probability that it will be (i) red (ii) yellow (iii) blue ?

cos ^(3) x sin 2x= sum _(x=0) ^(n) a _(r) sin (rx) AA x in R, then

For non null sets A and B, Acap(AcapB )'=…. .

The maximum value of f(x)=100-|45-x| is

Write the first five terms of the sequence using the given rule. In each case, the initial value of the index is 1. a_(n)= 2n

Prove that 16 cos ^(5) theta - 20 cos ^(3) theta+ 5 cos theta = cos 5 theta.

If origin is the orthocentre of a triangle formed bythe points (cos alpha, sin alpha,0), (cos beta, sin beta,0), (cos gamma, sin gamma,0)then sumcos(2alpha-beta-gamma)=-

Find theperiodof cos^(2) x+ cos^(4) x

State the converse and contrapositive of each of the following statements: r: If it is hot outside, then you feel thirsty.

Assertion (A) : Approximate value of (1.0002)^(3000) is 1.6 Reason (R ) : For the differentiable function f(x+deltax)~~f(x)+f^(1)(x).deltax where deltax is change in x The correct answer is

Write the first five terms of the sequence using the given rule. In each case, the initial value of the index is 1. a_(n) =((-1)^(n-1))/(n^(3))

A man on a wharf 20 mt above the water level, pulls in a rope to which a boat is attached, at the rate of 4 mt per second. At what rate is the boat approaching the shore, when there is still 25 mt of rope out.

Write the first five terms of the sequence using the given rule. In each case, the initial value of the index is 1. a_(n) = nth prime number for all natural numbers n .

An urn contains 8 white and 5 black balls while another urn contains 5 white and 6 black balls.One urn is chosen at random and two balls are drawn from it. Find the probability that the balls are white.

Write the first five terms of the sequence using the given rule. In each case, the initial value of the index is 1. a_(n)=3n-2

The straight line L-=X+Y+1=0and L_1-=X+2Y+3=0 " are intersectiong, m is the slope of the straight line " L_2 " such that L is the bisector of the angle between " L_1 and L_2 " The value of " m^2 is .

Write the first five terms of the sequence using the given rule. In each case, the initial value of the index is 1. a_(n) = n^(2) +5

If 2"sinh"^(-1)((a)/(sqrt(1-a^(2))))=log((1+x)/(1-x)) then x =

If p gt q gt r gt 0 then sum Cot^(-1)((pq+1)/(p-q))=

If the radius of a sphere is raised from 10 cm to 11 cm when heated then the percentage increase in volume is

cos A =(3)/4 implies 32 sin""((A)/(2)) sin""((5A)/(2))=

Solve 3x-6≥0 graphically in two dimensional plane.

The vlaue ofsin ^(2) 12^(@) + sin ^(@) 21^(@) + sin ^(2) 39^(@) + sin ^(2) 48^(@) - sin ^(2) 9^(@) - sin ^(2) 18^(@) is "______"

If 1lrf(x)x^(2)+2x+2,Aax in R then lim_(xto-1)f(x)=…………

It is not true that 'Ram is claver OR Ram is bold. Then logical from of these statement is ……. .

Let alpha and beta be any two positive values of x for which 2 cos x,|cos x|, and 1-3cos^(2)x are in G.P. The minimum value of |alpha-beta| is

One Indinaand fourAmericanmenand theirwivesare to beseated randomly around acirculartable . Theconditionalprobabiltiy that thegiventhat eachAmericanman isseated adjecent to his wife is ,

If the point (a,a) is placed in between the lines abs(x+y)=4, then sum of integral values of a is

If H is the orthocentre of Delta ABC, then : cos(angle AHB)=

Write Negation of the following statements: Each rectangle is a parallelogram.

y = f(x), Where f satisfies the relation f(x + y) = 2f(x) + xf(y) + ysqrt(f(x)) AA x, y in R and f'(0) = 0. Then f(6) is equal to ………

"cosec" theta =1/2

Find the coordinates of the focus , axis, the question of the directrix and latus rectum of the parabola y^(2)=8x.

If A, B, C, D be the angle of a quadrilateral, then (tan A + tan B + tan C + tan D)/( cot A + cot B + cot C + cot D) =

If Negation of p then q has symbolic from

Differentiate the following functions: (3)/(x^5)

Let f(x) = x^(2) and g(x) = sin xfor all x in R. Then the set of all x satisfying (fogogog)(x) = (gogof)(x), where (fog)(x) = f(g(x)), is

If f(x)= x^(2 )+ 2x + 3 then find f(1), f(2), f(3)

sum a^(3)cos (B-C)=

If (a + b)^(2) = c^(2) + ab " in a " Delta ABC " andif " sqrt2 (sin A + cos A) = sqrt3 then ascending order of angles A, B, C is

If A+B+C=pi prove that "tan"A/2"tan"B/2+"tan"B/2"tan"C/2+"tan"C/2"tan"A/2=1

If the lines 2x+y-3=0,5k+ky-3=0 and3x-y-2=0 areconcurrent ,find the value of K ?