14949 + Interview Questions in Maths in Class 11 Page 189 InterviewSolution

9401.	Find the circumcentre of the triangle whose vertices are (1,3) (-3,5) and (5,-1).
Answer» ANSWER :`(-8,-10)`

Discussion

9402.	The number of solutions of equation tanx+secx=2cosx lying in the interval [0,2pi] is
Answer» ANSWER :FALSE STATEMENT

Discussion

9403.	If A= {-1, 2, 3} and B= {1, 3}, the determine A xx A
Answer» ANSWER :`{(-1,-1),(-1,2),(-1, 3), (2,-1), (2,2), (2,3),(3,-1),(3,2),(3,3)}`

Discussion

9404.	Let f(x)= sin( cot ^(-1)x) + tan ((pi )/(2) [x]) ,where [x] is the greatest integer funcitons less than or equal to x Then which of the following altermatives is/are true
Answer» `f(X)` is many-one but not an even FUNCTION `f(x)` is a periodic function. `f(x)` is a BOUNDED function. The graph of `f(x)` remains aove the x-axis. Answer :A::B::C::D

Discussion

9405.	For arithmetic sequence a_(8) =23 common difference d = 5 then a = ...............
Answer» ANSWER :`-12`

Discussion

9406.	In the series 1/(1+sqrt(2)) + 1/(sqrt(2)+sqrt(3)) + 1/(sqrt(3) + sqrt(4)) + ... some of first 24 number is:
Answer» 4 `sqrt(24)` `1/sqrt(24)` `1/(sqrt(25) - sqrt(24))` ANSWER :a

Discussion

9407.	Find the absolute maximum and absolute minimum of f(x) = 2x^(3) - 3x^(2) - 36x + 2 on the interval [0, 5].
Answer» ANSWER :ABSOLUTE minimum= -79, Absolute maximum = 2

Discussion

9408.	Find the domain of each of the following functions given by f(x)= (x^(3)-x+3)/(x^(2)-1)
Answer» ANSWER :`R- {-1, 1}`

Discussion

9409.	Solve2 sin theta cos theta = cos theta. ( 0^(@) < theta lt 360^(@)).
Answer» ANSWER :`THETA = 30^(@), 90^(@), 150^(@), 270&(@)`

Discussion

9410.	If f(x + 1/2) + f(x - 1/2)= f(x) for all x in R, then the period of f(x) is
Answer» 1 2 3 4 Answer :C

Discussion

9411.	If the lines passing through (3,y) and (2,7) are perpendicular find the value of y
Answer» SOLUTION :`y = 13/2`

Discussion

9412.	If a point P lies in YZ - plane, then the coordinates of a point on YZ-plane is of the form _____ .
Answer» ANSWER :(o, y, Z)

Discussion

9413.	Let a kind of bacteria grow by t^(3) (t in sec). At what time the rate of growth of the bacteria is 300 bacteria per sec?
Answer» ANSWER :180

Discussion

9414.	If max{5 sin theta+3sin(theta-alpha)}=7, alpha=2n pi +-(pi)/K, n in I then the value of K(theta in R) is
Answer» ANSWER :3

Discussion

9415.	Find the cofficient of x in the expansion of log(1/(1-5x+6x^(2)))
Answer» ANSWER :`(2^(N) + 3^(n))/n`

Discussion

9416.	sec h^(-1)(sin theta) =
Answer» `"log tan " (THETA)/(2)` `"log SIN "(theta)/(2)` `"log COS "(theta)/(2)` `"log cot "(theta)/(2)` Answer :D

Discussion

9417.	Find the derivative of the w.r.t.x (1- cos 2x)/( 1 + cos 2x)
Answer» ANSWER :`2 TAN X SEC ^(2)x `

Discussion

9418.	Determine real values of x and y for which each statement is true (x^(4) + 2x i)- (3x^(2) + yi)= (3-5i) + (1 + 2yi)
Answer» ANSWER :`X=2,y= 3, x= -2Y, y= (1)/(3)`

Discussion

9419.	The probability that a car being filled with petrol will also need an oil change is 0.30, the probability that it needs a new oil filter is 0.40, and the probability that both the oil and filter need changing is 0.15.(i)If the oil had to be changed, what is the probability that a new oil filter is needed?(ii)If a new oil filter is needed, what is the probability that the oil has to be changed?
Answer» ANSWER :(i)`0.5` (II)`0.375`

Discussion

9420.	Find the value of n such that,""^(n)P_(2)=30
Answer» ANSWER :(i) -5, (II) 6

Discussion

9421.	Rewrite each of the following statements in the form p if and only if q: r: If a quadrilaterals equiangular, then it is a rectangle and if a quadrilateral is a rectangle, then it is equiangular.
Answer» ANSWER :A QUADRILATERAL is a RECTANGLE if and only if it is EQUIANGULAR.

Discussion

9422.	If a=3,b =4,c= 5 ,thensin 2Bis
Answer» `(25)/(24)` ` (24)/( 25) ` ` (12)/(25) ` ` (25)/(12) ` ANSWER :B

Discussion

9423.	The polar coordinate of complex number z=1+isqrt3 is (2,(pi)/3) .
Answer» ANSWER :TRUE STATEMENT

Discussion

9424.	A= {a, b ,{c, d}, e} which of the following statements are correct? {a, b, e} sub A
Answer» ANSWER :CORRECT

Discussion

9425.	Find equation of line passes from point of intersection at lines 4x-3y - 1 =0 and 2x - 5y+3=0 which makes equal angle with axis.
Answer» ANSWER :`X + y - 2 = 0, x = y`

Discussion

9426.	Write the n^(th) term of the sequence (3)/(1^(2)2^(2)), (5)/(2(2)3^(2)), (7)/(3^(2)4^(2)),….. as a difference of two terms.
Answer» ANSWER :`=(1)/(N^(2))-(1)/((n+1)^(2))`

Discussion

9427.	Express each of the complex number given in the form of a+ib (1-i)^(4)
Answer» ANSWER :`-4 + I0`

Discussion

9428.	In triangle ABC, range of (a^(2)+b^(2)+c^(2))/(ab+bc+ca) is (a,b,c are sides of triangle)
Answer» (0,1] [1,2) [1,4] None Answer :B

Discussion

9429.	cot (- (15pi)/(4))
Answer» ANSWER :1

Discussion

9430.	Find the values of theta lying between 0^(@) and 360^(@) when sin theta=1/2
Answer» ANSWER :`30^(@),150^(@)`

Discussion

9431.	If f(x)={:[(\|x\|", "x le 1),(2-x", "x gt 1):} then f(f(x))=
Answer» `{:{(2-\|x\|","x lt -1),(\|x\|","-1 LE x le 1),(\|2-x\|","x GT 1):}` `{:{(" "\|x\|","x lt -1),(2-\|x\|","-1 le x le 1),(" "\|2-x\|","x gt 1):}` `{:{(\|2-x\|","x lt -1),(\|x\|","-1 le x le 1),(2-\|x\|","x gt1):}` Cannot SAY Answer :A

Discussion

9432.	lim_(n to oo)(n!)/((n+1)!-n!)
Answer» `0` `2` `-1` `-2` ANSWER :A

Discussion

9433.	An experiment consists of tossing a coin and then throwing it second time if a head occurs. If a tail occurs on the first toss, then a die is rolled once. Find the sample space.
Answer» ANSWER :`S={HH,HT,T1,T2,T3,T4,T5,T6}`

Discussion

9434.	Which of the following sentences are statements? Give reasons for your answer: Answer this question.
Answer» ANSWER :It is an ORDER and THEREFORE, is not a STATEMENT.

Discussion

9435.	If A, B, C are the angles of a triangle such that "cot"(A)/(2)="3 tan"(C )/(2), then sin A, sin B, sin C are in
Answer» A.B G.P. H.P. NONE of these ANSWER :A

Discussion

9436.	Express the following as functions of angles less than 45^(@) : sin348^(@)
Answer» ANSWER :`-SIN 12^(@)`

Discussion

9437.	Let f(x) =a_(1)cos(alpha_(1)+x)+a_2cos(alpha_2+x)+............+ a_ncos(a_n+x) . If f(x) vanishes for x = 0 andx=x_1 (where x_1 ne kpi, k in Z) then
Answer» `a_(1)cosalpha_(1)+a_(2)cos alpha_(2)+..........+a_(n)cos alpha_(n)=0` `alpha_(1) sinalpha_(1)+a_(2)sinalpha_(2)+.........+a_(n)sinalpha_(n)=0` `f(X) = 0 ` has only two SOLUTION `0,x_1` f(x) is IDENTICALLY zero `AA x` Answer :A::B::D

Discussion

9438.	State whether each of the following statement is true or false. Justify your answer. { 2, 6, 10 } and { 3, 7, 11} are disjoint sets.
Answer» ANSWER :1

Discussion

9439.	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)/7tan^2""(2pi)/7tan^2""(3pi)/7
Answer» 8 `(35)/(3)` `(21)/(3)` none of these Answer :C

Discussion

9440.	To find the sum "sin"^(2) (2pi)/(7) + "sin"^(2) (4pi)/(7) + "sin"^(2) (8pi)/(7), we follow the following method. Put 7 theta = 2 n pi, where n is any integer. Then sin 4 theta = sin (2n pi - 3 theta) = - sin 3 theta""…(i) This means that sin theta takes the values 0. +- sin (2pi//7), +- sin (4pi//7), and +- sin (8pi//7). From Eq. (i), we now get 2 sin 2theta cos 2 theta = 4 sin^(3) theta - 3 sin theta or 4 sin theta cos theta(1 - 2 sin^(2) theta) = (4 sin^(2) theta - 3) sin theta Rejecting the value sin theta = 0, we get 4 cos theta (1-2 sin^(2) theta) = 4 sin^(2) theta - 3 or 16 cos^(2) theta (1-2sin^(2)theta)^(2) = (4 sin^(2) theta - 3)^(2) or 16(1-sin^(2)theta)(1-4 sin^(2)theta + 4 sin^(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 is "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

9441.	To find the sum "sin"^(2) (2pi)/(7) + "sin"^(2) (4pi)/(7) + "sin"^(2) (8pi)/(7), we follow the following method. Put 7 theta = 2 n pi, where n is any integer. Then sin 4 theta = sin (2n pi - 3 theta) = - sin 3 theta""…(i) This means that sin theta takes the values 0. +- sin (2pi//7), +- sin (4pi//7), and +- sin (8pi//7). From Eq. (i), we now get 2 sin 2theta cos 2 theta = 4 sin^(3) theta - 3 sin theta or 4 sin theta cos theta(1 - 2 sin^(2) theta) = (4 sin^(2) theta - 3) sin theta Rejecting the value sin theta = 0, we get 4 cos theta (1-2 sin^(2) theta) = 4 sin^(2) theta - 3 or 16 cos^(2) theta (1-2sin^(2)theta)^(2) = (4 sin^(2) theta - 3)^(2) or 16(1-sin^(2)theta)(1-4 sin^(2)theta + 4 sin^(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 is "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)
Answer» -3 7 -5 none of these Answer :B

Discussion

9442.	Express each of the complex number given in the form of a+ib (5i)(-3/5i)
Answer» ANSWER :`3+i0`

Discussion

9443.	Six new employees, two of whom are married to each other, are to be assigned six desks that are lined up in a row. If the assignment of employees to desks is made randomly, what is the probability that the married couple will have nonadjacent desks?
Answer» ANSWER :`=(2)/(3)`

Discussion

9444.	A(1, 2, 3), B(0, 4, 1) and C(-1, -1, -3) are verticies of DeltaABC. Find point on bar(BC) at which bisector of angleBAC intersects.
Answer» ANSWER :`(-3/10,5/2,-1/5)`

Discussion

9445.	Giventhat f(x)= (4-7x)/((3x+4)) , I = Lim_(x to 2 ) f(x)and m = Lim_(x to 0) f(x), form the equation whoseare 1/l , 1/m
Answer» ANSWER :`X^(2) - 1 = 0 `

Discussion

9446.	Write the component statements of the following compound statements and check whether the compound statement is true or false. 24 is a multiple of 4 and 6.
Answer» ANSWER :1

Discussion

9447.	Write the component statements of the following compound statements and check whether the compound statement is true or false. 2 is an even number and a prime number.
Answer» ANSWER :1

Discussion

9448.	Write the component statements of the following compound statements and check whether the compound statement is true or false. 57 is divisible by 2 or 3.
Answer» ANSWER :1

Discussion

9449.	The number of values of theta in the interval (-(pi)/(2),(pi)/(2)) such that theta ne (n pi)/(5) "for " n = 0 , pm 1, pm 2 and tan theta = cot 5 thetaas well as sin 2 theta = cos 4 thetais
Answer» ANSWER :3

Discussion

9450.	Write the component statements of the following compound statements and check whether the compound statement is true or false: A line is straight and extends indefinitely in both directions.
Answer» ANSWER :TRUE.

Discussion

Explore topic-wise InterviewSolutions in .

Find the circumcentre of the triangle whose vertices are (1,3) (-3,5) and (5,-1).

The number of solutions of equation tanx+secx=2cosx lying in the interval [0,2pi] is

If A= {-1, 2, 3} and B= {1, 3}, the determine A xx A

Let f(x)= sin( cot ^(-1)x) + tan ((pi )/(2) [x]) ,where [x] is the greatest integer funcitons less than or equal to x Then which of the following altermatives is/are true

For arithmetic sequence a_(8) =23 common difference d = 5 then a = ...............

In the series 1/(1+sqrt(2)) + 1/(sqrt(2)+sqrt(3)) + 1/(sqrt(3) + sqrt(4)) + ... some of first 24 number is:

Find the absolute maximum and absolute minimum of f(x) = 2x^(3) - 3x^(2) - 36x + 2 on the interval [0, 5].

Find the domain of each of the following functions given by f(x)= (x^(3)-x+3)/(x^(2)-1)

Solve2 sin theta cos theta = cos theta. ( 0^(@) < theta lt 360^(@)).

If f(x + 1/2) + f(x - 1/2)= f(x) for all x in R, then the period of f(x) is

If the lines passing through (3,y) and (2,7) are perpendicular find the value of y

If a point P lies in YZ - plane, then the coordinates of a point on YZ-plane is of the form _____ .

Let a kind of bacteria grow by t^(3) (t in sec). At what time the rate of growth of the bacteria is 300 bacteria per sec?

If max{5 sin theta+3sin(theta-alpha)}=7, alpha=2n pi +-(pi)/K, n in I then the value of K(theta in R) is

Find the cofficient of x in the expansion of log(1/(1-5x+6x^(2)))

sec h^(-1)(sin theta) =

Find the derivative of the w.r.t.x (1- cos 2x)/( 1 + cos 2x)

Determine real values of x and y for which each statement is true (x^(4) + 2x i)- (3x^(2) + yi)= (3-5i) + (1 + 2yi)

Find the value of n such that,""^(n)P_(2)=30

Rewrite each of the following statements in the form p if and only if q: r: If a quadrilaterals equiangular, then it is a rectangle and if a quadrilateral is a rectangle, then it is equiangular.

If a=3,b =4,c= 5 ,thensin 2Bis

The polar coordinate of complex number z=1+isqrt3 is (2,(pi)/3) .

A= {a, b ,{c, d}, e} which of the following statements are correct? {a, b, e} sub A

Find equation of line passes from point of intersection at lines 4x-3y - 1 =0 and 2x - 5y+3=0 which makes equal angle with axis.

Write the n^(th) term of the sequence (3)/(1^(2)2^(2)), (5)/(2(2)3^(2)), (7)/(3^(2)4^(2)),….. as a difference of two terms.

Express each of the complex number given in the form of a+ib (1-i)^(4)

In triangle ABC, range of (a^(2)+b^(2)+c^(2))/(ab+bc+ca) is (a,b,c are sides of triangle)

cot (- (15pi)/(4))

Find the values of theta lying between 0^(@) and 360^(@) when sin theta=1/2

If f(x)={:[(|x|", "x le 1),(2-x", "x gt 1):} then f(f(x))=

lim_(n to oo)(n!)/((n+1)!-n!)

An experiment consists of tossing a coin and then throwing it second time if a head occurs. If a tail occurs on the first toss, then a die is rolled once. Find the sample space.

Which of the following sentences are statements? Give reasons for your answer: Answer this question.

If A, B, C are the angles of a triangle such that "cot"(A)/(2)="3 tan"(C )/(2), then sin A, sin B, sin C are in

Express the following as functions of angles less than 45^(@) : sin348^(@)

Let f(x) =a_(1)cos(alpha_(1)+x)+a_2cos(alpha_2+x)+............+ a_ncos(a_n+x) . If f(x) vanishes for x = 0 andx=x_1 (where x_1 ne kpi, k in Z) then

State whether each of the following statement is true or false. Justify your answer. { 2, 6, 10 } and { 3, 7, 11} are disjoint sets.

Express each of the complex number given in the form of a+ib (5i)(-3/5i)

Six new employees, two of whom are married to each other, are to be assigned six desks that are lined up in a row. If the assignment of employees to desks is made randomly, what is the probability that the married couple will have nonadjacent desks?

A(1, 2, 3), B(0, 4, 1) and C(-1, -1, -3) are verticies of DeltaABC. Find point on bar(BC) at which bisector of angleBAC intersects.

Giventhat f(x)= (4-7x)/((3x+4)) , I = Lim_(x to 2 ) f(x)and m = Lim_(x to 0) f(x), form the equation whoseare 1/l , 1/m

Write the component statements of the following compound statements and check whether the compound statement is true or false. 24 is a multiple of 4 and 6.

Write the component statements of the following compound statements and check whether the compound statement is true or false. 2 is an even number and a prime number.

Write the component statements of the following compound statements and check whether the compound statement is true or false. 57 is divisible by 2 or 3.

The number of values of theta in the interval (-(pi)/(2),(pi)/(2)) such that theta ne (n pi)/(5) "for " n = 0 , pm 1, pm 2 and tan theta = cot 5 thetaas well as sin 2 theta = cos 4 thetais

Write the component statements of the following compound statements and check whether the compound statement is true or false: A line is straight and extends indefinitely in both directions.