14949 + Interview Questions in Maths in Class 11 Page 259 InterviewSolution

12901.	Domain of f(x)=sin^(-1)[2-4x^(2)] is ([.] denotes the greatest integer function)
Answer» `[ - (SQRT(3))/(2), (sqrt(3))/(2)]-{0}` `[ - (sqrt(3))/(2),1)` `[ - (sqrt(3))/(2), 0) uu (0, (sqrt(3))/(2)]` `[- (sqrt(3))/(2), 8]` Answer :A::C

Discussion

12902.	If b= 3, c= 4 angle B = (pi )/(3)then number of triangles that can be constructed is
Answer» `0` `1` ` 3` `2` ANSWER :A

Discussion

12903.	Are the following pair of sets equal ? Give reasons. A = {2, 3}, B ={x : x is solution of x^(2) + 5x + 6 = 0}
Answer» ANSWER :`A NE B`

Discussion

12904.	If f(x)=Sin^(-1)x+Cos^(-1)x, then(pi)/2 is the value of
Answer» 1)`f(-2)` 2)`f(-3/2)` 3)`f(1/(1+k^(2))),kinR` 4)`f(k^(2)-2k+3),kinR` ANSWER :C

Discussion

12905.	A tower leans towards west making an angle alpha with the vertical. The angular elevation of B, the top most point of the tower is beta as observed from a point C due east of A at distance d from A. If the angular elevation of B from a point due east of C a distance 2d from C isgamma , " then " 2tan alpha can be written as
Answer» `3cotbeta-2cot GAMMA` `3COT gamma-2cotbeta` `3cotbeta-cot gamma` `cotbeta-3cot gamma` ANSWER :C

Discussion

12906.	If y=tan^(-1)""1/2+tan^(-1)b, (0 lt b lt 1) and 0 lt y le pi/4, then the maximum value of b is
Answer» `1//4` `1//3` `1//4` `2//3` ANSWER :B

Discussion

12907.	If the lines 3x-y = 2 and x+2y = 3 are two diameters of a circle and if the circle passes through (2,0), find the equation of the circle.
Answer» SOLUTION :`x^2+y^2-2x-2y = 0`

Discussion

12908.	Discuss the continuity of f(x) in [0,2] wheref(x) = {{:([cos pi x]", " x le 1),(\| 2x - 3 \|.[ x- 2]" ," x gt 1):} where [.] denotes the G.I.F.
Answer» Answer :CONTINUOUS when `x in {0,2]-{0,(1)/(2),2}`

Discussion

12909.	Co - ordinates of the point in YZ plane are in the form of (a,y,z) where a in R - {0} .
Answer» ANSWER :FALSE STATEMENT

Discussion

12910.	if 1/(7!)+1/(9!) =x/(10!) then find x.
Answer» ANSWER :730

Discussion

12911.	A die is thrown, find the probability of following events : A number less then 6 will appear.
Answer» ANSWER :`(5)/(6)`

Discussion

12912.	If (alpha, beta) is the centroid of the triangle, whose sides are ax^(2)+2hxy+by^(2)=0 and lx+my=1, then show that (alpha)/(bl-hm)=(beta)/(am-hl)=(2)/(3(bl^(2)-2hlm+am^(2)))
Answer» ANSWER :`(2)/(3(BL^(2)-2hlm+am^(2)))`

Discussion

12913.	The ortho centre of triangle formed by the points (2,1,5),(3,2,3), (4,0,4) is
Answer» (2, 1, 5) (2, 2, 3) (4, 0, 4) (3, 1, 4) ANSWER :d

Discussion

12914.	Convert each of the complex number in the polar form: i
Answer» ANSWER :`"cos"(PI)/(3)+i"sin"(pi)/(2)`

Discussion

12915.	The sides of a Delta ^("le') ABCbe 8, 7, 6 and smallest angle is C then The length of altitude from vertex C is
Answer» `SQRT(30)` `2 sqrt6` `14/5` `(7sqrt15)/4` ANSWER :d

Discussion

12916.	If the distance from P to the points (2,3),(2,-3) are in the ratio 2:3 the find the locus of P.
Answer» ANSWER :`5X^(2)+5Y^(2)-20x-78y+65=0`

Discussion

12917.	The radius and height of a cylinder are measured as 5 cm and 10 cm respectively and there is an error of 0.02 cm in both the measurements. The approximate error in the volume is
Answer» `4PI` C.C `2.5pi C.C` `0.06 C. C` `0.6 C.C` ANSWER :B

Discussion

12918.	Evaluate the following limits : Lim_( x to 1) (e^(x)-e)/(x-1)
Answer» ANSWER :E

Discussion

12919.	Find the derivative of the function e ^(x) (x ^(2) + 1 )
Answer» ANSWER :`E ^(X) (x +1) ^(2)`

Discussion

12920.	Which term of the following sequences: 2, 2 sqrt2, 4…..is 128?
Answer» ANSWER :`13^(TH)`

Discussion

12921.	Find the angle in radian through which a pendulum swingsif its length is 75 cm and the tip describes an arc of length (i) 10 cm (ii) 15 cm (iii) 21cm.
Answer» ANSWER :`(i) (2)/(15)` (II) `1/5` (III) `7/25`

Discussion

12922.	If A = (3, 81) and f: A rarr B is a surjection defined by f(x)=log_(3)x then B=
Answer» `[1, 4]` `(1, 4]` `(1, 4)` `[1, OO)` ANSWER :C

Discussion

12923.	.......... is the transform form of equation x^2-y^2-2x+2y=0 by shifting origin at (1,1)
Answer» ANSWER :`x^2-y^2=0`

Discussion

12924.	Expandthe expression (x+1/x)^6
Answer» ANSWER :`x^6` + `6x^4` + 15x^2` + `20+ 15/x^2` + `6/x^4` + `1/x^6`

Discussion

12925.	An open cylinder of given surface will have maximum volume if radius =
Answer» HEIGHT `(1)/(2)("height")` 2 (height) 3 (height) ANSWER :A

Discussion

12926.	Evaluate the following limits in Exercises lim_(xtopi)(sin (pi-x))/(pi(pi-x))
Answer» ANSWER :`(1)/(PI)`

Discussion

12927.	List all the elements of the following sets : C= {x : The solution of x^(2)+5x+6=0}
Answer» ANSWER :`C= {-2, -3}`

Discussion

12928.	Iff(x)={:(ax^(2)-b",",-1 ltxlt1 ),(1/(\|x\|)",","elsewhere"):}isdifferentiableat x = 1, then………..
Answer» `a = 1/2 , B = (-3)/2 ` `a = (-1)/2 , b = 3/2` `a = -1/2 , b = 3/2 ` ` a = -1/2 , b = - 3/2 ` ANSWER :`a = 1/2b = 3/2 `

Discussion

12929.	In a triangle ABC, medians AD and BE are drawn.IF angle D=4, angle DAB=pi//6, angle ABE=pi//3 then the area of Delta ABC is
Answer» `(16)/(3)` `(32)/(3 SQRT(3))` `(64)/(3 sqrt(3))` `(8)/(3)` Answer :B

Discussion

12930.	In triangleABC, lfloor(A) = pi/4 and tanB.tanC= P, then all possible value of P is:
Answer» `(-INFTY,3-2sqrt(2)) CUP (3+2sqrt(2), infty)` `(-infty,3-2sqrt(2)) cup [3+2sqrt(2), infty)` `(3-2sqrt(2),3+2sqrt(2))` `[3-2sqrt(2),3+2sqrt(2)]` ANSWER :B

Discussion

12931.	Slope of line is non zero real number .
Answer» ANSWER :FALSE STATEMENT

Discussion

12932.	A and B are mutually exclusive event. If P(A)=(1)/(4),P(B)=(2)/(5) and P(AuuB)=(1)/(2).
Answer» ANSWER :`(3)/(20),(1)/(10)`

Discussion

12933.	If 2x^(2) - 3xy + y^(2) + x + 2y - 8= 0, then (dy)/(dx) is equal to
Answer» `(3Y - 4X + 1)/(2y - 3x + 2)` `(3y + 4x + 1)/(2y + 3x + 2)` `(3y - 4x + 1)/(2y - 3x - 2)` `(3y - 4x + 1)/(2y + 3x + 2)` ANSWER :A

Discussion

12934.	The range of f(x)=[\|sin x\|+\|cos x\|], where [.] denotes the greast integer function, is
Answer» `{0}` `{0, 1}` `{0}` `{1,2}` ANSWER :C

Discussion

12935.	Period of cos (x+ (x)/(3) + (x)/(3^2) + …..) is
Answer» `(PI)/(3)` `(2PI)/(3)` `pi` `(4PI)/(3)` ANSWER :D

Discussion

12936.	The polar form of ((i)^(25))^(3) is....
Answer» `cos((pi)/(2))+I SIN((pi)/(2))` `cos pi+I sin pi` `cospi-sinpi` `cos((pi)/(2))-isin((pi)/(2))` ANSWER :D

Discussion

12937.	Find the equation at line passes from point of intersection at lines x+2y=5 and 3x+7y = 12. which is perpendicular to line 3x+4y=10.
Answer» ANSWER :`4X - 3Y + 2 = 0`

Discussion

12938.	Find the 9^(th) term of the G.P. whose 3^(rd) term is 18 and 6^(th) term is 486.
Answer» ANSWER :13122

Discussion

12939.	IFA and Bare independent eventsof a randomexperiment suchthatP( A nn B) = (1)/(6) andP(barAnn barB) = (1)/(3) , then P(A) is equalto
Answer» `(1)/(4)` `(1)/(3)` `(1)/(6)` `(2)/(3)` Answer :B

Discussion

12940.	If \|z_(1)\|=1(z_(1) ne -1) and z_(2)=(z_(1)-1)/(z_(1)+1) then show that the real part of z_(2) is zero.
Answer» ANSWER :`0+(2yi)/((x+1)^(2)+y^(2))`

Discussion

12941.	Find the derivative at x = 2 of the function f(x) = 3x.
Answer» ANSWER :3

Discussion

12942.	Which of the following are examples of the null set { y : yis a point common to any two parallel lines}
Answer» ANSWER :it is an EMPTY SET

Discussion

12943.	Out of 500 car owners investigated, 400 owned car A and200 owned car B, 50 owned both A and B cars. Is this data correct?
Answer» ANSWER :This is a CONTRADICTION DATA is INCORRECT.

Discussion

12944.	If tan(A+B)=p and tan(A-B)=q, then show that tan2A=(p+q)/(1-pq).
Answer» ANSWER :`(p+q)/(1-pq)`

Discussion

12945.	Which of the following statement is a conjuction?
Answer» RAM and Shayan are friends Both Ram and SHAYAM are tall. Both Ram and Shayam are enemies. None of the above Answer :D

Discussion

12946.	A tangent to the parabola y^(2)=16x makes an angle of 60^(@) with the x-axis. Find its point of contact.
Answer» ANSWER :`(4/3,8/(SQRT(3)))`

Discussion

12947.	For some constants a and b, find the derivative of (x-a)/(x-b)
Answer» ANSWER :`(a-b)/((x-b)^(2))`

Discussion

12948.	Write the following sets in the set-builder form : {5, 25, 125, 625}
Answer» ANSWER :`{ X : x = 5^(N), n∈N and 1 ≤ n ≤ 4}`

Discussion

12949.	Given statements in (a) and (b). Identify the statements given below as contrapositive or converse of each other. (b) If a quadrilateral is a parallelogram, then its diagonals bisect each other. (i) If the diagonals of a quadrilateral do not bisect each other, then the quadrilateral is not a parallelogram. (ii) If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.
Answer» ANSWER :(i) CONTRAPOSITIVE (II) CONVERSE

Discussion

12950.	Given statements in (a) and (b). Identify the statements given below as contrapositive or converse of each other. (a) If you live in Delhi, then you have winter clothes. (i) If you do not have winter clothes, then you do not live in Delhi. (ii) If you have winter clothes, then you live in Delhi.
Answer» ANSWER :(i) CONTRAPOSITIVE (II) CONVERSE

Discussion

Explore topic-wise InterviewSolutions in .

Domain of f(x)=sin^(-1)[2-4x^(2)] is ([.] denotes the greatest integer function)

If b= 3, c= 4 angle B = (pi )/(3)then number of triangles that can be constructed is

Are the following pair of sets equal ? Give reasons. A = {2, 3}, B ={x : x is solution of x^(2) + 5x + 6 = 0}

If f(x)=Sin^(-1)x+Cos^(-1)x, then(pi)/2 is the value of

If y=tan^(-1)""1/2+tan^(-1)b, (0 lt b lt 1) and 0 lt y le pi/4, then the maximum value of b is

If the lines 3x-y = 2 and x+2y = 3 are two diameters of a circle and if the circle passes through (2,0), find the equation of the circle.

Discuss the continuity of f(x) in [0,2] wheref(x) = {{:([cos pi x]", " x le 1),(| 2x - 3 |.[ x- 2]" ," x gt 1):} where [.] denotes the G.I.F.

Co - ordinates of the point in YZ plane are in the form of (a,y,z) where a in R - {0} .

if 1/(7!)+1/(9!) =x/(10!) then find x.

A die is thrown, find the probability of following events : A number less then 6 will appear.

If (alpha, beta) is the centroid of the triangle, whose sides are ax^(2)+2hxy+by^(2)=0 and lx+my=1, then show that (alpha)/(bl-hm)=(beta)/(am-hl)=(2)/(3(bl^(2)-2hlm+am^(2)))

The ortho centre of triangle formed by the points (2,1,5),(3,2,3), (4,0,4) is

Convert each of the complex number in the polar form: i

The sides of a Delta ^("le') ABCbe 8, 7, 6 and smallest angle is C then The length of altitude from vertex C is

If the distance from P to the points (2,3),(2,-3) are in the ratio 2:3 the find the locus of P.

The radius and height of a cylinder are measured as 5 cm and 10 cm respectively and there is an error of 0.02 cm in both the measurements. The approximate error in the volume is

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

Find the derivative of the function e ^(x) (x ^(2) + 1 )

Which term of the following sequences: 2, 2 sqrt2, 4…..is 128?

Find the angle in radian through which a pendulum swingsif its length is 75 cm and the tip describes an arc of length (i) 10 cm (ii) 15 cm (iii) 21cm.

If A = (3, 81) and f: A rarr B is a surjection defined by f(x)=log_(3)x then B=

.......... is the transform form of equation x^2-y^2-2x+2y=0 by shifting origin at (1,1)

Expandthe expression (x+1/x)^6

An open cylinder of given surface will have maximum volume if radius =

Evaluate the following limits in Exercises lim_(xtopi)(sin (pi-x))/(pi(pi-x))

List all the elements of the following sets : C= {x : The solution of x^(2)+5x+6=0}

Iff(x)={:(ax^(2)-b",",-1 ltxlt1 ),(1/(|x|)",","elsewhere"):}isdifferentiableat x = 1, then………..

In a triangle ABC, medians AD and BE are drawn.IF angle D=4, angle DAB=pi//6, angle ABE=pi//3 then the area of Delta ABC is

In triangleABC, lfloor(A) = pi/4 and tanB.tanC= P, then all possible value of P is:

Slope of line is non zero real number .

A and B are mutually exclusive event. If P(A)=(1)/(4),P(B)=(2)/(5) and P(AuuB)=(1)/(2).

If 2x^(2) - 3xy + y^(2) + x + 2y - 8= 0, then (dy)/(dx) is equal to

The range of f(x)=[|sin x|+|cos x|], where [.] denotes the greast integer function, is

Period of cos (x+ (x)/(3) + (x)/(3^2) + …..) is

The polar form of ((i)^(25))^(3) is....

Find the equation at line passes from point of intersection at lines x+2y=5 and 3x+7y = 12. which is perpendicular to line 3x+4y=10.

Find the 9^(th) term of the G.P. whose 3^(rd) term is 18 and 6^(th) term is 486.

IFA and Bare independent eventsof a randomexperiment suchthatP( A nn B) = (1)/(6) andP(barAnn barB) = (1)/(3) , then P(A) is equalto

If |z_(1)|=1(z_(1) ne -1) and z_(2)=(z_(1)-1)/(z_(1)+1) then show that the real part of z_(2) is zero.

Find the derivative at x = 2 of the function f(x) = 3x.

Which of the following are examples of the null set { y : yis a point common to any two parallel lines}

Out of 500 car owners investigated, 400 owned car A and200 owned car B, 50 owned both A and B cars. Is this data correct?

If tan(A+B)=p and tan(A-B)=q, then show that tan2A=(p+q)/(1-pq).

Which of the following statement is a conjuction?

A tangent to the parabola y^(2)=16x makes an angle of 60^(@) with the x-axis. Find its point of contact.

For some constants a and b, find the derivative of (x-a)/(x-b)

Write the following sets in the set-builder form : {5, 25, 125, 625}

Given statements in (a) and (b). Identify the statements given below as contrapositive or converse of each other. (a) If you live in Delhi, then you have winter clothes. (i) If you do not have winter clothes, then you do not live in Delhi. (ii) If you have winter clothes, then you live in Delhi.