14949 + Interview Questions in Maths in Class 11 Page 1 InterviewSolution

1.	Let f:RtoR, defined by f(x)={{:(1",",ifx""inQ),(-1",",ifx""inQ):} Find (i) f(1)/(2) (ii) f(0.34) (iii) f(sqrt2) (iv) f(pi) (v) range(f) (vi) f^(-1)(1) (vii) f^(-1){1}
Answer» Solution :Since each one of `(1)/(2)` and 0.34 is rational, we have (i) `f((1)/(2))=1AND(II)f(0.34)=1`. Since each one of `sqrt2andphi` is IRRATIONAL, we have (iii) `f(sqrt2)=-1and(IV)f(pi)=-1`. (v) range `(f)={f(x):x""inR}` `={f(x):x""INQ}uu{f(x):x""inR-Q}={1,-1}`. (vi) `f^(1){1}={x:f(x)=1}=Q`. (vii) `f^(1){-1}={x:f(x)=-1}=(R-Q)`.

Discussion

2.	The reflection of the point a in the plane vecr.vecn=q is
Answer» `veca + ((VECQ - veca .VECN))/(\|vecn\|)` `veca + 2 (((vecq - veca.vecn))/(\|vecn\|^(2))) vecn` `veca + (2 (vecq + veca.vecn))/(\|vecn\|) vecn` `veca- (2 ( vecq - veca.vecn))/(\|vecn\|)` ANSWER :B

Discussion

3.	Ifsin y = x sin (y - a) and (dy)/(dx) = A/(1 + x^2 - 2x cos a) then the value of A is
Answer» `2` `COS a` `-SIN a` `-2` ANSWER :C

Discussion

4.	A point moves so that the differerence of the squares of its distance from the x-axis and the y-axis is constant. Find the equation of its locus.
Answer» ANSWER :`X^(2) - y ^(2) =a `

Discussion

5.	Find r(x,y) if cov (x,y) =-16.5, var(x)=2.25 and sigma_(y)=12
Answer» ANSWER :`-0.92`

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6.	For set {(a, b) : 2a^(2)+3b^(2)= 35, a, b in Z} the number of its elements is………..
Answer» 2 4 8 12 Answer :C

Discussion

7.	If the rate of change in the perimeter of a square is K times the rate of change in its side then k =
Answer» 2 3 4 1 Answer :C

Discussion

8.	The locus represented by the equation x^(2)+y^(2)+4x+2y-8=0 is
Answer» hyperbola circle ellipse parabola Answer :4

Discussion

9.	Identify the Quantifiers in the following statements: For all real numbers x with xgt3,x^(2) is greater than 9.
Answer» ANSWER :UNIVERSAL QUANTIFIER is USED

Discussion

10.	If A, B C are three events associated with a random experiment, prove that P(AcupBcupC)=P(A)+P(B)+P(C)-P(AcapB)-P(AcapC)- P(BcapC)+ P(AcapBcapC).
Answer» ANSWER :` = 1/10`

Discussion

11.	Find the radius and hence the area of the circle x^2+y^2-6x+12y+15 = 0
Answer» SOLUTION :`x^2+y^2-6x+12y-15 = 0`

Discussion

12.	The sum of first n even natural numbers is k times the sum of first n odd natural numbers then k= …….
Answer» `(1)/(N)` `(n-1)/(n)` `(n+1)/(2N)` `(n+1)/(n)` ANSWER :D

Discussion

13.	If two lines in 2x^(2)+2(k-1)xy-3y^(2)=0 are equally inclined to axes then k=
Answer» 0 1 2 `-1` ANSWER :B

Discussion

14.	If (sin alpha)x^(2)-2x+bge2 for all the real values of x le1 and alpha in (0,pi//2)uu(pi/2,pi) then the possible real values of b is /are
Answer» 2 3 4 5 Answer :C::D

Discussion

15.	If A=(2sinx)/(sin3x)+(tanx)/(tan3x), B=cos10^(@)cos30^(@)cos50^(@)cos70^(@) C=tan20^(@)tan40^(@)tan60^(@)tan80^(@) Then the ascending order of A,B,C is
Answer» A,B,C B,C,A B,A,C C,A,B Answer :C

Discussion

16.	If the axes are rotated through an angle30^(0) then find the coordinates of (-2,4) in the new system.
Answer» ANSWER :`(2-sqrt,1+2 SQRT3)`

Discussion

17.	Exhibit graphically the solution set of the lineat inequations :
Answer» Solution :(I ) First, we draw the GRAPH of`x + 2Y le 10 ` Consider the linex+ 2y 10 Clearly, the points A(0, 5) and B(l0, 0) satisfy, x + 2y = 10 Then, line AB represents x + 2y = 10. Clearly, (0, 0) satisfies the inequation ` x+ 2y le 10 ` THUS, the line AB and PART of the plane containing 0(0, 0) represent the solution set of `x + 2y le10` (ii) Next, we draw the graph of `x + y le 6`. Consider the line, x + y = 6. Clearly, the points C(O, 6) and D(6, 0) satisfy x + y = 6. So, line CD represents x + y = 6. Clearly, (0, 0) satisfies the inequation, `x + y le 6` So, the line CD and part of the plane containing 0(0, 0) represent the solution set of `x + y le 6` (iii) Next, we draw the graph of `x le 4` We know that x = 4 is the line EF parallel to the y-axis and passing through the point E(4, 0). Clearly, (0, 0) satisfies the inequation, `x le 4` Thus, the line EF and part of the plane containing 0(0, 0) represent the solution set of `x le 4` (IV)`x ge 0 ` is represented by the y-axis and the plane on its right. (v)`y ge 0 ` is represented by the x-axis and the plane above the x-axis. The intersection of all these planes is the shaded part, which together with its boundary represents the solution of the given systemof inequations.

Discussion

18.	If msintheta=nsin(theta+2alpha), then prove that tan(theta+alpha)cotalpha=(m+n)/(m-n).
Answer» ANSWER :`(m+n)/(m-n)`

Discussion

19.	The approximate value of (1.0002)^(3000) is
Answer» only I only II both I and II neither I nor II Answer :B

Discussion

20.	(1-tan^(2)(45^(@)-theta))/(1+tan^(2)(45^(@)-theta))=
Answer» `sin 2THETA` `COS 2 theta` `tan 2theta` `cot2 theta` ANSWER :A

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21.	Find the eccentricity, vertices, foci, equations to the directrices, length of transverse axis and conjugate axis and the length of latus rectum of the hyperbola 3x^2-y^2=4
Answer» SOLUTION :`2, [+-2/sqrt3,0], [+-4/sqrt3,0], sqrt3x-1=0` and `sqrt3x+1=0, 4/sqrt3,4,4sqrt3`

Discussion

22.	Find the domains of the following functionsf(x) = ( 1)/( [x]) ( [ ] denotes the GIF)
Answer» ANSWER :R-[0,1)

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23.	Two anglesofa trianglesare (pi)/(6)and (pi)/(4)includedside issqrt3+ 1cmthen areaof triangles is
Answer» ` (sqrt3+1)/(2 ) CM ^(2) ` ` (sqrt3-1)/( 2sqrt 2 ) cm ^(2) ` ` (sqrt3+1)/( 2sqrt 2 ) cm ^(2) ` ` (sqrt3-1)/( 2sqrt 2 ) cm ^(2) ` ANSWER :A

Discussion

24.	Two dice, one black and one white arerolled. The probability that sum of two no is7 and no. of black greater than the no. ofwhite is
Answer» `(1)/(12)` `(1)/(6)` `(1)/(4)` `(1)/(2)` Answer :A

Discussion

25.	Two persons go in a railways carriage where there are 6 vacant seats. In how manydifferent ways can they seat themselves?
Answer» ANSWER :` 30`

Discussion

26.	Radius of the sphere is _____ if its end points of diameter are (3, 4, -1) and (-1, 2, 3).
Answer» 2 3 6 7 Answer :B

Discussion

27.	Therangeof sin^(2) x+4 sinx + 5lies in
Answer» `[-2,10]` `[10,15]` `[5,10]` `[2,10]` ANSWER :1

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28.	Find a unit vector perpendicular to the plane containing the vector bar(a) = 4bar(i) + 3bar(j) - bar(k), bar(b) = 2bar(i) - 6bar(j) - 3bar(k)
Answer» ANSWER :`+- ((-3 bar(i)+ 2BAR(j)- 6 bar(K))/(7))`

Discussion

29.	Find the most general value of theta that satisfying both the equations tan x = (-1)/(sqrt(3)), Sec x = (2)/(sqrt(3))
Answer» ANSWER :`2N PI - (pi)/(6)`

Discussion

30.	Evaluate : cos ""(pi)/(8) sin ""(pi)/(8)
Answer» ANSWER :`(1)/(2SQRT2)`

Discussion

31.	If f(x)= x^(3)+3x^(2)+4x + a sin x +bcos x AA x in Ris an injection then the greatest value of a^(2)+ b^(2)is
Answer» 1 2 `SQRT(2)` `2sqrt(2)` ANSWER :A

Discussion

32.	A particle moves along a line by s = (t^(3))/(3) - 3t^(2) + 8t then the distance travelled by the particle before if first comes to rest is
Answer» 20 20/3 3 60 Answer :B

Discussion

33.	If bar a and bar b are two unit vectors inclined at an angle alpha to each other then match the following lists The correct match is
Answer» a,B,C b,c,a a,c,a c,a,b Answer :A

Discussion

34.	Let bara= 2bari+3barj+k,barb = 4bari+barj and bari = bari - 3barj-bark. " Find vector " barr " such that " barr.bara = 9, barr .barb = 7 and barr .barc =6.
Answer» `bari+3barj+2bark` `bari+3barj-2bark` `bari-2barj+3bark` `bari+2barj+5bark` ANSWER :B

Discussion

35.	If bara,barb are two units vectors inclined at an angle pi/3 then {axx(barb+baraxxbarb)}.barb=
Answer» `(-3)/4` `1/4` `3/4` `1/2` ANSWER :A

Discussion

36.	IfA = {:[ ( 1,a) , ( 0,1)]:}, then computeA^(4)
Answer» ANSWER :` A^(4) = {:[ ( 1,4a) , ( 0,1)]:}`

Discussion

37.	For non-zero vectors bara,barb,barc,abs(baraxxbarb.barc)=abs(bara)abs(barb)abs(barc) holds if and only if
Answer» `bara.barb=barb.barc=barc.bara=0` `bara.barb+barb.barc+barc.bara=0` `bara+barb+barc=0` `[BARABARBBARC]=0` ANSWER :A

Discussion

38.	An integer is chosen at random from first 200 natural numbers. What is the probability that the integer chosen is divisible by 6 or 8 ?
Answer» ANSWER :`(49)/(200)`

Discussion

39.	Find the equation of lines passing through (1, 2) and making angle 30° with Y- axis. Thinking Process : Equation of a line passing through the point (x_(1) , y_(1) ) and having slope m is y-y_1 = m( x- x_1).
Answer» ANSWER :`sqrt(3) X - y + 2 - sqrt(3) = 0`

Discussion

40.	The setof all real numbers satisfying e^((1/x - 1)) lt 1 is
Answer» `(0, oo)` `(-oo,0) UU (1, oo)` `(-oo, oo)` `(0, 1)` ANSWER :B

Discussion

41.	If A, B and C are three sets such that A cup B = A cup C and A cap B = A cap C, then prove that B = C.
Answer»

Discussion

42.	If y = (sinx + cosecx)^(2) + (cos x + sec x)^(2).then the minimum value of y,AA x in R is
Answer» 7 3 9 0 Answer :C

Discussion

43.	The radius of an air bubble is increasing at the rate of 1/2 cm/sec. At what rate is the volume of the bubble increasing when the radius is 1 cm?
Answer» ANSWER :`2PI CM^(3)//SEC`

Discussion

44.	How many words, with or without meaning , can be made from the letters of the word MONDAY, assuming that no letters is repeated , if (i) 4 letters are used at a time (ii) all letters are used at a time
Answer» Answer :(i) 360, (II) 720, (iii) 240

Discussion

45.	The maximum value of the funtion f(x)=2x^(3)-15x^(2)+36x-48 on the set A={x\|x^(2)+20le9x} is
Answer» ANSWER :7

Discussion

46.	Consider the points A (2,3) and B (6,5) Find the equation of the perpendicular bisector of the line segment AB
Answer» SOLUTION :`X - 2Y - 6 = 0`

Discussion

47.	The product of perpendiculars from origin to the pair of lines 12x^(2)+25xy+12y^(2)+10x+11y+2=0
Answer» `(1)/(25)` `(2)/(25)` `(3)/(25)` `(4)/(25)` Answer :B

Discussion

48.	Find theroots of x^(2) + x + 1/sqrt(2)=0
Answer» ANSWER :`(-1 +-SQRT((2sqrt(2)-1)i))/2`

Discussion

49.	Evaluate Lt_(xtooo)((x^(2)+ax+b)/(x^(2)+cx+d))^(x) where a, b, c, d are constants.
Answer» ANSWER :`E^(a-c)`

Discussion

50.	A and B are two sets (A - B) cup (B - A) cup (A cap B)="……….."
Answer» `A CUP B` `A CAP B` `A` `B'` ANSWER :A

Discussion

Explore topic-wise InterviewSolutions in .

Let f:RtoR, defined by f(x)={{:(1",",ifx""inQ),(-1",",ifx""inQ):} Find (i) f(1)/(2) (ii) f(0.34) (iii) f(sqrt2) (iv) f(pi) (v) range(f) (vi) f^(-1)(1) (vii) f^(-1){1}

The reflection of the point a in the plane vecr.vecn=q is

Ifsin y = x sin (y - a) and (dy)/(dx) = A/(1 + x^2 - 2x cos a) then the value of A is

A point moves so that the differerence of the squares of its distance from the x-axis and the y-axis is constant. Find the equation of its locus.

Find r(x,y) if cov (x,y) =-16.5, var(x)=2.25 and sigma_(y)=12

For set {(a, b) : 2a^(2)+3b^(2)= 35, a, b in Z} the number of its elements is………..

If the rate of change in the perimeter of a square is K times the rate of change in its side then k =

The locus represented by the equation x^(2)+y^(2)+4x+2y-8=0 is

Identify the Quantifiers in the following statements: For all real numbers x with xgt3,x^(2) is greater than 9.

If A, B C are three events associated with a random experiment, prove that P(AcupBcupC)=P(A)+P(B)+P(C)-P(AcapB)-P(AcapC)- P(BcapC)+ P(AcapBcapC).

Find the radius and hence the area of the circle x^2+y^2-6x+12y+15 = 0

The sum of first n even natural numbers is k times the sum of first n odd natural numbers then k= …….

If two lines in 2x^(2)+2(k-1)xy-3y^(2)=0 are equally inclined to axes then k=

If (sin alpha)x^(2)-2x+bge2 for all the real values of x le1 and alpha in (0,pi//2)uu(pi/2,pi) then the possible real values of b is /are

If A=(2sinx)/(sin3x)+(tanx)/(tan3x), B=cos10^(@)cos30^(@)cos50^(@)cos70^(@) C=tan20^(@)tan40^(@)tan60^(@)tan80^(@) Then the ascending order of A,B,C is

If the axes are rotated through an angle30^(0) then find the coordinates of (-2,4) in the new system.

Exhibit graphically the solution set of the lineat inequations :

If msintheta=nsin(theta+2alpha), then prove that tan(theta+alpha)cotalpha=(m+n)/(m-n).

The approximate value of (1.0002)^(3000) is

(1-tan^(2)(45^(@)-theta))/(1+tan^(2)(45^(@)-theta))=

Find the eccentricity, vertices, foci, equations to the directrices, length of transverse axis and conjugate axis and the length of latus rectum of the hyperbola 3x^2-y^2=4

Find the domains of the following functionsf(x) = ( 1)/( [x]) ( [ ] denotes the GIF)

Two anglesofa trianglesare (pi)/(6)and (pi)/(4)includedside issqrt3+ 1cmthen areaof triangles is

Two dice, one black and one white arerolled. The probability that sum of two no is7 and no. of black greater than the no. ofwhite is

Two persons go in a railways carriage where there are 6 vacant seats. In how manydifferent ways can they seat themselves?

Radius of the sphere is _____ if its end points of diameter are (3, 4, -1) and (-1, 2, 3).

Therangeof sin^(2) x+4 sinx + 5lies in

Find a unit vector perpendicular to the plane containing the vector bar(a) = 4bar(i) + 3bar(j) - bar(k), bar(b) = 2bar(i) - 6bar(j) - 3bar(k)

Find the most general value of theta that satisfying both the equations tan x = (-1)/(sqrt(3)), Sec x = (2)/(sqrt(3))

Evaluate : cos ""(pi)/(8) sin ""(pi)/(8)

If f(x)= x^(3)+3x^(2)+4x + a sin x +bcos x AA x in Ris an injection then the greatest value of a^(2)+ b^(2)is

A particle moves along a line by s = (t^(3))/(3) - 3t^(2) + 8t then the distance travelled by the particle before if first comes to rest is

If bar a and bar b are two unit vectors inclined at an angle alpha to each other then match the following lists The correct match is

Let bara= 2bari+3barj+k,barb = 4bari+barj and bari = bari - 3barj-bark. " Find vector " barr " such that " barr.bara = 9, barr .barb = 7 and barr .barc =6.

If bara,barb are two units vectors inclined at an angle pi/3 then {axx(barb+baraxxbarb)}.barb=

IfA = {:[ ( 1,a) , ( 0,1)]:}, then computeA^(4)

For non-zero vectors bara,barb,barc,abs(baraxxbarb.barc)=abs(bara)abs(barb)abs(barc) holds if and only if

An integer is chosen at random from first 200 natural numbers. What is the probability that the integer chosen is divisible by 6 or 8 ?

Find the equation of lines passing through (1, 2) and making angle 30° with Y- axis. Thinking Process : Equation of a line passing through the point (x_(1) , y_(1) ) and having slope m is y-y_1 = m( x- x_1).

The setof all real numbers satisfying e^((1/x - 1)) lt 1 is

If A, B and C are three sets such that A cup B = A cup C and A cap B = A cap C, then prove that B = C.

If y = (sinx + cosecx)^(2) + (cos x + sec x)^(2).then the minimum value of y,AA x in R is

The radius of an air bubble is increasing at the rate of 1/2 cm/sec. At what rate is the volume of the bubble increasing when the radius is 1 cm?

How many words, with or without meaning , can be made from the letters of the word MONDAY, assuming that no letters is repeated , if (i) 4 letters are used at a time (ii) all letters are used at a time

The maximum value of the funtion f(x)=2x^(3)-15x^(2)+36x-48 on the set A={x|x^(2)+20le9x} is

Consider the points A (2,3) and B (6,5) Find the equation of the perpendicular bisector of the line segment AB

The product of perpendiculars from origin to the pair of lines 12x^(2)+25xy+12y^(2)+10x+11y+2=0

Find theroots of x^(2) + x + 1/sqrt(2)=0

Evaluate Lt_(xtooo)((x^(2)+ax+b)/(x^(2)+cx+d))^(x) where a, b, c, d are constants.

A and B are two sets (A - B) cup (B - A) cup (A cap B)="……….."