28278 + Interview Questions in Maths in Class 12

1.	If the minor axis of an ellipse subtends an angle 90^(@) at each focus then the eccentricity of the ellipse is
Answer» ANSWER :`(1)/(SQRT(2))`

Discussion

2.	Evaluate the following integrals. int(x^(8))/(1+x^(18))dx
Answer» Answer :`(1)/(9)tan^(-1)(x^(9))+C`

Discussion

3.	If veca, vecb, cecc are non-coplanar vectors and lamda is a real number, then [lamda (veca + vecb) lamda ^(2) vecb lamda vecc]=[veca vecb + vecc vecb] for :
Answer» no value of `lamda` eactly ONE value of `lamda` ecactly TWO VALUES of `lamda` EXACTLY three values of `lamda.` ANSWER :A

Discussion

4.	Prove that if the function f(x) is continuous on the interval (a, b) and x_1, x_2, ..., x_n, are any values from this open interval, then we can find among them a number epsi such that f(epsi)=1/n [f(x_1)+f(x_(2)+....+f(x_n)]
Answer» ANSWER :`[F(x_(1))....,f(x_(N))]`

Discussion

5.	The normal to the curve at P(x, y) meets the x-axis at G. If the distance of G from the origin is twice the abscissa of P, then the curve is
Answer» ELLIPSE PARABOLA CIRCLE HYPERBOLA or ellipse Answer :D

Discussion

6.	If overline(a), overline(b), overline(c) are three coplanar vectors, the \|[overline(a), overline(b), overline(c)], [overline(a)overline(a), overline(a)overline(b), overline(a)overline(c)], [overline(b)overline(a), overline(b)overline(b), overline(b)overline(c)]\|=
Answer» `-1` `OVERLINE(0)` `1` `0` ANSWER :B

Discussion

7.	Let be a binary operation on the set Q of rational numbers as followsab=a+ab. Is the binary operation commutative and associative ?
Answer» Solution :`a(BC)=a(b^2+c^2)` `=a^2+(b^2+c^2)^2` `(a+b)+c=(a^2+b^2)+c` `=a^2+b^2+(c^2)^2` `=a^2+b^2+c^4` `THEREFORE a(bc)ne (ab)c` `therefore ` is not associative

Discussion

8.	AB and CD are equal and parallel chords of a circle. KN is a diameter of the circle, and K is equidistant from A and B. Then bar(KA) + bar(KB) + bar(KC) + bar(KD) =
Answer» `BAR(KN)` 2`bar(KN)` 3`bar(KN)` 4`bar(KN)` Answer :B

Discussion

9.	For events E and F if P(E) le P(F)and P(E cap F) gt 0 then …………
Answer» E OCCURS `RIGHTARROW` F occurs F occurs `Rightarrow` E occurs E does not occurs `Rightarrow` F does not occurs None of above is valid Answer :D

Discussion

10.	If f(x)={:{(x,x inQ),(0,x !inQ):}andg(x)={:{(x, !inQ),(0,x inQ):} then (f-g) will be :
Answer» one-one onto one-one into many-one onto many-one into Answer :A

Discussion

11.	If \|{:(,b+c,c+a,a+b),(,c+a,a+b,b+c),(,a+b,b+c,c+a):}\|ge 0, "where a ,b,c,"inR,"then"(a+b)/(c)"is"
Answer» ANSWER :2

Discussion

12.	Find dy/dx of x=2at^2 , y=at^4
Answer» SOLUTION :`dy/dt=4AT^3dx/dt=4atdy/dx=(dy/dt)/(dx/dt)=(4at^3)/(4at)=t^2`

Discussion

13.	Three numbers are chosen at random (without replace ment) from the numbers 1, 2,... 20. The probability that the numbers are not consecutive are
Answer» `3/190` `7/190` `171/190` `187/190` ANSWER :D

Discussion

14.	If (1+x)(1+x+x^2)(1+x+x^2+x^3)……(1+x+x^2+……+x^(n-1)) = a_0 + a_1x + a_2x^2 +…….+a_m x^mthen a_0 +a_1 + …..+ a_m =
Answer» N! 2N! 3N! 4N! ANSWER :A

Discussion

15.	int_(log_t2)^x (dt)/sqrt(e^t-1)=pi/6impliesx=
Answer» `2.log_e 2` `3. log_e 2` `4. log_e 2` `8. log_e 2` ANSWER :A

Discussion

16.	A conical vessel whose height is 10 meters and the radius of whose base is half that of the height is being filled with a liquid at a uniform rate of 1.5m^(3)//"min". Find the rate which the level of the water in the vessel is rising when it is 3m below the top of the vessel.
Answer» ANSWER :`(6)/(49 PI)` m/min

Discussion

17.	Coefficient of x^18 in (x^2 + 1)(x^2 + 4)(x^2 + 9)….(x^2 + 100) is
Answer» `-385` `385` `285` `-285` ANSWER :B

Discussion

18.	If n is a positive integer then 49^n + 16n-1 is divided by
Answer» 64 56 72 83 Answer :A

Discussion

19.	Evaluate the following:lim_(ntoinfty) ((sqrtn-1)/(sqrtn+1))
Answer» SOLUTION :`lim_(ntoinfty) ((sqrtn-1)/(sqrtn+1))=lim_(ntoinfty)(1-1/(sqrtn))/(1+1/sqrtn)=1`

Discussion

20.	For theta in (0, (pi)/(2)) "sech"^(-1) (cos theta) is equal to
Answer» `log\|tan ((X)/(6) + (THETA)/(2))\|` `log\|tan ((pi)/(3) + (theta)/(2))\|` `log\|tan ((pi)/(4) + (theta)/(2))\|` `log\|tan((pi)/(4) - (theta)/(2))\|` Answer :c

Discussion

21.	Which of the following is/are redox reaction
Answer» `KCl+K_(2)Cr_(2)O_(7)+con. H_(2)SO_(4)rarrCrO_(2)Cl_(2)+K_(2)SO_(4)+H_(2)O` `K_(2)Cr_(2)O_(7)+H_(2)O_(2)+con. H_(2)SO_(4)+rarrK_(2)SO_(4)+CrO_(5)+H_(2)O` `K_(2)Cr_(2)O_(7)+H_(2)O_(2)+dil. H_(2)SO_(4)rarrK_(2)SO_(4)+Cr_(2)(SO_(4))_(3)+7H_(2)O+3O_(2)` `K_(2)Cr_(2)O_(7)+2KOHrarr2K_(2)CrO_(4)+H_(2)O` ANSWER :abc

Discussion

22.	I : sum_(k=1)^(6)[sin((2kpi)/(7))-icos((2kpi)/(7))]=iII : sum_(r=1)^(8)[sin((2pir)/(9))+icos((2pir)/(9))]=iWhich of the above statements are true
Answer» A) only I B) only II C) Both I and II D) neither I nor II ANSWER :B

Discussion

23.	y=Ae^(x)+Be^(2x)+Ce^(3x) satisfies the differential equation
Answer» `y_(3) - 6y_(2) + 11 y_(1) - 6Y = 0` `y_(3) + 6y_(2) + 11 y_(1) + 6y = 0` `y_(3) + 6y_(2) - 11 y_(1) + 6y = 0` `y_(3) - 6y_(2) - 11 y_(1) + 6y = 0` Answer :A

Discussion

24.	Findthe values ofx,y and z so that the vectors veca=xhati+2hatj+zhatkandvecb=2hati+yhatj+hatkare equal .
Answer» ANSWER :X = 2, y = 2, Z = 1

Discussion

25.	For the probability density function f(x) ={(2e""^(-2x),x gt0),(0,xlt=0):} find F(2)
Answer» ANSWER :`(E^(4)-1)/e^(4)`

Discussion

26.	[(cos alpha-cos beta)+i(sin alpha-sinbeta)]^n+[(cos alpha-cos beta)-i(sin alpha-sin beta)]^n=
Answer» `2^(n+1).sin^n((alpha-beta)/(2))COS[(pi/2+(alpha+beta)/(2))]` `2^(n-1).sin^n((alpha-beta)/(2))cos[(pi/2+(alpha+beta)/(2))]` `2^(n+1).sin^n((alpha+beta)/(2))cos[(pi/2+(alpha-beta)/(2))]` `2^(n-1).sin^n((alpha+beta)/(2))cos[(pi/2+(alpha-beta)/(2))]` ANSWER :A

Discussion

27.	If C_(r ) denotes the binomial coefficient .^(n)C_(r+) then (-1) C_(0)^(2) + 2C_(1)^(2) + 5C_(2)^(2) + ….. + (3n - 1) C_(n)^(2) is equal to
Answer» `(3n - 2) .^(2n)C_(N)` `((3n - 2)/(2)) .^(2n)C_(P)` `(5 + 3n) .^(2nC_(n)` `((3n - 5)/(2)) .^(2n)C_(a + 1)` Answer :B

Discussion

28.	Let A={1,3,5} and B = {x:x is an odd natural number less than 6}. Then, which of the following are true? I. AsubB II. BsubA III. A=B IV. "AB"
Answer» I and II are TRUE I and III are true I, II and III are true I, II and IV are true ANSWER :C

Discussion

29.	If the probability of choosing an integer k out of '2m' integers 1,2,3,….2m is inversely proportional to k^(4) ( 1 le k le 2m), then the probability that chosen number is odd , is .
Answer» `GT 1` `gt 1//2` `=1//2` `LT 1//3`. ANSWER :B

Discussion

30.	Determine the unknown coordinates of theT(x,0,z) in y"-axis"
Answer» SOLUTION :x=0,z=0,

Discussion

31.	Let x_(1), x_(2),…,x_(n) be n observations such that sum x_(i)^(2) = 400 and sum x_(i) = 80. Then a possible value of n among the following is
Answer» 15 18 9 12 Answer :B

Discussion

32.	Integration of some particular functions : int(x-2)/(x^(2)-4x+5)dx=......+c
Answer» `LOG\|X^(2)-4x+5\|` `log sqrt(x^(2)-4x+5)` `(1)/(2)(x^(2)-4x+5)^(2)` `log((x-3)/(x-1))` ANSWER :B

Discussion

33.	If two concentric elipse be such that the foci of one be on the and if e and e' be their eccentricities. Prove that the angle between their axes is cos^(-1){(sqrte^(2)+e'^(2)-1)/(ee')}
Answer» ANSWER :A::B::C

Discussion

34.	If the mappings f and g are given be f = {(1,2),(3,5),(4,1)} and g = {(2,3),(5,1),(1,3)}, write fog .
Answer» SOLUTION :N/A

Discussion

35.	Differentiate the functions given in Exercises 1 to 11 w.r.t. x. (log x)^(cos x)
Answer» ANSWER :`(LOG X)^(COS x) [(cos x)/(x log x)-SIN x log(log x)]`

Discussion

36.	IF overlinea,overlineb,overlinec are non-coplanar, then prove that the points with position vectors 2overlinea+3overlineb-overlinec,overlinea-2overlineb+3overlinec,3overlinea+4overlineb-2overlinec,overlinea-6overlineb+6overlinec are coplanar.
Answer» <P> ANSWER :P,Q,R are COLLINEAR

Discussion

37.	Write down and simplify Find the 4th term the end in (2a + 5b)^8
Answer» ANSWER :`""^8C_(5) 2^(3) 5^5 a^3 b^5`

Discussion

38.	Evalute the following integrals int (sqrt(3x -2)) dx
Answer» ANSWER :`(2)/(9)(3x-2)^(3//2)+C`

Discussion

39.	d/dx [sqrt(3x +4)]
Answer» 1/`2[sqrt(3x +4)]` 1/`[sqrt(3x +4)]` 3/`2[sqrt(3x +4)]` 3/`[sqrt(3x +4)]` ANSWER :C

Discussion

40.	Let alpha ne 1 be a real root of the equation x^(3) - ax^(2) + ax - 1 = 0, where a ne - 1 is a real number, then a root of this equation, among the following , is :
Answer» `alpha^2` `-1/(alpha^2)` `1/alpha` `(1)/(alpha^2)` ANSWER :C

Discussion

41.	Let p in IR, then the differential equation of the family of curves y=(alpha +beta x)3e^(px), where alpha,beta are arbitary constants , is
Answer» `y^(n)+4py^(1)+p^(2)y=` `y^(n)-2py^(1)+p^(2)y=0` `y^(n)+2py^(1)-p^(2)y=0` `2^(in)+2py^(1)+p^(2)y=0`. Answer :B

Discussion

42.	The solution of(dy)/(dx) + (x (1+y^(3)))/(y^(2) (1 + x^(2))) = 0 is
Answer» `(1 + X^(2))^(3) (1 + y^(3))^(2) = C` `(1 -x^(2))^(3) (1 + y^(3))^(2) = c` `(1 + x^(2))^(3) (1 -y^(3))^(2) = c` `(1 -x^(2))^(3) (1-y^(3))^(2) =c` Answer :A

Discussion

43.	Prove that : \|veca + vecb\|le\|veca\|+\|vecb\|.
Answer» Solution : Let ABC be the triangle where `vec(AB) = VECA. vec(BC) = vecb` Then `vec(AC) = veca=vecb` Now `\|veca\| = AB, \|vecb\| = BC` and `\|veca+vecb\| = AC` In the triangle ABC, `AC `implies \|veca+vecb\|<\|veca\|+\|vecb\|` Now AC = AB+BC when A,B,C LIE on a straight line A,B,C are collinear. Hence `\|veca+vecb\| = \|veca\|+\|vecb\|` When `veca` and `vecb` are like collinear vectors or ZERO vectors.

Discussion

44.	Prove that A nn(B uu C) =(A nn B) uu (A nn C)
Answer» SOLUTION :Let `X in A NN (B uu C) `` ` ` ``:. A nn (B UUC)=(A nn B) uu (A nn C)`

Discussion

45.	S and T are the foci of an ellipse and B is one end of the minor axis. IF STB is an equilateral traingle , then find the eccentricity of the ellipse.
Answer» ANSWER :`1/2`

Discussion

46.	If \|{:(-1,7,0),(2,1,-3),(3,4,1):}\|=A" then"\|{:(13,-11,5),(-7,-1,25),(-21,-3,15):}\| is
Answer» `A^2` `A^2-A+I^3` `A^2-3A+I_3` `3A^2+5A-4I_3` ANSWER :A

Discussion

47.	Let n in N which one of the following is true?
Answer» `47^(n) + 16n-1` is divisible by 4 `2(4^(2n+1))-3^(3n+1)` is divisible by 9 `4^(n) -3n-1` is divisible by 11 `3(5^(2n+1)) + 2^(3n+1)` is divisible by 17 Answer :D

Discussion

48.	Find the area of a parallelogram whose adjacent sides are given by the vectors vec(a)=3hati+5hatj-2hatk and vec(b)=2hati+hatj+3hatk.
Answer» `(1)/(2)SQRT(507)` `sqrt(387)` `sqrt(507)` 25 Answer :C

Discussion

49.	A company producing soft drinks has a contract which requires a minimum of 80 units of chemical A and 60 units of chemical B to go in each bottle of the drink. The chemicals are available in a prepared mix from two different suppliers.Suppleer X has a mix of 4 units of A and 2 units of B that costs Rs.10, and the supplier Y has a mix of 1 unit of A and 1 unit of B that costs Rs4. How many mixes from X and Y should the company purchase to honour the contract requirement and yet minimize the cost ?
Answer» SOLUTION :Let the COMPANY purchase X mixes from X and y mixes from Y. Then, minimize `Z=10x+4y,` SUBJECT to the CONSTRAINTS `xge0,yge0,4x+yge80and2x+3yge60.`

Discussion

50.	If f(x)=(1+2x)^(frac[1][x]),xne0 is continuous at x=0, then what is the value of f(0) ?
Answer» Ex-situ conservation In-situ conservation in VITRO conservation in VIVO conservation Answer :B

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

If the minor axis of an ellipse subtends an angle 90^(@) at each focus then the eccentricity of the ellipse is

Evaluate the following integrals. int(x^(8))/(1+x^(18))dx

If veca, vecb, cecc are non-coplanar vectors and lamda is a real number, then [lamda (veca + vecb) lamda ^(2) vecb lamda vecc]=[veca vecb + vecc vecb] for :

Prove that if the function f(x) is continuous on the interval (a, b) and x_1, x_2, ..., x_n, are any values from this open interval, then we can find among them a number epsi such that f(epsi)=1/n [f(x_1)+f(x_(2)+....+f(x_n)]

The normal to the curve at P(x, y) meets the x-axis at G. If the distance of G from the origin is twice the abscissa of P, then the curve is

If overline(a), overline(b), overline(c) are three coplanar vectors, the |[overline(a), overline(b), overline(c)], [overline(a)*overline(a), overline(a)*overline(b), overline(a)*overline(c)], [overline(b)*overline(a), overline(b)*overline(b), overline(b)*overline(c)]|=

Let ** be a binary operation on the set Q of rational numbers as followsa**b=a+ab. Is the binary operation commutative and associative ?

AB and CD are equal and parallel chords of a circle. KN is a diameter of the circle, and K is equidistant from A and B. Then bar(KA) + bar(KB) + bar(KC) + bar(KD) =

For events E and F if P(E) le P(F)and P(E cap F) gt 0 then …………

If f(x)={:{(x,x inQ),(0,x !inQ):}andg(x)={:{(x, !inQ),(0,x inQ):} then (f-g) will be :

If |{:(,b+c,c+a,a+b),(,c+a,a+b,b+c),(,a+b,b+c,c+a):}|ge 0, "where a ,b,c,"inR,"then"(a+b)/(c)"is"

Find dy/dx of x=2at^2 , y=at^4

Three numbers are chosen at random (without replace ment) from the numbers 1, 2,... 20. The probability that the numbers are not consecutive are

If (1+x)(1+x+x^2)(1+x+x^2+x^3)……(1+x+x^2+……+x^(n-1)) = a_0 + a_1x + a_2x^2 +…….+a_m x^mthen a_0 +a_1 + …..+ a_m =

int_(log_t2)^x (dt)/sqrt(e^t-1)=pi/6impliesx=

A conical vessel whose height is 10 meters and the radius of whose base is half that of the height is being filled with a liquid at a uniform rate of 1.5m^(3)//"min". Find the rate which the level of the water in the vessel is rising when it is 3m below the top of the vessel.

Coefficient of x^18 in (x^2 + 1)(x^2 + 4)(x^2 + 9)….(x^2 + 100) is

If n is a positive integer then 49^n + 16n-1 is divided by

Evaluate the following:lim_(ntoinfty) ((sqrtn-1)/(sqrtn+1))

For theta in (0, (pi)/(2)) "sech"^(-1) (cos theta) is equal to

Which of the following is/are redox reaction

I : sum_(k=1)^(6)[sin((2kpi)/(7))-icos((2kpi)/(7))]=iII : sum_(r=1)^(8)[sin((2pir)/(9))+icos((2pir)/(9))]=iWhich of the above statements are true

y=Ae^(x)+Be^(2x)+Ce^(3x) satisfies the differential equation

Findthe values ofx,y and z so that the vectors veca=xhati+2hatj+zhatkandvecb=2hati+yhatj+hatkare equal .

For the probability density function f(x) ={(2e""^(-2x),x gt0),(0,xlt=0):} find F(2)

[(cos alpha-cos beta)+i(sin alpha-sinbeta)]^n+[(cos alpha-cos beta)-i(sin alpha-sin beta)]^n=

If C_(r ) denotes the binomial coefficient .^(n)C_(r+) then (-1) C_(0)^(2) + 2C_(1)^(2) + 5C_(2)^(2) + ….. + (3n - 1) C_(n)^(2) is equal to

Let A={1,3,5} and B = {x:x is an odd natural number less than 6}. Then, which of the following are true? I. AsubB II. BsubA III. A=B IV. "AB"

If the probability of choosing an integer k out of '2m' integers 1,2,3,….2m is inversely proportional to k^(4) ( 1 le k le 2m), then the probability that chosen number is odd , is .

Determine the unknown coordinates of theT(x,0,z) in y"-axis"

Let x_(1), x_(2),…,x_(n) be n observations such that sum x_(i)^(2) = 400 and sum x_(i) = 80. Then a possible value of n among the following is

Integration of some particular functions : int(x-2)/(x^(2)-4x+5)dx=......+c

If two concentric elipse be such that the foci of one be on the and if e and e' be their eccentricities. Prove that the angle between their axes is cos^(-1){(sqrte^(2)+e'^(2)-1)/(ee')}

If the mappings f and g are given be f = {(1,2),(3,5),(4,1)} and g = {(2,3),(5,1),(1,3)}, write fog .

Differentiate the functions given in Exercises 1 to 11 w.r.t. x. (log x)^(cos x)

IF overlinea,overlineb,overlinec are non-coplanar, then prove that the points with position vectors 2overlinea+3overlineb-overlinec,overlinea-2overlineb+3overlinec,3overlinea+4overlineb-2overlinec,overlinea-6overlineb+6overlinec are coplanar.

Write down and simplify Find the 4th term the end in (2a + 5b)^8

Evalute the following integrals int (sqrt(3x -2)) dx

d/dx [sqrt(3x +4)]

Let alpha ne 1 be a real root of the equation x^(3) - ax^(2) + ax - 1 = 0, where a ne - 1 is a real number, then a root of this equation, among the following , is :

Let p in IR, then the differential equation of the family of curves y=(alpha +beta x)3e^(px), where alpha,beta are arbitary constants , is

The solution of(dy)/(dx) + (x (1+y^(3)))/(y^(2) (1 + x^(2))) = 0 is

Prove that : |veca + vecb|le|veca|+|vecb|.

Prove that A nn(B uu C) =(A nn B) uu (A nn C)

S and T are the foci of an ellipse and B is one end of the minor axis. IF STB is an equilateral traingle , then find the eccentricity of the ellipse.

If |{:(-1,7,0),(2,1,-3),(3,4,1):}|=A" then"|{:(13,-11,5),(-7,-1,25),(-21,-3,15):}| is

Let n in N which one of the following is true?

Find the area of a parallelogram whose adjacent sides are given by the vectors vec(a)=3hati+5hatj-2hatk and vec(b)=2hati+hatj+3hatk.

If f(x)=(1+2x)^(frac[1][x]),xne0 is continuous at x=0, then what is the value of f(0) ?

If overline(a), overline(b), overline(c) are three coplanar vectors, the |[overline(a), overline(b), overline(c)], [overline(a)overline(a), overline(a)overline(b), overline(a)overline(c)], [overline(b)overline(a), overline(b)overline(b), overline(b)overline(c)]|=

Let be a binary operation on the set Q of rational numbers as followsab=a+ab. Is the binary operation commutative and associative ?