28278 + Interview Questions in Maths in Class 12

1.	The two curves x=y^2, xy=a^3 cut orthogonally at a point, then a^2 is equal to
Answer» `1/3` `1/2` 1 1 Answer :B

Discussion

2.	Statement-1: The hydrogen carbonates of the alkali metals are soluble in water, but are less soluble than the corresponding normal carbonates. Statement-2: The hydrogen carbonates of the alkali metals have H-bonding.
Answer» Statement-1 is TRUE, statement-2 is true and statement-2 is correct explanation for statement-1 . Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for statement-1. Statement-1is true, statement-2 is FALSE. Statement-1 is false, statement-2 is true. Solution :In Alkali metal bicarbonates intemolecular hydrogen bonding involved and terefore more energy is reauired dissociate metal bicarbonate LATTICE by `H_(2)O`.

Discussion

3.	If y= x^(tan x) + sqrt((x^(2) + 1)/(x)) then find (dy)/(dx)
Answer» ANSWER :`X^(tan x) [(tan x)/(x) + SEC^(2)x.log x] + (1)/(2) SQRT((x)/(x^(2) + 1)) ((x^(2)-1)/(x^(2)))`

Discussion

4.	int (dx)/(x [ 6 (log x)^(2) + 7 log x + 2] )=
Answer» `LOG \|(6 log x + 3)/(6 log x + 4)\| ` + C `- log \|(3 log x + 2)/(log x + 4)\| + c ` `\|(3x + 2)/(2- 3)\| + c ` `- log \|(6 log x + 3)/(6 log x + 4)\| + c ` Answer :A

Discussion

5.	Find the value of tan["sin"^(-1)3/5+"cot"^(-1)3/2]
Answer» ANSWER :`17/6`

Discussion

6.	Ifalpha, beta , gammaarethe rootsof theequationx^3 +px^2 +qx +r=0thensum alpha^2 ( beta + gamma)=
Answer» `p^2 -2Q` `-p^3 +3PQ -3R` `p^4 -4p^2 q+4pr +2q^2` `3r-pq` ANSWER :D

Discussion

7.	Find the second order derivatives of the functions given in Exercises 1 to 10. log (log x).
Answer» ANSWER :`-(1)/(x^2)`

Discussion

8.	The point on the curve x^(2) = 2y which is nearest to the point (0, 5) is
Answer» `(2sqrt(2),4)` `(2sqrt(2),0)` `(0,0)` (2,2) ANSWER :A

Discussion

9.	Evaluate the following definite integrals : int_(1)^(3)(dx)/(x^(2)(x+1))
Answer» ANSWER :`log2-log3+(2)/(3)`

Discussion

10.	Integrate the following functions with respect to x. sqrt(1-sin2x), x in((5pi)/(4),(9pi)/(4))
Answer» ANSWER :`sinx+cosx+c`

Discussion

11.	Integration by partial fraction : int(dx)/(x[(logx)^(2)+4log(x)-1)])=....
Answer» `(1)/(2sqrt(5))LOG[(logx+2- SQRT(5))/(logx+2+sqrt(5))]+c` `(1)/(sqrt(5))log[(logx+2- sqrt(5))/(logx+2+sqrt(5))]+c` `(1)/(2sqrt(5))log[(logx+2+ sqrt(5))/(logx+2-sqrt(5))]+c` `(1)/(sqrt(5))log[(logx+2+ sqrt(5))/(logx+2-sqrt(5))]+c` Answer :A

Discussion

12.	Find the area bounded by curves {(x,y): y ge x^(2) and y = \|x\|}
Answer» ANSWER :`1/3`

Discussion

13.	If the system of equations lambdax + 3y + z = 0 , 4x+lambday+3z=0, 2x+3y+lambdaz=0 has non-trival solution, then lambda =
Answer» 6 3 2 None Answer :D

Discussion

14.	A chord through P cut the circle x^(2)+y^(2)+2gx+2fy+c=0 in A and B another chord through P in c and D, then
Answer» `PA.PBltPC.PD` `PA.PB=PC.PD` `PA.PC=PB.PD` `PA.PBgtPC.PD` ANSWER :B

Discussion

15.	Ifalpha, beta , gammaare the rootsof theequationx^3 +4x^2 -5x +3=0thensum (1)/( alpha^2beta^2)=
Answer» `-9/2` `-(38 )/( 49 )` `(26 )/(9)` `98` Answer :C

Discussion

16.	Find the area under the given curves and given lines: (i) y = x^(2), x = 1, x = 2 and x-axis (ii) y = x^(4), x = 1, x = 5 and x-axis
Answer» ANSWER :(i) `7/3` (II) 624.8

Discussion

17.	Proceeding from the definiton of the limit of a function after Cauchy (ie, in the term of e-deltal e-M'' etc). Prove that (a) underset(x to 1)lim (3x-8)=-5, (b) underset(x to oo)lim (5x+1)/(3x+9)=5/3 (c) underset(x to 1)lim (1)/((1-x)^(2))=+oo, (d) underset(x to oo)lim log_(a) x=oo (a gt 1), (e) underset( x to oo)lim arc tan x=pi/2, (f) underset(x to pi/6) sin x=1/2
Answer» ANSWER :`1/X (x GT 0)`

Discussion

18.	For minimum curved surface area and given volume, the ration of the height and radius of base of a cone is :
Answer» `1 : SQRT2` `sqrt2 : 1` `1 : 2` None of these Answer :B

Discussion

19.	If A^(-1) ={:[( 3,-1,1),(-15,6,-5),(5,-2,2) ]:}and B= {:[( 1,2,-2),( -1,3,0),( 0,-2,1) ]:} ,find (AB) ^(-1)
Answer» ANSWER :`{:[( 9,-3,5),(-2,1,0),(1,0,2)]:}`

Discussion

20.	Ifalpha, beta, gammaare therootsofx^3 +px^2 +qx +r=0then find sum alpha^2beta^2
Answer» ANSWER :`q^2 -2pr`

Discussion

21.	If the roots of the equation x^(2)+px+c=0 are 2,-2 and the roots of the equation x^(2)+bx+q=0 are -1,-2, then the roots of the equation x^(2)+bx+c=0 are
Answer» `-3,-2` `-3,2` `1,-4` `-5,1` Answer :C

Discussion

22.	Solve system of linear equations ,using matrix method5x+2y =3 3x+ 2y = 5
Answer» ANSWER :`x=-1,y=4`

Discussion

23.	Using elementary transformations, find the inverse of the matrix. ({:(0,0,-1),(3,4,5),(-2,-4,-7):})
Answer» Answer :`A^(-1)=(1)/(4) [{:(-8,4,4),(11,-2,-3),(-4,0,0):}]`

Discussion

24.	Two balanced dice are tossed. Find probability of the event that sum of the numbers obtain on both dice is 3 or it is multiple of 5.
Answer» ANSWER :`(19)/(36)`

Discussion

25.	The volume of tetrahedron with vertices -hat(i)+hat(k),2hat(i)-hat(j),hat(i)+2hat(j)+5hat(k),hat(i)+2hat(j)+hat(k) is
Answer» `3//16` `16//3` `15//2` `2//15` ANSWER :B

Discussion

26.	Using elementary row transformations , find the inverse of [{:(2,3),(5,7):}]
Answer» ANSWER :`thereforeA^(-1)=[{:(-7,3),(5,-2):}]`

Discussion

27.	If ax^(3)-cx+bge0AAxepsilonR^(+)-{0} where a,b,cepsilonR^(+). Then the minimum value of ((27ab^(2))/(c^(3))) is………
Answer» Solution :Let `F(X)=AX^(2)+B/x-C f^(')(x)=2ax-b/(x^(2))` `f^(')(x)=0, x=(b/(2a))^(1/3)impliesa(b/(2a))^(2/3)+b/((b/(2a))^(1/3))gecimplies(27ab^(2))/(c^(3))ge4`

Discussion

28.	For any two events A and B, P(A cup B) cap (bar(A) cap bar(B)) is :
Answer» `LE 1/3` `GT 1/3` ` gt 1/2 ` `GE 1/2` ANSWER :A

Discussion

29.	lim_(xto1)(sqrt(1-cos2(x-1)))/(x-1) is
Answer» `SQRT2` `-sqrt2` does not EXIST `sqrt1` ANSWER :C

Discussion

30.	C is the centre, AA' and BB' are Major and minor Axes of the ellipse (x^(2))/(aA^(2))+(y^(2))/(b^(2))=1respectively. If PN a b is the ordinate of a point P on the ellipse then show that (PN)^(2)/(A'N)(AN)=(BC)^(2)/(CA)^(2)
Answer» ANSWER :`(BC)^2/(CA)^2`

Discussion

31.	{:("Column A","a and b are the digits of a two digit number ab, and a = b + 3" ,"Column B"),("The two-digit number ab", ,"40"):}
Answer» If COLUMN A is LARGER If column B is larger If the COLUMNS are EQUAL If there is not ENOUGH information to decide Answer :D

Discussion

32.	Match the lengths of the focal chords drawn to y^(2)=8x from points having parameters {:("List-I", "","List-II"),((A)2,1.,8),((B) -3,2.,(25)/(2)),((C)1,2.,(289)/(8)),((D)-4,4.,(200)/(9)):} The correct match is
Answer» `{:(A,B,C,D),(4,2,3,1):}` `{:(A,B,C,D),(2,4,3,1):}` `{:(A,B,C,D),(2,4,1,3):}` `{:(A,B,C,D),(1,2,3,4):}` ANSWER :C

Discussion

33.	The position vectors of points of intersection of three planes rcdotn_1=q_1, rcdotn_2=q_2, rcdotn_3=q_3, where n_1, n_2 and n_3 are non coplanar vectors, is
Answer» `(1)/([n_1 n_2 n_3])[q_3(n_1timesn_2)+q_1(n_2timesn_3)+q_2(n_3timesn_1)]` `(1)/([n_1 n_2 n_3])[q_1(n_1timesn_2)+q_1(n_2timesn_3)+q_3(n_3timesn_1)]` `-(1)/([n_1 n_2 n_3])[q_1(n_1timesn_2)+q_1(n_2timesn_3)+q_3(n_3timesn_1)]` NONE of these Answer :(a)

Discussion

34.	A 5 -digit number divisble by 30 us to be formed using the digits 0,1,2,3,4,5 without repetition to the digit.The numbers of ways it can be done is
Answer» 36 24 48 60 Answer :B

Discussion

35.	The unit vector perpendicualr to (3, 4)is ……………….
Answer» `((4)/(5),(3)/(5))` `(-(4)/(5),(3)/(5))` `(-(3)/(5),(4)/(5))` `((3)/(5),(4)/(5))` ANSWER :B

Discussion

36.	Find the vector equation of the line perpendicular to the lines(x-1)/( 2) = ( y-1)/(2)= (z-3)/( 4) and ( x+1)/( 4)= ( y)/(3)= z-1and which passes through the point (2,1,2)
Answer» ANSWER :` ( x-2)/(5)= (y - 1)/(-7)=(2-2)/( 1)`

Discussion

37.	Integrate the following functions sqrt(1-4x^2)
Answer» SOLUTION :`int sqrt(1-4x^2) dx = int sqrt(1^2-(2x^2))dx` =`1/2[(2x)/2 sqrt(1^2-(2x^2)) +1^2/2 sin^-1(2x)/1]+c` =`1/2[X sqrt(1-4x^2) +1/2 sin^-1(2x)]+c`

Discussion

38.	int_(-pi//2)^(pi//2) ln((2-sin theta)/(2+sin theta))d theta=
Answer» 0 1 2 -1 Answer :A

Discussion

39.	Find the equation of plane through the line of intersection of the planes 3x – 4y + 5z = 10,2x +2y-3z=4 and parallel to the line x=2y=3z
Answer» ANSWER :`x-20y+27z-14=0`

Discussion

40.	Find the area of the region bounded by the curves x=\|y^(2)-1\| and y=x-5.
Answer» ANSWER :`(109)/(6)`

Discussion

41.	Two men A and B start with velocities v at the same time from the junction of two roads inclined at 45^(@) to each other. If they travel by different roads, find the rate at which they are being seperated.
Answer» ANSWER :`(SQRT(2-sqrt(2)))V`.

Discussion

42.	The value of the expression
Answer» 0 2 3 1 Answer :D

Discussion

43.	Choose the correct answer If f(x)=int_(0)^(x)tsintdt, then f' (x) is
Answer» cosx + x sin x x sinx x cosx sinx + x cosx Answer :B

Discussion

44.	Draw scatter diagram of the following paris of observations: (a) (1,28), (2,26), (4,22), (5,20), (6,18), (7,16), (8,14), (10,10) (b) (1,15), (2,3), (4,14), (5,1), (6,15), (7,4), (8,3), (9,2), (10,15)
Answer» ANSWER :CON (X,Y)=1.34

Discussion

45.	Integrate the functions tan^(2)(2x-3)
Answer» ANSWER :`1/2tan(2x-3)-x+C`

Discussion

46.	If the function y = ae^(x) + bx^(2)+3x is maximum at x = 0 and minimum at x = - 3, then find the values of a and b.
Answer» ANSWER :`a = - 3, B = 1/2 (1-e^(-3))`

Discussion

47.	Evaluate the following determinants. [[sectheta,tantheta],[tantheta,sectheta]]
Answer» SOLUTION :`[[SECTHETA,TANTHETA],[tantheta,sectheta]]=sec^2theta-tan^2theta=1`

Discussion

48.	Assumethat alpha, beta, gamma are the roots of 2x^3+5x^2+5x+2=0 "for " h in R, if alpha +h , beta+h, gamma+h are roots of a(h)x^3+b(h)x^2+c(h)x+d(h)=0 then
Answer» `c(H) ne 0 , AA h in R` `b(-5/6)=0` `c(-2)=0` d (h) VANISHES for these distinctreal values of h ANSWER :A

Discussion

49.	Let P,Q,R be three points on parabola y^2=4x and normal P and R meet at Q, then the locus of the mid-points of the chord PR is a parabola whose vertex is at
Answer» (2,0) (0,-2) (-2,0) NONE of these Answer :C

Discussion

50.	Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius R is (2R)/(sqrt(3)) . Also find the maximum volume.
Answer» ANSWER :`(4PI R^(3))/(3sqrt(3))`

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

The two curves x=y^2, xy=a^3 cut orthogonally at a point, then a^2 is equal to

Statement-1: The hydrogen carbonates of the alkali metals are soluble in water, but are less soluble than the corresponding normal carbonates. Statement-2: The hydrogen carbonates of the alkali metals have H-bonding.

If y= x^(tan x) + sqrt((x^(2) + 1)/(x)) then find (dy)/(dx)

int (dx)/(x [ 6 (log x)^(2) + 7 log x + 2] )=

Find the value of tan["sin"^(-1)3/5+"cot"^(-1)3/2]

Ifalpha, beta , gammaarethe rootsof theequationx^3 +px^2 +qx +r=0thensum alpha^2 ( beta + gamma)=

Find the second order derivatives of the functions given in Exercises 1 to 10. log (log x).

The point on the curve x^(2) = 2y which is nearest to the point (0, 5) is

Evaluate the following definite integrals : int_(1)^(3)(dx)/(x^(2)(x+1))

Integrate the following functions with respect to x. sqrt(1-sin2x), x in((5pi)/(4),(9pi)/(4))

Integration by partial fraction : int(dx)/(x[(logx)^(2)+4log(x)-1)])=....

Find the area bounded by curves {(x,y): y ge x^(2) and y = |x|}

If the system of equations lambdax + 3y + z = 0 , 4x+lambday+3z=0, 2x+3y+lambdaz=0 has non-trival solution, then lambda =

A chord through P cut the circle x^(2)+y^(2)+2gx+2fy+c=0 in A and B another chord through P in c and D, then

Ifalpha, beta , gammaare the rootsof theequationx^3 +4x^2 -5x +3=0thensum (1)/( alpha^2beta^2)=

Find the area under the given curves and given lines: (i) y = x^(2), x = 1, x = 2 and x-axis (ii) y = x^(4), x = 1, x = 5 and x-axis

For minimum curved surface area and given volume, the ration of the height and radius of base of a cone is :

If A^(-1) ={:[( 3,-1,1),(-15,6,-5),(5,-2,2) ]:}and B= {:[( 1,2,-2),( -1,3,0),( 0,-2,1) ]:} ,find (AB) ^(-1)

Ifalpha, beta, gammaare therootsofx^3 +px^2 +qx +r=0then find sum alpha^2beta^2

If the roots of the equation x^(2)+px+c=0 are 2,-2 and the roots of the equation x^(2)+bx+q=0 are -1,-2, then the roots of the equation x^(2)+bx+c=0 are

Solve system of linear equations ,using matrix method5x+2y =3 3x+ 2y = 5

Using elementary transformations, find the inverse of the matrix. ({:(0,0,-1),(3,4,5),(-2,-4,-7):})

Two balanced dice are tossed. Find probability of the event that sum of the numbers obtain on both dice is 3 or it is multiple of 5.

The volume of tetrahedron with vertices -hat(i)+hat(k),2hat(i)-hat(j),hat(i)+2hat(j)+5hat(k),hat(i)+2hat(j)+hat(k) is

Using elementary row transformations , find the inverse of [{:(2,3),(5,7):}]

If ax^(3)-cx+bge0AAxepsilonR^(+)-{0} where a,b,cepsilonR^(+). Then the minimum value of ((27ab^(2))/(c^(3))) is………

For any two events A and B, P(A cup B) cap (bar(A) cap bar(B)) is :

lim_(xto1)(sqrt(1-cos2(x-1)))/(x-1) is

C is the centre, AA' and BB' are Major and minor Axes of the ellipse (x^(2))/(aA^(2))+(y^(2))/(b^(2))=1respectively. If PN a b is the ordinate of a point P on the ellipse then show that (PN)^(2)/(A'N)(AN)=(BC)^(2)/(CA)^(2)

{:("Column A","a and b are the digits of a two digit number ab, and a = b + 3" ,"Column B"),("The two-digit number ab", ,"40"):}

Match the lengths of the focal chords drawn to y^(2)=8x from points having parameters {:("List-I", "","List-II"),((A)2,1.,8),((B) -3,2.,(25)/(2)),((C)1,2.,(289)/(8)),((D)-4,4.,(200)/(9)):} The correct match is

The position vectors of points of intersection of three planes rcdotn_1=q_1, rcdotn_2=q_2, rcdotn_3=q_3, where n_1, n_2 and n_3 are non coplanar vectors, is

A 5 -digit number divisble by 30 us to be formed using the digits 0,1,2,3,4,5 without repetition to the digit.The numbers of ways it can be done is

The unit vector perpendicualr to (3, 4)is ……………….

Find the vector equation of the line perpendicular to the lines(x-1)/( 2) = ( y-1)/(2)= (z-3)/( 4) and ( x+1)/( 4)= ( y)/(3)= z-1and which passes through the point (2,1,2)

Integrate the following functions sqrt(1-4x^2)

int_(-pi//2)^(pi//2) ln((2-sin theta)/(2+sin theta))d theta=

Find the equation of plane through the line of intersection of the planes 3x – 4y + 5z = 10,2x +2y-3z=4 and parallel to the line x=2y=3z

Find the area of the region bounded by the curves x=|y^(2)-1| and y=x-5.

Two men A and B start with velocities v at the same time from the junction of two roads inclined at 45^(@) to each other. If they travel by different roads, find the rate at which they are being seperated.

The value of the expression

Choose the correct answer If f(x)=int_(0)^(x)tsintdt, then f' (x) is

Draw scatter diagram of the following paris of observations: (a) (1,28), (2,26), (4,22), (5,20), (6,18), (7,16), (8,14), (10,10) (b) (1,15), (2,3), (4,14), (5,1), (6,15), (7,4), (8,3), (9,2), (10,15)

Integrate the functions tan^(2)(2x-3)

If the function y = ae^(x) + bx^(2)+3x is maximum at x = 0 and minimum at x = - 3, then find the values of a and b.

Evaluate the following determinants. [[sectheta,tantheta],[tantheta,sectheta]]

Assumethat alpha, beta, gamma are the roots of 2x^3+5x^2+5x+2=0 "for " h in R, if alpha +h , beta+h, gamma+h are roots of a(h)x^3+b(h)x^2+c(h)x+d(h)=0 then

Let P,Q,R be three points on parabola y^2=4x and normal P and R meet at Q, then the locus of the mid-points of the chord PR is a parabola whose vertex is at

Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius R is (2R)/(sqrt(3)) . Also find the maximum volume.