28278 + Interview Questions in Maths in Class 12 Page 118 InterviewSolution

5851.	Find the two equation of regression line for the given data: n=102, sumx=510, sumy=7140, sumx^(2)=4150, sumy^(2)=740200, sumxy=54900 Also estimate the value of y when x = 7.
Answer» ANSWER :Regression EQUATION of y on X: y = 12x + 10, Regression equation of x on `y: x = 0.08y - 0.6;y = 94`

Discussion

5852.	An edge of a variable cube is increasing at the rate of 3 cm/s. How fast is the volume of the cube increases when the edge is 10 cm long ?
Answer» ANSWER :`= 900 CM^(3)//SEC`.

Discussion

5853.	If a,b,c are non -zero then number of solutions of solutions of (2x^(2))/(a^(2))-(y^(2))/(b^(2))-(z^(2))/(c^(2))=0 -(x^(2))/(a^(2))+(2y^(2))/(b^(2))-(z^(2))/(c^(2))=0 -(x^(2))/(a^(2))-(y^(2))/(b^(2))+(2z^(2))/(c^(2))=0 is
Answer» 6 8 9 infinite Answer :D

Discussion

5854.	Prove the existence of limits of the following sequences and find them. (a) sqrt2, sqrt(2 sqrt(2)), sqrt(2 sqrt(2 sqrt(2)))......, (b) x_n=c^(n)//rootk(n!) (c gt 0, k gt 0, (c) x_n=alpha_n/n, where alpha_n is the nth of the number pi.
Answer» ANSWER :(a) 2; (B) 0; (C) 0

Discussion

5855.	{:(" "Lt),(n rarr oo):} ((1^(m)+2^(m)+3^(m)+.........+n^(m))/(n^(m+1)))=
Answer» `(1)/(m+1)` `(1)/(m+2)` `(1)/(m)` `(1)/(m+3)` ANSWER :A

Discussion

5856.	An ellipse of eccentricity (2sqrt(2))/(3)is inscribed in a circle and a point within the circle is chosenat random. The probability that this point lies outside the ellipse is
Answer» `1//9` `4//9` `1//3` `2//3` ANSWER :D

Discussion

5857.	The probability that a bulb produced by a factory will fuse after 150 days of use is 0.05. Find the probability that out of 5 such bulbs.(i) none (ii) not more than one (iii) more than fuse after 150 days of use.
Answer» Answer :(i) `(0.95)^(5)` (ii) `(45)/(512)` (iii) `(243)/(1024)` (iv) `1-(0.95)^(5)`

Discussion

5858.	A vanadium electrically, if the magnetic moment (spin only) of the vanadium product is 1.73 B.M. and the mass of electrode decreases by 102 mg during the process, then what will be the amount of current in ampere if it flowed for 8 seconds ? (Assume current efficiency 100%, At. wt. of V = 51)
Answer» ANSWER :`40.3`

Discussion

5859.	Evalute the following integrals int (x tan^(-1))/((1 + x^(2))^(3//2)dx
Answer» ANSWER :`(1)/(SQRT(1 + x^(2))) [ x - TAN^(-1) x ] ` + x

Discussion

5860.	Eliminates (i) a,b, and c (ii) x,y,z from the equations -a+(by)/(z)+(cz)/(y)=0,-b+(cz)/(x)+(ax)/(z)=0 and-c+(ax)/(y)+(by)/(x)=0.
Answer» Answer :(i) `(yz)/(X^(2))+(ZX)/(y^(2))+(xy)/(z^(2))+1=0` (ii) `a^(3)+B^(3)+c^(3)=5abc`

Discussion

5861.	Is the function [x] differentiable at x=2?
Answer» SOLUTION :[X] is DIFFERENTIABLE at x=2.

Discussion

5862.	Find the area of the region enclosed by the curves y^(2)-1 =2x and x=0
Answer» ANSWER :`((2)/(3))`

Discussion

5863.	int(cospx+cosqx)/(sinpx+sinqx)dx
Answer» SOLUTION :`INT(cospx+cosqx)/(sinpx+sinqx)dx` =`int(2COS((p+q)/2)x.cos((p-q)/2)x)/(2SIN((p+q)/2)x.cos((p-q)/2)x)dx` =`intcot((p+q)/2)xdx` =2/(p+q) Inabs(sin((p+q)/2)x)+C`

Discussion

5864.	A rectangle has two opposite vertices at (1, 2) and (5,5). If the other vertices lie on the line x = 3 then their coordinates are
Answer» (3, 1), (3, 3) (3,1),(3,6) (3,1),(3,4) (3,2), (3,3) Answer :B

Discussion

5865.	Using elementary transformations, find the inverseof the matrix [(2,1),(7,4)]
Answer» ANSWER :`[(4,-1),(-7,2)]`

Discussion

5866.	Find the number of ways of arranging the letters of the word ORGANIC so that the relative positions of vowels and consonants are not disturbed
Answer» ANSWER :144

Discussion

5867.	(cottheta + "cosec" theta-1)/( cot theta - "cosec" theta +1) is
Answer» `cosec theta+ COTTHETA ` `COSECTHETA- COT theta ` ` cot theta` `cosec theta` ANSWER :A

Discussion

5868.	Find the area of the region bounded by y=sinx and the x - axis in the interval [0,2pi]
Answer» ANSWER :4

Discussion

5869.	The newspaper headline below tells about a power outage. If there are 63,000 residences in Springfield , how many residences were affected by the outage ?
Answer» `10,500` `21,000` `31,500` `42,000` ANSWER :D

Discussion

5870.	P is a point onx^(2)//a^(2) -y^(2)//b^(2) =1andA_2 A' are the vertices of the conic .If PA ,PA' meet an asymptotes at K and L then(KL)^(2)
Answer» `2A^(2) ` `2B^(2) ` `a^(2) -B^(2)` `a^(2)+b^(2) ` ANSWER :D

Discussion

5871.	The potential energy 'U' of a particle veries with distance 'x' from a fixed origin as U=(AX)/(x^(2)+B). Where A and B are dimensional constants. Find the dimension of length in AB.
Answer» Solution :`U=(AX)/(X^(2)+B)` `therefore[B] =L^(2)` `ML""^(2)T^(-2)=([A]L)/(L^(2))` `therefore[A] =ML""^(3)T^(-2)` `[AB]=ML""^(5)T^(-2)""]`

Discussion

5872.	Show that "sin"^(-1)3/5-"sin"^(-1)8/17="cos"^(-1)84/85
Answer» ANSWER :`84/85`

Discussion

5873.	{:("Column A","", "Column B"),("The number of distinct prime factor of x",,"The number of distinct prime factors of 4x"):}
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

5874.	If we change the central atom from S to Se in SO_4^(2-) then which of the following property does NOT changes.
Answer» dipole moment number of `SIGMA` & `pi` BONDS overlapping for `pi`-BOND(s) Bond ORDER of E-O bond (E=S/Se) Answer :A,B,D

Discussion

5875.	In triangle ABC , AD is perpendicular to BC . If AB = 3, AC = 4 , AD = 60 / 25 and length of perpendiculars fron D to AB and AC is 36/25and 48/25 respectively , then
Answer» triangle is isosceles circumradius is 2.5 UNITS triangle is right angled INRADIUS is 2.5 units Answer :B,C

Discussion

5876.	A point P moves such that PA/PB = p where A and B are two fixed pints with AB=a, the locus of P is a circle with radius
Answer» `a. (1- p^(2))` ` p //(1-a ^(2))` `AP (1 - p ^(2))` `ap //(1- a ^(2))` ANSWER :C

Discussion

5877.	Find the second order derivatives of the functions x^(3) log x
Answer» ANSWER :`X(5 + 6 LOG x)`

Discussion

5878.	Find [vec(a)vec(b)vec(c)], where vec(a)=hat(i),vec(b)=hat(j),vec(c)=hat(k).
Answer» 1 4 2 3 Answer :A

Discussion

5879.	A coins is tossed three times,where E:aleast two heads,F: atmost two heads. Find P(E/F)
Answer» Solution :Here,S = {HHH,HHT,HTH,HTT,THH,THT,TTH,TTT} E={HHT,HTH,THH,HHH} (because at LEAST two HEADS means two heads or three heads) F = {TTT,THT,TTH,HTT,HHT,HTH,THH} (because at the most two heads means zero head or one head or two heads) `rArr ENNF = {HHT,HTH,THH}therefore P (EnnF)=3/8 and P(F)=7/8`. Thus,P(E/F)=`(P(EnnF))/(P(F))`=3/8/7/8=3/7

Discussion

5880.	P and Q are points on the straight line passing to the vector 2 hat(i)-hat(j)- hat (k) and parallel to the vector 2 hat(i)-hat(j)+2 hat (k) , If AP=AQ=3 , then the vector equation of the plane OPQ is
Answer» `R=(s+5t) HAT(i)+2s hat(J)+ (t-3s) hat (k)` `r= (3 hat(i)+ hat(j)- hat(k))+s(2 hat(i)- hat(j)+2 hat(k))+t (5 hat(i)+hat(k))` `r= (s+5t)hat(i)+2s hat(j)+(5S +t)hat(k)` `r= (3t-s)hat(i)+2s hat(j)+(t-3s)hat (k)` Answer :A

Discussion

5881.	If x = a (cos t + t sin t) y = a (sin t - t cos t) find (d^2y)/(dx^2).
Answer» Answer :`(SEC^(3)t)/(at), 0 LT t lt (pi)/(2)`.

Discussion

5882.	obtain the equation of hyperbola in each of the following cases: centre at (0,0) transverse axis is along y-axis the distance between the foci is 14 and distance between the vertices is 12.
Answer» Solution :Here 2C =14 2a =12 `therefore` c=7, a=6 `therefore` b^2=c^2-a^2=13` `therefore` EQN of the ELLIPSE is `y^2/a62-x^2/b^2=1` or `y^2/36-x^2/13=1`

Discussion

5883.	Find the equation of plane passes through the pointA ( 1,2,1) ,B ( 2,3,1) and C( 2,1,0)Also find the distance of the point (1,1,1)
Answer» ANSWER :` x-y +2Z -1 =0; 0.41` UNITS

Discussion

5884.	( sin(n+1) alpha - sin (n-1)alpha )/( cos (n+1) alpha + 2 cos n alpha + cos (n-1) alpha )=
Answer» ANSWER :RHS

Discussion

5885.	A number x is chosen at random from first 100 natural numbers. {:((a),x^(2) - 25x - 150 le 0,(b),x^(2) - 30 x gt 0),((c),x+(30)/(x) ge 17,(d),x + (100)/(x) gt 50):}
Answer» ANSWER :(a) 0.3 (B) 0.7 (C) 0.88 (d) `(11)/(20)`

Discussion

5886.	A swimming pool is to be drained for cleaning. If L represents the number of litres of water in the pool t seconds after the pool has been plugged off to drain and L = 200 (10-t)^(2). How fast is the water running out at the end of 5 seconds ? What is the average rate at which the water flows out during the first 5 seconds ?
Answer» ANSWER :3000 liter/sec.

Discussion

5887.	Statewhichof the following statement is false ?
Answer» the feasible regionis thecolllection of all feasible solutoin given the lpp maximize : z=2x+3y subject to the constraints `3x+y le3` and `X GE 0, y ge 0` The MAXIMUM value of z is 19 Given the lpp mainimize z =5x -2y subject to the constriants `2x+3y ge1` and `x ge 0,y ge0` the MINIMUMVALUE of z is `2/3` the collectionof all feasible solutionis called convex set Answer :D

Discussion

5888.	Statewhich of the followingstatementis false ?
Answer» the objective function of an lpp may ASSUME its optimal VALUE at more than one corner POINTS of the feasible region the feasible region of a linear programming problem is a convex set `s={(X,y: x^(2) +yy^(2) le4}` is a convexset any solutionto a generallpp which satisfies the non negative restrictions of the problem is called a optimal solution Answer :D

Discussion

5889.	The points (-6,2),(-3,1) w.r.t the circle x^(2)+y^(2)=20 are
Answer» EXTREMITIES of a diameter conjugate points inverse points lie on the circle Answer :C

Discussion

5890.	If functions f : R to R and g: R to R are given by f(x) = \|x\| and g(x) = [x], ( where [x] is greatest function) find fog (-(1)/(2) ) and "gof" (- (1)/(2) )
Answer» ANSWER :`"GOF" ( - 1//2) =0`

Discussion

5891.	Average Marginal cost is
Answer» `(d)/(dx)(AC)` `(d)/(dx)(MC)` `(MC)/(x)` `(d)/(dx)(AC + MC)` ANSWER :C

Discussion

5892.	If z is a comple numbersuch that-(pi)/(2) lt "arg z" le (pi)/(2), thenwhich of the followinginequalities is ture ?
Answer» `\|z - BARZ\| LE \|z\| (arg z - arg barz)` `\|z-barz\| GE \|z\| (argz -arg barz)` `\|z -bar z\| LT (arg z - arg barz)` NONE of these Solution : `\|z-barz\|=AB` while `\|z\|(argz-arg barz)=" Arc "AB` `therefore"" \|z-barz\\|le\|z\|("arg "z-"arg "barz)`

Discussion

5893.	Discuss the continuity of the function f, where f is defined by f(x)={{:(-2," if "x le -1),(2x," if "-1 lt x le 1),(2," if "x gt 1):}.
Answer» ANSWER :Continuos

Discussion

5894.	In 2013, there are 28 days in February and there are 365 days in the year, In 2004, there are 29 days in February and there are 366 days in the year. If the date March 11, 2003 is a Tuesday, then which one of the following would the date March 11, 2004 be ?
Answer» Monday Tuesday Wednesday Thursday Answer :D

Discussion

5895.	Match the following.I . Ifx^(2) + y^(2) - 6x - 8y + 12 =0 , x^(2) + y^(2) - 4x + 6y + k= 0 "a) 1" Cut othogonally then k = II . Ifx^(2) + y^(2) + 2x + 3y + k = 0 , x^(2) + y^(2) + 8x - 6y - 7 = 0 "b) - 10" cut orthognal then k = III. Ifx^(2) + y^(2) + 2x - 2y + 4 = 0 , x^(2) + y^(2) + 4x - 2ky + 2 = 0 " c) - 24" cut orthogonally then k =
Answer» a,B,C b,c,a c,b,a a,c,b Answer :A::C

Discussion

5896.	Angle between the lines (x-2)/(3)=(y+1)/(-2) = z-2 and (x-1)/(2)=(y+(3)/(2))/(3)=(z+5)/(4) is
Answer» `(PI)/(2)` `(pi)/(3)` `(pi)/(6)` `(pi)/(4)` ANSWER :A

Discussion

5897.	Let I=int_(0)^(pi//2)(dx)/(1+sin x), then int_(0)^(pi)(x^(2)cos x)/((1+sin x)^(2))dx .
Answer» `-PI^(2)` `pi^(2)-2PI I` `2pi I` `2pi I - pi^(2)` ANSWER :D

Discussion

5898.	If P(A) =0.25 , P(B)=0.5, P(A nn B)=0.14then P(barA nn barB)=
Answer» ANSWER :0.39

Discussion

5899.	If the chords of contact of the tangents from two pointsto the hyperbola4x^(2)-5y^(2)=a^(2) are at right angles then 16x_(1)x_(2)+25y_(1)y_(2) is equal to
Answer» `-1` 0 `a^(2)` 1 Answer :B

Discussion

5900.	Determine the ranges of sine and cosine functions.
Answer» SOLUTION :The MAXIMUM and minimum values of SINE and cosine are 1 and -1, respectively. `therefore` Ranges of sine and cosine are [-1, 1].

Discussion

Explore topic-wise InterviewSolutions in .

Find the two equation of regression line for the given data: n=102, sumx=510, sumy=7140, sumx^(2)=4150, sumy^(2)=740200, sumxy=54900 Also estimate the value of y when x = 7.

An edge of a variable cube is increasing at the rate of 3 cm/s. How fast is the volume of the cube increases when the edge is 10 cm long ?

If a,b,c are non -zero then number of solutions of solutions of (2x^(2))/(a^(2))-(y^(2))/(b^(2))-(z^(2))/(c^(2))=0 -(x^(2))/(a^(2))+(2y^(2))/(b^(2))-(z^(2))/(c^(2))=0 -(x^(2))/(a^(2))-(y^(2))/(b^(2))+(2z^(2))/(c^(2))=0 is

Prove the existence of limits of the following sequences and find them. (a) sqrt2, sqrt(2 sqrt(2)), sqrt(2 sqrt(2 sqrt(2)))......, (b) x_n=c^(n)//rootk(n!) (c gt 0, k gt 0, (c) x_n=alpha_n/n, where alpha_n is the nth of the number pi.

{:(" "Lt),(n rarr oo):} ((1^(m)+2^(m)+3^(m)+.........+n^(m))/(n^(m+1)))=

An ellipse of eccentricity (2sqrt(2))/(3)is inscribed in a circle and a point within the circle is chosenat random. The probability that this point lies outside the ellipse is

The probability that a bulb produced by a factory will fuse after 150 days of use is 0.05. Find the probability that out of 5 such bulbs.(i) none (ii) not more than one (iii) more than fuse after 150 days of use.

A vanadium electrically, if the magnetic moment (spin only) of the vanadium product is 1.73 B.M. and the mass of electrode decreases by 102 mg during the process, then what will be the amount of current in ampere if it flowed for 8 seconds ? (Assume current efficiency 100%, At. wt. of V = 51)

Evalute the following integrals int (x tan^(-1))/((1 + x^(2))^(3//2)dx

Eliminates (i) a,b, and c (ii) x,y,z from the equations -a+(by)/(z)+(cz)/(y)=0,-b+(cz)/(x)+(ax)/(z)=0 and-c+(ax)/(y)+(by)/(x)=0.

Is the function [x] differentiable at x=2?

Find the area of the region enclosed by the curves y^(2)-1 =2x and x=0

int(cospx+cosqx)/(sinpx+sinqx)dx

A rectangle has two opposite vertices at﻿ (1, 2) and (5,5). If the other vertices lie on﻿ the line x = 3 then their coordinates are﻿

Using elementary transformations, find the inverseof the matrix [(2,1),(7,4)]

Find the number of ways of arranging the letters of the word ORGANIC so that the relative positions of vowels and consonants are not disturbed

(cottheta + "cosec" theta-1)/( cot theta - "cosec" theta +1) is

Find the area of the region bounded by y=sinx and the x - axis in the interval [0,2pi]

The newspaper headline below tells about a power outage. If there are 63,000 residences in Springfield , how many residences were affected by the outage ?

P is a point onx^(2)//a^(2) -y^(2)//b^(2) =1andA_2 A' are the vertices of the conic .If PA ,PA' meet an asymptotes at K and L then(KL)^(2)

The potential energy 'U' of a particle veries with distance 'x' from a fixed origin as U=(AX)/(x^(2)+B). Where A and B are dimensional constants. Find the dimension of length in AB.

Show that "sin"^(-1)3/5-"sin"^(-1)8/17="cos"^(-1)84/85

{:("Column A","", "Column B"),("The number of distinct prime factor of x",,"The number of distinct prime factors of 4x"):}

If we change the central atom from S to Se in SO_4^(2-) then which of the following property does NOT changes.

In triangle ABC , AD is perpendicular to BC . If AB = 3, AC = 4 , AD = 60 / 25 and length of perpendiculars fron D to AB and AC is 36/25and 48/25 respectively , then

A point P moves such that PA/PB = p where A and B are two fixed pints with AB=a, the locus of P is a circle with radius

Find the second order derivatives of the functions x^(3) log x

Find [vec(a)vec(b)vec(c)], where vec(a)=hat(i),vec(b)=hat(j),vec(c)=hat(k).

A coins is tossed three times,where E:aleast two heads,F: atmost two heads. Find P(E/F)

P and Q are points on the straight line passing to the vector 2 hat(i)-hat(j)- hat (k) and parallel to the vector 2 hat(i)-hat(j)+2 hat (k) , If AP=AQ=3 , then the vector equation of the plane OPQ is

If x = a (cos t + t sin t) y = a (sin t - t cos t) find (d^2y)/(dx^2).

obtain the equation of hyperbola in each of the following cases: centre at (0,0) transverse axis is along y-axis the distance between the foci is 14 and distance between the vertices is 12.

Find the equation of plane passes through the pointA ( 1,2,1) ,B ( 2,3,1) and C( 2,1,0)Also find the distance of the point (1,1,1)

( sin(n+1) alpha - sin (n-1)alpha )/( cos (n+1) alpha + 2 cos n alpha + cos (n-1) alpha )=

A number x is chosen at random from first 100 natural numbers. {:((a),x^(2) - 25x - 150 le 0,(b),x^(2) - 30 x gt 0),((c),x+(30)/(x) ge 17,(d),x + (100)/(x) gt 50):}

Statewhichof the following statement is false ?

Statewhich of the followingstatementis false ?

The points (-6,2),(-3,1) w.r.t the circle x^(2)+y^(2)=20 are

If functions f : R to R and g: R to R are given by f(x) = |x| and g(x) = [x], ( where [x] is greatest function) find fog (-(1)/(2) ) and "gof" (- (1)/(2) )

Average Marginal cost is

If z is a comple numbersuch that-(pi)/(2) lt "arg z" le (pi)/(2), thenwhich of the followinginequalities is ture ?

Discuss the continuity of the function f, where f is defined by f(x)={{:(-2," if "x le -1),(2x," if "-1 lt x le 1),(2," if "x gt 1):}.

In 2013, there are 28 days in February and there are 365 days in the year, In 2004, there are 29 days in February and there are 366 days in the year. If the date March 11, 2003 is a Tuesday, then which one of the following would the date March 11, 2004 be ?

Angle between the lines (x-2)/(3)=(y+1)/(-2) = z-2 and (x-1)/(2)=(y+(3)/(2))/(3)=(z+5)/(4) is

Let I=int_(0)^(pi//2)(dx)/(1+sin x), then int_(0)^(pi)(x^(2)cos x)/((1+sin x)^(2))dx .

If P(A) =0.25 , P(B)=0.5, P(A nn B)=0.14then P(barA nn barB)=

If the chords of contact of the tangents from two pointsto the hyperbola4x^(2)-5y^(2)=a^(2) are at right angles then 16x_(1)x_(2)+25y_(1)y_(2) is equal to

Determine the ranges of sine and cosine functions.

A rectangle has two opposite vertices at (1, 2) and (5,5). If the other vertices lie on the line x = 3 then their coordinates are