14949 + Interview Questions in Maths in Class 11 Page 5 InterviewSolution

201.	The shortest distance between the straight line passing through the point A = (6, 2, 2) and parallel to the vector (1, -2, 2) and the straight line passing through A^(1) = ( -4, 0, -1) and parallel to the vector (3, -2, -2) is
Answer» 3 6 9 12 Answer :C

Discussion

202.	Define compressibility.
Answer» Solution :(i) The reciprocal of the BULK modulus is called 6. compressibility. It is DEFINED as the fractional CHANGE in volume per unit increase in PRESSURE. (ii) From the equation `K = -(sigma_n)/(epsi_v) = - ((Delta P)/(DeltaV))/(V) `we can say that the compressibility `C = 1/K = (epsi_v)/(sigma_n) = - ((Delta V)/(V))/(Delta P)` .

Discussion

203.	A and B are two fixed points such that AB=3unit. P is a point such that (PA)/(PB)=2 then the maximum area of triangle PAB is (in sq.units)
Answer» ANSWER :3

Discussion

204.	If m= ""^(n) C_(2), then ""^(m) C_(2) is equal to
Answer» `3.""^(N) C_(4)` `""^(n+1)C_4` `3.""^(n+1)C_4` `3.""^(n+1)C_3` ANSWER :C

Discussion

205.	Let a function f be defined as f(x) = {:{(x," if " 0 le x lt 1/2),(0," if "x=1/2),(x-1," if" 1/2 lt x le 1):} Establish the existence of Lim_(x to 1/2) f(x) .
Answer» Answer :Since L.H.L `!= ` R.H.L . THEREFORE `Lim_(x to 1/2) F(x)` does not exist .

Discussion

206.	O, A, B are vertices of triangle whose sides are given by (5x+12y)^(2)-3(12x-5y)^(2)=0, 5x+12y-78=0 then AB =
Answer» `SQRT(3)` `2sqrt(3)` `3sqrt(3)` `4sqrt(3)` ANSWER :D

Discussion

207.	Show that the function f(x) = x cos (1//x), x ne 0 f(0) = 1 is discontinuous at x = 0.
Answer» ANSWER :x=0

Discussion

208.	An Index of retail prices is the mean of the five other price index numbers which are weighted as follows: The original index of retail prices are established at 100. If the following percentage increases in the various indices have occurred since that time, find the index of retail prices now. A=55% , B= 180%, C=60%, D=45%, E=90%.
Answer» ANSWER :`=179.635`.

Discussion

209.	If bara=bari+barj+bark,bara.barb=1,baraxxbarb=2bari+barj-3bark then 3barb=
Answer» `5bari-4barj+2bark` `3bari-6barj` `4bari-5barj+1k` `4bari+barj+bark` ANSWER :A

Discussion

210.	If there is an error of 0.05cm in the measurement of the side as 2cm of a cube, then relative error in the volume is
Answer» 0.075 0.0075 7.5 0.75 Answer :A

Discussion

211.	If the point P(tan^2, tan theta) lie in the region corresponding to the acute angle between the lines 2y=x and 4y=x, then [(tantheta)/2] is equal to (where [.] denotes greatest interger function)
Answer» ANSWER :1

Discussion

212.	If A(2, 2, -3), B(5, 6, 9) and C(2, 7, 9) be the vertices of a triangle. The internal bisector of the angle A meets BC at the point D. Find the coordinates of D.
Answer» ANSWER :`(7/2,13/2,9)`

Discussion

213.	Complete the table using calculator and use the result to estimate the limit. lim_(xrarr2)(x-2)/(x^2 -4)
Answer» ANSWER :0.25

Discussion

214.	Which unit is used to measure electrical energy?
Answer» Solution :In circular motion the centripetal FORCE does not dowork on the OBJECT MOVING on a circle as it is ALWAYS perpendicular to the displacement. `F dr cos 90^@ [ cos 90^@ = 0]` ` therefore W = 0`

Discussion

215.	Find equation of the line through the point (0,2) making an angle (2pi)/( 3) with the positive X -axis. Also, find the equation of line parallel to it and crossing the Y -axis at a distance of 2 units below the origin.
Answer» ANSWER :Required EQUATION of the line are `sqrt(3) x + y -2 =0 and sqrt(3) x +y+2=0`.

Discussion

216.	If Sin x Cosy = 1/4 and 3Tanx = 4 Tany then Sin (x - y) =
Answer» `(1)/(16)` `(7)/(16)` `(3)/(4)` `(3)/(4)` Answer :A

Discussion

217.	Find the sum of: 10 terms of 5 +8 + 11+ ....,
Answer» ANSWER :185

Discussion

218.	If A=[(5a,-b),(3,2)] and A. adjA = A.A^(T) then 5a+b is equal to
Answer» 13 `-1` 5 4 Answer :C

Discussion

219.	Let L be the distance between the line x =0, y/b + z/c =1 and y =0, x/a - z/c =1. Then L ^(2) ((1)/( a ^(2)) + (1)/( b ^(2)) + (1)/(c ^(2))) is
Answer» ANSWER :4

Discussion

220.	An iron rod of length 2l is sliding on two mutually perpendicular lines. Find the locus of the midpoint of the rod.
Answer» ANSWER :`L^(2)`

Discussion

221.	Two balls are drawn from an urn containing 2 white , 3 red and 4 black balls , one by one without replacement . Whatis the probability that both balls are of the same colour ,
Answer» ANSWER :`(5)/(18)`

Discussion

222.	Two balls are drawn from an urn containing 2 white , 3 red and 4 black balls , one by one without replacement . Whatis the probability that at least one ball is red ?
Answer» ANSWER :`(7)/(12)`

Discussion

223.	Find a point on the x-axis, which is equidistant from the points (7,6) and (3, 4).
Answer» ANSWER :`(15/2, 0)`

Discussion

224.	In Delta ABC, if sin^2 A+sin^2 B+sin^2 C =9//4, then the triangle is
Answer» isosceles right angled Equilateral SCALENE triangle. Answer :C

Discussion

225.	Determine the point on ZX plane which is equidistance from points (1,-1,0),(2,1,2),(3,2,-1)
Answer» ANSWER :`(31/10,0,1/5)`

Discussion

226.	The radii r_(1),r_(2),r_(3)of the escribed circles of the triangle ABC are in H.P. If the area of the triangle is 24cm and its perimeter is 24 cm, then the length of its largest side is
Answer» 10 9 8 none of these Answer :A

Discussion

227.	(d)/(dx){log(x+sqrt(a^2+x^2))} =
Answer» `1/(X+SQRT(a^2+x^2))` `x/(sqrt(a^2+x^2))` `1/(x(x+sqrt(a^2+x^2)))` `1/sqrt(a^2+x^2)` ANSWER :D

Discussion

228.	Solve for n : ((2n)!)/( 3!( 2n-3) !): ( n!)/( 2!( n-2)!) = 44 : 3
Answer» ANSWER :` N= 6`

Discussion

229.	Dividing 5^(99)by 13 , the remainder is …………
Answer» 8 9 10 0 Answer :A

Discussion

230.	lim_(x to3)lfloorx rfloor =
Answer» 2 3 does not EXIST 0 Answer :does not exist

Discussion

231.	If there is an error of 0.01 cm in the diameter of a sphere when its radius 5 cm, then the percentage error in its surface area is
Answer» 0.2 0.6 0.05 `(PI)/(10)` ANSWER :A

Discussion

232.	Find the ratio in which the point P(5, 4, -6) divides the line segement joining the points A(3, 2, -4) and (B(9, 8, -10). Also, find the harmonic conjugate of P.
Answer» ANSWER :`1:2` and `(-3,-4,2)`

Discussion

233.	Which term of the series 8+1.6+0.32+ . . . . is 0.00256 ?
Answer» (a)`7^(th)` (B)`6^(th)` (C)`5^(th)` (d)NONE of these ANSWER :B

Discussion

234.	lim_(xto(pi)/(2))(sin(cosx))/((pi)/(2)-x)=……….
Answer» 0 1 -1 None of these Answer :B

Discussion

235.	Evaluate cos^(2)45^(@)+cos^(2)135^(@)+cos^(2)225^(@)+cos^(2)315^(@).
Answer» ANSWER :2

Discussion

236.	Find the stationary points and stationary values for the following functions. (x-2)^(2//3) (2x-4)
Answer» ANSWER :(2, 0), 0

Discussion

237.	Arrange the following values in the ascending order of P,Q,R. If A+B+C=pi then (i) P=(cos A)/(sin B sin C)+(cos B)/(sin A sin C)+(cos C)/(sin A sin B)(ii) Q = sum cot A.cot B(iii) R=tan3A+tan3B+tan3C-tan3A tan 3B tan3C=
Answer» <P>R,Q,P Q,P,R P,Q,R P,R,Q Answer :A

Discussion

238.	If the vectors 2veci+vecj-veck, veci+3vecj-4veck and -veci-4vecj+lambda veck form a triangle then lambda is:
Answer» -4 2 -3 3 Answer :D

Discussion

239.	Using the mathematical induction, showthat forany natural numbern le 2( 1 - 1/2^(2)) (1 - 1/3^(2))( 1 - 1/4^(2)) …( 1- 1/n^(2)) = ( n +1)/( 2n )
Answer» ANSWER :N

Discussion

240.	Which of the following are examples of the null set Set of even prime numbers
Answer» ANSWER :III

Discussion

241.	Four candidates A, B, C, D have applied for the assignment to coach a school cricket team. If A is twice as likely to be selected as B, and B and C are given about the same chance of being selected, while C is twice as likely to be selected as D, what are the probabilities that (i) C will be selected ? (ii) A will not be selected ?
Answer» ANSWER :`(5)/(9)`

Discussion

242.	If each side of length a of an equilateral triangle subtends an angle of 60^(@) at the top of a tower h meter high situated at the centre of the triangle, then
Answer» `3a^(2)=h^(2)` `2A^(2)=3H^(2)` `a^(2)=3h^(2)` `3a^(2)=h^(2)` ANSWER :B

Discussion

243.	Find the new coordinates of the point in each of the following cases if origin is shifted to the point (-3,-2) by translation of axes. (i) (1,1)
Answer» ANSWER :`=(4,3)`

Discussion

244.	Find the new coordinates of the point in each of the following cases if origin is shifted to the point (-3,-2) by translation of axes. (ii) (0,1)
Answer» ANSWER :`=(3,3)`

Discussion

245.	Find the new coordinates of the point in each of the following cases if origin is shifted to the point (-3,-2) by translation of axes. (iii) (5,0)
Answer» ANSWER :`=(8,2)`

Discussion

246.	Find the new coordinates of the point in each of the following cases if origin is shifted to the point (-3,-2) by translation of axes. (iv) (-1,-2)
Answer» ANSWER :` = (2,0)`

Discussion

247.	Find the new coordinates of the point in each of the following cases if origin is shifted to the point (-3,-2) by translation of axes. (v) (3,-5)
Answer» ANSWER :`=(6,-3)`

Discussion

248.	A fair coin with 1 marked on one face and 6 on the other and a fair die are both tossed. Find the probability that the sum of numbers that turn up is (i9ii) 12.
Answer» ANSWER :(i) `1/12` (II) `1/12`

Discussion

249.	The unit vector perendicular to the plane determined by P (1,-1,2) ,C(3,-1,2) is ________.
Answer» Solution :Required unit vector `hata= (VEC(PQ)xxvec(PR))/(\|vec(PQ) XX vec(PR)\|)` `vec(PQ) = hati-hatj -3hatk, vec(PR)= -hati+3hatj-hatk` `vec(PQ)xx vec(PR)=\|{:(hati,hatj,hatk),(1,1,-3),(-1,3,-1):}\|` ` 8hati + 4hatj + 4hatk` `\|vec(PQ) xx vec(PR)\|=SQRT(64+16+16)=sqrt96 + 4sqrt6` `hatn = (8hati+4hatj+4hatk)/(4sqrt6)=(2hati+hatj+hatk)/sqrt6`

Discussion

250.	If there is a possible error of 0.02 cm in the measurement of the diameter of a sphere then the possible percentage error in its volume when the radius 10 cm is
Answer» 0.1 0.2 0.3 0.4 Answer :C

Discussion

Explore topic-wise InterviewSolutions in .

The shortest distance between the straight line passing through the point A = (6, 2, 2) and parallel to the vector (1, -2, 2) and the straight line passing through A^(1) = ( -4, 0, -1) and parallel to the vector (3, -2, -2) is

Define compressibility.

A and B are two fixed points such that AB=3unit. P is a point such that (PA)/(PB)=2 then the maximum area of triangle PAB is (in sq.units)

If m= ""^(n) C_(2), then ""^(m) C_(2) is equal to

Let a function f be defined as f(x) = {:{(x," if " 0 le x lt 1/2),(0," if "x=1/2),(x-1," if" 1/2 lt x le 1):} Establish the existence of Lim_(x to 1/2) f(x) .

O, A, B are vertices of triangle whose sides are given by (5x+12y)^(2)-3(12x-5y)^(2)=0, 5x+12y-78=0 then AB =

Show that the function f(x) = x cos (1//x), x ne 0 f(0) = 1 is discontinuous at x = 0.

If bara=bari+barj+bark,bara.barb=1,baraxxbarb=2bari+barj-3bark then 3barb=

If there is an error of 0.05cm in the measurement of the side as 2cm of a cube, then relative error in the volume is

If the point P(tan^2, tan theta) lie in the region corresponding to the acute angle between the lines 2y=x and 4y=x, then [(tantheta)/2] is equal to (where [.] denotes greatest interger function)

If A(2, 2, -3), B(5, 6, 9) and C(2, 7, 9) be the vertices of a triangle. The internal bisector of the angle A meets BC at the point D. Find the coordinates of D.

Complete the table using calculator and use the result to estimate the limit. lim_(xrarr2)(x-2)/(x^2 -4)

Which unit is used to measure electrical energy?

Find equation of the line through the point (0,2) making an angle (2pi)/( 3) with the positive X -axis. Also, find the equation of line parallel to it and crossing the Y -axis at a distance of 2 units below the origin.

If Sin x Cosy = 1/4 and 3Tanx = 4 Tany then Sin (x - y) =

Find the sum of: 10 terms of 5 +8 + 11+ ....,

If A=[(5a,-b),(3,2)] and A. adjA = A.A^(T) then 5a+b is equal to

Let L be the distance between the line x =0, y/b + z/c =1 and y =0, x/a - z/c =1. Then L ^(2) ((1)/( a ^(2)) + (1)/( b ^(2)) + (1)/(c ^(2))) is

An iron rod of length 2l is sliding on two mutually perpendicular lines. Find the locus of the midpoint of the rod.

Two balls are drawn from an urn containing 2 white , 3 red and 4 black balls , one by one without replacement . Whatis the probability that both balls are of the same colour ,

Two balls are drawn from an urn containing 2 white , 3 red and 4 black balls , one by one without replacement . Whatis the probability that at least one ball is red ?

Find a point on the x-axis, which is equidistant from the points (7,6) and (3, 4).

In Delta ABC, if sin^2 A+sin^2 B+sin^2 C =9//4, then the triangle is

Determine the point on ZX plane which is equidistance from points (1,-1,0),(2,1,2),(3,2,-1)

The radii r_(1),r_(2),r_(3)of the escribed circles of the triangle ABC are in H.P. If the area of the triangle is 24cm and its perimeter is 24 cm, then the length of its largest side is

(d)/(dx){log(x+sqrt(a^2+x^2))} =

Solve for n : ((2n)!)/( 3!( 2n-3) !): ( n!)/( 2!( n-2)!) = 44 : 3

Dividing 5^(99)by 13 , the remainder is …………

lim_(x to3)lfloorx rfloor =

If there is an error of 0.01 cm in the diameter of a sphere when its radius 5 cm, then the percentage error in its surface area is

Find the ratio in which the point P(5, 4, -6) divides the line segement joining the points A(3, 2, -4) and (B(9, 8, -10). Also, find the harmonic conjugate of P.

Which term of the series 8+1.6+0.32+ . . . . is 0.00256 ?

lim_(xto(pi)/(2))(sin(cosx))/((pi)/(2)-x)=……….

Evaluate cos^(2)45^(@)+cos^(2)135^(@)+cos^(2)225^(@)+cos^(2)315^(@).

Find the stationary points and stationary values for the following functions. (x-2)^(2//3) (2x-4)

Arrange the following values in the ascending order of P,Q,R. If A+B+C=pi then (i) P=(cos A)/(sin B sin C)+(cos B)/(sin A sin C)+(cos C)/(sin A sin B)(ii) Q = sum cot A.cot B(iii) R=tan3A+tan3B+tan3C-tan3A tan 3B tan3C=

If the vectors 2veci+vecj-veck, veci+3vecj-4veck and -veci-4vecj+lambda veck form a triangle then lambda is:

Using the mathematical induction, showthat forany natural numbern le 2( 1 - 1/2^(2)) (1 - 1/3^(2))( 1 - 1/4^(2)) …( 1- 1/n^(2)) = ( n +1)/( 2n )

Which of the following are examples of the null set Set of even prime numbers

If each side of length a of an equilateral triangle subtends an angle of 60^(@) at the top of a tower h meter high situated at the centre of the triangle, then

Find the new coordinates of the point in each of the following cases if origin is shifted to the point (-3,-2) by translation of axes. (i) (1,1)

Find the new coordinates of the point in each of the following cases if origin is shifted to the point (-3,-2) by translation of axes. (ii) (0,1)

Find the new coordinates of the point in each of the following cases if origin is shifted to the point (-3,-2) by translation of axes. (iii) (5,0)

Find the new coordinates of the point in each of the following cases if origin is shifted to the point (-3,-2) by translation of axes. (iv) (-1,-2)

Find the new coordinates of the point in each of the following cases if origin is shifted to the point (-3,-2) by translation of axes. (v) (3,-5)

A fair coin with 1 marked on one face and 6 on the other and a fair die are both tossed. Find the probability that the sum of numbers that turn up is (i9ii) 12.

The unit vector perendicular to the plane determined by P (1,-1,2) ,C(3,-1,2) is ________.

If there is a possible error of 0.02 cm in the measurement of the diameter of a sphere then the possible percentage error in its volume when the radius 10 cm is