28278 + Interview Questions in Maths in Class 12 Page 28 InterviewSolution

1351.	Let A be a non-empty set such that AxA has 9 elements among which are found (-1, 0) and (0, 1). Then,
Answer» A = {-1, 0} A = (0, 1} A = (-1, 0, 1} A = {-1, 1) ANSWER :C

Discussion

1352.	Letf(x)be differentiable for all x. If f(1)=-2 and f'(x) ge 2 for x in [1, 6] then -
Answer» ANSWER :C

Discussion

1353.	Ifthe range of random veriable X is {0,1,2,3,4….} withP(X = k) = ((k +1)a)/(3^(k)) " for " k ge 0, then a is equal to
Answer» `2/3` `4/9` `(8)/(27)` `(16)/(81)` ANSWER :B

Discussion

1354.	Which type of overlapping is NOT possible (when internuclear axis is z-axis) ?
Answer» `p_x +d_(YZ)` `d_(yz)+d_(yz)` `d_(z^2) +d_(z^2)` `d_(x^2-y^2) +d_(x^2-y^2)`

Discussion

1355.	Evaluate the following integrals int_1^3(dx/x^3)dx
Answer» SOLUTION :`int_1^3dx/X^3=[(x^(-3)+1)/(-3+1)]_1^3=[-1/(2x^2)]_1^3` (-1/2)[(1/9)-1)]=4/9

Discussion

1356.	Sketch the graphs of the following functions. f(x) = x^3
Answer» SOLUTION :

Discussion

1357.	If the tangents to y^(2)= 2x at 3 points have inclinations 30^(@), 40^(@), 50^(@)and the ordinatesof corresponding points are y_(1),y_(2),y_(3) then the ascending order of y_(1),y_(2),y_(3) is
Answer» `y^(1),y_(2),y_(3)` `y_(3),y_(2),y_(1)` `y_(1),y_(3),y_(2)` `y_(3),y_(1),y_(2)` ANSWER :B

Discussion

1358.	The range of values of x for which the inequality (x-1)/(4x+5) lt (x-3)/(4x-3) holds is
Answer» `((-4)/(3). (5)/(8))` `((-4)/(3), (1)/(2))` `((-5)/(4), (3)/(4))` (3, 8) Answer :C

Discussion

1359.	Equation of curve in polar coordinates is I/r=2 sin^(2)""theta/2 then it represents
Answer» a STRAIGHT LINE a parabola a circle an ellipse Answer :B

Discussion

1360.	If z_(1),z_(2),z_(3) are vertices ofa Delta such that \|z_(1)\|=\|z_(2)\|=\|z_(3)\|=20andz_(1)z_(2)+z_(3)=12-5i distance of orthocentre from origin is:
Answer» ANSWER :13

Discussion

1361.	A binary operation defined on Q^(+) the set of all positive is given ab = (ab) /2 Then the inverse of 3 is :
Answer» `4/3` `3/4` 3 `1/3` ANSWER :A

Discussion

1362.	If Integration using rigonometric identities : int(1)/(1+cotx)dx=px+q
Answer» <P>`p=(1)/(2),Q=(1)/(2)` `p=-(1)/(2),q=(1)/(2)` `p=-(1)/(2),q=-(1)/(2)` `p=(1)/(2),q=-(1)/(2)` ANSWER :D

Discussion

1363.	Statement I Two non-zero, non-collinear vectors are linearly independent Statement II Any three coplanar vectors are linearly dependent Which of the above statement is/are true?
Answer» Only I Only II Both I and II Neither I nor II ANSWER :C

Discussion

1364.	Points A(3,2,4), B ((33)/(5),(28)/(5),(38)/(5)) and C(9,8,10) are given. The ratio in which B divides overline(AC) is
Answer» `5 : 3` `2 : 1` `1 : 3` `3 : 2` ANSWER :d

Discussion

1365.	Whichof the followingoptions is theonly INCORRECT combination ?
Answer» `(I), (III) (P)` `(II) (iv) (Q)` `(II), (iii) (P)` `(III) (i) (R)` ANSWER :D

Discussion

1366.	Evaluate the following integrals intx^(2)sin^(-1)x dx
Answer» ANSWER :`(X^(3))/(3)sin^(-1)x+(1)/(3)sqrt(1-x^(2))-(1)/(9)(1-x^(2))^((2)/(3))+C`

Discussion

1367.	Let A (2, -3) and B (-2, 1) be vertices of a triangle ABC. If the centroid of this triangle moves on the line 2x + 3y=1, then the locus of the vertex C is the line
Answer» 3x + 2Y = 5 2x - 3Y = 7 2x + 3y = 9 3x – 2y = 3 Answer :C

Discussion

1368.	If a_(1) is the greatest value of f(x) , where f(x) =((1)/(2+[sinx])) (where [.] denotes greatest integer function) and a_(n-1)=((-1)^(n-2))/((n+1))+a_(n)(where n in N), then lim_(nrarroo)(a_(n))is
Answer» `1` `E^(2)` `In^(2)` NONE of these Solution :`a_(1)=1` IMPLIES a_(2)=1-(1)/(2)` `impliesa_(3)=1-(1)/(2)+(1)/(3)` `…………………….` `……………………..` `a_(ALPHA) = 1-(1)/(2)+(1)/(3)-(1)/(4)+…………….. =ln 2`

Discussion

1369.	Solve (x+y)dy+(x-y)dx=0
Answer» ANSWER :`log (x^(2) + y^(2)) + 2 tan^(-1) (y)/(x) = (pi)/(2) + log 2`

Discussion

1370.	Consider a regular polygon of 12 sides each of length one until, then which of the following is not true?
Answer» The area of polygon is `(6+3sqrt(3))` The circum-radius of polygon is `1/2(sqrt(6)+sqrt(2))` The radius of incircle is `(2+sqrt(3))/(2)` Each internal ANGLE is of `135^(@)` ANSWER :D

Discussion

1371.	A tunnel is dug along a chord of Earth having length sqrt(3R) where R is radius of Earth. A small block is released in the tunnel from the surface of Earth. The particle comes to rest centre of tunnel. If the coefficient of friction between the block and the surface of tunnel is mu=(2sqrt(3))/(n), then find n. Ignore the effect of rotation of Earth.
Answer» Solution :`a_(x)=(GM)/(R^(3))(R//2)/(cosphi)cosphi=GM//(2R^(2))` `V_(L)=-GM//R` `V_(f)=-(GM)/(2R^(3))(3R^(2)-(R^(2))/(4))=-(GM)/(2R^(3))xx(11R^(2))/(4)=-(11GM)/(8R)` `(SQRT(3)Rmu)/(2)(GM)/(2R^(2))=(3)/(8)(GM)/(R)` `MU(sqrt(3))/(2)""]`

Discussion

1372.	Five digit numbers can be formed from the digits 1,2,3,4,5. If one number is selected at random , the probability that it is an even number is
Answer» `(4)/(7)` `(2)/(5)` `(7)/(16)` `(1)/(16)` Answer :B

Discussion

1373.	If ""^(n)C_(r-1)=36,""^(n)C_(r)=84 and ""^(n)C_(r+1)=126, then r is equal to
Answer» 1 2 3 4 Answer :C

Discussion

1374.	((cosalpha-cos 3 alpha)(sin8alpha+sin 2alpha))/((sin 5alpha-sin alpha)(cos 4 alpha-cos 6alpha))=
Answer» `-1` `-2` `2` `1` ANSWER :D

Discussion

1375.	Graphof functions are given in the following figure. Check the functions forabsolute extremum.
Answer» Solution :(a) Function has no absolute minima nor absolute maxima. (b) Function has absolute minima but no absolute maxima. (C) Function has local maxima atx = 0as `F(0 - H) f(0+h) LT f(0) (=2)`.

Discussion

1376.	Probability distribution of random variable X is as follows: Find P(X lt 3), P(X ge 3)andP(0 lt X lt 5).
Answer» ANSWER :`(1)/(9),(8)/(9),(8)/(27)`

Discussion

1377.	Observed the following statements I: The intercepts of the circle x^(2)+y^(2)-4x+13=0 on y-axis is sqrt(7) II: The intercept made by the circle x^(2)+y^(2)-4x-8y+13=0 on x-axis is 15 III: The straight line y=x+1 cuts the circle x^(2)+y^(2)=1 in two, two distinct points, then truness, falseness of the above statements are
Answer» F,T,F F,F,T T,T,F T,T,T Answer :B

Discussion

1378.	The sum of the series (.^(101)C_(1))/(.^(101)C_(0)) + (2..^(101)C_(2))/(.^(101)C_(1)) + (3..^(101)C_(3))/(.^(101)C_(2)) + "….." + (101..^(101)C_(101))/(.^(101)C_(100)) is "____".
Answer» Solution :Here `T_(r) = (r^(.1001)C_(r))/(.^(100)C_(r-1))= (r.(1001-r+1))/(r)= 102 -r` `:.` Given sum `= underset(r=1)overset(101)sum(102-r)` `= 101+100+99+"...."+2+1` `=5151`

Discussion

1379.	A doctor is to visit a patient. From the pastexperience, it is known that the probabilities that he will come by train, bus, scooter or by other means of transport are respectively (3)/(10),(1)/(5),(1)/(10) and (2)/(5). The probabilities that he will belate are (1)/(4),(1)/(3) and (1)/(12), is he comes by train, bus and scooter respectively, but if he comes by other means of transport, then he willnot be late. Whenhe arrives, he is late. The the probability that he comes by train is
Answer» `(1)/(2)` `(1)/(3)` `(2)/(3)` `(3)/(5)` ANSWER :A

Discussion

1380.	sqrt((x)/(x-3))+sqrt((x-3)/(x))=(5)/(2)," when "x ne 0and x ne 3
Answer» `{1,2}` `{1,-1}` `{1,5}` `{4,-1}` ANSWER :D

Discussion

1381.	inta^(x+2)dx
Answer» SOLUTION :`INTA^(x+2)dx=inta^2a^xdx` =`a^2.a^x/(INA)+C=a^(x+2)/(Ina)+C`

Discussion

1382.	Solve (1+2e^(x//y))dx + 2e^(x//y) (1-(x)/(y))dy = 0
Answer» ANSWER :`x+2y E^(x/y) = C`

Discussion

1383.	The point does not lie in half plane x + 2y le 10 is
Answer» (2,1) (1,4) (5,3) (3,2) ANSWER :C

Discussion

1384.	Which of the following is logically equivalent to p ^^ q ?
Answer» <P>`p rarr ~Q` `~p VV ~q` `~(p rarr ~q)` `~(~p ^^ ~q)` Answer :C

Discussion

1385.	Also find the condition of having two common roots.
Answer» ANSWER :or`a_1/a_2=b_1/b_2`

Discussion

1386.	Prove that .^(n)C_(0)- .^(n)C_(1) + .^(n)C_(2)- .^(n)C_(3) + "……" + (-1)^(r) + .^(n)C_(r) + "……" = (-1)^(r ) xx .^(n-1)C_(r ).
Answer» Solution :`.^(N)C_(0) - .^(n)C_(1) + .^(n)C_(2) - .^(n)C_(3)+"…"+(-1)^(R ) xx ,^(n)C_(r ) + "…"` Coeffciint of `x^(r )` in `(.^(n)C_(0) - .^(n)C_(1)x + .^(n)C_(2)x^(2) - .^(n)C_(3)x^(3) + "….." + (-1)^(r) xx .^(n)C_(r) + "…..") xx (1+x + x^(2)+x^(3)+"…."+x^(r ) + "....")` `=` Coefficient of `x^(r)` in `(1-x)^(n)(1-x)^(-1)` `=` Coefficient of `x^(r )`in `(1-x)^(n-1)` `= (-1)^(r) xx .^(n-1)C_(r )`.

Discussion

1387.	Evalute the following integrals int sqrt(3 + 8x - 3x^(3)) dx
Answer» ANSWER :`(3X - 4)/(6)sqrt(3 + 8x - 3x^(2)) + (25)/(6 sqrt(3)) SIN^(-1) ((3x - 4)/(5)) + c `

Discussion

1388.	Given that for each a epsilon(0,1),lim(hto 0^(+)) int_(h)^(1-h)f^(-a)(1-t)^(a-1)dt exists. Let this limit be g(a). In addition it is given the function g(a) is differentiable on(0,1). The value of g'(1/2) is
Answer» `(PI)/2` `pi` `-(pi)/2` `0` SOLUTION :NA

Discussion

1389.	In triangleABC, sin((A)/(2))sin((B)/(2))sin((C)/(2))=
Answer» `(A(TRIANGLEABC))/(ABC)` `(A(triangleABC))/(ABCS)` `(A(triangleABC)^(2))/(abc)` `(A(triangleABC)^(2))/(abcs)` ANSWER :D

Discussion

1390.	A survey is conducted in which 60% of the individuals who responded indicated that they do not support issuing a bond to help raise money to fund the construction of a new sports arena in their city. A statistician calculates the confidence level to be 95% foran interval of 5% below and above the 60% mark. What conclusions is best supported by this information?
Answer» 95% of the people SURVEYED do not support the issuing of the bond. The probability that a person selected at random from the sample does not support the issing of the bond RANGES from 0.57 to 0.63. The probability that a person selected at random from the sample supports the issuing of the bond is 0.4. If the survey were to be repeated 100 times, 95% of the times the number of people who would not support the issuing of the bond would RANGE from 55% to 65% of those surveyed. Answer :D

Discussion

1391.	If f={(1,2),(2,-3),(3,-1) then find (ii) sqrt(f).
Answer» ANSWER :`(1,SQRT(2))`

Discussion

1392.	Let N be the number of integer solutions of the equation n_(1) + n_(2) + n_(3) + n_(4)= 17 when n ge 1, n_(2) ge -1, n_(3) ge 3, n_(4) ge 0. If N= ""^(17)C_(K), then find K.
Answer» ANSWER :3

Discussion

1393.	A(2,3,5), B(a,3,3) and C(7,5,beta) are the vertices of a triangle. If the median through A is equally inclined with the co-ordinate axes, then cos^-1(alpha/beta)=
Answer» `cos^-1((-1)/9)` `pi/2` `pi/3` `cos^-1(2/5)` ANSWER :A

Discussion

1394.	If f: N rarr R be the function defined by f(x) = (2x-1)/2 and g : Q rarr R be another function defined by g(x) = x+2. Then , gof (3/2) is .......
Answer» 1 `-1` 3 None of these Solution :N/A

Discussion

1395.	A man speaks truth 2 out of 3 times. He picks one of the natural numbers in the set S={1,2,3,4,5,6,7} and reports that it is even. The probability that it is actually even is
Answer» 1)`1/10` 2)`2/5` 3)`3/5` 4)`1/5` ANSWER :C

Discussion

1396.	Evaluate the following integrals (iii) int_(0)^(pi/2)(sqrt(sec x))/(sqrt(sec x)+sqrt(cosec x))dx
Answer» ANSWER :`(PI)/(4)`

Discussion

1397.	The vector veca = alpha hati + 2 hatj + beta hatk lies in the plance of the vectors vecb = hati + hatj and vecc= ahtj + hatk and bisects the angle between vecbg and vecc. Then which one of the following gives possible values of alpha and beta ?
Answer» `ALPHA =1 , BETA =1` `alpha=2 , beta=2` `alpha =1, beta =2` `alpha=2, beta=1.` ANSWER :A

Discussion

1398.	Find the area bounded by y = [-0. 01 x^(4) - 0.02 x^(2)], (where [*]G.I.F.) and curve 3x^(2)+4y^(2) = 12,which lies below y = - 1.
Answer» SOLUTION :N//A

Discussion

1399.	2 + (5)/(2!3) + (5.7)/(3!3^2) + (5.7.9)/(4!3^2) + …..oo =
Answer» `sqrt3` `ROOT(3)(3)` `3SQRT3` `2sqrt3` ANSWER :C

Discussion

1400.	Integrate the following functions : intsqrt(2x^(2)+3x+4)dx
Answer» Answer :`(4x+3)/(8)sqrt(2x^(2)+3x+4)+(23)/(16sqrt2)LOG[(4x+3)/(4)+sqrt(X^(2)+(3)/(2)x+2)]+c`

Discussion

Explore topic-wise InterviewSolutions in .

Let A be a non-empty set such that AxA has 9 elements among which are found (-1, 0) and (0, 1). Then,

Letf(x)be differentiable for all x. If f(1)=-2 and f'(x) ge 2 for x in [1, 6] then -

Ifthe range of random veriable X is {0,1,2,3,4….} withP(X = k) = ((k +1)a)/(3^(k)) " for " k ge 0, then a is equal to

Which type of overlapping is NOT possible (when internuclear axis is z-axis) ?

Evaluate the following integrals int_1^3(dx/x^3)dx

Sketch the graphs of the following functions. f(x) = x^3

If the tangents to y^(2)= 2x at 3 points have inclinations 30^(@), 40^(@), 50^(@)and the ordinatesof corresponding points are y_(1),y_(2),y_(3) then the ascending order of y_(1),y_(2),y_(3) is

The range of values of x for which the inequality (x-1)/(4x+5) lt (x-3)/(4x-3) holds is

Equation of curve in polar coordinates is I/r=2 sin^(2)""theta/2 then it represents

If z_(1),z_(2),z_(3) are vertices ofa Delta such that |z_(1)|=|z_(2)|=|z_(3)|=20andz_(1)z_(2)+z_(3)=12-5i distance of orthocentre from origin is:

A binary operation ** defined on Q^(+) the set of all positive is given a**b = (ab) /2 Then the inverse of 3 is :

If Integration using rigonometric identities : int(1)/(1+cotx)dx=px+q

Statement I Two non-zero, non-collinear vectors are linearly independent Statement II Any three coplanar vectors are linearly dependent Which of the above statement is/are true?

Points A(3,2,4), B ((33)/(5),(28)/(5),(38)/(5)) and C(9,8,10) are given. The ratio in which B divides overline(AC) is

Whichof the followingoptions is theonly INCORRECT combination ?

Evaluate the following integrals intx^(2)sin^(-1)x dx

Let A (2, -3) and B (-2, 1) be vertices of﻿ a triangle ABC. If the centroid of this﻿ triangle moves on the line 2x + 3y=1, then﻿ the locus of the vertex C is the line﻿

If a_(1) is the greatest value of f(x) , where f(x) =((1)/(2+[sinx])) (where [.] denotes greatest integer function) and a_(n-1)=((-1)^(n-2))/((n+1))+a_(n)(where n in N), then lim_(nrarroo)(a_(n))is

Solve (x+y)dy+(x-y)dx=0

Consider a regular polygon of 12 sides each of length one until, then which of the following is not true?

Five digit numbers can be formed from the digits 1,2,3,4,5. If one number is selected at random , the probability that it is an even number is

If ""^(n)C_(r-1)=36,""^(n)C_(r)=84 and ""^(n)C_(r+1)=126, then r is equal to

((cosalpha-cos 3 alpha)(sin8alpha+sin 2alpha))/((sin 5alpha-sin alpha)(cos 4 alpha-cos 6alpha))=

Graphof functions are given in the following figure. Check the functions forabsolute extremum.

Probability distribution of random variable X is as follows: Find P(X lt 3), P(X ge 3)andP(0 lt X lt 5).

The sum of the series (.^(101)C_(1))/(.^(101)C_(0)) + (2..^(101)C_(2))/(.^(101)C_(1)) + (3..^(101)C_(3))/(.^(101)C_(2)) + "….." + (101..^(101)C_(101))/(.^(101)C_(100)) is "____".

sqrt((x)/(x-3))+sqrt((x-3)/(x))=(5)/(2)," when "x ne 0and x ne 3

inta^(x+2)dx

Solve (1+2e^(x//y))dx + 2e^(x//y) (1-(x)/(y))dy = 0

The point does not lie in half plane x + 2y le 10 is

Which of the following is logically equivalent to p ^^ q ?

Also find the condition of having two common roots.

Prove that .^(n)C_(0)- .^(n)C_(1) + .^(n)C_(2)- .^(n)C_(3) + "……" + (-1)^(r) + .^(n)C_(r) + "……" = (-1)^(r ) xx .^(n-1)C_(r ).

Evalute the following integrals int sqrt(3 + 8x - 3x^(3)) dx

Given that for each a epsilon(0,1),lim(hto 0^(+)) int_(h)^(1-h)f^(-a)(1-t)^(a-1)dt exists. Let this limit be g(a). In addition it is given the function g(a) is differentiable on(0,1). The value of g'(1/2) is

In triangleABC, sin((A)/(2))sin((B)/(2))sin((C)/(2))=

If f={(1,2),(2,-3),(3,-1) then find (ii) sqrt(f).

Let N be the number of integer solutions of the equation n_(1) + n_(2) + n_(3) + n_(4)= 17 when n ge 1, n_(2) ge -1, n_(3) ge 3, n_(4) ge 0. If N= ""^(17)C_(K), then find K.

A(2,3,5), B(a,3,3) and C(7,5,beta) are the vertices of a triangle. If the median through A is equally inclined with the co-ordinate axes, then cos^-1(alpha/beta)=

If f: N rarr R be the function defined by f(x) = (2x-1)/2 and g : Q rarr R be another function defined by g(x) = x+2. Then , gof (3/2) is .......

A man speaks truth 2 out of 3 times. He picks one of the natural numbers in the set S={1,2,3,4,5,6,7} and reports that it is even. The probability that it is actually even is

Evaluate the following integrals (iii) int_(0)^(pi/2)(sqrt(sec x))/(sqrt(sec x)+sqrt(cosec x))dx

The vector veca = alpha hati + 2 hatj + beta hatk lies in the plance of the vectors vecb = hati + hatj and vecc= ahtj + hatk and bisects the angle between vecbg and vecc. Then which one of the following gives possible values of alpha and beta ?

Find the area bounded by y = [-0. 01 x^(4) - 0.02 x^(2)], (where [*]G.I.F.) and curve 3x^(2)+4y^(2) = 12,which lies below y = - 1.

2 + (5)/(2!3) + (5.7)/(3!3^2) + (5.7.9)/(4!3^2) + …..oo =

Integrate the following functions : intsqrt(2x^(2)+3x+4)dx

A binary operation defined on Q^(+) the set of all positive is given ab = (ab) /2 Then the inverse of 3 is :

Let A (2, -3) and B (-2, 1) be vertices of a triangle ABC. If the centroid of this triangle moves on the line 2x + 3y=1, then the locus of the vertex C is the line