28278 + Interview Questions in Maths in Class 12 Page 25 InterviewSolution

1201.	A bag contains 5 white and 4 black balls. 3 balls are drawn and laid aside. Without noting their colour. Then one more ball is drawn. Find the probability that it is white.
Answer» ANSWER :`(5)/(9)`

Discussion

1202.	Match the following
Answer» b,a,c,e a,b,c,d a,b,c,e b,a,c,d ANSWER :D

Discussion

1203.	Sum of the series 2.5+(1)/(2)+(1)/(3)+(1)/(2^(2))+(1)/(3^(2))+(1)/(3^(3))+... is
Answer» ANSWER :4

Discussion

1204.	Let V = Volume of the tetrahedron whose vertices are A(1,0,0),B(0,0,1),C(0,0,2)andD(1,2,3) then 3V = ___________
Answer» ANSWER :1

Discussion

1205.	Differentiate cos(ax+b)
Answer» SOLUTION :LET `y=cos(ax+b)` `Then `dy/dx=-SIN(ax+b)xxd/dx(ax+b) "by CHAIN RULE". `=-sin(ax+b) cdota=-asin(ax+b)`

Discussion

1206.	If A (x) = \|{:(x + 1, 2x + 1, 3x + 1),(2x + 1, 3x + 1, x + 1),(3x + 1, x + 1, 2x + 1):}\| then int_(0)^(1) A (x) dx is equal to
Answer» `-15` `- (15)/(2)` `-30` `-5` ANSWER :B

Discussion

1207.	Find the cartesian equation of the line which passes through the point (-2, 4, -5) and parallel to the line given by(x+3)/(3)=(y-4)/(5)=(z+8)/(6)
Answer» ANSWER :`THEREFORE =(z+5)/(6)`

Discussion

1208.	Determine the area of parallelogram whose adjacent sides are the vector hati+hatj, -hati+2hatj
Answer» SOLUTION :Let `veca = hati+hatj, vecb = -hati+2hatj` Then `vecaxxvecb = (hati+hatj)XX(-hati+2hatj)` =`-hatixxhati+2hatixxhatj-hatjxxhati+2hatixxhatj` `2hatk+hatk = 3hatk` AREA of the PARALLELOGRAM =`\|vecaxxveca\| = \|3hatk\|` = 3 square units.

Discussion

1209.	Let the vectors veca, vecb, vecc and vecd be such that (veca xx vecb) xx (veccxx vecd) = vec0. Let P_(1), P_(2) be planes determined by the pairs of vectors veca, vecb and vecc, vecd respectively. Then the between P _(1) and P _(2) is :
Answer» 0 `pi//4` `pi//3` `pi//2.` ANSWER :A

Discussion

1210.	The shadowof atowerisfoundto be60metershorterwhenthe sun'saltitudechangesfrom30^@ to60^@the height ofthetowerfromthe groundis appoximately equal to
Answer» 62cm 301 m 101 m 75m Answer :C

Discussion

1211.	Evaluation of definite integrals by subsitiution and properties of its : int_(0)^(2)f(x)dx=......... where f(x)=max{x,x^(2)}
Answer» `(8)/(3)` `(13)/(6)` `(17)/(6)` `(19)/(6)` ANSWER :A

Discussion

1212.	The marginal cost MC of a product is given to be a constant multiple of number of units (x) produced. Find the total cost function if the fixed cost is Rs. 1000 and the cost of producing 30 units is Rs. 2800.
Answer» ANSWER :`C(X)=2X^(2)+1000`

Discussion

1213.	The nature of inter cepts made on the axes by the tangent at the point ((16)/( 5) ,(9)/(5))to the ellipse 9x^(2) +16y^(2)=144are
Answer» equal UNEQUAL equal in MAGNITUDE but OPPOSITE in sign interpts in the RATIO 1:2 ANSWER :A

Discussion

1214.	If ath , bth , cth terms are the middle terms in the expansion of (x+1//x)^10, (a//x-x//a)^12, (x^2-1//x^2)^8 then the ascending order of a, b, c is
Answer» a, B, C b, c, a c, a, b a, c, b Answer :C

Discussion

1215.	Solve ye^(y) dx = (y^(4)=3xe^(y))dy
Answer» ANSWER :` X = -y^(3) E^(-y) + CY^(3)`

Discussion

1216.	The position vector of a particle is given by vecr=10hati+(20-5t)hatj(m) where t is in seconds and vecr is in meters. Choose the correct statement(s) :
Answer» Velocity of PARTICLE is of MAGNITUDE 10 m/s Velocity of particle is of magnitude 5 m/s Direction of motion of particle is parallel to x-axis. Direction of motion of particle is parallel to z-axis.

Discussion

1217.	Given the following frequency distribution with some missing frequencies . {:("Class",10-20,20-30,30-40,40-50,50-60,60-70,70-80),(" "f," "180," "-," "34," "180," "136," "-," "50):}If the total frequency is 685 and median is 42.6 then the missing frequencies are
Answer» 81,24 80,25 82,23 83,22 Answer :C

Discussion

1218.	Prove that for any givenintegral with finite limits a and b onecanalways choose the linear substitution x = pt + q (p,q constants) so as totransformthis integral into a newone withlimits 0 and 1
Answer» ANSWER :`int_(a)^(b) f(X) dx = (b - a) int_(0)^(1) f[(b -a) t + a] DT`

Discussion

1219.	Consider the following statement I: The negation of the statement "The number 2 is greater then 7" is"The number 2 is not greater then 7". II: The negation of the statement "Every natural number is an integer" is every natural number is not an integer". Choose the correct option.
Answer» Only I is true Only II is true Both are true Both are false Answer :C

Discussion

1220.	If x is real, then the range of (x^(2)+2x+1)/(x^(2)+2x+7) is
Answer» `0,1` `1,2` `0,2` `2,3` ANSWER :A

Discussion

1221.	Find (dy)/(dx)" if "y=(log x)^("cos x)
Answer» Answer :`=(LOGX)^(COS x) [(cos x)/(x LOG x)-sin x log (log x)]`

Discussion

1222.	If the line 2x + 5y = 12 intersects the ellipse 4x^(2)+5y^(2) = 20 in two distinct points A and B, then the mid point of AB is
Answer» 0,1 1,2 1,0 2,1 Answer :B

Discussion

1223.	If the total cost function is given by C(x), where x is the quality of the output, then (d)/(dx)(AC) =
Answer» `(1)/(X)(AC - MC)` `(d)/(DX) (MC)` `(1)/(x^(2)) (MC - AC)` NONE of these Answer :D

Discussion

1224.	The sum of(1)/( 2sqrt1+1 sqrt2 ) + (1)/( 3 sqrt2 + 2 sqrt3 ) + (1)/( 4 sqrt3 + 3 sqrt4 ) +...+(1)/( 25 sqrt 24 + 24 sqrt25) is
Answer» ANSWER :`4/5`

Discussion

1225.	A variable plane in space moves in such a way that the sum of its reciprocal of intercepts on the x and y-axes exceed the reciprocal of its intercept on the z-axis by 2. If all these planes passing through a fixed point F(alpha,beta,gamma), then alpha^(2)+beta^(2)+gamma^(2) = ____________
Answer» ANSWER :`0.75`

Discussion

1226.	Connect int x^(m-1)(a+bx^(n))^(p)dx with int x^(m-n-1)(a+bx^(n))^(p)dx and evaluate int(x^(8)dx)/((1-x^(3))^(1//3)).
Answer» ANSWER :`-1/8 x^(6)(1-x^(3))^(2//3)-(3)/(20)x^(3)(1-x^(3))^(2//3)-(9)/(40)(1-x^(3))^(2//3)+C`

Discussion

1227.	Let f(x) = cos ((pi)/(x)) xne 0 then assuming k as an integer ,
Answer» F(x) INCREASE in the interval `((1)/(2K+1),(1)/(2k))` f(x) decreases in the interval `((1)/(2k+1),(1)/(2k))` f(x) decrease in the interval `((1)/(2k+2),(1)/(2k+1))` f(x) increases in the interval `((1)/(2k+2),(1)/(2k+1))` Answer :A::C

Discussion

1228.	Let 0 le beta_r le 1 and sum_(r=1)^(k) cos^(-1) beta_r =(kpi)/2 for any k ge 1 and A=sum_(r=1)^k (beta_r)^r , then lim_(x to A) ((1+x^2)^(1//3) -(1-2x)^(1//4))/(x+x^2) is equal to
Answer» ANSWER :`0.50`

Discussion

1229.	int_(0)^(oo)(1)/(1+x^(n))dx, AA n gt 1 equals
Answer» `2int_(0)^(oo)(1)/(1+x)dx` `int_(-oo)^(oo)(1)/(1+x^(N))dx` `int_(1)^(oio)(dx)/((x^(n)-1)^(1//n))` `int_(0)^(1)(1)/((1-x^(n))^(1//n))dx` ANSWER :D

Discussion

1230.	If int_(0)^(pi) f(tan x) dx= lambda then int_(0)^(2pi) f(tan x) dx=
Answer» `LAMBDA/2` `-2 lambda` `2 lambda` `- lambda/2` ANSWER :C

Discussion

1231.	When two dice are thrown n number of times, the probability of getting a doublet atleast once in greater than 80% and the least value of n is lambda, then the value of lambda is equal to
Answer» 62 71 80 91 Answer :D

Discussion

1232.	The minimum number of elements that must be added to the relation R={(1,2),(2,3)} on the set {1, 2, 3} so that it is an equivalence relation
Answer» 3 5 6 7 Answer :D

Discussion

1233.	Let a, b and c bereal numbers such that 4a+2b+c=0 andab gt 0. Then the quadratic equation ax^(2)+bx+c=0 has
Answer» REAL ROOTS COMPLEX roots purely IMAGINARY roots only ONE root Answer :a

Discussion

1234.	If int_(0)^(2Pi) sin^(2020) x.cos^(2019) x dx = 1 then the value of f(I), (where f(x) = x cos(I) – x^(2) sin2(I)) is equal to:-
Answer» 0 `(Pi)/(4sqrt(2))-(Pi^2)/4` 1 `cos 1 - sin 2` Solution :Let `p(x) = sin^(2020)x.cos^(2019)x` `implies p(2pi-x)=p(x)` `implies I = 2.int_(0)^(pi) sin^(2020)(pi-x).cos^(2019)(pi-x) dx` `implies I = -2int_(0)^(pi)sin^(2020)x cos^(2019)x dx` `implies 3I = 0 or I = 0 implies f (I) = 0`.

Discussion

1235.	Integrate the functions 1/sin(x+alpha))
Answer»

Discussion

1236.	Integrate the following functions: tan^4x
Answer» Solution :`tan^4x = tan^2 X tan^2 x` =`tan^2 x sec^2 x-(sec^2 x-1)` =`tan^2 x sec^2 x -sec^2 x+1` THEREFORE `INT tan^4 x dx` =`int (ta_n^2x sec^2 x-sec^2 x+1)dx` `int t^2dt-TANX+x+c`, if we PUT tanx =t =`t^3/3-tanx+x+c` =`tan^3 x/3 -tanx+x+c`

Discussion

1237.	A lot contains 15 items of which 5 are defective. If three items are drawn at random, find the probability that (i) all three are defective
Answer» SOLUTION :A LOT contains 15 items of which 5 are defective. THREE items are drawn at random. As the items are drawn ONE after another, their probability `=5/15xx4/14xx3/13`

Discussion

1238.	A lot contains 15 items of which 5 are defective. If three items are drawn at random, find the probability thatnone of the three is defective. Do this problem directly.
Answer» SOLUTION :As none of the 3 items are defective we have to draw 3 non-defective items one after another.`therefore` Their PROBABILITY=`10/15xx9/14xx8/13`

Discussion

1239.	Let u = (1)/(2) (-1 + sqrt(3)i) and z = u - u^(2) - 2. Then the value of z^(4) + 3z^(3) + 2z^(2) - 11z - 6 is :
Answer» 1 -1 2 -2 Answer :A

Discussion

1240.	Write minors and cofactors of the elements of following determinant \|{:(4,3,8),(6,7,5),(3,1,2):}\|
Answer» Answer :`M_(11)=9,M_(12)=-3,M_(13)=-15,M_(21)=-2,M_(22)=-16,M_(23)=-5,M_(31)=-41,M_(32)=-28,M_(33)=10` `A_(11)=9,A_(12)=-3,A_(13)=-15,A_(21)=2,A_(22)=-16,A_(23)=-5,A_(31)=-41,A_(32)=-28,A_(33)=10`

Discussion

1241.	Find an approximate value of (i) (1)/(root(3)(999)) (ii) (627)^((1)/(4)) corrected to 5 decimal places
Answer» SOLUTION :N/A

Discussion

1242.	If the range of real values of k for which equation 2"log"_3^2x-\|log_3x\|+k=0 has four distinct solutions is (p,s) , then the value of ((s+p)/2) is
Answer» ANSWER :0.12 or 0.13

Discussion

1243.	If C_(r) stands for ""^(n)C_(r) then the sum of the series (2(n/2)!(n/2)!)/(n!)[C_(0)^(2)-2C_(1)^(2)+....+(-1)^(n)(n+1)C_(n)^(2)] where n is an even positive integer, is equal to:
Answer» 0 `(-1)^(N//2)(n+1)` `(-1)^(n//2)(n+2)` `(-1)^(n)n` ANSWER :C

Discussion

1244.	Randomly selected one person from rural area for the following study. It is found that probability of an event that person has botanical allergy (i.e. plants allergy) is (7)/(20) & probability by sand and plant is (3)/(17). If person has allergy by plants then find the probability that person has allergy by sand.
Answer» ANSWER :`(60)/(119)`

Discussion

1245.	If A and Bare two events such thatP(A)= (1)/(4),P(B)= (1)/(2)and P(A nnB)= (1)/(8) ,then P ( not A and not B) =
Answer» ` (3)/(8)` ` ( 5)/(8)` ` ( 7)/(8)` None of these ANSWER :A

Discussion

1246.	You have one knight, one king, one queen, one rook and one pawn each of the same colour. Arrange all five of these pieces on the chessboard shown such that the following conditions are satisfied: (i)The no. of pieces attacking a square(with a number on it) should be equal to the number written on it. (ii)There should not be any piece on a square which has a number written on it. [Note: A king can only attack its adjacent squares, a pawn attacks its diagonally adjacent squares, a rook on its horizontal and vertical lines, a queen on its horizontal, vertical and diagonal lines and a knight as explained in question 1. Lastly, rook and queen cannot attack a square if there is a some other piece in the path of attack.] What should be the position of the Queen?
Answer» B1 B2 A1 A2 Solution :(C) The above diagram shows ONE of the POSSIBLE solution but CLEARLY the QUEENS’s position must be A1 in EVERY possible solution.

Discussion

1247.	A function y=(ax+b)/((x-1)(x-4)) has maximum or minimum at P(2,-1) then find a and b. Also show that y has maximum value at P.
Answer» ANSWER :a = 1, B = 0

Discussion

1248.	If a number x is selected from natural numbers 1 to 100, then the probability for x +100//x gt 29 is
Answer» ANSWER :`(39)/(50)`

Discussion

1249.	Evaluate : int(sinx+cosx)/(sqrt(sinxcosx))dx.
Answer» ANSWER :`sqrt2sin^(-1)(sinx-cosx)+C.`

Discussion

1250.	A ladder 13 m long is leaning against a wall. The bottom of the ladder is pulled along the ground, away from the wall, at the rate of 2m/sec. How fast is the height on the wall decreasing when the foot of the ladder is 5 m away from the wall ?
Answer» ANSWER :DECREASING at the RATE of `(5)/(6)` m/sec

Discussion

Explore topic-wise InterviewSolutions in .

A bag contains 5 white and 4 black balls. 3 balls are drawn and laid aside. Without noting their colour. Then one more ball is drawn. Find the probability that it is white.

Match the following

Sum of the series 2.5+(1)/(2)+(1)/(3)+(1)/(2^(2))+(1)/(3^(2))+(1)/(3^(3))+... is

Let V = Volume of the tetrahedron whose vertices are A(1,0,0),B(0,0,1),C(0,0,2)andD(1,2,3) then 3V = ___________

Differentiate cos(ax+b)

If A (x) = |{:(x + 1, 2x + 1, 3x + 1),(2x + 1, 3x + 1, x + 1),(3x + 1, x + 1, 2x + 1):}| then int_(0)^(1) A (x) dx is equal to

Find the cartesian equation of the line which passes through the point (-2, 4, -5) and parallel to the line given by(x+3)/(3)=(y-4)/(5)=(z+8)/(6)

Determine the area of parallelogram whose adjacent sides are the vector hati+hatj, -hati+2hatj

Let the vectors veca, vecb, vecc and vecd be such that (veca xx vecb) xx (veccxx vecd) = vec0. Let P_(1), P_(2) be planes determined by the pairs of vectors veca, vecb and vecc, vecd respectively. Then the between P _(1) and P _(2) is :

The shadowof atowerisfoundto be60metershorterwhenthe sun'saltitudechangesfrom30^@ to60^@the height ofthetowerfromthe groundis appoximately equal to

Evaluation of definite integrals by subsitiution and properties of its : int_(0)^(2)f(x)dx=......... where f(x)=max{x,x^(2)}

The marginal cost MC of a product is given to be a constant multiple of number of units (x) produced. Find the total cost function if the fixed cost is Rs. 1000 and the cost of producing 30 units is Rs. 2800.

The nature of inter cepts made on the axes by the tangent at the point ((16)/( 5) ,(9)/(5))to the ellipse 9x^(2) +16y^(2)=144are

If ath , bth , cth terms are the middle terms in the expansion of (x+1//x)^10, (a//x-x//a)^12, (x^2-1//x^2)^8 then the ascending order of a, b, c is

Solve ye^(y) dx = (y^(4)=3xe^(y))dy

The position vector of a particle is given by vecr=10hati+(20-5t)hatj(m) where t is in seconds and vecr is in meters. Choose the correct statement(s) :

Given the following frequency distribution with some missing frequencies . {:("Class",10-20,20-30,30-40,40-50,50-60,60-70,70-80),(" "f," "180," "-," "34," "180," "136," "-," "50):}If the total frequency is 685 and median is 42.6 then the missing frequencies are

Prove that for any givenintegral with finite limits a and b onecanalways choose the linear substitution x = pt + q (p,q constants) so as totransformthis integral into a newone withlimits 0 and 1

Consider the following statement I: The negation of the statement "The number 2 is greater then 7" is"The number 2 is not greater then 7". II: The negation of the statement "Every natural number is an integer" is every natural number is not an integer". Choose the correct option.

If x is real, then the range of (x^(2)+2x+1)/(x^(2)+2x+7) is

Find (dy)/(dx)" if "y=(log x)^("cos x)

If the line 2x + 5y = 12 intersects the ellipse 4x^(2)+5y^(2) = 20 in two distinct points A and B, then the mid point of AB is

If the total cost function is given by C(x), where x is the quality of the output, then (d)/(dx)(AC) =

The sum of(1)/( 2sqrt1+1 sqrt2 ) + (1)/( 3 sqrt2 + 2 sqrt3 ) + (1)/( 4 sqrt3 + 3 sqrt4 ) +...+(1)/( 25 sqrt 24 + 24 sqrt25) is

A variable plane in space moves in such a way that the sum of its reciprocal of intercepts on the x and y-axes exceed the reciprocal of its intercept on the z-axis by 2. If all these planes passing through a fixed point F(alpha,beta,gamma), then alpha^(2)+beta^(2)+gamma^(2) = ____________

Connect int x^(m-1)(a+bx^(n))^(p)dx with int x^(m-n-1)(a+bx^(n))^(p)dx and evaluate int(x^(8)dx)/((1-x^(3))^(1//3)).

Let f(x) = cos ((pi)/(x)) xne 0 then assuming k as an integer ,

Let 0 le beta_r le 1 and sum_(r=1)^(k) cos^(-1) beta_r =(kpi)/2 for any k ge 1 and A=sum_(r=1)^k (beta_r)^r , then lim_(x to A) ((1+x^2)^(1//3) -(1-2x)^(1//4))/(x+x^2) is equal to

int_(0)^(oo)(1)/(1+x^(n))dx, AA n gt 1 equals

If int_(0)^(pi) f(tan x) dx= lambda then int_(0)^(2pi) f(tan x) dx=

When two dice are thrown n number of times, the probability of getting a doublet atleast once in greater than 80% and the least value of n is lambda, then the value of lambda is equal to

The minimum number of elements that must be added to the relation R={(1,2),(2,3)} on the set {1, 2, 3} so that it is an equivalence relation

Let a, b and c bereal numbers such that 4a+2b+c=0 andab gt 0. Then the quadratic equation ax^(2)+bx+c=0 has

If int_(0)^(2Pi) sin^(2020) x.cos^(2019) x dx = 1 then the value of f(I), (where f(x) = x cos(I) – x^(2) sin2(I)) is equal to:-

Integrate the functions 1/sin(x+alpha))

Integrate the following functions: tan^4x

A lot contains 15 items of which 5 are defective. If three items are drawn at random, find the probability that (i) all three are defective

A lot contains 15 items of which 5 are defective. If three items are drawn at random, find the probability thatnone of the three is defective. Do this problem directly.

Let u = (1)/(2) (-1 + sqrt(3)i) and z = u - u^(2) - 2. Then the value of z^(4) + 3z^(3) + 2z^(2) - 11z - 6 is :

Write minors and cofactors of the elements of following determinant |{:(4,3,8),(6,7,5),(3,1,2):}|

Find an approximate value of (i) (1)/(root(3)(999)) (ii) (627)^((1)/(4)) corrected to 5 decimal places

If the range of real values of k for which equation 2"log"_3^2x-|log_3x|+k=0 has four distinct solutions is (p,s) , then the value of ((s+p)/2) is

If C_(r) stands for ""^(n)C_(r) then the sum of the series (2(n/2)!(n/2)!)/(n!)[C_(0)^(2)-2C_(1)^(2)+....+(-1)^(n)(n+1)C_(n)^(2)] where n is an even positive integer, is equal to:

If A and Bare two events such thatP(A)= (1)/(4),P(B)= (1)/(2)and P(A nnB)= (1)/(8) ,then P ( not A and not B) =

A function y=(ax+b)/((x-1)(x-4)) has maximum or minimum at P(2,-1) then find a and b. Also show that y has maximum value at P.

If a number x is selected from natural numbers 1 to 100, then the probability for x +100//x gt 29 is

Evaluate : int(sinx+cosx)/(sqrt(sinxcosx))dx.

A ladder 13 m long is leaning against a wall. The bottom of the ladder is pulled along the ground, away from the wall, at the rate of 2m/sec. How fast is the height on the wall decreasing when the foot of the ladder is 5 m away from the wall ?