28278 + Interview Questions in Maths in Class 12 Page 562 InterviewSolution

28051.	Method of integration by parts : If int_(n)=int(sinx)^(n)dx, x in N then the value (5I_(4)-6I_(6)) is.....
Answer» `SIN x(cosx^(5)+C` `sin2x-cos2x+c` `(Sin2x)/(8)(cos^(2)2X+1-cos 2x)+c` None of these Answer :C

Discussion

28052.	Calculate the weight of lime (CaO) obtained by heating 200 kg of 95% pure limestone (CaCO_(3)) :
Answer» 104.4 kg 105.4 kg 212.8 kg 106.4 kg Answer :A

Discussion

28053.	Assertion (A) : (3^2)/(2!) +(3^4)/(4!)+(3^6)/(4!)+ .... = Cosh 3 -1 Reason (R) : Cosh x =1 +(x^2)/(2!) +x^4/(4!) + .....
Answer» A is true, R is true and R is CORRECTEXPLANATION of A A is true, R is true and R is not correct EXPLANATION of A A is true , R is false A is false, R is true ANSWER :A

Discussion

28054.	If 10 coins are tossed, find the odds against the event of getting atleast 2 heads.
Answer» ANSWER :`11 : 1013`

Discussion

28055.	Integrate the functions (x)/((1+x)^(2))
Answer»

Discussion

28056.	Find the range of x for which the binomial expansions of the following are valid .(2 + 5x)^(-1//2)
Answer» ANSWER :`((-2)/(5), 2/5)`

Discussion

28057.	Solve for x tan^(-1) ((1-x)/(1+x))=(1)/(2) tan^(-1)x, x gt 0
Answer» ANSWER :`1/sqrt3`

Discussion

28058.	Two circles are such that one is inscribed in and the other is circumscribed about a square A _(1), A _(2), A _(3), A_(4), If the length of each side of the square is a and P, Q are two points respectively on these circles, then \|sum_(i =1) ^(4) (PAi) ^(2) -sum_(i =1) ^(4) (AQi) ^(2) \|=
Answer» `a ^(2) //4` `a ^(2) //2` `a ^(2) ` `2A^(2)` ANSWER :C

Discussion

28059.	For the parabola y=-x^(2), let a lt 0 and b gt 0,P(a, -a^(2)) and Q(b, -b^(2)). Let M be the mid-point of PQ and R be the point of intersection of the verticalline through M, with the parabola. If the ratio of the area of the region bounded by the parabolaand the line segmentPQ to the area of the triangle PQR be (lambda)/(mu), where lambda and mu are relatively prime positive integers, then find the value of (lambda+mu):
Answer» ANSWER :7

Discussion

28060.	The probability distribution of random variable X is as follows: Find value of k.
Answer» ANSWER :`K= (1)/(10)`

Discussion

28061.	Integration using rigonometric identities : int sin 4xe^(tan^(2)x)dx=a cos^(b)xe^(tan^(2)x)+c then the value of a^(2a) is ....
Answer» 256 265 285 156 Answer :A

Discussion

28062.	If alpha, beta are the irrational roots of the equation x^(5)-5x^(4)+9x^(3)-9x^(2)+5x-1=0 then the roots of the equation (alpha+beta)x^(2)+2alphabetax-alphabeta=0are
Answer» `-1,(1)/(3)` `(3+-sqrt(3))/(2)` `(1+-isqrt(3))/(2)` `1,-(1)/(3)` ANSWER :A

Discussion

28063.	Let f and g be differentiable functions on R such that fog is the identity function. If for some a,b in R,g'(a)=5 and g(a)=b, then f'(b) is equal to :
Answer» `2/5` `1/5` 1 5 Answer :D

Discussion

28064.	Evaluate the following determinants. [[1,1,1],[1,1,1],[1,1,1]]
Answer» SOLUTION :`[[1,1,1],[1,1,1],[1,1,1]]`=0 as the ROW are IDENTICAL.

Discussion

28065.	Let x be a non-zero real number. A determinant is chosen from the set of all determinants of order 2 with entries x or -x only. The probability that the value of the determinant is non-zero is
Answer» `(3)/(16)` `(1)/(4)` `(1)/(2)` `(1)/(3)` Answer :C

Discussion

28066.	If (m_(1),1//m_(1)), i=1,2,3,4 are concyclic points, then the value of m_(1)m_(2)m_(3)m_(4)" is"
Answer» 1 `-1` 0 `OO` ANSWER :A

Discussion

28067.	Show that the circles x^(2) +y^(2) + 2ax + c=0 and x ^(2) + y^(2)+ 2by + c=0to touch each other if(1)/(a^(2)) + (1)/( b^(2)) = (1)/( c )
Answer» Answer :i.e. if ` (1)/( a^(2)) + (1)/( B^(2)) = (1)/( C ) ` which is TRUE

Discussion

28068.	If f(x) = (x-1)/(x+1), x ne -1, 1, then "fof"^(-1) is
Answer» IDENTITY FUNCTION Even function Odd function NONE of these Answer :A

Discussion

28069.	Let an object be placed at some height h cm and let P and Q two points of observation which are at a distance 10 cm a part on a line inclined at angle 15° to the horizontal. If the angles of elevation of the object from P and Q are 30^@ and 60^@ respectively then find h.
Answer» ANSWER :`5sqrt(2)CM`

Discussion

28070.	Let A = N xx N and be the binary opertion on A defined by (a,b) (c,d) = (a + c, b+d) Show that is commutative and associative. Find the identity element for on A, if any.
Answer» ANSWER :IDENTITY ELEMENT does not EXIST.

Discussion

28071.	Find the probability distribution of (i) number of heads in two tosses of a coin. (ii) number of tails in the simultaneous tosses of three coins. (iii) number of heads in four tosses of a coin.
Answer» ANSWER :`(##NCERT_GUJ_MAT_XII_P2_C13_E04_004_A01##)` `(##NCERT_GUJ_MAT_XII_P2_C13_E04_004_A02##)`

Discussion

28072.	Using the second Guldin theorem, find the coordinates of the centre of gravity of the figure bounded by the x-axis and one are of the cycloid: x=a (t -sin t), y = a (1- cos t).
Answer» ANSWER :`(5A)/(6)`

Discussion

28073.	cot^(-1)((sqrt(1+x^(2))-1)/(x))=
Answer» `(PI)/(2)-(1)/(2)COT^(-1)x` `cot^(-1)x` `-(1)/(2)TAN^(-1)x` `(pi)/(2)-(1)/(2)tan^(-1)x` ANSWER :D

Discussion

28074.	In the cartesian plane, O is the origin of the coordinate axes. A person starts at O and walks a distance of 3 units in the NORTH - EAST direction and reaches the point P. From P he walks 4 units distance parallel to NORTH - WEST direction and reaches the point Q. Express the vector bar(OQ) interms of bar(i) and bar(j) (Observe angleXOP=45^(@))
Answer» ANSWER :`(1)/(SQRT(2))(-BAR(i)+7bar(j))`

Discussion

28075.	If eccentricity of conjugate hyperbola of the given hyperbola : \|sqrt((x-1)^(2)+(y-2)^(2))-sqrt((x-5)^(2)+(y-5)^(2))\|=3 is e', then value of 8e' is :
Answer» 12 14 17 10 Answer :D

Discussion

28076.	Prove statement "tan"^(-1)((a-b)/(1+ab)) +"tan"^(-1)((b-c)/(1+bc)) ="tan"^(-1)a-"tan"^(-1) c.
Answer» SOLUTION :"TAN"^(-1)((a-B)/(1+ab)) +"tan"^(-1)((b-C)/(1+bc)) `="tan"^(-1) a- "tan"^(-1)b+"tan"^(-1)b-"tan"^(-1)c` `"tan"^(-1)a-"tan"(-1)c`

Discussion

28077.	Find x and y :[[x+3],[2-y]]=[[1],[-3]]
Answer» SOLUTION :`[[x+3],[2-y]]=[[1],[-3]]` `:. x+3=1,2-y=-3` `:.x=-2,y=5`

Discussion

28078.	Construct Collection of all integers of multiples of 3 in the form of set and describe it with the help of proposition.
Answer» SOLUTION :`D ={0,+-3,+- 6}`

Discussion

28079.	There are 30 boys and 20 girls in a class. The mean and variance of their marks in maths are, respectively, 65 and 100. If 5 grace marks are added to the score of each students, then the revised mean and variance will be respectively.
Answer» `70, 100` ` 70, "variance " gt 100` ` 65, "variance " LT 100` ` 65, 100` ANSWER :A

Discussion

28080.	Find the variance of the number obtained on a throw of an unbiased die.
Answer» ANSWER :`(35)/(12)`

Discussion

28081.	If A = {x\|x inN, xle5}, B = {x\|x in Z, x^(2) – 5x +6=0}, then the number of onto functions from A to B is
Answer» 30 2 32 23 Answer :A

Discussion

28082.	int sec^(2)x*cosec^2(x)dx=.....+c
Answer» `tanx+cotx` `tanx-cotx` `sec^(2)x+"COSEC"^(2)x` `cotx-tanx` ANSWER :B

Discussion

28083.	Let function f(x) be defined as f(x) = \|sin^(-1)x\| + cos^(-1) (1/x) .Then which of the following is /are TRUE.
Answer» f(X) is injective in its domain. f(x) is MANY - one in its domain. Range of f is SINGLETON set sgn (f(x)) =1 , where sgn x DENOTES signum function of x. Answer :A::D

Discussion

28084.	Using differentials, find the approximate value of each of the up to 3 places of decimal. (0.0999)^((1)/(10))
Answer» ANSWER :0.999

Discussion

28085.	A set of values of theta for which the system of equations (sin 3theta ) x +4y+3z=0,2x+7y+7z=0 has non -trivial solutions is
Answer» `(n+1)^(pi)/(2)+(-1)^(n)(pi)/(4)` (here n is any INTEGER) `(n-1)^(pi)/(2)+(-1)^(n)(pi)/(4)` (here n is any integer) `(npi)/(2)+(-1)^(n)(pi)/(6)` ( here n is any integer ) `npi +(-1)^(n)(pi)/(6)` ( here n is any integer ) Answer :D

Discussion

28086.	For Delta ABC,if 81 + 144 a ^(4) + 16b ^(4) + 9c ^(4) =144 abc, (where notations have their usual meaning), then :
Answer» `a GT b gt C` `A lt B lt C` Area of `Delta ABC = (3 SQRT3)/(8)` Triangle ABC is RIGHT angled Answer :B::C::D

Discussion

28087.	Solve system of linear equations , using matrix method if exists 2/x-3/y+3/z=10 1/x+1/y+1/z=10 3/x-1/y+2/z=13
Answer» ANSWER :`x=1/2,y=1/3,z=1/5`

Discussion

28088.	If \|x-5\| lt 1 then the range of f(x) = (x)/(X+10) is
Answer» `(2/3 , 3/8)` `(0 , OO)` `(3/7, 3/4)` `(1, oo)` ANSWER :A

Discussion

28089.	If the lengths of tangents drawn to the circlesx^(2) + y^(2) -8x + 40 = 0 , 5x^(2) + 5y^(2) - 25x + 80 = 0 , x^(2) + y^(2) - 8x + 16y+ 160 = 0from the point P are equal, then P =
Answer» `(8, (15)/(2))` `(-8,(15)/(2))` `(8, (-15)/(2))` `(-8, (-15)/(2))` ANSWER :C

Discussion

28090.	Study the following statements. I. The vertex of the parabola x=ly^(2)+my+n is (n-m^(2)/(4 l), -m/(2l)) II. The focus of the parabola y=l x^(2) +mx+n is (n+(1-m^(2))/(4l), -m/(2l)) III. The pole of the line lx+my+n=0 with respect to the parabola x^(2)=4ay is (-(2 al)/m, n/m) Then the correct option among the following is
Answer» A.All the three STATEMENT are TRUE B.Statement I & II are true but III is false C.Statement I & III are true but II is false D.Statement II & III are true but I is false Answer :C

Discussion

28091.	Maximum slope of the curve y=-x^(3)+3x^(2)+9x-27 is ………….
Answer» 0 12 16 32 Answer :B

Discussion

28092.	Integrate the functions 1/(xsqrt(ax-x^(2))) [Hint: Put x =a/t]
Answer» ANSWER :`(-2)/(a) SQRT((a-X)/(x))+C`

Discussion

28093.	If the chord of contact of a point P with respect to thecirclesx ^(2) + y ^(2)= a ^(2)cut the circle at A and B such thatangle AOB =90 ^(@).Find the locus of P.
Answer» Answer :` THEREFORE (x_1.y_1) ` LIES on the circle `X ^(2) +y^(2)=2A^(2) `

Discussion

28094.	The solution of cos x(dy)/(dx) + y = sin x is
Answer» `y(sec X + TAN x) = sec x + Tan x + x + C` `y(sec x + Tan x) = sec x + Tan x - x + c` `y(sec x + Tan x) = sec x - Tan x - x + c` `y(sec x - Tan x) = sec x + Tan x + x - c` ANSWER :B

Discussion

28095.	Which of the following is correct combination
Answer» (i) (II) (Q) (III) (i) (S) (II) (iv) (S) (IV) (iii) (R) ANSWER :B

Discussion

28096.	Which of the following is correct combination
Answer» (II) (ii) (P) (i) (ii) (Q) (I) (ii) (R) (IV) (III) (R) Answer :C

Discussion

28097.	If line (x-2)/(3)=(y-4)/(4)=(z+2)/(1)is parallel to planesmux+3y-2z+d=0and x-2lambda y+z=0,then value oflambdaand mu are
Answer» `mu=4, lambda=-(2)/(3)` `mu=-6, lambda=-2` `mu=(-10)/(3), lambda=(-1)/(2)` `mu=(-10)/(3), lambda=(1)/(2)` SOLUTION :`3xxmu+4xx3+1xx(-2)=0` `3mu=2-12` `mu=(-10)/(3) and3xx1+4xx(-2lambda)+1xx1=0` `-8lambda=-4,""lambda=(1)/(2)`

Discussion

28098.	bar(a)=a_(1)hati+a_(2)hatj+a_(3)hatk,bar(b)=b_(1)hati+b_(2)hatj+b_(3)hatk,bar( c )=c_(1)hati+c_(2)hatj+c_(3)hatk are three non zero vectors. The unit vector bar( c ) is perpendicular to bar(a) and bar(b). The angle between bar(a) and bar(b) is (pi)/(6) then, \|{:(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3)):}\| = .............
Answer» 0 1 `(1)/(4)\|BAR(a)\|^(2)\|bar(B)\|^(2)` `(3)/(4)\|bar(a)\|^(2)\|bar(b)\|^(2)` Answer :C

Discussion

28099.	The solution of y dx - x dy + log x dx = 0 is
Answer» `y - LOG x - 1 = CX` `x + log y + 1 = cx` `y + log x + 1 = cx` `y + log x - 1 = C x` ANSWER :C

Discussion

28100.	Out of 8 given points .3 are collinear.How many different straight lines can be drawn by joining any two points from those 8 points ?
Answer» 26 28 27 25 Answer :A

Discussion

Explore topic-wise InterviewSolutions in .

Method of integration by parts : If int_(n)=int(sinx)^(n)dx, x in N then the value (5I_(4)-6I_(6)) is.....

Calculate the weight of lime (CaO) obtained by heating 200 kg of 95% pure limestone (CaCO_(3)) :

Assertion (A) : (3^2)/(2!) +(3^4)/(4!)+(3^6)/(4!)+ .... = Cosh 3 -1 Reason (R) : Cosh x =1 +(x^2)/(2!) +x^4/(4!) + .....

If 10 coins are tossed, find the odds against the event of getting atleast 2 heads.

Integrate the functions (x)/((1+x)^(2))

Find the range of x for which the binomial expansions of the following are valid .(2 + 5x)^(-1//2)

Solve for x tan^(-1) ((1-x)/(1+x))=(1)/(2) tan^(-1)x, x gt 0

Two circles are such that one is inscribed in and the other is circumscribed about a square A _(1), A _(2), A _(3), A_(4), If the length of each side of the square is a and P, Q are two points respectively on these circles, then |sum_(i =1) ^(4) (PAi) ^(2) -sum_(i =1) ^(4) (AQi) ^(2) |=

The probability distribution of random variable X is as follows: Find value of k.

Integration using rigonometric identities : int sin 4x*e^(tan^(2)x)dx=a cos^(b)x*e^(tan^(2)x)+c then the value of a^(2a) is ....

If alpha, beta are the irrational roots of the equation x^(5)-5x^(4)+9x^(3)-9x^(2)+5x-1=0 then the roots of the equation (alpha+beta)x^(2)+2alphabetax-alphabeta=0are

Let f and g be differentiable functions on R such that fog is the identity function. If for some a,b in R,g'(a)=5 and g(a)=b, then f'(b) is equal to :

Evaluate the following determinants. [[1,1,1],[1,1,1],[1,1,1]]

Let x be a non-zero real number. A determinant is chosen from the set of all determinants of order 2 with entries x or -x only. The probability that the value of the determinant is non-zero is

If (m_(1),1//m_(1)), i=1,2,3,4 are concyclic points, then the value of m_(1)m_(2)m_(3)m_(4)" is"

Show that the circles x^(2) +y^(2) + 2ax + c=0 and x ^(2) + y^(2)+ 2by + c=0to touch each other if(1)/(a^(2)) + (1)/( b^(2)) = (1)/( c )

If f(x) = (x-1)/(x+1), x ne -1, 1, then "fof"^(-1) is

Let an object be placed at some height h cm and let P and Q two points of observation which are at a distance 10 cm a part on a line inclined at angle 15° to the horizontal. If the angles of elevation of the object from P and Q are 30^@ and 60^@ respectively then find h.

Let A = N xx N and ** be the binary opertion on A defined by (a,b) ** (c,d) = (a + c, b+d) Show that ** is commutative and associative. Find the identity element for ** on A, if any.

Find the probability distribution of﻿ (i) number of heads in two tosses of a coin. ﻿ (ii) number of tails in the simultaneous tosses of three coins.﻿ (iii) number of heads in four tosses of a coin.﻿

Using the second Guldin theorem, find the coordinates of the centre of gravity of the figure bounded by the x-axis and one are of the cycloid: x=a (t -sin t), y = a (1- cos t).

cot^(-1)((sqrt(1+x^(2))-1)/(x))=

If eccentricity of conjugate hyperbola of the given hyperbola : |sqrt((x-1)^(2)+(y-2)^(2))-sqrt((x-5)^(2)+(y-5)^(2))|=3 is e', then value of 8e' is :

Prove statement "tan"^(-1)((a-b)/(1+ab)) +"tan"^(-1)((b-c)/(1+bc)) ="tan"^(-1)a-"tan"^(-1) c.

Find x and y :[[x+3],[2-y]]=[[1],[-3]]

Construct Collection of all integers of multiples of 3 in the form of set and describe it with the help of proposition.

There are 30 boys and 20 girls in a class. The mean and variance of their marks in maths are, respectively, 65 and 100. If 5 grace marks are added to the score of each students, then the revised mean and variance will be respectively.

Find the variance of the number obtained on a throw of an unbiased die.﻿

If A = {x|x inN, xle5}, B = {x|x in Z, x^(2) – 5x +6=0}, then the number of onto functions from A to B is

int sec^(2)x*cosec^2(x)dx=.....+c

Let function f(x) be defined as f(x) = |sin^(-1)x| + cos^(-1) (1/x) .Then which of the following is /are TRUE.

Using differentials, find the approximate value of each of the up to 3 places of decimal. (0.0999)^((1)/(10))

A set of values of theta for which the system of equations (sin 3theta ) x +4y+3z=0,2x+7y+7z=0 has non -trivial solutions is

For Delta ABC,if 81 + 144 a ^(4) + 16b ^(4) + 9c ^(4) =144 abc, (where notations have their usual meaning), then :

Solve system of linear equations , using matrix method if exists 2/x-3/y+3/z=10 1/x+1/y+1/z=10 3/x-1/y+2/z=13

If |x-5| lt 1 then the range of f(x) = (x)/(X+10) is

If the lengths of tangents drawn to the circlesx^(2) + y^(2) -8x + 40 = 0 , 5x^(2) + 5y^(2) - 25x + 80 = 0 , x^(2) + y^(2) - 8x + 16y+ 160 = 0from the point P are equal, then P =

Maximum slope of the curve y=-x^(3)+3x^(2)+9x-27 is ………….

Integrate the functions 1/(xsqrt(ax-x^(2))) [Hint: Put x =a/t]

If the chord of contact of a point P with respect to thecirclesx ^(2) + y ^(2)= a ^(2)cut the circle at A and B such thatangle AOB =90 ^(@).Find the locus of P.

The solution of cos x(dy)/(dx) + y = sin x is

Which of the following is correct combination

Which of the following is correct combination

If line (x-2)/(3)=(y-4)/(4)=(z+2)/(1)is parallel to planesmux+3y-2z+d=0and x-2lambda y+z=0,then value oflambdaand mu are

The solution of y dx - x dy + log x dx = 0 is

Out of 8 given points .3 are collinear.How many different straight lines can be drawn by joining any two points from those 8 points ?

Integration using rigonometric identities : int sin 4xe^(tan^(2)x)dx=a cos^(b)xe^(tan^(2)x)+c then the value of a^(2a) is ....

Let A = N xx N and be the binary opertion on A defined by (a,b) (c,d) = (a + c, b+d) Show that is commutative and associative. Find the identity element for on A, if any.

Find the probability distribution of (i) number of heads in two tosses of a coin. (ii) number of tails in the simultaneous tosses of three coins. (iii) number of heads in four tosses of a coin.

Find the variance of the number obtained on a throw of an unbiased die.