28278 + Interview Questions in Maths in Class 12 Page 156 InterviewSolution

7751.	By using the properties of definite integrals, evaluate the integrals int_((-pi)/2)^(pi/2)sin^(7)xdx
Answer» ANSWER :`overset((pi)/(2) UNDERSET(-(pi)/(2)int sin^(7)x dx=0`

Discussion

7752.	Evaluate by Simpson's formula the integral int_(a.5)^(1.5) (e^(1.1.x))/(x) dxaccurate tofourdecimal places.
Answer» ANSWER :1.2038

Discussion

7753.	Let BC to be chord of contact of the tangents from a point A to the circle x^2+y^2=1. P is any point on the arc BC . Let PX,PY, PZ be the lengths of perpendicular from P on the AB,BC,CA respectivelythen PX,PY,PZ are in
Answer» A.P. G.P H.P none of these ANSWER :B

Discussion

7754.	By using the properties of definite integrals evaluate the integrals in exercise. overset((pi)/(2))underset(o)int(sin^((3)/(2))x dx)/(sin^((3)/(2))x+cos^((3)/(2))x)
Answer» ANSWER :`:. I=(PI)/(4)`

Discussion

7755.	20 persons are arranged along a row and 4 of them are selected at random. Find the probability that (a) all the selected 4 are not consecutive (b) no two of the selected 4 are consecutive. (c) the first person of the linear arrangement must be selected and no two of the selected 4 are consecutive. (d) exactly three persons of the selected 4 are consecutive. (e) exactly two persons of the selected 4 are consecutive.
Answer» Answer :(a) `(4828)/(4845)` (B) `(.^(17)C_(4))/(.^(20)C_(4))` (C) `(.^(16)C_(3))/(.^(20)C_(4))` (d) `(272)/(.^(20)C_(4))` (e) `(2040)/(.^(20)C_(4))`

Discussion

7756.	Two coins whose faces are mared 1 and 2 are tossed. Let X be the total value of the numbers. Find mean and variance of X.
Answer» ANSWER :`3, (1)/(2)`

Discussion

7757.	int_(0)^(2pi) cos^(7) x sin^(5) x dx=
Answer» 1 0 `(5pi)/(16)` `(3pi)/(8)` ANSWER :B

Discussion

7758.	A steel rod at 25^(@)C is bolted at both ends and then cooled. By how many^(@)C should the rod be cooled so that it will rupture? Assume that till rupture, Hooke's law is obeyed. (alpha_("steel")=10xx10^(-6)//^(@)C,Y=2xx10^(11)N//m^(2)" and "sigma_(b)("breaking stress of steel rod")=4xx10^(8)N//m^(2))
Answer» SOLUTION :`Deltal=alphalDeltaT` `(Deltal)/(l)=alphaDeltaT` `sigma_(b)=(T)/(A)=(yDeltal)/(l)=yalphaDeltaT=DeltaT=(sigma_(b))/(yalpha)=(4xx10^(8))/(2xx10^(11)xx10^(-5))=200^(@)C`

Discussion

7759.	Integrate the following function : int(x^(2))/(sqrt(x^(6)-1))dx
Answer» Answer :`(1)/(3)log\|X^(3)+sqrt(x^(6)-1)\|+C`

Discussion

7760.	Find the vector equations of the plane passing through the points R(2, 5, -3), S(-2,-3, 5) and T(5, 3, -3).
Answer» ANSWER :`[VECR-(2hati+5hatj-3hatk)].[(-4hati-8hat+8hatk)XX(3hati-2hatj)]=0`

Discussion

7761.	Let f and g be functions defined by f(x) =1/(x+1), x in R, x ne -1 and g(x) =x^(2) =1, x in R. Then g.f is
Answer» one-one but not onto onto but not one-one both one-one and onto neither one-one nor onto Answer :D

Discussion

7762.	If \|x\|gt1,then sum of the series(1)/(1+x)+(2)/(1+x^(2))+(2^(2))/(1+x^(4))+(2^(3))/(1+x^(8))+"......"" upto n terms "oo is (1)/(x-lambda),then the value of lambda is
Answer» Solution :LET `P=lim_(N to oo)((1)/(1+x)+(2)/(1+x^(2))+(2^(2))/(1+x^(4))+""....." upto n terms ")` `=lim_(n to oo)sum_(r=0)^(n)((2^(r ))/(1+x^(2^(r )))+(2^(r ))/(1-x^(2^(r )))-(2^(r ))/(1-x^(2^(r ))))` `=lim_(n to oo)sum_(r=0)^(n)((2^(r+1))/(1-x^(2^(r+1)))-(2^(r ))/(1+x^(2^( r))))` `=lim_(n to oo)((2^(n+1))/(1-x^(2^(n+1)))-(1)/(1+x))` `=lim_(n to oo)((2^(n+1))/(1-x^(2^(n+1))))/((1)/(x^(2^(n+1))-1))-(1)/(1+x)=0-(1)/(1-x)` `=(1)/(x-1)=(1)/(x-lambda) "" [" given "]` `:.lambda=1`.

Discussion

7763.	The sumof divisorsof2 ^5 3^4 5^3 is
Answer» 60 120 1189188 1378154 Answer :C

Discussion

7764.	int(dx)/((x-1)sqrt(x^2-1)) is equal to
Answer» `-SQRT((x-1)/(x+1))+C` `sqrt((x-1)/(x^2+1))+C` `-sqrt((x+1)/(x-1))+C` `sqrt((x^2+1)/(x-1))+C` ANSWER :C

Discussion

7765.	Following table shows the marks obtained by 8 students in English and Mathematics. A candidate scored 85 marks in Y but was absent from the X test. Estimate his probable score for other test.
Answer» ANSWER :153.25

Discussion

7766.	Statement I f(x)=xe^-x has the maximum at x = 1. Statement II f'(1) = 0 and f"(1) < 0
Answer» Both I and II are TRUE and II is the CORRECT explanation for I Both I and II are true and II is not the correct explanation for I I is true but II is FALSE I is false but II is true Answer :A

Discussion

7767.	Thenumberof waysin whichoneor moreballscanbeselectedoutof10 white, 9greenand7blueballsis
Answer» 892 881 891 879 Answer :D

Discussion

7768.	Show that the relation R in the set {1,2,3} given by R ={(1,2),(2,1 )} is symmetric but neither reflexive nor transitive
Answer» SOLUTION :`(1,1),(2,2),(3,3),!in R` `THEREFORE `R is not reflexive `(1,2) in R `and `(2,1) in R ` `therefore `R is SYMMETRIC `(1,2) in R, (2,1) in R` but `(1,1) !in R` `therefore `R is not TRANSITIVE

Discussion

7769.	int (tan ^-1 x^2) x dx
Answer» ANSWER :`(1+x^4)+C`

Discussion

7770.	Let a,b be the solutions of x^(2)+px+1=0 and c, d be the solutions of x^(2)+qx+1=0. If (a-c)(b-c) and (a+d)(b+d) are the solutions of x^(2)+ax+beta=0, then beta equals
Answer» <P>`p+Q` `p-q` `p^(2)+q^(2)` `p^(2)-q^(2)` ANSWER :D

Discussion

7771.	Expand the binomial ((2)/(x) +x)^(10) up to four terms
Answer» ANSWER :`""^(10)C_(0) ((2)/(X))^(10) + ""^(10)C_(1) ((2)/(x))^(9) x + ""^(10)C_(2) ((2)/(x))^(8) x^(2) + ""^(10)C_(3) ((2)/(x))^(7) x^(3)+ …`

Discussion

7772.	A box contains 5 black, 4 white and 6 red balls. Two balls are drawn one after another without replacement. What is the probability that the first will be white and the second will be balck ?
Answer» ANSWER :`(2)/(21)`

Discussion

7773.	If a,b,c are in H.P. , then
Answer» `(a)/(B + C - a) , (b)/(c + a - b), (c)/(a + b - c)` are in H.P. `(2)/(b) = (1)/(b-a) + (1)/(b-c)` `a - (b)/(2),(b)/(2) , c (b)/(2) ` are in G.P. `(a)/(b+c),(b)/(c+a),(c)/(a +b)` are in H.P. Answer :1,2,3,4

Discussion

7774.	Find theareaof theregionboundedbyparabolay=(x^2)/(4)and the linesy=x ,y=1in the firstquadrant .
Answer» ANSWER :`5/6` SQ . UNITS

Discussion

7775.	If sum_(i=1)^(18)(x_(i) - 8) = 9 and sum_(i=1)^(18)(x_(i) - 8)^(2) = 45 then find the standard deviation of x_(1), x_(2),….x_(18)
Answer» ANSWER :`(3)/(2)`

Discussion

7776.	Find k if the cirlces x^(2)+y^(2)-5x-14y-34=0 and x^(2)+y^(2)+2x+4y+k=0 are orthogonal to each other.
Answer» ANSWER :1

Discussion

7777.	If u = sin ( xy ) + e ^(x ^(2+y ^(2))) Find u _(xy) and u _(yx) are they are equal ?
Answer» ANSWER :`F _(XY) =f _(YX) in A.`

Discussion

7778.	A=[{:(-5,1,3),(7,1,-5),(1,-1,1):}]and B=[{:(1,1,2),(3,2,1),(2,1,3):}] then find AB. Hence, solve the system of equation {:(x+y+2z=1),(3x+2y+z=7),(2x+y+3z=2):}}
Answer» ANSWER :x=2,y=1, z=-1

Discussion

7779.	Solve the following linear programming problems graphically : Maximise : Z = 10x + 6y subject to constraints 3x+y le 12, 2x+5y le 34, x, y ge 0
Answer» Answer :MAXIMUM Z = 56 at (2, 6)

Discussion

7780.	Find the solution of equations: (3x+y)(x+3y) sqrt(xy) = 14 and (x+y)(x^(2)+14xy + y^(2)) = 36, where x,y in R
Answer» ANSWER :`(X,y) =(3/2 + SQRT(2),3/2 - sqrt(2))` or `(3/2 -sqrt(2),3/2 + sqrt(2))`

Discussion

7781.	int(1-sin^3 x)/(sin^2 x)dx
Answer» SOLUTION :`INT(1-sin^3x)/(sin^2x)DX=int(cosec^2 x-sinx)dx =-COT x+cos x+C`

Discussion

7782.	If ax^2+2hxy+by^2+2gx+2fy+c=0 represents two parallel lines then prove that the distance between the parallel lines is 2sqrt((g^2-ac)/(a(a+b)))" or "2sqrt((f^2-bc)/(b(a+b))).
Answer» ANSWER :`2=sqrt((G^(2)-AC)/(a(a+b)))`

Discussion

7783.	If the vector equation of a line (x-2)/2=(2y-5)/(-3) =z+1 is vecr=2hati+5/2hatj-hatk+lambda(2hati-3/2 hatj+phatk) then p is equal to
Answer» 0 1 2 3 Answer :B

Discussion

7784.	What is the arithmetic mean of 4, 8, 12, 16, and 20 ?
Answer» ANSWER :12

Discussion

7785.	Observe the following statements : (A) : The median of 100 items is 52. The value of the largest item is 100. It was later found that it actually 110. Therefore the true median is 52. (R ) : The median is not effected by the extreme observations.
Answer» both A, R are TRUE and `R RARR A` both A, R are true and `R cancelrArr A` A is true, R is FALSE A is false, R is true Answer :A

Discussion

7786.	int_(2)^(3) (dx)/(x^2 - x) is equal to
Answer» `log.(2)/(3)` `log.(4)/(3)` `log.(8)/(3)` `log .(1)/(4)` Answer :B

Discussion

7787.	Evaluate the following integrals int (x)/(1+cosx)dx
Answer» ANSWER :`2xtan (x/2) - 4LOG SEC (x/2) + C`

Discussion

7788.	Three persons A, B and C are to speak at a function along with 7 other persons. The probability that A, B, and C speak together
Answer» `3/70` `1/15` `3/7` `1/(7!)` ANSWER :B

Discussion

7789.	Whichof the followingformsof the equation belowdirectly givesthe coordinatesof thecoordinates ofthe vertex of the graph ofthe quadraticexpressionshownabovewithouthavingto doanyadditionalsteps ?
Answer» `y= (X -1)(x-4)` `y = x^(2) + 4` `y = (x -1)^(2) + 3` `y = 2(x -1)^(2) + 3` Answer :C

Discussion

7790.	Find the points of extremum of the function F(x) = int_(0)^(x) (sin t)/(t)dtin the domain x gt 0
Answer» ANSWER :`(1)/(n pi) (-1)^(n) NE 0`

Discussion

7791.	The mean age of 25 teanchers of a school is 40 years. A teacher retires at the age of 60 years and a new teachers is appointed in his place. If now the mean age of the teachers in the school is 39 years. Then the age of the newly appointed teacher is
Answer» 25 30 35 40 Answer :C

Discussion

7792.	A dice is tossed twice. A 'success' is getting an even number on a toss. Find the variance of the number of successes.
Answer» ANSWER :`(1)/(2)`

Discussion

7793.	A particle moves along the curve 6y=x^(3)+2. Find the points on the curve at which the y-coordinate is changing 8 times as fast as the x-coordinate.
Answer» ANSWER :(4, 11) and `(-4,-(31)/(3))`

Discussion

7794.	int(cos^4x-sin^4x)/(cosx-sinx)dx
Answer» SOLUTION :`INT(cos^4-sin^4x)/(cosx-sinx)DX` =int((cos^2x+sin^2x)(cosx-sinx)(cosx+sinx)dx)/(cosx-sinx)` =`int(cosx+sinx)dx=sinx-cosx+C`

Discussion

7795.	int_(0)^(pi) (x tan x)/(sec x + tan x) dx=
Answer» `(PI -2)/(2)` `(pi + 2)/(2)` `(pi (pi + 2))/(2)` `(pi(pi -2))/(2)` ANSWER :D

Discussion

7796.	The value of lim_(x rarr 1) ((x^(3) + 2x^(2) + x + 1)/(x^(2) + 2x + 3))^((1-log(x-1))/((x-1)^(2))) is equal to : then f is :
Answer» E `e^(1//2)` 1 `SQRT(5//6)` ANSWER :D

Discussion

7797.	Evaluate int (x-2)/(sqrt(x + 5)) dx
Answer» ANSWER :50 `sqrt(X + 5) `+ c

Discussion

7798.	Let A = ((a,b),(c,d)) wherea,b,c,d in R . Then
Answer» det (A) `LT= sqrt(a^(2)+B^(3))sqrt(C^(3)+d^(2))` det(A ) `lt= (a+b) (c+d)` det(A) `lt = ac +BD` det (A) `lt= (\|a\|-\|b\|) (\|c\|-\|d\|)` Answer :A

Discussion

7799.	Write Minors and Cofactors of the elments of following determinants : \|{:(a,c),(b,d):}\|
Answer» ANSWER :`M_(11)=d,M_(12)=B,M_(21)=c,M_(22)=a` `A_(11)=d,A_(12)=-b,A_(21)=-c,A_(22)=a`

Discussion

7800.	Show that the points A(a,b), B(a+alpha+ b,+ beta), C(a+alpha+ p, b+beta+ q) and D(a+p,b+q) when joined in order, form a parallelogram. Find the cooditions for which the paralleogram is a(i)rectangle (ii) rhombus.
Answer» <P> ANSWER :`(i)a ALPHA+ beta q=0` (ii) `alpha^(2)+ beta^(2)=p^(2)+q^(2)`

Discussion

Explore topic-wise InterviewSolutions in .

By using the properties of definite integrals, evaluate the integrals int_((-pi)/2)^(pi/2)sin^(7)xdx

Evaluate by Simpson's formula the integral int_(a.5)^(1.5) (e^(1.1.x))/(x) dxaccurate tofourdecimal places.

Let BC to be chord of contact of the tangents from a point A to the circle x^2+y^2=1. P is any point on the arc BC . Let PX,PY, PZ be the lengths of perpendicular from P on the AB,BC,CA respectivelythen PX,PY,PZ are in

By using the properties of definite integrals evaluate the integrals in exercise. overset((pi)/(2))underset(o)int(sin^((3)/(2))x dx)/(sin^((3)/(2))x+cos^((3)/(2))x)

Two coins whose faces are mared 1 and 2 are tossed. Let X be the total value of the numbers. Find mean and variance of X.

int_(0)^(2pi) cos^(7) x sin^(5) x dx=

Integrate the following function : int(x^(2))/(sqrt(x^(6)-1))dx

Find the vector equations of the plane passing through the points R(2, 5, -3), S(-2,-3, 5) and T(5, 3, -3).

Let f and g be functions defined by f(x) =1/(x+1), x in R, x ne -1 and g(x) =x^(2) =1, x in R. Then g.f is

If |x|gt1,then sum of the series(1)/(1+x)+(2)/(1+x^(2))+(2^(2))/(1+x^(4))+(2^(3))/(1+x^(8))+"......"" upto n terms "oo is (1)/(x-lambda),then the value of lambda is

The sumof divisorsof2 ^5 3^4 5^3 is

int(dx)/((x-1)sqrt(x^2-1)) is equal to

Following table shows the marks obtained by 8 students in English and Mathematics. A candidate scored 85 marks in Y but was absent from the X test. Estimate his probable score for other test.

Statement I f(x)=xe^-x has the maximum at x = 1. Statement II f'(1) = 0 and f"(1) < 0

Thenumberof waysin whichoneor moreballscanbeselectedoutof10 white, 9greenand7blueballsis

Show that the relation R in the set {1,2,3} given by R ={(1,2),(2,1 )} is symmetric but neither reflexive nor transitive

int (tan ^-1 x^2) x dx

Let a,b be the solutions of x^(2)+px+1=0 and c, d be the solutions of x^(2)+qx+1=0. If (a-c)(b-c) and (a+d)(b+d) are the solutions of x^(2)+ax+beta=0, then beta equals

Expand the binomial ((2)/(x) +x)^(10) up to four terms

A box contains 5 black, 4 white and 6 red balls. Two balls are drawn one after another without replacement. What is the probability that the first will be white and the second will be balck ?

If a,b,c are in H.P. , then

Find theareaof theregionboundedbyparabolay=(x^2)/(4)and the linesy=x ,y=1in the firstquadrant .

If sum_(i=1)^(18)(x_(i) - 8) = 9 and sum_(i=1)^(18)(x_(i) - 8)^(2) = 45 then find the standard deviation of x_(1), x_(2),….x_(18)

Find k if the cirlces x^(2)+y^(2)-5x-14y-34=0 and x^(2)+y^(2)+2x+4y+k=0 are orthogonal to each other.

If u = sin ( xy ) + e ^(x ^(2+y ^(2))) Find u _(xy) and u _(yx) are they are equal ?

A=[{:(-5,1,3),(7,1,-5),(1,-1,1):}]and B=[{:(1,1,2),(3,2,1),(2,1,3):}] then find AB. Hence, solve the system of equation {:(x+y+2z=1),(3x+2y+z=7),(2x+y+3z=2):}}

Solve the following linear programming problems graphically : Maximise : Z = 10x + 6y subject to constraints 3x+y le 12, 2x+5y le 34, x, y ge 0

Find the solution of equations: (3x+y)(x+3y) sqrt(xy) = 14 and (x+y)(x^(2)+14xy + y^(2)) = 36, where x,y in R

int(1-sin^3 x)/(sin^2 x)dx

If ax^2+2hxy+by^2+2gx+2fy+c=0 represents two parallel lines then prove that the distance between the parallel lines is 2sqrt((g^2-ac)/(a(a+b)))" or "2sqrt((f^2-bc)/(b(a+b))).

If the vector equation of a line (x-2)/2=(2y-5)/(-3) =z+1 is vecr=2hati+5/2hatj-hatk+lambda(2hati-3/2 hatj+phatk) then p is equal to

What is the arithmetic mean of 4, 8, 12, 16, and 20 ?

Observe the following statements : (A) : The median of 100 items is 52. The value of the largest item is 100. It was later found that it actually 110. Therefore the true median is 52. (R ) : The median is not effected by the extreme observations.

int_(2)^(3) (dx)/(x^2 - x) is equal to

Evaluate the following integrals int (x)/(1+cosx)dx

Three persons A, B and C are to speak at a function along with 7 other persons. The probability that A, B, and C speak together

Whichof the followingformsof the equation belowdirectly givesthe coordinatesof thecoordinates ofthe vertex of the graph ofthe quadraticexpressionshownabovewithouthavingto doanyadditionalsteps ?

Find the points of extremum of the function F(x) = int_(0)^(x) (sin t)/(t)dtin the domain x gt 0

The mean age of 25 teanchers of a school is 40 years. A teacher retires at the age of 60 years and a new teachers is appointed in his place. If now the mean age of the teachers in the school is 39 years. Then the age of the newly appointed teacher is

A dice is tossed twice. A 'success' is getting an even number on a toss. Find the variance of the number of successes.

A particle moves along the curve 6y=x^(3)+2. Find the points on the curve at which the y-coordinate is changing 8 times as fast as the x-coordinate.

int(cos^4x-sin^4x)/(cosx-sinx)dx

int_(0)^(pi) (x tan x)/(sec x + tan x) dx=

The value of lim_(x rarr 1) ((x^(3) + 2x^(2) + x + 1)/(x^(2) + 2x + 3))^((1-log(x-1))/((x-1)^(2))) is equal to : then f is :

Evaluate int (x-2)/(sqrt(x + 5)) dx

Let A = ((a,b),(c,d)) wherea,b,c,d in R . Then

Write Minors and Cofactors of the elments of following determinants : |{:(a,c),(b,d):}|

Show that the points A(a,b), B(a+alpha+ b,+ beta), C(a+alpha+ p, b+beta+ q) and D(a+p,b+q) when joined in order, form a parallelogram. Find the cooditions for which the paralleogram is a(i)rectangle (ii) rhombus.