28278 + Interview Questions in Maths in Class 12 Page 560 InterviewSolution

27951.	Ifone ofx^3 +3x^2 +5x +k=0is sumof the othertworootsthenk=
Answer» `11/4` `17/6` `25/9` `33/8` ANSWER :D

Discussion

27952.	Find the area of the smaller region bounded by the ellipse x^(2)/a^(2) + y^(2)/b^(2) =1 and the line x/a + y/b =1.
Answer» ANSWER :`(AB)/(4) (pi-2)`

Discussion

27953.	The solution of x (dy)/(dx) + y = y^(2) x^(3)ln x is
Answer» `(X^(2))/(4) (2 In x - 1) + (1)/(xy) = c` `(x^(2))/(4) (In x + 1) + (1)/(xy) = c` `(x^(2))/(4) (2 In x + 1) + (1)/(xy) = c` `(x)/(4) (In x + 1)+ (1)/(xy) = c` Answer :A

Discussion

27954.	The equation of the chord of contact of the point (4,2) with respect to the circle x^(2)+y^(2)-5x+4y-3=0 is
Answer» ANSWER :` THEREFORE ` PLIES OUTSIDE S =0

Discussion

27955.	The point of intersection of the asymptotes with the directrices lie on
Answer» ANSWER :HENCE the points lie on the AUXILLARY LINE

Discussion

27956.	Discuss the maximum possibel number of positive the negative zeros of the polynomials x^2 - 5x + 6 and x^2 - 5x + 16. Also draw rough sketch of the graphs.
Answer» ANSWER :`x^2-5x+16`

Discussion

27957.	If1/a,1/b,1/c are in A.P. and a+b+cne0_2 prove that (b+c)/a,(c+a)/b,(a+b)/care in A.P.
Answer» SOLUTION :`1/a.1/B,1/C` are in A.P.`IMPLIES(a+b+c)/a,(a+b+c)/b,(a+b+c)/c` are in A.P. `implies(a+b+c)/a-1,(a+b+c)/b-1,(a+b+c)/c-1` are in A.P. `implies(b+c)/a,(c+a)/b,(a+b)/c` are in A.P.

Discussion

27958.	How much heat ( in kcal ) will be required at constant pressure to form 1.28 kg of CaC_(2) from CaO(s) & C(s) ? Given: Delta_(f)H^(@)(CaO,s)=-152 kcal/mol. DeltaH_(f)(CaC_(2),s)=-14 kcal/mol DeltaH_(f)(CO,g)=-26 kcal/mol
Answer» Solution :[2240] `CaO(s)+3C(s) to CaC_(2)(s)+CO_(g)` `Delta_(f)H^(@)=(-14-26)-(-152)=+112 KCAL//mol` TOTAL heat required `=((1280)/(64))xx112implies 2240 kcal`

Discussion

27959.	Number of non - negative integral solutions of a+b+c+d=n,n in N, is :
Answer» <P>`""^(n+3)P_2` `((n+1)(n+2)(n+3))/6` `""^(n+1)P_(n-4)` NONE of these Answer :B

Discussion

27960.	Let veca=hati+hatj and vecb=2hati-hatk. Then the point of intersection of the lines vecrxxveca=vecbxxveca and vecrxxvecb=vecaxxvecb is (A) (3,-1,10 (B) (3,1,-1) (C) (-3,1,1) (D) (-3,-1,-10
Answer» `(-1,1,1)` `(3,-1,1)` `(3,1,-1)` `(1,-1,-1)` ANSWER :C

Discussion

27961.	Choose the corréct answer in each of the following The mean of the numbers obtained on throwing a die having written 1 on three faces, 2 on two faces and 5 on one face is
Answer» 1 2 5 44263 Answer :B

Discussion

27962.	The shortest destance between vecr = veca_1 + lambdavecb and vecr = veca_2 + muvecb is abs((vecbxx(veca_2-veca_1))/absvecb)
Answer» ANSWER :T

Discussion

27963.	A couple has two children. Find the probability that both children are males, if it is known that atleast one of the children is male. ii. Find the probability that both children are females, if it is known that the eIder chiId is a female.
Answer» ANSWER :(i) `(1)/(3)` (II) `(1)/(2)`

Discussion

27964.	If a coin is tossed twice and X is the number of tails, then var(X)=
Answer» 0 1 `1/2` `1/3` ANSWER :C

Discussion

27965.	Locate the position of the point P with respect to the circle S =0 whenP ( 1,2) and S = x^(2) +y^(2) + 6x + 8y -96
Answer» ANSWER : INTERIOR

Discussion

27966.	Find the values of k so that the function f is continuous at the indicated point f(x)= {(kx+1",","if" x le 5),(3x-5",","if" x gt 5):} at x=5
Answer» ANSWER :`K= (9)/(5)`

Discussion

27967.	Two tangents OA and OB are drawn to the circle x^(2)+y^(2)+4x+6y+12=0from origin O. The circumradius of DeltaOAB is :
Answer» `(1)/(2)` 1 2 `(SQRT(13))/(2)` SOLUTION :Circum radius `=(sqrt((0+2)^(2)+(0+3)^(2)))/(2)=(sqrt(13))/(2)`UNIT

Discussion

27968.	Let U=R. If A={x inR:0ltxlt2},B={x inR:1ltxle3}, Which of the following is false?
Answer» `A'={x INR:xle0orxge2}` `B'={x inR:xle1orxgt3}` `AuuB={x inR:0lexle3}` `AuuB={x inR:1ltxlt2}` ANSWER :C

Discussion

27969.	Integrate the functions (sinx)/((1+cosx)^(2))
Answer» ANSWER :`1/(1+cosx)+C`

Discussion

27970.	Argument of ((1+i)(sqrt(3)+i))/((i-sqrt(3))(1-i)) is
Answer» `(pi)/(3)` `(pi)/(6)` `(-pi)/(6)` `5(pi)/(6)` Answer :C

Discussion

27971.	Given the sum of the perimeters of a square is equal to the diameter of the circle .
Answer» ANSWER :At the END of 4 SECONDS

Discussion

27972.	If a line makes angle 90^(@), 60^(@) and 30^(@) with the positive direction of x,y and z axis respectively , find its direction cosines.
Answer» ANSWER :`0, (1)/(2), (sqrt(3))/(2)`

Discussion

27973.	Using the properties of determinants, prove the following \|{:((a+b)^2,ca,cb),(ca,(b+c)^2,ab),(bc,ab,(c+a)^2):}\|=2abc(a+b+c)^3
Answer» ANSWER :`2ABC(a+b+c)^3`

Discussion

27974.	Find the area of the triangle whose vertices are the roots of z^(3) + iz^(2) + 2i= 0
Answer» ANSWER :B

Discussion

27975.	If n = 2hati-3hati+4hatk,m=hati-hatj,I=2hati-hatj+hatk, then the Cartesian equation of the plane passing through the line of intersection of two planes r.n = 1 and r.m =-4 and perpendicular to the plane r.1= -8 is
Answer» 5x-20y-12z-44=0 x-2y-12z-45=0 5x-20y-12z-47=0 5x-2y-12z+47=0 Answer :D

Discussion

27976.	Four bad oranges are mixed accidently with 16 good oranges in box. Find probability distribution of bad oranges in a draw of two oranges.
Answer» ANSWER :`(##KPK_AIO_MAT_XII_P2_C13_E01_053_A01##)`

Discussion

27977.	If A is 3 xx 4 matrix and B is a matrix such that A^(1)B and B A^(1) are both defined, then B is of the type
Answer» `4 XX 4` `3 xx 4` `4 xx 3` `3 xx 3` ANSWER :B

Discussion

27978.	Verify mean value theorem for each of the functions: f(x)= sin x- sin (2x), "in " x in [0, pi]
Answer» ANSWER :`COS^(-1) ((1 +- sqrt33)/(8))`

Discussion

27979.	Solve the following equations : tan^(-1)(2x)+tan^(-1)(3x)=pi/4
Answer» ANSWER :`x=1/6orx=-1`

Discussion

27980.	If f(x) = x^(3) + a x^(2) + b x + c has a maximum at x = -1 and minimum at x = 3. Find a + b.
Answer» 12 `-12` 9 3 Answer :B

Discussion

27981.	The differential equation of the family of ellipses having centres at the origin and whose axes are the coordinate axes is
Answer» ANSWER :`X y y_(2) + x(y_(1))^(2) - y y_(1) = 0`

Discussion

27982.	Integrate the follwing functions: (2x)/(x^2+3x+2)
Answer» Solution :Let `(2X)/(X^2+3x+2) = (2x)/((x+1)(x+2)) = A/(x+1) + B/(x+2)` Then 2x = A(x+2)+b(x+1)....(a) Putting x = -1 and x = -2 in (a) we have -2 = `Axx1 gtA = -2`, -4 = `Bxx-1 gt B = 4` THEREFORE `int (2x)/(x^2+3x+2) dx` = `-2log\|x+1\|+4 log\|x+2\|+c`

Discussion

27983.	From the point (-1,2), tangent lines are to the parabola y^(2)=4x. If the area of the triangle formed by the chord of contact and the tangents is A, then the value of A//sqrt(2) is ___________ .
Answer» Solution :(8) The chord of contact w.r.t point O(-1,2) is `y=(x-1)"[Using "yy_(1)=2a(x+x_(1))]` Solving y=x-1 with the parabola, we get the point of intersection as `P(3+2sqrt(2),2+2sqrt(2))andQ(3-2sqrt(2),2-2sqrt(2))` `:." "PQ^(2)=32+32=64` `:." "PQ=8` ALSO, the length of perpendicular from O(-1,2) on PQ is `4//sqrt(2)`. Then the required AREA of triangle is `A=(1)/(2)xx8xx((4)/(sqrt(2)))=8sqrt(2)` sq. units

Discussion

27984.	Solvethe equation 3x^3 -4x^2 +x +88 =0giventhat2- sqrt(-7)isa root .
Answer» ANSWER :`2+- SQRT(7) i`

Discussion

27985.	Let the roots f(x)=x be alpha and beta where f(x) is quadratic polynomial ax^(2)+bx+c. alpha and beta are alos the roots of f(f(x))=x. Let the other two roots of f(f(x))=x be lambda and delta. If alpha and beta are real and equal then
Answer» `LAMBDA and DELTA` are IMAGINARY `lambda and delta` are REAL `lambda and delta` MAY be real or imaginary can't say Answer :A

Discussion

27986.	IfP(E_(1))=1//2, P(E_(2))=1//2" and "P(A//E_(1))=1//2, P(A/E_(2))=1//4. Find P(E_(1)//A).
Answer» ANSWER :`2//3`

Discussion

27987.	Let the roots f(x)=x be alpha and beta where f(x) is quadratic polynomial ax^(2)+bx+c. alpha and beta are alos the roots of f(f(x))=x. Let the other two roots of f(f(x))=x be lambda and delta. If alpha +beta+lambda+delta, then the correct statements are I : alpha and beta are real II : lambda and delta are real IIIalpha and beta are imaginary IV : lambda and delta are imaginary
Answer» I and II III and IV II and III I and IV Answer :B

Discussion

27988.	Given three statements : S_(1) : "log"_(0.6) ("log"_(e )(x^(2)+x)/(x^(2)+4))lt 0, then x in (8, oo) S_(2) : log_(10)(x^(2)-16)le log_(10)(4x-11), then x in (4,5) S_(3) : If log_(3)(x+2)(x+4)+log_(((1)/(3)))(x+2)lt(1)/(2)log_(sqrt(3))7 then x in (-2, -1)uu(0, 1], then which of the following option(s) is/are incorrect ?
Answer» `S_(1)` is FALSE `S_(2)` is true `S_(3)` is true `S_(4)` is false Solution :Given THREE ………… Obvious

Discussion

27989.	Let the roots f(x)=x be alpha and beta where f(x) is quadratic polynomial ax^(2)+bx+c. alpha and beta are alos the roots of f(f(x))=x. Let the other two roots of f(f(x))=x be lambda and delta. The correct statements are I : if alpha and beta are real and unequal then lambda and delta are also real II : If alpha and beta are imaginary then lambda and delta and also imaginary
Answer» I only II only II and III I and IV Answer :B

Discussion

27990.	Let A_(n) and B_(n) be square matrices of order 3, which are defined as : A_(n)=[a_(ij)] and B_(n)=[b_(ij)] where a_(ij)=(2i+j)/(3^(2n)) and b_(ij)=(3i-j)/(2^(2n)) for all i and j, 1 le i, j le 3. Ifl=lim_(n to oo) Tr. (3A_(1)+3^(2)A_(2)+3^(3)A_(3)+........+3^(n)A_(n)) andm=lim_(n to oo) Tr. (2B_(1)+2^(2)B_(2)+2^(3)B_(3)+.....+2^(n)B_(n)), then find the value of ((l+m))/(3) [Note : Tr (P) denotes the trace of matrix P.]
Answer» ANSWER :7

Discussion

27991.	Which of the following compound produces only basic products on hydrolysis ?
Answer» `Mg_(3)N_(2)`<BR>`NCl_(3)` `B Br_(3)` `PCl_(5)` Solution :`Mg_(3)N_(2)+6H_(2)O to underset(("Both are basic"))(3 Mg(OH)_(2)+2NH_(3)` `NCl_(3)+3H_(2)O to underset(("ONE is basic and other is acidic"))(NH_(3)+3HOCl)` `BBr_(3)+3H_(2)O to underset(("Both are acidic"))(H_(3)BO_(3)+3HBr)` `PCl_(5)+4H_(2)O to underset(("Both are acidic"))(H_(3)PO_(4)+5HCl)`.

Discussion

27992.	Let f be a functionon [0,1] defined by f(x)=(1//2)^n , (1//2)^(n+1) le x lt (1//2)^n, n=0,1,2,… Then
Answer» f is a continuous function f is continuous except x=1/2 f is continuous except for finitely MANY points The SETS of points where f is not continuous is infinite. ANSWER :D

Discussion

27993.	f(x)= {((tan 2x)/(x)",",x ne 0),(K",",x=0):} If a function f is continuous at x=0 then find k.
Answer» ANSWER :k=2

Discussion

27994.	If [(I,0),(3,-i)] + A = [ (I,2),(3,4+i)] - A, then A equals :
Answer» `[ (0,1),(0,2+i)] ` `[(0,-1),(3,i)] ` `[(1,0),(0,2-i)] ` NONE of these ANSWER :A

Discussion

27995.	Evaluate the following integrals int x sec^(2) x dx
Answer» ANSWER :`X TAN x - LOG \|secx\|+c`

Discussion

27996.	(1+costheta-isintheta)^(n)
Answer» `2^ncos^n((THETA)/(2))CIS(ntheta)/(2)` `2^ncos^n((theta)/(2))cis (-(ntheta)/(2))` `2^nsin^n(theta/2) cis(ntheta)/(2)` `2^nsin^n(theta/2)-cis(ntheta)/(2)` ANSWER :B

Discussion

27997.	The statement "n^(5)-5n^(3)+4n is divisible by 120" is true for
Answer» n = 1 only n = 10 only n = 100 only All positive integer VALUES of n Answer :D

Discussion

27998.	If (pi)/6 and (pi)/2 are the ends of chord of the circle x^(2)+y^(2)=16 then its length is
Answer» 2 4 6 8 Answer :B

Discussion

27999.	underset(x to 0)"Lt" (Sin^(-1)x-Tan^(-1))/(x)=
Answer» 2 1 `-1` `1//2` ANSWER :D

Discussion

28000.	Water is filowing into right circular conical vessel, 10 inch deep and 10 inch in diameter atthe rate of 4 (inch)""^(3) /min, How fast is the water-level rising when the water is 8 inch deep?
Answer» `(PI)/(4)` inch/min `4PI` inch/min `(1)/(4pi)` inch/min `(1)/(2PI)` inch/min Solution :N/A

Discussion

Explore topic-wise InterviewSolutions in .

Ifone ofx^3 +3x^2 +5x +k=0is sumof the othertworootsthenk=

Find the area of the smaller region bounded by the ellipse x^(2)/a^(2) + y^(2)/b^(2) =1 and the line x/a + y/b =1.

The solution of x (dy)/(dx) + y = y^(2) x^(3)ln x is

The equation of the chord of contact of the point (4,2) with respect to the circle x^(2)+y^(2)-5x+4y-3=0 is

The point of intersection of the asymptotes with the directrices lie on

Discuss the maximum possibel number of positive the negative zeros of the polynomials x^2 - 5x + 6 and x^2 - 5x + 16. Also draw rough sketch of the graphs.

If1/a,1/b,1/c are in A.P. and a+b+cne0_2 prove that (b+c)/a,(c+a)/b,(a+b)/care in A.P.

How much heat ( in kcal ) will be required at constant pressure to form 1.28 kg of CaC_(2) from CaO(s) & C(s) ? Given: Delta_(f)H^(@)(CaO,s)=-152 kcal/mol. DeltaH_(f)(CaC_(2),s)=-14 kcal/mol DeltaH_(f)(CO,g)=-26 kcal/mol

Number of non - negative integral solutions of a+b+c+d=n,n in N, is :

Let veca=hati+hatj and vecb=2hati-hatk. Then the point of intersection of the lines vecrxxveca=vecbxxveca and vecrxxvecb=vecaxxvecb is (A) (3,-1,10 (B) (3,1,-1) (C) (-3,1,1) (D) (-3,-1,-10

Choose the corréct answer in each of the following The mean of the numbers obtained on throwing a die having written 1 on three faces, 2 on two faces and 5 on one face is

The shortest destance between vecr = veca_1 + lambdavecb and vecr = veca_2 + muvecb is abs((vecbxx(veca_2-veca_1))/absvecb)

A couple has two children. Find the probability that both children are males, if it is known that atleast one of the children is male. ii. Find the probability that both children are females, if it is known that the eIder chiId is a female.

If a coin is tossed twice and X is the number of tails, then var(X)=

Locate the position of the point P with respect to the circle S =0 whenP ( 1,2) and S = x^(2) +y^(2) + 6x + 8y -96

Find the values of k so that the function f is continuous at the indicated point f(x)= {(kx+1",","if" x le 5),(3x-5",","if" x gt 5):} at x=5

Two tangents OA and OB are drawn to the circle x^(2)+y^(2)+4x+6y+12=0from origin O. The circumradius of DeltaOAB is :

Let U=R. If A={x inR:0ltxlt2},B={x inR:1ltxle3}, Which of the following is false?

Integrate the functions (sinx)/((1+cosx)^(2))

Argument of ((1+i)(sqrt(3)+i))/((i-sqrt(3))(1-i)) is

Given the sum of the perimeters of a square is equal to the diameter of the circle .

If a line makes angle 90^(@), 60^(@) and 30^(@) with the positive direction of x,y and z axis respectively , find its direction cosines.

Using the properties of determinants, prove the following |{:((a+b)^2,ca,cb),(ca,(b+c)^2,ab),(bc,ab,(c+a)^2):}|=2abc(a+b+c)^3

Find the area of the triangle whose vertices are the roots of z^(3) + iz^(2) + 2i= 0

If n = 2hati-3hati+4hatk,m=hati-hatj,I=2hati-hatj+hatk, then the Cartesian equation of the plane passing through the line of intersection of two planes r.n = 1 and r.m =-4 and perpendicular to the plane r.1= -8 is

Four bad oranges are mixed accidently with 16 good oranges in box. Find probability distribution of bad oranges in a draw of two oranges.

If A is 3 xx 4 matrix and B is a matrix such that A^(1)B and B A^(1) are both defined, then B is of the type

Verify mean value theorem for each of the functions: f(x)= sin x- sin (2x), "in " x in [0, pi]

Solve the following equations : tan^(-1)(2x)+tan^(-1)(3x)=pi/4

If f(x) = x^(3) + a x^(2) + b x + c has a maximum at x = -1 and minimum at x = 3. Find a + b.

The differential equation of the family of ellipses having centres at the origin and whose axes are the coordinate axes is

Integrate the follwing functions: (2x)/(x^2+3x+2)

From the point (-1,2), tangent lines are to the parabola y^(2)=4x. If the area of the triangle formed by the chord of contact and the tangents is A, then the value of A//sqrt(2) is ___________ .

Solvethe equation 3x^3 -4x^2 +x +88 =0giventhat2- sqrt(-7)isa root .

Let the roots f(x)=x be alpha and beta where f(x) is quadratic polynomial ax^(2)+bx+c. alpha and beta are alos the roots of f(f(x))=x. Let the other two roots of f(f(x))=x be lambda and delta. If alpha and beta are real and equal then

IfP(E_(1))=1//2, P(E_(2))=1//2" and "P(A//E_(1))=1//2, P(A/E_(2))=1//4. Find P(E_(1)//A).

Which of the following compound produces only basic products on hydrolysis ?

Let f be a functionon [0,1] defined by f(x)=(1//2)^n , (1//2)^(n+1) le x lt (1//2)^n, n=0,1,2,… Then

f(x)= {((tan 2x)/(x)",",x ne 0),(K",",x=0):} If a function f is continuous at x=0 then find k.

If [(I,0),(3,-i)] + A = [ (I,2),(3,4+i)] - A, then A equals :

Evaluate the following integrals int x sec^(2) x dx

(1+costheta-isintheta)^(n)

The statement "n^(5)-5n^(3)+4n is divisible by 120" is true for

If (pi)/6 and (pi)/2 are the ends of chord of the circle x^(2)+y^(2)=16 then its length is

underset(x to 0)"Lt" (Sin^(-1)x-Tan^(-1))/(x)=

Water is filowing into right circular conical vessel, 10 inch deep and 10 inch in diameter atthe rate of 4 (inch)""^(3) /min, How fast is the water-level rising when the water is 8 inch deep?