28278 + Interview Questions in Maths in Class 12 Page 247 InterviewSolution

12301.	If P=sum_(r=3n)^(r=4n-1)[(r^(2)+13n^(2)-7m)/(n^(3))] & Q=sum_(r=3n+1)^(r=4n)[(r^(2)+13n^(2)-7m)/(n^(3))] Then
Answer» `Pgt5/6` `Qlt5/6` `Qgt5/6` `Plt5/6` Solution :`F(x)=x^(2)-7x+13` In both CASES GAIN `gt` loss `impliesP gt int_(3)^(4)f(x)dx` & `Qgtint_(3)^(4)f(x)dx`

Discussion

12302.	Equation of the common tangents of (x^(2))/( y^(2)) +- (y^(2))/( b^(2)) =1 ,( x^(2))/( b^(2)) +- (y^(2))/( a^(2)) =+- 1 are
Answer» ` y=+- X+- SQRT( a^(2)-B^(2)) ` ` y=+-x +- 2sqrt(a^(2) +b^(2)) ` ` y=+- x+- sqrt(a^(2) +b^(2) ) ` ` y= +- x+- 2 sqrt( a^(2)- b^(2))` ANSWER :A

Discussion

12303.	int (sin x + 8 cos x )/(4 sn x + 6 cos x ) dx =
Answer» ` x + (1)/(2) " log " ` (4 sin x + 6 COS x ) + c `2X + log ` ( 2 sin x + 3 cos x ) +c `(1)/(2)`log ( 4 sin x + 6 cos x ) + c Answer :A

Discussion

12304.	Let f(x)=(f(x))^(2)+(f'(x))^(2),F(0)=0 where f(x) is thrice differentiable function such that \|f(x)\|le1 for all x in [-1, 1], then choose the correct statement(s)
Answer» There is atleast and point in each of the intervals `(-1, 0)` and (0, 1)where `\|f'(x)\|le 2` There is atleast one point in each of the intervals `(-1, 0)` and 0, 1) where `F(x)le5` There is no point of local maxima of F(x) in `(-1, 1)` For some `c in (-1, 1), F(c)GE 6, F'(c) =0 and F''(c) LE0` ANSWER :A::B::D

Discussion

12305.	Two points A and B are selected at random on a segment of length l. Find the probability that a triangle can be constructed from these three segments.
Answer» ANSWER :`(1)/(4)`

Discussion

12306.	Solve the following linear programming problem graphically: Maximize :z=4x+3y Subject to: 2x+yge40 x+2yge50 x+yge35 xge0 yge0
Answer» SOLUTION :NA

Discussion

12307.	A curve y = f(x) is such that f(x)ge 0 and f(0)=0 and bounds a curvilinear triangle with the base [0,x] whose area is proportional to (n+1)^(th) power of f(x)cdot" If "f(1)=1 then find f(x).
Answer» Solution :ACCORDING to the question `OVERSET(x)underset(0)intf(x)dx=lamda{F(x)}^(n+1)` Where `lamda` is constant of proportionality Differentiating both sides w.r.t x, `f(x)=lamda(n+1)(f(x))^(n)f'(x)` `"or "(f(x)^(n-1))f'(x)=(1)/(lamda(n+1))` Integrating both sides w.r.t x, `((f(x))^(n))/(n)=(x)/(lamda(n+1))+C` `f(0)=0, THEREFORE C=0` `(f(x))^(n)=(nx)/(lamda(n+1))` `f(1)=1` `therefore""(n)/(lamda(n+1))=1` `therefore""f(x)=x^(1//n)`

Discussion

12308.	Show that thevolume of the largest cone that can be inscribed in a sphere of radius R is (8)/(27) of the volume of the sphere .
Answer» Answer :`=(8)/(27)XX` volume of THESPHERE.

Discussion

12309.	A tankcontains 1000 liters of water in which 100 grams of saltsis dissolved brineruns in a rate of 10 liter per minute and each litre contains 5 grams of dissolved salt the mixtureof the tank is kept uniform by stirring brine runs out at 10 liter per minute find the amount of salt at any time t
Answer» ANSWER :in FLOWRATE - OUTFLOW RATE

Discussion

12310.	Catalyst used in conversion of n-hexane into benzene in:
Answer» `AlCl_(3)` `SiO_(2)-Al_(2)O_(3)` `Cr_(R)O_(3)-Al_(2)O_(3)` `MnO_(2)` Answer :C

Discussion

12311.	Write down the first three terms is the following expansions(1 + 4x)^(-4)
Answer» ANSWER :`1, -16X, 160x^2`

Discussion

12312.	Findthe order anddegree of the followingdifferential equations (i) (dy)/(dx)+y=x^(2) (ii) y'+y^(2)=x (iii) y'+3y^(2)+y^(3)=0 (iv) (d^(2)y)/(dx^(2))+x=sqrt(y+(dy)/(dx)) (v) (d^(2)y)/(dx^(2))-y+(dy)/(dx)+(d^(3)y)/(dx^(3))^(3/2)=0 (vi)y'=(y-y'3)^(2//3) (vii)y'+(y^(2))=(x+y^(2)) (viiii)y'+(y)^(2)=x(x+y")^(2) (ix)(dy)/(dx)^(2)+x=(dx)/(dy)+x^(2) (x) sin x (dx+dy)=cos x(dx-dy)
Answer» Answer :(i) 1 (II) 1 (iii) 1 (iv) 2 (V) 0 (vi) 3 (VII) 1 (viii)2 (ix)3 (x) 3

Discussion

12313.	Find the derivative of f givenby f(x)= sin^(-1)x assuming it exists.
Answer» ANSWER :`=(1)/(SQRT(1-x^2))`

Discussion

12314.	Find the polar of (1,2) with respect to x^(2) + y^(2) = 7
Answer» ANSWER :` X+ 2Y = 7`

Discussion

12315.	If \|3z-1\|=3\|z-2\|, then z lies on
Answer» 6Re(Z) =7 On the PERPENDICULAR bisector of LINE JOINING ` (1/3 ,0) and ( 2,0) ` A line PARALLEL to x-axis A line parallel to y-axis Answer :A::B::D

Discussion

12316.	Find the area of the region bounded by the ellipse x^(2)/16 + y^(2)/9=1.
Answer» ANSWER :`12pi`

Discussion

12317.	int_(0)^(1)\|sin 2 pi x\|dx=
Answer» `2PI` `2/PI` `pi/2` `pi` ANSWER :B

Discussion

12318.	Evaluation of definite integrals by subsitiution and properties of its : If int_(0)^(a)f(2a-x)dx=mu and int_(0)^(a)f(x)dx=lamda then int_(0)^(2a)f(x)dx=..........
Answer» `2lamda+mu` `lamda+mu` `mu-lamda` `lamda-2mu` ANSWER :B

Discussion

12319.	If P(E ) = 0.8, P(F)= 0.5 and P(E cap F) = 0.4 then P( E//F)=….......
Answer» `0.80` `0.32` `0.64` `0.98` ANSWER :C

Discussion

12320.	If a,b,c are in A.P then the determinant \|{:(x+2,x+3,x+2a),(x+3,x+4,x+2b),(x+4,x+5,x+2c):}\| is …..
Answer» 0 1 x 2x Answer :a

Discussion

12321.	For each of the differential equations in find the particular solution satisfying the given condition : (dy)/(dx)-(y)/(x)+cosec((y)/(x))=0,y=0 when x=1
Answer» ANSWER :`COS ((y)/(X)) = LOG \|EX\|`

Discussion

12322.	A wire of length 20 cm can be bent in the form of a sector then its maximum area is
Answer» 15 sq. CM 25 sq.cm 5 sq. cm none Answer :B

Discussion

12323.	Determine order and Degree(if defined) of differential equations given y''' + 2y'' + y' = 0
Answer» ANSWER :ORDER 3; DEGREE 1

Discussion

12324.	A wedge B of mass 2 m is placed on a rough horizontal suface. The coefficient of friction between wedge and the horizontal surface is mu_(1). A block of mass m is placed on wedge as shown in the figure. The coefficient of friction between block and wedge is mu_(2). The block and wedge are released from rest. Q. Suppose the inclined surface of the wedge is at theta=37^(@) angle from horizontal and mu_(2)=0.9 then the wedge:
Answer» will remain in equilibrium if `mu_(1)=0.5` will accelerate TOWARDS left if `mu_(1)=0` will acceleration TOWARD left if `mu_(1)=0.25` will remain in equilibrium if `mu_(1)=0.3` Solution :Since `mu_(2)gttantheta` so block will remain at REST, so net content force onblock will be vertically upward. Net contact force on wedge DUE to block will be vertically downward. There is no tendency of sliding of wedge so wedge will remain in EQULIBRIUM for any value of `mu_(1)`

Discussion

12325.	In which one pair, both the plants can be vegetatively propagated by leaf pieces ?
Answer» BRYOPHYLLUM and Kalanchoe Chrysanthemum and Agave Agave and Dioscorea Bryophyllum and Asparagus Answer :A

Discussion

12326.	Let O be the origin and A be a point on the cune y^(2)=4x then locus of the midpoint of OA is
Answer» `X^(2)=4Y` `x^(2)=2y` `y^(2)=16X` `y^(2)=2x` Answer :D

Discussion

12327.	If y=sec^(-1)(sqrtx+1)/sqrtx+sin^(-1)fracsqrtx(sqrtx+1)then dy/dx=____
Answer» 0 undefined `pi/2` 1 Answer :A

Discussion

12328.	Fundamental theorem of definite integral : f(x)=int_(1)^(x)sqrt(2-t^(2))dt then real roots of the equation x^(2)-f'(x)=0 are ……….
Answer» `pm1` `PM(1)/(SQRT3)` `pm(1)/(2)` 0 and 1 ANSWER :A

Discussion

12329.	If vec(a)=i-2 j + 3k, vec(b) is a vector such that vec(a).vec(b)= \|vec(b)\|^(2) \|vec(a)-vec(b)\|= sqrt7, then \|vec(b)\|= ________
Answer» a.21 B.`SQRT7` c.14 d.7 Answer :B

Discussion

12330.	An unbiased die is rolled 4 times. Out of 4 face values obtained, the probability thatthe minimum face value is not less than 2 and the maximum face value is not greater than5 is
Answer» `(16)/(81)` `(1)/(81)` `(80)/(81)` `(65)/(81)` ANSWER :A

Discussion

12331.	The slope of the normal to the curve y = 3x^(2) at the point whose abscissa is 2 is:
Answer» `(1)/(12)` `-(1)/(12)` `(1)/(13)` `(1)/(14)` ANSWER :B

Discussion

12332.	If a,b,c in R and equations ax^2 + bx + c = 0 and x^2 + 2x + 9 = 0 have a common root, show that a:b:c=1 : 2 : 9.
Answer» ANSWER :`a:B:c=1:2:9`

Discussion

12333.	If a fair coin is tossed 10 times, find the probability of exactly six heads
Answer» Answer :(i) `(105)/(512)`, (II) `(193)/(512)` and (iii) `(53)/(64)`

Discussion

12334.	STATEMENT-1 If A cup B=A cup C, A cap B= A cap C, then B=C STATEMENT-2: A-(B cup C)=(A-B) cup (A-C) STATEMENT-3: If A cap (B' cap C')= A cap B cap C.
Answer» ANSWER :B

Discussion

12335.	Construct truth tables for the following and indicate which of these are tautologies (p < implies q) ^^ (q < impliesr) rarr (p < impliesr)
Answer» SOLUTION :

Discussion

12336.	The value of (1 - omega + omega^(2))^(5) + (1 + omega - omega^(2))^(5), where ro and ro2 are the complex cube roots of unity is
Answer» 0 `32omega` `-32` 32 Answer :D

Discussion

12337.	Two integers x and y are chosen one by one with replacement from 1, 2, 3, 4, 5,…., 10. Find the probability that 0 lt \|x"- "y\| lt 5.
Answer» ANSWER :`(3)/(5)`

Discussion

12338.	The mean and standard deviation of 100 observations were calculated as 40 and 5.1, respectivey by a student who took by mistake 50 instead of 40 for one observations. The correct standard deviation is
Answer» ANSWER :MEAN = 15.6 and s.d = 5.04

Discussion

12339.	Integrate the rational functions (5x)/((x+1)(x^(2)-4))
Answer» ANSWER :`(5)/(3)log\|x+1\|-(5)/(2)log\|x+2\|+(5)/(6)log\|x-2\|+c`

Discussion

12340.	{ x in R : cos 2x + 2cos^2 x =2} is equal to
Answer» `{2npi+pi/3: NINI}` `{npi PM pi/6 : N in I}` `{npi+pi/3:n in I}` `{2 n pi -pi/3 : n in I}` Answer :B

Discussion

12341.	Match the following{:("List - I "," List II "),( (A) int (f^(1)(x))/(f(x)) dx = ,(1) 2 sqrt(f(x)) +c ),((B) int (f^(1)(x))/(sqrt(f(x))) dx= , (2) (2)/(3) (f(x))^(3//2) + c ),((C) int f^(1) (x) sqrt(f(x)) dx =, (3)" log \| f(x)\| + c"),((D) int f^(1) (x).(f(x))^(2) dx = , (4) (1)/(3) (f(x))^(3) + c ):} The correct match for list -I from List - II is
Answer» `{:(A,B,C,D),(1,2,3,4):}` `{:(A,B,C,D),(3,1,2,4):}` `{:(A,B,C,D),(3,5,2,4):}` `{:(A,B,C,D),(5,4,3,1):}` ANSWER :B

Discussion

12342.	Find the order and degree of the differential equation ((d^(2) y )/( dx^2) )^(2) + cos ((dy)/( dx) ) =0
Answer» ANSWER :ORDER is 2 DEGREES is not DEFINED.

Discussion

12343.	For each positve real number k, let C _(k) denotes the circle with centre at origin and radius k units. On a circle C _(k) particle alpha moves k units in the counter-clockwise direction. After completing its motion on C_(k), the particle moves onto the circle C _(k+1) in same well defined manner, where r gt 0. The motion of particle continues in this manner. Let the particle starts from the point A (2,0) and moves pi/2 units on circle C_(2) in the counter clockwise direction, then moves on circle C_(3) along tangential peth, let this straight the (tangential path traced by particle) intersect the circle C_(3) at points A and B. then tangents at A and B intersect at
Answer» `(SQRT2, sqrt2) `(9,9)` `((9)/(2SQRT2), (9)/(2sqrt2))` `(9 sqrt2, 9 sqrt2)` ANSWER :C

Discussion

12344.	For each positve real number k, let C _(k) denotes the circle with centre at origin and radius k units. On a circle C _(k) particle alpha moves k units in the counter-clockwise direction. After completing its motion on C_(k), the particle moves onto the circle C _(k+1) in same well defined manner, where r gt 0. The motion of particle continues in this manner. Let k in l^(+) and r in R, particle moves tangentially from C_(k)to C_(k+r') such that length of tangent is equal to k units itself. If particle starts from teh point (2,0), then
Answer» the particle will cross positive X-AXIS again for `2 sqrt2 lt x lt 4` the particle will cross positive x -axis again at `x =2 sqrt2` the particle will cross positive x-axis again for `4 lt x lt 4 sqrt2 the particle will cross positive x-axis again at `x =3` Answer :C

Discussion

12345.	For each positve real number k, let C _(k) denotes the circle with centre at origin and radius k units. On a circle C _(k) particle alpha moves k units in the counter-clockwise direction. After completing its motion on C_(k), the particle moves onto the circle C _(k+1) in same well defined manner, where r gt 0. The motion of particle continues in this manner. Let k in l' and r=1, particle moves in the radial direction from C _(k) to C_(k+1). If particle starts from the point (-1, 0), then
Answer» It will CROSS the x-axis again at `(3,0)` It will cross the x-axis again at `(4,0)` It will cross the POSITIVE y-axis again at `(0,4)` It will cross the positive y-axis again at `(0,5)` ANSWER :B

Discussion

12346.	There are 3 bags each containing 5 white and 3 black balls. Also there are two bags each contains 2 white and 4 black balls. A white ball is drawn at random. Find the probability at the event that white ball is from a bag of the first group.
Answer» ANSWER :`(45)/(61)`

Discussion

12347.	If X is random variable with distribution given below x:1234P(X=x):kk2k3kThe value of k and its mean are
Answer» ANSWER :B

Discussion

12348.	If the pairs of lines x^(2) – 2nxy - y^(2) = 0 and x^(2) – 2mxy - y^(2) = 0 are such that one of them represents the bisectors of the angles between the other, then
Answer» `(1)/(N)+(1)/(m)=0` `(1)/(n)-(1)/(m)=0` NM - 1 = 0 mn + 1 = 0 Answer :D

Discussion

12349.	By the definition of the definite integral, the value of lim_(n rarr oo)((1)/(sqrt(n^(2))-1) + (1)/(sqrt(n^(2))-2^(2)) +....+(1)/(sqrt(n^(2)-(n-1)^(2)))) is equal to
Answer» `pi` `(pi)/(2)` `(pi)/(4)` `(pi)/(6)` Answer :B

Discussion

12350.	If n is odd natural number , then coefficient of x^n in (e^(5x)+e^x)/(e^(3x)) is
Answer» `2^N/(n!)` `2/n` `n/2` 0 Answer :D

Discussion

Explore topic-wise InterviewSolutions in .

If P=sum_(r=3n)^(r=4n-1)[(r^(2)+13n^(2)-7m)/(n^(3))] & Q=sum_(r=3n+1)^(r=4n)[(r^(2)+13n^(2)-7m)/(n^(3))] Then

Equation of the common tangents of (x^(2))/( y^(2)) +- (y^(2))/( b^(2)) =1 ,( x^(2))/( b^(2)) +- (y^(2))/( a^(2)) =+- 1 are

int (sin x + 8 cos x )/(4 sn x + 6 cos x ) dx =

Let f(x)=(f(x))^(2)+(f'(x))^(2),F(0)=0 where f(x) is thrice differentiable function such that |f(x)|le1 for all x in [-1, 1], then choose the correct statement(s)

Two points A and B are selected at random on a segment of length l. Find the probability that a triangle can be constructed from these three segments.

Solve the following linear programming problem graphically: Maximize :z=4x+3y Subject to: 2x+yge40 x+2yge50 x+yge35 xge0 yge0

A curve y = f(x) is such that f(x)ge 0 and f(0)=0 and bounds a curvilinear triangle with the base [0,x] whose area is proportional to (n+1)^(th) power of f(x)cdot" If "f(1)=1 then find f(x).

Show that thevolume of the largest cone that can be inscribed in a sphere of radius R is (8)/(27) of the volume of the sphere .

A tankcontains 1000 liters of water in which 100 grams of saltsis dissolved brineruns in a rate of 10 liter per minute and each litre contains 5 grams of dissolved salt the mixtureof the tank is kept uniform by stirring brine runs out at 10 liter per minute find the amount of salt at any time t

Catalyst used in conversion of n-hexane into benzene in:

Write down the first three terms is the following expansions(1 + 4x)^(-4)

Find the derivative of f givenby f(x)= sin^(-1)x assuming it exists.

Find the polar of (1,2) with respect to x^(2) + y^(2) = 7

If |3z-1|=3|z-2|, then z lies on

Find the area of the region bounded by the ellipse x^(2)/16 + y^(2)/9=1.

int_(0)^(1)|sin 2 pi x|dx=

Evaluation of definite integrals by subsitiution and properties of its : If int_(0)^(a)f(2a-x)dx=mu and int_(0)^(a)f(x)dx=lamda then int_(0)^(2a)f(x)dx=..........

If P(E ) = 0.8, P(F)= 0.5 and P(E cap F) = 0.4 then P( E//F)=….......

If a,b,c are in A.P then the determinant |{:(x+2,x+3,x+2a),(x+3,x+4,x+2b),(x+4,x+5,x+2c):}| is …..

For each of the differential equations in find the particular solution satisfying the given condition : (dy)/(dx)-(y)/(x)+cosec((y)/(x))=0,y=0 when x=1

A wire of length 20 cm can be bent in the form of a sector then its maximum area is

Determine order and Degree(if defined) of differential equations given y''' + 2y'' + y' = 0

In which one pair, both the plants can be vegetatively propagated by leaf pieces ?

Let O be the origin and A be a point on the cune y^(2)=4x then locus of the midpoint of OA is

If y=sec^(-1)(sqrtx+1)/sqrtx+sin^(-1)fracsqrtx(sqrtx+1)then dy/dx=____

Fundamental theorem of definite integral : f(x)=int_(1)^(x)sqrt(2-t^(2))dt then real roots of the equation x^(2)-f'(x)=0 are ……….

If vec(a)=i-2 j + 3k, vec(b) is a vector such that vec(a).vec(b)= |vec(b)|^(2) |vec(a)-vec(b)|= sqrt7, then |vec(b)|= ________

An unbiased die is rolled 4 times. Out of 4 face values obtained, the probability thatthe minimum face value is not less than 2 and the maximum face value is not greater than5 is

The slope of the normal to the curve y = 3x^(2) at the point whose abscissa is 2 is:

If a,b,c in R and equations ax^2 + bx + c = 0 and x^2 + 2x + 9 = 0 have a common root, show that a:b:c=1 : 2 : 9.

If a fair coin is tossed 10 times, find the probability of﻿ exactly six heads﻿

STATEMENT-1 If A cup B=A cup C, A cap B= A cap C, then B=C STATEMENT-2: A-(B cup C)=(A-B) cup (A-C) STATEMENT-3: If A cap (B' cap C')= A cap B cap C.

Construct truth tables for the following and indicate which of these are tautologies (p < implies q) ^^ (q < impliesr) rarr (p < impliesr)

The value of (1 - omega + omega^(2))^(5) + (1 + omega - omega^(2))^(5), where ro and ro2 are the complex cube roots of unity is

Two integers x and y are chosen one by one with replacement from 1, 2, 3, 4, 5,…., 10. Find the probability that 0 lt |x"- "y| lt 5.

The mean and standard deviation of 100 observations were calculated as 40 and 5.1, respectivey by a student who took by mistake 50 instead of 40 for one observations. The correct standard deviation is

Integrate the rational functions (5x)/((x+1)(x^(2)-4))

{ x in R : cos 2x + 2cos^2 x =2} is equal to

Find the order and degree of the differential equation ((d^(2) y )/( dx^2) )^(2) + cos ((dy)/( dx) ) =0

There are 3 bags each containing 5 white and 3 black balls. Also there are two bags each contains 2 white and 4 black balls. A white ball is drawn at random. Find the probability at the event that white ball is from a bag of the first group.

If X is random variable with distribution given below x:1234P(X=x):kk2k3kThe value of k and its mean are

If the pairs of lines x^(2) – 2nxy - y^(2) = 0 and﻿ x^(2) – 2mxy - y^(2) = 0 are such that one of﻿ them represents the bisectors of the angles﻿ between the other, then

By the definition of the definite integral, the value of lim_(n rarr oo)((1)/(sqrt(n^(2))-1) + (1)/(sqrt(n^(2))-2^(2)) +....+(1)/(sqrt(n^(2)-(n-1)^(2)))) is equal to

If n is odd natural number , then coefficient of x^n in (e^(5x)+e^x)/(e^(3x)) is

If a fair coin is tossed 10 times, find the probability of exactly six heads

If the pairs of lines x^(2) – 2nxy - y^(2) = 0 and x^(2) – 2mxy - y^(2) = 0 are such that one of them represents the bisectors of the angles between the other, then