28278 + Interview Questions in Maths in Class 12 Page 563 InterviewSolution

28101.	(sin 7 theta+ 6 sin 5 theta+17sin 3 theta+12sin theta)/(sin 6 theta+5 sin 4 theta+12sin 2theta)
Answer» `2 COS THETA` `cos theta` `2 SIN theta` `sin theta` ANSWER :A

Discussion

28102.	Find x if abs[[2,4],[5,1]]=abs[[2x,4],[6,x]]
Answer» Solution :The given equation may be WRITTEN as 2-20 = `2x^2 - 24 IMPLIES -18 = 2x^2 - 24 implies 2x^2 = 6 implies x^2 = 3`

Discussion

28103.	If f(x)={((sin([x]+x))/([x]+x),x!=0),(1,x=0):} when [.] denotes the greatest integer function, then:
Answer» `lim_(xto0)(f(x)=SIN1` `lim_(xto0)f(x)=1` `lim_(xto0)f(x)` does not EXIST `lim_(xto0)f(x)` EXISTS but `f(x)` is not CONTINUOUS at x=0 Answer :C

Discussion

28104.	A square is inscribed in the circlex^(2)+y^(2)-4x+6y-5=0 whose sides are parallel to co-ordinate axes then vetices of square are
Answer» (5,0),(5,-6),(-1,0),(-1,-6) (5,1),(5,-6),(-,1),(-1,-6) (5,-1),(5,6),(-1,0),(1,-6) (0,5),(-6,5),(0,-1),(6,1) ANSWER :A

Discussion

28105.	(1-omega +omega^2)(1+omega-omega^2)=4
Answer» SOLUTION :L.H.S.`=(1-omega+omega^2)(1+omega-omega^2)` `= (-omega-omega)(-omega^2-omega^2)(:' 1+omega+omega^2=0)` `(-2omega-2omega^2)=4omega^3=4=`R.H.S.

Discussion

28106.	z = x + iy and w = (1 - iz)/(z-i) , then \|w\| = 1 implies in the complex plane
Answer» z lies on the imaginary AXIS z lies on the real axis z lies on the unit circle z lies on the PARABOLA ANSWER :B

Discussion

28107.	Let f(x) = x^3 + ax^2 + bx + c and g(x) = x^3 + bx^2 + cx + a, where a, b, c are integers. Suppose that the following conditions hold- (a) f(1) = 0, (b) the roots of g(x) = 0 are the squares of the roots of f(x) = 0. Find the value of: a^(2013) + b^(2013) + c^(2013)
Answer» ANSWER :`-1`

Discussion

28108.	Evaluate the following determinants. [[1,0,0],[0,1,0],[0,0,1]]
Answer» SOLUTION :`[[1,0,0],[0,1,0],[0,0,1]]=1[[1,0],[0,1]]`=1-0=1

Discussion

28109.	Removesecondterm( secondhigherpowerof x )fromthe equation x^3-6x^2 +4x -7=0
Answer» ANSWER :`x^3 -8x-15=0`

Discussion

28110.	If A is the set of students of a school then write, which of following relations are Universal, Empty or neither of the two. R_(1)={(a,b):a,b " are ages of students and" \|a-b\| gt 0} R_(2)={(a,b):a,b " are weights ofstudents, and "\|a-b\|lt0} R_(3)={(a,b):a,b " are students studying in same class"}
Answer» ANSWER :`R_(1)` : is universal RELATION. `R_(2)`: is EMPTY relation. `R_(3)`: is NEITHER universal nor empty

Discussion

28111.	int_(0)^(2)[x^(2)]dx=
Answer» 1)`5-sqrt2+sqrt3` 2)`5-sqrt2-sqrt3` 3)`-5-sqrt2-sqrt3` 4)`5+sqrt2-sqrt3` Answer :B

Discussion

28112.	As he reaches the exit of the market, Mario notices five people who are gathered for an eat-as-much-as-you-can competition. There is a clear order in their hunger (i.e. no two people are identically hungry) and the person who was more hungry initially (at the beginning of the competition) wins in a face-off. How many face-offs are required to rank everyone according to their initial hunger? Note : Face-offs should be sufficient to guarentee rank of everyone in any case
Answer» Solution :Note : The faceoffs are independent of each other (their hungers will have their initialvalues before each faceoff). at least 7 matches are needed. Denote the players by A, B, C, D and E. 1. First, A playsagainst B, while C plays against D. Without loss of generality, suppose Aand C are the winners. 2. Then, let A play C in the winners’ match. Without loss of generality, suppose A WINS. Upto this point, we have determined that A gt B and A gt C gt D. 3. Now, we determine the position of E within the A gt C gt D CHAIN. This can be achieved intwo matches. First let E play against C. If E wins, then let him play against A. Otherwise lethim play against D. After this, we have a complete ORDERING of A, C, D and E.4. Finally we have to find the position of B using only two more matches.So far we only have A gt B. There are two cases. If the previous step PRODUCED E gt A gt C gt D.Then we can simply play B against C and D to complete the ordering. If A gt E occurs instead,then we may, without loss of generality, ASSUME that A gt E gt C gt D since none of E, C or Dhave played against B. Now we can simply repeat the method used in the previous step tofind the position of B amongst E gt C gt D, by first matching B against C, then E or Ddepending on the outcome. In all cases, we have determined the complete ordering in 7 matches.

Discussion

28113.	If perpendicular from the point P(a,b,c) drawn to YZ- and ZX- plane meet tham in the points L and M respectively, then equation of plane OLM is
Answer» ax+by +cz=abc bcx + CAY = abc bcx + cay= abc ax+ by + cz=1 Answer :C

Discussion

28114.	Find the angle between two vectorsoversetrarra"and"oversetrarrb with magnitudes sqrt3"and"2 respectively havingoversetrarra.oversetrarrb=sqrt6.
Answer» SOLUTION :`COS THETA =(veca.vecb)/(\|veca\|.\|vecb\|)` `SQRT6/(sqrt3xx2)=sqrt2/2 =1/sqrt2` ` IMPLIES theta=pi/4`

Discussion

28115.	A coin is tossed three times. Find the probability of getting at least 2 heads
Answer» ANSWER :A coin is tossed three TIMES. `S={HHH,HT T, HTH,THH,T TH, THT,HHT,T T T}` `\|S\|=8` LET C be the event of GETTING at least 2 HEADS `thereforeC={HTH,THH,HHT,HHH}` `implies \|C\|=4` `therefore P(C)=\|C\|/\|S\|=4/8=1/2`

Discussion

28116.	A random variable X has the following probability distribution : find the value of k
Answer» ANSWER :0.15

Discussion

28117.	The smallest positive angle which satisfies the equation 2sin^(2)theta+sqrt(3)costheta+1=0, is
Answer» `(5pi)/(6)` `(2PI)/(3)` `(pi)/(3)` `(pi)/(6)` ANSWER :A

Discussion

28118.	P(2, -1, 4) and Q (4, 3, 2) are given points. Find the prove which divides the line joining P and Q in the ratio 2 : 3. (i) Internally (ii) Externally (Using vector method).
Answer» Answer :(i) `((14)/(5),(3)/(5),(16)/(5))`(II) `(-2,-9,8)`

Discussion

28119.	A teacher wants to take 20 students to a park. He can take exactly 5 students at a time and will not take the same group more than once. Find the number of times that the teacher can go to the park
Answer» ANSWER :`""^(20)C_5`

Discussion

28120.	A teacher wants to take 20 students to a park. He can take exactly 5 students at a time and will not take the same group more than once. Find the number of times each student can go to the park.
Answer» ANSWER :`""^(19)C_4`

Discussion

28121.	Refer to Question 8. If the grower wants to maximise the amount of nitrogen added to the garden, how many bags of each brand should be added ? What is the maximum amount of nitrogen added ?
Answer» ANSWER :The MAXIMUM AMOUNT of NITROGEN is 595 KG.

Discussion

28122.	If P = (1, 5, 4) and Q = (4, 1, -2) then find the d.r. of PQ.
Answer» `LT3, 4, 6gt` `lt3, -4, -6gt` `larr3, -4, -6gt` `lt3, 4, -6gt` ANSWER :B

Discussion

28123.	Evaluate the following integrals int_0^2x^2e^(x^3)dx
Answer» SOLUTION :`int_0^2e^(x^3)x^2dx` `int_0^8e^6(1/3)dt=1/3(e^8-1)`

Discussion

28124.	The maximum value of variance in binomial distribution withparameters n and p is_____.
Answer» Solution :VARIANCE =npq where Q = 1 -p, and `0LTPLT1` Now variance is maxium when `p=q=1/2` Thus maximum value of variance `=n/4` Let the number of trails =n and P(succes)=P.

Discussion

28125.	Solve the following systems of linear inequalities graphically : x gt y , x lt 1, y gt 0.
Answer» Solution : Step-2 : Let us consider a point (2,1) that does not lie on any of the lines. Putting x = 2, y = 2 In the inequalities we get `RARR` (2,1) satisfies x `gt` y and y `gt` 0 but does not satisfy x `lt` 1 thus the SHADED REGION is the solution region.

Discussion

28126.	Find int(x^(4)dx)/((x-1)(x^(2)+1))
Answer» ANSWER :`(X^(2))/(2)+x+(1)/(2)log\|x-1\|-(1)/(4)log (x^(2)+1)-(1)/(2)TAN^(-1)x+c`

Discussion

28127.	Find the equation of the circle which cuts the following circles orthogonally. x^(2)+y^(2)+4x-7=0,2x^(2)+2y^(2)+3x+5y-9=0,x^(2)+y^(2)+y=0
Answer» ANSWER :`X^(2)+y^(2)-26/5 x+34/5 y-17/5=0`

Discussion

28128.	An aeroplane flying with uniform speed horizontally one kilometer above the ground id observed at an elevation of 60^(@). Aftar 10s if the elevation is observed to be 30^(@), then the speed of the aeroplane (in km/h) is
Answer» `240//SQRT3` `200 sqrt3` `240 sqrt3` `120//sqrt3` ANSWER :C

Discussion

28129.	If a_0, a_1 , a_2 …..a_n are binomial coefficients then (1 + a_1/a_0)(1 +a_2/a_1) …………….(1 + (a_n)/(a_(n-1)) ) =
Answer» `((N -1)^n)/(n!)` `((n + 1)^n)/(n!)` `((n +1)^(2N))/(n!)` `((n - 1)^n)/(2n!)` ANSWER :B

Discussion

28130.	If p,q are roots of the quadratic equationx^(2)-10rx -11s =0 and r,sare roots of x^(2)-10px -11q=0 then find the value ofp+q +r+s.
Answer» ANSWER :1210

Discussion

28131.	Find the equation of a curve passing through the point (0,0) and whose differentialequation is y' = e^(x) sin x.
Answer» ANSWER :`2y - 1 = e^(X)(sin x - COS x)`

Discussion

28132.	int (secx+ tan x)^(2)dx=...
Answer» `2(SEC X+tanx)-x+c` `(1)/(3) (secx+tanx)^(3)+c` `sec x(secx+tanx)+c` `2(secx+tanx)+c` Answer :A

Discussion

28133.	Let m be the smallest odd positive iteger for which 1 + 2+ …..+ m is a square of an integer and let n be the smallest even positive integer for which 1 + 2+ ……+ n is a square of an integer. What is the value of m + n ?
Answer» ANSWER :9

Discussion

28134.	int_(1//e)^(e)\|logx\|dx=
Answer» `1 - 1/e` `1+ 1/e` `2( 1- 1/e)` `(1+ 1/e)` ANSWER :C

Discussion

28135.	The probability of getting atleast two heads, when tossing a coin three times is……….
Answer» `(1)/(8)` `(3)/(8)` `(1)/(2)` `(5)/(8)` Answer :C

Discussion

28136.	If \|(a,a^(2),1+a^(3)),(b,b^(2),1+b^(3)),(c,c^(2),1+c^(3))\|=0 and vectors (1,a,a^(2)),(1,b,b^(2)) and (1,c,c^(2)) are non coplanar then the product abc=
Answer» only I is true only II is true both I and II are true neither I nor II true Answer :C

Discussion

28137.	Using the method of integration find the area of the triangle ABC, coordinates of whose vertices are A(2, 0), B (4, 5) and C (6, 3).
Answer» ANSWER :7

Discussion

28138.	f: R rarr R, f(x) is a differentiable function such that all its successive derivatives exist. f'(x) can be zero at discrete points only and f(x)f''(x) le 0 AA x in R If alpha and beta are two consecutive roots of f(x) = 0, then
Answer» `f''(GAMMA) = 0 gamma in(alpha , beta)` `f'''(gamma) = 0 gamma in(alpha , beta)` `f''''(gamma) = 0 gamma in(alpha , beta)` `f'''''(gamma) = 0 gamma in(alpha , beta)` Answer :B

Discussion

28139.	If area of triangle is 35 sq. units with vertices (2,-6), (5,4)and (k,4), then k=…......
Answer» `-12,-2` `-20` `1.2` `12,-2` ANSWER :D

Discussion

28140.	Integrate the functions cos^(3)xe^(logsinx)
Answer» ANSWER :`-1/4cos^(4)x+C`

Discussion

28141.	Find the number of radians in cos^(-1)(-0.5624)
Answer» `-0.97` `0.97` `1.77` 2.17 Solution :SET you calculator to RADIAN mode, and ENTER 2ND `COS^(-1)(-0.5624)`.

Discussion

28142.	(a + b) xx c + (b + c) xx a + (c + a) xx b =
Answer» 0 `- [a B C]` 2 [a b c] [a b c] ANSWER :D

Discussion

28143.	If ((1 + i)/(1- i))^(x) = 1 then
Answer» x = 4N where n is any POSITIVE integer x = 2n where n is any positive integer x = 4n + 1 where n is any positive integer x = 2n + 1 where n is any positive integer Answer :A

Discussion

28144.	If anebnecand \|{:(a,a^3,a^4-1),(b,b^3,b^4-1),(c,c^3,c^4-1):}\|=0 then prove that abc(ab+bc+ca)=a+b+c
Answer» ANSWER :ABC(ab+bc+ca)=a+b+c

Discussion

28145.	Find the general solution of e^(x) tan ydx + (1 - e^(x))sec^(2)y dy = 0
Answer» ANSWER :`TAN y = C (1 - E^(X))`

Discussion

28146.	A ladder rests against a wall at an angle of 35^(@). Its foot is pulled away through a distance a, so that it slides a distance b down the wall, finally making an angle of 25^(@) with the horizontal, then a/b =
Answer» 1 `1//SQRT(3)` `sqrt(3)` `sqrt(3)//2` ANSWER :B

Discussion

28147.	If vec(alpha)=(1)/(a)hati+(4)/(b)hatj+b hatk and vec(beta)=b hati+a hatj+(1)/(b)hatk then the maximum value (10)/(5+vec(alpha).vec(beta) is …………
Answer» 1 5 2 3 Answer :A

Discussion

28148.	If ""^(n)C_(4)=""^(n)C_(6), find n.
Answer» ANSWER :10

Discussion

28149.	Find values of x for which \|{:(3,x),(x,1):}\|=\|{:()3,2),(4,1):}\|
Answer» ANSWER :`(x=+-2sqrt2)`

Discussion

28150.	Let ABCD be a quadrilateral with /_CBD=2/_ADB, /_ABD=2/_CDB, AB=BC, then
Answer» `AD=CD` `/_ADB=/_CDB` `/_CBD=/_ABD` `/_ADC` is`(2pi)/3` Solution :`2x=/_CBD` `2y=/_ABD` In `/_\CBD` `(sin(pi-(2y+x)))/(sinx)=(BD)/(BA)=(BD)/(BC)=(sin(pi-(2x+y)))/(SINY)` `impliessin(2+x)siny=sin(2x+y)sinx` `=1/2[cos(y+x)-cos(3y+x)]=1/2[cos(x+y)-cos(3x+y)]` `0ltx+y=1/2ABClt(pi)/2` `0LT(3y+x)+(3x+y)lt2pi` `=:. 3y+x=3x+yimpliesx=y` `implies/_ABD=/_CBDimpliesAD=CD`

Discussion

Explore topic-wise InterviewSolutions in .

(sin 7 theta+ 6 sin 5 theta+17sin 3 theta+12sin theta)/(sin 6 theta+5 sin 4 theta+12sin 2theta)

Find x if abs[[2,4],[5,1]]=abs[[2x,4],[6,x]]

If f(x)={((sin([x]+x))/([x]+x),x!=0),(1,x=0):} when [.] denotes the greatest integer function, then:

A square is inscribed in the circlex^(2)+y^(2)-4x+6y-5=0 whose sides are parallel to co-ordinate axes then vetices of square are

(1-omega +omega^2)(1+omega-omega^2)=4

z = x + iy and w = (1 - iz)/(z-i) , then |w| = 1 implies in the complex plane

Let f(x) = x^3 + ax^2 + bx + c and g(x) = x^3 + bx^2 + cx + a, where a, b, c are integers. Suppose that the following conditions hold- (a) f(1) = 0, (b) the roots of g(x) = 0 are the squares of the roots of f(x) = 0. Find the value of: a^(2013) + b^(2013) + c^(2013)

Evaluate the following determinants. [[1,0,0],[0,1,0],[0,0,1]]

Removesecondterm( secondhigherpowerof x )fromthe equation x^3-6x^2 +4x -7=0

If A is the set of students of a school then write, which of following relations are Universal, Empty or neither of the two. R_(1)={(a,b):a,b " are ages of students and" |a-b| gt 0} R_(2)={(a,b):a,b " are weights ofstudents, and "|a-b|lt0} R_(3)={(a,b):a,b " are students studying in same class"}

int_(0)^(2)[x^(2)]dx=

If perpendicular from the point P(a,b,c) drawn to YZ- and ZX- plane meet tham in the points L and M respectively, then equation of plane OLM is

Find the angle between two vectorsoversetrarra"and"oversetrarrb with magnitudes sqrt3"and"2 respectively havingoversetrarra.oversetrarrb=sqrt6.

A coin is tossed three times. Find the probability of getting at least 2 heads

A random variable X has the following probability distribution : find the value of k

The smallest positive angle which satisfies the equation 2sin^(2)theta+sqrt(3)costheta+1=0, is

P(2, -1, 4) and Q (4, 3, 2) are given points. Find the prove which divides the line joining P and Q in the ratio 2 : 3. (i) Internally (ii) Externally (Using vector method).

A teacher wants to take 20 students to a park. He can take exactly 5 students at a time and will not take the same group more than once. Find the number of times that the teacher can go to the park

A teacher wants to take 20 students to a park. He can take exactly 5 students at a time and will not take the same group more than once. Find the number of times each student can go to the park.

Refer to Question 8. If the grower wants to maximise the amount of nitrogen added to the garden, how many bags of each brand should be added ? What is the maximum amount of nitrogen added ?

If P = (1, 5, 4) and Q = (4, 1, -2) then find the d.r. of PQ.

Evaluate the following integrals int_0^2x^2e^(x^3)dx

The maximum value of variance in binomial distribution withparameters n and p is_____.

Solve the following systems of linear inequalities graphically : x gt y , x lt 1, y gt 0.

Find int(x^(4)dx)/((x-1)(x^(2)+1))

Find the equation of the circle which cuts the following circles orthogonally. x^(2)+y^(2)+4x-7=0,2x^(2)+2y^(2)+3x+5y-9=0,x^(2)+y^(2)+y=0

An aeroplane flying with uniform speed horizontally one kilometer above the ground id observed at an elevation of 60^(@). Aftar 10s if the elevation is observed to be 30^(@), then the speed of the aeroplane (in km/h) is

If a_0, a_1 , a_2 …..a_n are binomial coefficients then (1 + a_1/a_0)(1 +a_2/a_1) …………….(1 + (a_n)/(a_(n-1)) ) =

If p,q are roots of the quadratic equationx^(2)-10rx -11s =0 and r,sare roots of x^(2)-10px -11q=0 then find the value ofp+q +r+s.

Find the equation of a curve passing through the point (0,0) and whose differentialequation is y' = e^(x) sin x.

int (secx+ tan x)^(2)dx=...

Let m be the smallest odd positive iteger for which 1 + 2+ …..+ m is a square of an integer and let n be the smallest even positive integer for which 1 + 2+ ……+ n is a square of an integer. What is the value of m + n ?

int_(1//e)^(e)|logx|dx=

The probability of getting atleast two heads, when tossing a coin three times is……….

If |(a,a^(2),1+a^(3)),(b,b^(2),1+b^(3)),(c,c^(2),1+c^(3))|=0 and vectors (1,a,a^(2)),(1,b,b^(2)) and (1,c,c^(2)) are non coplanar then the product abc=

Using the method of integration find the area of the triangle ABC, coordinates of whose vertices are A(2, 0), B (4, 5) and C (6, 3).

f: R rarr R, f(x) is a differentiable function such that all its successive derivatives exist. f'(x) can be zero at discrete points only and f(x)f''(x) le 0 AA x in R If alpha and beta are two consecutive roots of f(x) = 0, then

If area of triangle is 35 sq. units with vertices (2,-6), (5,4)and (k,4), then k=…......

Integrate the functions cos^(3)xe^(logsinx)

Find the number of radians in cos^(-1)(-0.5624)

(a + b) xx c + (b + c) xx a + (c + a) xx b =

If ((1 + i)/(1- i))^(x) = 1 then

If anebnecand |{:(a,a^3,a^4-1),(b,b^3,b^4-1),(c,c^3,c^4-1):}|=0 then prove that abc(ab+bc+ca)=a+b+c

Find the general solution of e^(x) tan ydx + (1 - e^(x))sec^(2)y dy = 0

A ladder rests against a wall at an angle of 35^(@). Its foot is pulled away through a distance a, so that it slides a distance b down the wall, finally making an angle of 25^(@) with the horizontal, then a/b =

If vec(alpha)=(1)/(a)hati+(4)/(b)hatj+b hatk and vec(beta)=b hati+a hatj+(1)/(b)hatk then the maximum value (10)/(5+vec(alpha).vec(beta) is …………

If ""^(n)C_(4)=""^(n)C_(6), find n.

Find values of x for which |{:(3,x),(x,1):}|=|{:()3,2),(4,1):}|

Let ABCD be a quadrilateral with /_CBD=2/_ADB, /_ABD=2/_CDB, AB=BC, then