28278 + Interview Questions in Maths in Class 12 Page 245 InterviewSolution

12201.	Consider the equaitonof line abarz + abarz+ abarz + b=0, whereb is arealparameterand a isfixed non-zero complex number. Theinterceptof lineon real axis is given by
Answer» `(-2b)/(a+bara)` `(-b)/(2(a+ bara))` `(-b)/(a+bara)` `(b)/(a+bara)` Solution :Givenequationof line is `abarz + abarz + b =0AA b in R`. Let thePQbe thesegement intercept between AXES. Forintercept on real axis `Z_(R)`. `z =BARZ` `rArr Z_(R)(a+ bara) + b =0` ` rArr Z_(R) = (-b)/(a + bara)` For interceptonimaginary `Z_(1)` `z +barz = 0` `rArr Z_(1)(bara - a) + b=0` `rArr Z_(1)= (b)/(a+bara)` For mid-point, `z= (Z_(R) + Z_(I))/(2)` `rArr z =(-b)/(2)[(1)/(bara+a)+(1)/(bara +a)]` `z= (BARAB)/((a + bara)(a-bara))` `rArr z = (barab)/(a^(2) -(a)^(2))` `(z[a^(2)-(a)^(2)])/(bara) = barz((bara)^(2) - (a)^(2))/(a)` `rArr az + BAR(az) =0`

Discussion

12202.	Consider the equationof line abarz + baraz + b=0, whereb is arealparameterand a isfixed non-zero complex number. The locus of mid-point of thelineintercepted between real and imaginary axis is givenby
Answer» `az- BAR(az) =0` `az + bar(az) =0` `az-bar(az) + B =0` `az - bar(az) + 2B = 0` Solution :Givenequationof line is `abarz + abarz + b =0AA b in R`. Let thePQbe thesegement intercept between axes. Forintercept on real axis `Z_(R)`. `Z =barz` `rArr Z_(R)(a+ bara) + b =0` ` rArr Z_(R) = (-b)/(a + bara)` For interceptonimaginary `Z_(1)` `z +barz = 0` `rArr Z_(1)(bara - a) + b=0` `rArr Z_(1)= (b)/(a+bara)` For mid-point, `z= (Z_(R) + Z_(I))/(2)` `rArr z =(-b)/(2)[(1)/(bara+a)+(1)/(bara +a)]` `z= (barab)/((a + bara)(a-bara))` `rArr z = (barab)/(a^(2) -(a)^(2))` `(z[a^(2)-(a)^(2)])/(bara) = barz((bara)^(2) - (a)^(2))/(a)` `rArr az + bar(az) =0`

Discussion

12203.	Consider the following statements: S_(1): The antiderivative of every function is an odd function. S_(2): Primitive of (3x^(4)-1)/(x^(4)-x+1)^(2) w.r.t is x/(x^(4)+x+1) +C S_(3): int1/(sqrt(sinxcosx))dx = -2/sqrt(tanx)+C S_(4): The value of int(sqrt(a+x)/(a-x)-sqrt(a-x)/(a+x)) dx is equal to -2sqrt(a^(2)-x^(2))+C State, in order whether S_(1),S_(2),S_(3),S_(4) are true or false
Answer» FFTT TTTT FFFF TFTF Answer :a

Discussion

12204.	If a matrix has 18 elements, what are the possible orders it can have? What, if it has 5 elements?
Answer» ANSWER :`1xx18, 2xx9, 3xx6, 6xx3, 9xx2, 18xx1; 1xx5, 5xx1`

Discussion

12205.	If a=hat(i)+hat(j)+hat(k), b=hat(i)+3hat(j)+5hat(k) and c=7hat(i)+9hat(j)+11 hat(k), then the area of the parallelogram having diagonals a+b and b+c is
Answer» `4sqrt(6)` `1/2 sqrt(21)` `sqrt(6)/2` `sqrt(6)` SOLUTION :GIVEN that, `a = hati +HATJ +hatk, b =hati +3hatj +5 hatj ` and`c=7 hati +9 hatj +1 hatk` Let `A =1 +b=(hati + hatj +hatk) +(hati+3hatj +5 hatk)=2 hati +4 hatj+6hatk` and `=+=(hat+hat3+ha5)+(hat7+hat9+hat11)` `=hat8+hat12+hat16` If A and B are adagonals, then area of parallelogram `1/2\|AxxB\|=1/2\|\|{:(hati, hatj,hatk),(2,4,6),(8,12,16):}\|\|` `=1/2\|hati(64-72)-hatj(32-48)+hatk(24-32)\|` `1/2\|-8hati+16hatj-8hatk\|` `=\|-4hati+8hatj+4hatk\|` `=sqrt((-4)^(2)+(8)^(2)+(-4)^(2))` `=sqrt(16+64+16)` `=sqrt96=4sqrt6`

Discussion

12206.	If the function f(x) = {(x, if 0 le x le 2),(2, if x ge 2):} derivable at 2? Justify.
Answer» ANSWER :A::B::D

Discussion

12207.	I : The equation of the perpendicular bisecting plane of the line segment joining (-3,3, 2), (9, 5, 4) is x – 7y + 2z - 1 = 0 II : The equation of the plane passing through the points (1, 2, 1), (1, 1, 0), (- 2,2, - 1) is 2x – 3y + 2z – 11 = 0
Answer» only I is TRUE only II is true both I and II are true neither I nor II are true Answer :D

Discussion

12208.	int_(0)^(2x) sin^6 x cos^5 x dx is equal to
Answer» `2PI` `PI//2` 0 `-pi` ANSWER :C

Discussion

12209.	Integration by partial fraction : int(x^(2)-1)/(x^(4)+x^(2)+1)dx=...
Answer» `(1)/(2)LOG((x^(2)+x+1)/(x^(2)-x+1))+C` `(1)/(2)log((x^(2)-x-1)/(x^(2)+x+1))+c` `log((x^(2)-x+1)/(x^(2)+x+1))+c` `(1)/(2)log((x^(2)-x+1)/(x^(2)+x+1))+c` ANSWER :D

Discussion

12210.	If [sinx]+[sqrt(2)cosx]=-3,x in[0,2pi]([.]-GIF), "then" x in
Answer» `((5PI)/(4),2pi)` `[(5pi)/(4),2pi]` `(pi,(5pi)/(4))` `[pi,(5pi)/(4)]` Solution :`A^(n+2)-B^(n+2)=(A+B)(A^(n+1)-B^(n+1))-AB(A^(n)-B^(n))` `A^(n)-B^(n)=(A+B)(A^(n)-B^(n))-AB(A^(n)-B^(n))` `impliesI=A+B-AB""[becauseA^(n)-B^(n)"is INVERTIBLE"]` `IMPLIES (I-A)(I-B)=0` As A, `B ne l`, we get I-A and I-B are singluar MATRICES.

Discussion

12211.	If ""^(18)P_((r-1)):""^(17)P_((r-1))=9:7, find r.
Answer» ANSWER :5

Discussion

12212.	Thereare n pointsin a planeno threeofwhichare in thesamelineexceptingp pointswhich arecollinear. Thenumberof triangle fomedby joiningthem is
Answer» `""^(N)C_(2)` `""^(n)C_(2)-""^(p)C_(2)` `""^(n-p)C_(3)` `""^(n)C_(3)-""^(p)C_(3)+1` Answer :D

Discussion

12213.	The volume of a parallelopiped whose coterminous edges are 2a, 2b, 2c, is
Answer» `2 [(a,b,C)]` `4 [(a,b,c)]` `8 [(a, b, c)]` `[(a,b,c)]` SOLUTION :Volume of parallelopiped=`["2a2b 2C"]=8["ABC"]`

Discussion

12214.	The vector equation of the linepassing through the point i+j-k and parallel to the vector 2i+3j-k is
Answer» R=(i+j-k)+t(2i+3j-k) r=(i-j+k)+t(2i-3j-k) r=(i-j-k)+t(2i-3j-k) r=(-i-j+k)+t(-2i+3j+k) ANSWER :A

Discussion

12215.	Draw the graph of y = x sin x.
Answer» Solution :We have y = f(x) = x sin x. First draw the graph of `y = +-x`. Now CONSIDER the values of f(x) for quadrant angles. f(0) = 0 `f(pi//2) = pi//2` `f(pi) = 0` `f(3pi//2) = -3pi//2` `f(2pi) = 0` `f(5pi//2) = 5pi//2` ETC. POINTS `(pi//2, pi//2), (5pi//2, 5pi//2), ...` lie on the graph of y = x. Points `(3pi//2, 3pi//2), (7pi//2, 7pi//2),...` lie on the graph of y = -x. Further f(x) = f(-x), hence the function is EVEN and the graph is symmetrical about the y-axis. From the above discussion, the graph of the function is as shown in the following figure.

Discussion

12216.	If the co-ordinates of the points A, B, C, D be (1,2,3),(4,5,7) (-4,3,-6) and (2,9,2) respectively, then find the angle between the lines AB and CD
Answer» Answer :Direction ratios of AB are 4-1, 5-2, 7-3 i.e., 3, 3, 4 and the direction ratios of CD and 2+4, 9-3, 2+6 i.e., 6, 6, 8 Since 3/6 = 3/6 = 4/8, AB and CD are parallel `rArr` ANGLE between AB and CD = `0^@`

Discussion

12217.	If P and Q are the Points of intersection of the circles x^2 + y^2 + 3x + 7y -2p - 5 = 0 andx^2 +y^2 +2x +2y- p^2 =0 then there is a circle passing through P, Q and (1, 1) for
Answer» all EXCEPT ONE value of p all except twovalues of p exactly one value of p all values of p ANSWER :A

Discussion

12218.	On a multiple choice examination with three possible answers (out of which only one is correct) for each of the five questions, what is the probability that a candidate would get four or more correct answers just by guessing.
Answer» ANSWER :0.045

Discussion

12219.	The point of extremum of f(x)=int_(0)^(x)(t-2)^(2)(t-1)dt is a
Answer» max at X = 1 max at x = 2 min at x = 1 min at x = 2 ANSWER :3

Discussion

12220.	A tower leans towards west making an angle alpha with the vertical. The angular elevation of B, the top most point of the tower, is 75^(@) as observed from a point C due east of A at a distance of 20 units. If the angular elevation of B from a point due east of C at a distance of 20 units from C is 45^(@), then tan alpha is equal to
Answer» `(sqrt3+1)/(2)` `(sqrt3+1)/(sqrt3-1)` `3-2sqrt3` `(sqrt3-1)/(2)` ANSWER :C

Discussion

12221.	The volume of the parallelepiped with edges -12hati+alpha hatk,3hatj-hatk and 2hati+hatj-15hatk is 546 then alpha = ……………
Answer» 3 2 `-3` `-2` ANSWER :C

Discussion

12222.	If x is a real number then maximum value of (3x^(2)+9x+17)/(3x^(2)+9x+7) is …………
Answer» `(1)/(4)` 41 1 `(17)/(7)` Answer :B

Discussion

12223.	An experiment succeeds twice as often as it fails. Find the probability that in the next six trials, there will be atleast 4 successes.
Answer» Answer :`((2)/(3))^(4)[(31)/(9)]`

Discussion

12224.	Bag I contains 3 red and 4 black balls while another Bag II contains 5 red and 6 black balls. One ball is drawn at random from one of the bags and it is found to be red. Find the probability that it was drawn from Bag II.
Answer» ANSWER :`(35)/(68)`

Discussion

12225.	Integrate the functions 1/(x(logx)^(m)),xgt0,mne1
Answer» ANSWER :`((LOGX)^(1-m))/(1-m)+C`

Discussion

12226.	Findproducts : [[0,1],[1,0]][[a,b],[c,d]]
Answer» SOLUTION :`[[0,1],[1,0]][[a,B],[C,d]]` `=[[0.a+1.c""0.b+1.d],[1.a+0.c" "1.b+0.d]]=[[c,d],[a,b]]`

Discussion

12227.	If theta=pi/6, then the 10th term of the series 1+(costheta+isintheta)+(cos theta+i sin theta)^2+…. Is
Answer» i -1 1 `-i` ANSWER :D

Discussion

12228.	Let alpha !=1 be a real root of the equationx^(3)-ax^(2)+ax-1=0, where a != -1 is a real number. Then, a root of this equation, among the following, is
Answer» `ALPHA^(2)` `- 1/alpha` `1/alpha` `- 1/alpha^(2)` ANSWER :C

Discussion

12229.	1.C_0 + 3.C_1+ 3^2.C_2+….+3^n.C_n =
Answer» `4^n` `3^n` `5^n` `2^n` ANSWER :A

Discussion

12230.	A relation R on a finite set having n elements is reflexive. If R has m pairs then ............
Answer» `m GE N` `m LEN` `m=n` NONE of these Solution :N/A

Discussion

12231.	The vector (bar(a)+bar(b)) bisects the angle between the non-collinear vectors bar(a) and bar(b), if ……………
Answer» ANSWER :`:.BAR(a)=bar(B)`

Discussion

12232.	Integrate the functions (x^(3)-1)^(1/3)x^(5)
Answer» ANSWER :`1/7(X^(3)-1)^(7/3)+1/4(x^(3)-1)^(4/3)+C`

Discussion

12233.	If A and B are square matrices of order 3 x 3 such that \|A\|=2,\|B\|=3, then \|2AB\| =
Answer» 48 12 36 24 Answer :A

Discussion

12234.	Find the number of positive integral solutions of x_(1)x_(2)x_(3)x_(4)=1050.
Answer» ANSWER :640

Discussion

12235.	If A and B are two square matrices of order n , and A and B commute, then for any real number k
Answer» `A-kI,B-kI` COMMUTE A-kI,B-kI are equal A-kI,B-kI are not commute none Answer :A

Discussion

12236.	The equation of the line passing through the point P(1, 2) such that P bisects the part intercepted between the axes is
Answer» a, B, C c, a, b b, c, a c, b, a ANSWER :D

Discussion

12237.	State which of the foolowing statement is true?
Answer» The distance between the line `vecr=(2 HATI-2 hatj+3 HATK)+( hati- hatj+ 4hatk)` and the plane `vecr.( hati+5 hatj+ hatk) =5 is (10)/(3 sqrt3)` units . Distance between parallel to the plane`vecr. (6 hat i- 3 hatj +9 hat k)+13=0` units. A vector parallel to the plane `x+y+z-3=0 and 2x-y-3z=0 ishati- hatj-3 hatk`. The distance of a POINT `(2,5,-3)` from the plane ` vec r .( 6 hati- 3 hatj+2 hatk)=4 is (7)/(13)` units. Answer :A

Discussion

12238.	Consider the following sequence :a _(1) = a _(2) =1, a _(1) = 1 + minimum( a _(i-1) , a _(i-2)) for I gt 2. Then a _( 2006)=
Answer» ANSWER :`1003`

Discussion

12239.	If the locus of the mid points of the chords of the ellipse (x^(2))/(a^(2)) +(y^(2))/( b^(2)) =1, drawn parallel to y=m_1x is y=m_2xthen m_1m_2=
Answer» ` ( B^(2))/( a^(2))` ` ( a^(2))/( b^(2))` ` (-b^(2))/( a^(2))` ` ( -a^(2))/( b^(2))` ANSWER :C

Discussion

12240.	If sin (sin^(-1)""(1)/5 + cos^(-1)x) = 1, then find the value of x.a) 0 b) 1/5 c) 2/5 d) 3/5
Answer» 0 1/5 2/5 3/5 ANSWER :`X =(1)/5`

Discussion

12241.	If ""^(18)C_(15)+2(""^(18)C_(16))+""^(17)C_(16)+1=""^(n)C_(3), then n =
Answer» 19 20 18 24 Answer :B

Discussion

12242.	Evalute the following integrals int ((1 + log x)^(2))/(x )dx
Answer» ANSWER :`((X + LOG )^(3))/(3 ) + C `

Discussion

12243.	Let A={a,b,c} and Let R={(a,a),(a,b)}. then ,R is
Answer» REFLEXIVE and SYMMETRIC but TRANSITIVE Reflexive and transitive but not symmetric symmetric and transitive but not reflexive An EQUIVALENCE relation Answer :C

Discussion

12244.	Three friends Ram , Shyam and Rahul went to a shop .Ram purchased 12 dozen notebooks ,6 dozen pen and 10 dozen pencil .Shyam purchased 20 dozen notebooks , 10 dozen pen and 15 dozen pencils . If the price of 1 dozen notebooks , pen and pencil is respectively Rs 72, Rs. 48 and Rs. 18 . Using matrix equation find the amount paid by each person to shopkeepar .
Answer» ANSWER :RS. 1332 , Rs. 2190, Rs. 1650

Discussion

12245.	Find the number of (i) 6
Answer» ANSWER :`8^3`

Discussion

12246.	Integrate the functions xsinx
Answer» ANSWER :`-xcosx+sinx+C`

Discussion

12247.	Evaluate : (i) int_(0)^(2pi) {sin(sinx)+sin(cosx)}dx, (ii) int_(0)^(pi) (dx)/(5+4cos2x) (iii) int_(0)^(pi//2) (2lnsinx-ln sin2x)dx , (iv) int_(0)^(oo) ln(x+(1)/(x)).(dx)/(1+x^(2))
Answer» SOLUTION :N//A

Discussion

12248.	If S_(0),S_(1),S_(2),… are areas bounded by the x-axis and half-wave of the curve y=sin pi sqrt(x)," then prove that "S_(0),S_(1),S_(2),… are in A.P…
Answer» SOLUTION :`y= sin pi sqrt(x)` meets x-axis when `pisqrt(x)=npi or x=n^(2), n in N.` Therefore, area of half-wave between `x=n^(2) and x=(n+1)^(2)` is `S_(n)=\|overset((n+1)^(2))underset(n^(2))int sin pi sqrt(x)dx \|` `"Putting "pisqrt(x)=y and pi^(2) dx =2Y dy,`we get `therefore""S_(n)=\|(2)/(pi^(2))overset((n+1)pi)underset(npi)inty sin y dy \|` `=\|(2)/(pi^(2))[-y cos y + sin y ]_(npi)^((n+1)pi)\|` `=\|(2)/(pi^(2))[-(n+1)pi cos (n+1) pi +npi cos n pi ]\|` `=(2(2n+1))/(pi), n in N` `"Hence, "S_(0),S_(1),S_(2),...` are in A.P..

Discussion

12249.	int (tan x+tan^3 x)/(1+tan^3x) dx.
Answer» ANSWER :`1/6`

Discussion

12250.	Marks scored by 100 students in a 25 marks unit test ofMathematics is given below. Their median is {:("Marks " ,0-5,5-10,10-15,15-20,20-25),("Students "," "10," "18," "42," "23," "7):}
Answer» 12 `12.63` `12.3` `12.7` ANSWER :B

Discussion

Explore topic-wise InterviewSolutions in .

Consider the equaitonof line abarz + abarz+ abarz + b=0, whereb is arealparameterand a isfixed non-zero complex number. Theinterceptof lineon real axis is given by

Consider the equationof line abarz + baraz + b=0, whereb is arealparameterand a isfixed non-zero complex number. The locus of mid-point of thelineintercepted between real and imaginary axis is givenby

If a matrix has 18 elements, what are the possible orders it can have? What, if it has 5 elements?

If a=hat(i)+hat(j)+hat(k), b=hat(i)+3hat(j)+5hat(k) and c=7hat(i)+9hat(j)+11 hat(k), then the area of the parallelogram having diagonals a+b and b+c is

If the function f(x) = {(x, if 0 le x le 2),(2, if x ge 2):} derivable at 2? Justify.

I : The equation of the perpendicular bisecting plane of the line segment joining (-3,3, 2), (9, 5, 4) is x – 7y + 2z - 1 = 0 II : The equation of the plane passing through the points (1, 2, 1), (1, 1, 0), (- 2,2, - 1) is 2x – 3y + 2z – 11 = 0

int_(0)^(2x) sin^6 x cos^5 x dx is equal to

Integration by partial fraction : int(x^(2)-1)/(x^(4)+x^(2)+1)dx=...

If [sinx]+[sqrt(2)cosx]=-3,x in[0,2pi]([.]-GIF), "then" x in

If ""^(18)P_((r-1)):""^(17)P_((r-1))=9:7, find r.

Thereare n pointsin a planeno threeofwhichare in thesamelineexceptingp pointswhich arecollinear. Thenumberof triangle fomedby joiningthem is

The volume of a parallelopiped whose coterminous edges are 2a, 2b, 2c, is

The vector equation of the linepassing through the point i+j-k and parallel to the vector 2i+3j-k is

Draw the graph of y = x sin x.

If the co-ordinates of the points A, B, C, D be (1,2,3),(4,5,7) (-4,3,-6) and (2,9,2) respectively, then find the angle between the lines AB and CD

If P and Q are the Points of intersection of the circles x^2 + y^2 + 3x + 7y -2p - 5 = 0 andx^2 +y^2 +2x +2y- p^2 =0 then there is a circle passing through P, Q and (1, 1) for

On a multiple choice examination with three possible answers (out of which only one is correct) for each of the five questions, what is the probability that a candidate would get four or more correct answers just by guessing.

The point of extremum of f(x)=int_(0)^(x)(t-2)^(2)(t-1)dt is a

The volume of the parallelepiped with edges -12hati+alpha hatk,3hatj-hatk and 2hati+hatj-15hatk is 546 then alpha = ……………

If x is a real number then maximum value of (3x^(2)+9x+17)/(3x^(2)+9x+7) is …………

An experiment succeeds twice as often as it fails. Find the probability that in the next six trials, there will be atleast 4 successes.

Bag I contains 3 red and 4 black balls while another Bag II contains 5 red﻿ and 6 black balls. One ball is drawn at random from one of the bags and it is found to﻿ be red. Find the probability that it was drawn from Bag II.

Integrate the functions 1/(x(logx)^(m)),xgt0,mne1

Findproducts : [[0,1],[1,0]][[a,b],[c,d]]

If theta=pi/6, then the 10th term of the series 1+(costheta+isintheta)+(cos theta+i sin theta)^2+…. Is

Let alpha !=1 be a real root of the equationx^(3)-ax^(2)+ax-1=0, where a != -1 is a real number. Then, a root of this equation, among the following, is

1.C_0 + 3.C_1+ 3^2.C_2+….+3^n.C_n =

A relation R on a finite set having n elements is reflexive. If R has m pairs then ............

The vector (bar(a)+bar(b)) bisects the angle between the non-collinear vectors bar(a) and bar(b), if ……………

Integrate the functions (x^(3)-1)^(1/3)x^(5)

If A and B are square matrices of order 3 x 3 such that |A|=2,|B|=3, then |2AB| =

Find the number of positive integral solutions of x_(1)x_(2)x_(3)x_(4)=1050.

If A and B are two square matrices of order n , and A and B commute, then for any real number k

The equation of the line passing through the point P(1, 2) such that P bisects the part intercepted between the axes is

State which of the foolowing statement is true?

Consider the following sequence :a _(1) = a _(2) =1, a _(1) = 1 + minimum( a _(i-1) , a _(i-2)) for I gt 2. Then a _( 2006)=

If the locus of the mid points of the chords of the ellipse (x^(2))/(a^(2)) +(y^(2))/( b^(2)) =1, drawn parallel to y=m_1x is y=m_2xthen m_1m_2=

If sin (sin^(-1)""(1)/5 + cos^(-1)x) = 1, then find the value of x.a) 0 b) 1/5 c) 2/5 d) 3/5

If ""^(18)C_(15)+2(""^(18)C_(16))+""^(17)C_(16)+1=""^(n)C_(3), then n =

Evalute the following integrals int ((1 + log x)^(2))/(x )dx

Let A={a,b,c} and Let R={(a,a),(a,b)}. then ,R is

Find the number of (i) 6

Integrate the functions xsinx

Evaluate : (i) int_(0)^(2pi) {sin(sinx)+sin(cosx)}dx, (ii) int_(0)^(pi) (dx)/(5+4cos2x) (iii) int_(0)^(pi//2) (2lnsinx-ln sin2x)dx , (iv) int_(0)^(oo) ln(x+(1)/(x)).(dx)/(1+x^(2))

If S_(0),S_(1),S_(2),… are areas bounded by the x-axis and half-wave of the curve y=sin pi sqrt(x)," then prove that "S_(0),S_(1),S_(2),… are in A.P…

int (tan x+tan^3 x)/(1+tan^3x) dx.

Marks scored by 100 students in a 25 marks unit test ofMathematics is given below. Their median is {:("Marks " ,0-5,5-10,10-15,15-20,20-25),("Students "," "10," "18," "42," "23," "7):}

Bag I contains 3 red and 4 black balls while another Bag II contains 5 red and 6 black balls. One ball is drawn at random from one of the bags and it is found to be red. Find the probability that it was drawn from Bag II.