14949 + Interview Questions in Maths in Class 11 Page 10 InterviewSolution

451.	If alpha and beta ( alpha lt beta ) are two different real roots of the equation ax^(2) + bx + c = 0then
Answer» `alpha gt - ( B)/(2A)` `beta lt - ( b)/( 2a)` `alpha lt - ( b)/( 2a) lt beta` `beta lt- ( b )/( 2a ) lt alpha` ANSWER :C

Discussion

452.	The numbers 1,2 ,3 and 4 are written separately on four slips of paper. The slips are put in a box and mixed thoroughly. A person draws two slips from the box, one after the other, without replacement. Describe the sample space for the experiment.
Answer» ANSWER :`S={(1,2), (1,3), (1,4) ,(2,1) ,(2,3) ,(2,4),(3,1) ,(3,2),(3,4),(4,1) (4,2),(4,3)}`

Discussion

453.	Find the point of intersection of the lines 2x^(2)+xy+y^(2)-5x+3y+2=0
Answer» (-1,-1) (1,1) (1,0) (0,1) ANSWER :B

Discussion

454.	If the area of a triangle is 96 and the radii of the escribed circles are 8, 12, 24, then the greatest side of the triangle is
Answer» 18 20 16 30 Answer :B

Discussion

455.	If (a + b)^(2) = c^(2) + ab " in a " Delta ABC , Sin^(4) B + Sin^(4) C = Sin^(2) Bsin^(2) C + 2Sin^(2) Csin^(2)A = 2Sin^(2) B then A =
Answer» `pi/6, (5PI)/6` `pi/3, (5pi)/6` `pi/3, pi/2` `pi/4, (3PI)/4` ANSWER :A

Discussion

456.	A tower of x metres high, has a flagstaff at its top. The tower and the flagstaff subtend equal angles at a point distant ymetres from the foot of the tower. Then the length of the flagstaff in metres is
Answer» `(y(X^(2)-y^(2)))/((x^(2)+y^(2)))` `(y(y^(2)+x^(2)))/((y^(2)+x^(2)))` `(x(x^(2)+y^(2)))/((x^(2)-y^(2)))` `(x(x^(2)-y^(2)))/((x^(2)+y^(2)))` ANSWER :B

Discussion

457.	If R is the set of all real numbers, what do the cartesian products R xx R and R xx R xx R represent?
Answer» ANSWER :COORDINATES of all the POINTS in three-dimensional SPACE

Discussion

458.	Find the mean deviation using arithmetic mean from the following table:
Answer» SOLUTION : Arithmetic MEAN `barx=(sumf_(i)x_(i))/(sumf_(i))=1320/48=27.5` MENA devition `=(sumf_(i)\|x_(i)-barx\|)/(sumf_(i))` `=450/48=9.375`

Discussion

459.	The polynomial p(x)is such that for any polynomial q(x) we have p (q( x) ) = q(p (x) )then p(x) is
Answer» EVEN ODD of even degree of odd degree Answer :B::D

Discussion

460.	If m^(th), n^(th) and p^(th) terms of an A.P and G.P be equal and be respectively x,y, z then………......................................................a ) x^(y).y^(z).z^(x) =x^(z).Y^(x).z^(y)b ) (x-y)^(x).(y-z)^(y)= (z-x)^(z)c )(x-y)^(z) (y-z)^(x)= (z-x)^(y)d ) None of these
Answer» `X^(y).y^(Z).z^(x)= x^(z).Y^(x).z^(y)` `(x-y)^(x).(y-z)^(y)= (z-x)^(z)` `(x-y)^(z) (y-z)^(x)= (z-x)^(y)` NONE of these Answer :A

Discussion

461.	Find dy/dx if x=acos^(3)t,y=asin^(3)t.
Answer» ANSWER :TAN t

Discussion

462.	Write downthe slopes of the lines joining L(-p, q) and M(r, s)
Answer» ANSWER :`((s-q))/(r+p)`

Discussion

463.	By the principle of mathematical induction , prove that , for n in NN cos alpha + cos (alpha + beta)+cos (alpha + 2 beta) + .....+ cos (alpha +(n-1)beta) = cos (alpha + ((n-1)beta)/(2)) xx (sin((nbeta)/(2)))/(sin(beta/2))
Answer» Answer :`COS (alpha+((n-1)BETA)/(2))xxsin((nbeta)/(2))/(SIN(beta/(2))`

Discussion

464.	The point (-1,4,-2) lie in the octant
Answer» OX'YZ' OXY 'Z' OX'Y'Z OX'Y'Z' Answer :A

Discussion

465.	A cure is represented parametrically by the equation x=f(t)=a^(In(b^t)) and y=g(t)=b^(-In(a^t))a,b gt0 and a = ne 1, b ne 1wheret in R Which of the following is not a correct expression for (dy)/(dx) ?
Answer» `(-1)/(F(t))^2` `-(G(t))^2` `(-g(t))/(f(t))` `(-f(t))/(g(t))` ANSWER :D

Discussion

466.	A variable plane is at a constant distance p from the origin and meets the axes in A, B and C. The locus of the centroid of the triangle ABC is
Answer» <P>`x ^(2) + y ^(2) + z^(-2) = p ^(-2)` `x ^(2) + y ^(2) + z ^(-2) = 4p ^(-2)` `x ^(-2) + y ^(-2) + z ^(-2) = 16 p ^(-2)` `x %(2) + y ^(-2) + z ^(-2) = 9P ^(-2)` Answer :D

Discussion

467.	The ratio in which the line joining the ponts (2,5,4) and (3,5,4) is divided by the YZ plane is
Answer» (a) 3:2 INTERNALLY (B) 2:3 internally (C) 3:2 EXTERNALLY (d) 2:3 externally Answer :D

Discussion

468.	Match the following
Answer» ANSWER :d

Discussion

469.	A line cuts x-axis at A(7, 0) and y-axis at B(0, -5). A variable line PQ is drawn perpendicular to AB cutting x, y-axis at P and Q. If AQ, BP intersect in R, then locus of R is
Answer» `X^(2)+y^(2)+7x-5y=0` `x^(2)+y^(2)-7x+5y=0` `x^(2)+y^(2)-3x+4y=0` `x^(2)+y^(2)+6x+7y=0` ANSWER :B

Discussion

470.	Let f={(1,1),(2,3)(0,-1),(-1-3)} be a linear function from Z into Z. Find f(x) ?
Answer» ANSWER :`F(X) =(2x-1)`

Discussion

471.	If bara, barb, barc are non-coplanar, nonzero vectors and barr is any vector in space then [bara barb barc]barc+[barb barc bara]bara+[barc bara barb]barb=
Answer» `3[barabarbbarc]BARR` `[barabarbbarc]barr` `[barabarbbarc]` `bar0` Answer :B

Discussion

472.	A horse runs along with a speed of 20 km/hr. A lantern is at the centre of the circle. A fence is along the tangent to the circle at the point at which the horse starts. The speed with which the shadow of the horse moves along the fence at the moment when it covers 1/8 of the circle in km/hr is.
Answer» ANSWER :`theta=45^@`

Discussion

473.	The set {x in R : 1 le x lt 2} can be written as "…………".
Answer» ANSWER :`(1, 2)`

Discussion

474.	Express (13i)/(2-3i) in the form A + Bi
Answer» ANSWER :`-3+ 2I`

Discussion

475.	A box contains 10red marbles, 20 blue marbles and30 green marbles. 5 marbles are drawn at random. From the box, what is theprobability that i. all are blue? ii. at least one is green?
Answer» ANSWER :(i) `=34)/(11977)`. `(II) `=4367)/(4484)`.

Discussion

476.	If two sides of a triangle lie along 3x^(2)-xy-2y^(2)=0 and its orthocentre is (2,1) then equation to third side is
Answer» `10X+5y–1=0` `10x + 5y – 21 = 0` 5x – 10Y + 1 = 0 `5x - 10y - 21 = 0` ANSWER :B

Discussion

477.	A coin is tossed. If it shows a tail, we draw a balls from a box which contains 2 red and 3 black balls. If it shows head, we throw a die. Find the sample space for this experiment.
Answer» Answer :`{TR_(1), TR_(2), TB_(1), TB_(2), TB_(3), H1, H2, H3, H4, H5, H6}`

Discussion

478.	Assertion (A) : bara,barb,barc and bard are the position vectors of four coplanar points A, B, C, D. If abs(bard-bara)=abs(bard-barb) =abs(bard-barc), then D is the circumcentre of Delta ABC Reason ( R ) : In any triangle, the circumcentre is equidistant from the vertice. Then
Answer» Both A and R are TRUE and R is the CORRECT explanatioon A. Both A and R are true and R is not the correct explanatioon A. Ais true R is false A is false R is true ANSWER :A

Discussion

479.	Find the standard deviation of first n natural numbers.
Answer» Solution :Now`Sigmax_(i)=1+2+3+4+.....+n=(n(n+1))/2` `Sigmax_(i)^(2)=1^(2)+2^(2)+3^(3)+…..+n^(2)=(n(n+1)(2N+1))/(6)` `sigma=sqrt((Sigmax_(i)^(2))/N-(Sigma_(x_(i))/N)^(2)` `sqrt((n(n+1)(2n+1))/(6N)-(n^(2)(n+1)^(2))/(4N^(2))` `sqrt(((n+1)(2n+1))/(6)-((n+1)^(2))/(4)` `sqrt((2(2n^(2)+3n+1)-3(n^(2)+2n+1))/(12)` `sqrt((4n^(2)+6n+2-3n^(2)-6n-3)/(12)` `sqrt((n^(2)-1)/12)`

Discussion

480.	x ^(2) + y^(2) = t + 1/t, x ^(4) + y^(4) = t ^(2) + (1)/( t ^(2)) implies x ^(3) y (dy)/(dx) =
Answer» 0 1 `-1` 2 Answer :C

Discussion

481.	IfA and B are twosets such that AsubB , then write B^(c)-A^(c) interms of A and B.
Answer» ANSWER :`PHI`

Discussion

482.	The straight line 5x + 4y =0 passes through the point of intersection of the straight lines x+2y - 10 = 0 and 2x + y +5=0. True or False.
Answer» ANSWER :1

Discussion

483.	Find the derivative of the function wrt x. cos ^(-1) (2x ^(2) -1)
Answer» ANSWER :`(-2)/( SQRT (1- X ^(2)))`

Discussion

484.	Find the angle between the lines 2x + y + 4 = 0 and y - 3x = 7
Answer» ANSWER :`pi//4`

Discussion

485.	Find the derivative of sin2x from the first principle.
Answer» ANSWER :`2 COS 2X`

Discussion

486.	(1+(1)/1)(1+(1)/(2))(1+(1)/(3))......(1+(1)/n) n(n+1)
Answer» Solution :Let `P(n): (1+1) (1+(1)/(2))(1+(1)/(3))......(1+(1)/(n)) =(n+1)` for n=1 `L.H.S. =1+1=2` `R.H.S. =1+1=2` `:. L.H.S. =R.H.S.` `RARR` P (n)is truefor n=1 Let P (n)be true for n =K `:. P(k) : (1+1)(1+(1)/(2))(1+(1)/(3))......(1+(1)/(k)) =K+1` for n = K+1 `P(k+1) : (1+1)(1+(1)/(2))(1+(1)/(3))` ` ....(1+(1)/(k))(1+(1)/(K+1))` `=(k+1)(1+(1)/(K+1))` `=(k+1)((K+2)/(K+1))=K+2` `rArr` P(n) is ALSO true for n= k+1 Hence from the principle of mathematical INDUCTION P (n) is truefor all natural numbers n .

Discussion

487.	If (xy) is a variable point on the line y=2x lying between the line 2(x+1)+y=0 and x+3(y-1)-0, then
Answer» `X in (-1//2,6//7)` `XIN(-1//2,3//7)` `xin(-1,3//7)` `xin(-1,6//7)` ANSWER :B::D

Discussion

488.	Does the equation x^(2)+xy+y^(2)=0 represent a pair of lines?
Answer» ANSWER :No

Discussion

489.	Evaluate the following limits : Lim_(x to sqrt(2))(x^(4)-4)/(x^(2)+3xsqrt(2)-8)
Answer» ANSWER :`8/5`

Discussion

490.	Obtain equation of ellipse satisfying given conditions Eccentricity e = (2)/(3), length of the latus rectum = 5
Answer» ANSWER :`20X^(2) + 36Y^(2) = 405`

Discussion

491.	If bara =bari -2barj-3bark,barb =2bari + barj-bark, barc = bari +3barj-2barkand baraxx(barbxxbarc)=pbari+1barj+rbark then p+q+r=
Answer» `-4` `-2` 2 4 Answer :A

Discussion

492.	Let A=[(-1,1,1),(1,-1,1),(1,1,-1)] then \|"Adj (Adj A)"\|=
Answer» 64 256 8 6 Answer :B

Discussion

493.	Show that the statement " If x is a real number such thatx^(2) +4x=0 thenx is 0 true by ( 1) Direct method (2) method of contradiction (3) Method of contrapositive
Answer» ANSWER :` (3)/(4) `

Discussion

494.	If bara" is perpendicular to " bari,barj & bark, " then find " bara.
Answer» ANSWER :`BAR0`

Discussion

495.	Find the vertex, focus, directrix, latus rectum, equation of latus rectum, equation of axis and co-ordinates of ends of latus rectum for the following parabola : (i) y^(2)=20x , (ii)y^(2)=-8y (iii) x^(2)=16y , (iv) x^(2)=-8y (v) 2x^(2)=3y , (iv) 3y^(2)+4x=0
Answer» Answer :(i) VERTEX (0,0), focus (5,0), directrix X=-5, latus rectum = 20, equation of latus rectum x=5, equation of axis y=0, co-ordinates of the ends of latus rectum (5,10),(5-10). (II)Vertex (0,0), focus (-3,0), directrix x=3, latus rectum = 12, equation of latus rectum x=-3, equation of axis y=0, co-ordinates of the ends of latus rectum (-3,6),(-3-6). (iii)Vertex (0,0), focus (0,4), directrix x=-4, latus rectum y = 16, equation of latus rectum y=4, equation of axis x=0, co-ordinates of the ends of latus rectum (8,4),(-8-4). (iv)Vertex (0,0), focus (0,-2), directrix x=2, latus rectum = 8, equation of latus rectum y=-2, equation of axis x=0, co-ordinates of the ends of latus rectum (4,-2),(-4,-2). (v) Vertex (0,0), focus `(0,(3)/(8))`, directri x `y=-(3)/(8)`, latus rectum `=(3)/(2)`, equation of latus rectum `y=(3)/(8)`, equation of axis x=0, co-ordinates of the ends of latus rectum `((-3)/(4),(3)/(8)),((3)/(4),(3)/(8))`. (vi) Vertex (0,0) focus `(-(1)/(3),0)`, directrix `x-(1)/(3)`, latus rectum `=(4)/(3)`, equation of latus rectum `x=-(1)/(3)`, equation of directrix y = 0, co-ordinates of the ends of latus rectum `(-(1)/(3),(2)/(3)),(-(1)/(3),-(2)/(3))`.

Discussion

496.	Given that alpha and beta are the roots of the equation x^(2)=x+7. (i) Prove that (a) (1)/(alpha)=(alpha-1)/(7) and(b) alpha^(3)=8alpha+7. (ii) Find the numerical value of (alpha)/(beta)+(beta)/(alpha).
Answer» ANSWER :(II) `(-15)/(7)`.

Discussion

497.	If 0 le x le 2 piand \|cos x\| le sin x, then
Answer» the set of all VALUES of x is `[(pi)/(4), (3 pi)/(4)]` the NUMBER of solutions that are integral multiple of `(pi)/(4)` is four the sum of the LARGEST and the smallest solution is `pi` the set of all values of x is ` x in [(pi)/(4), (pi)/(2)) cup ((pi)/(2), (3 pi)/(4)]` ANSWER :A::C

Discussion

498.	To fill 12 vacancies there are 25 candidates of which 5 are from scheduled castes. If 3 of the vacanies are reserved for scheduled caste candidates while the rest are open to all, the number of ways in which the selection can be made is ""^5C_3 xx ""^22C_9.
Answer» ANSWER :`=""^5C_3 XX ""^22C_9.`

Discussion

499.	Find the co-efficient of x^(5) in (x+3)^(8) ?
Answer» ANSWER :1512

Discussion

500.	Find Delta y and dy for the following functions for the values of x and Delta x which are shown against each of the functions. y = cos (x), x = 60^(@) and Delta x = 1^(@)
Answer» ANSWER :`DELTA y = - 0.152 DY = - 0.01516`

Discussion

Explore topic-wise InterviewSolutions in .

If alpha and beta ( alpha lt beta ) are two different real roots of the equation ax^(2) + bx + c = 0then

The numbers 1,2 ,3 and 4 are written separately on four slips of paper. The slips are put in a box and mixed thoroughly. A person draws two slips from the box, one after the other, without replacement. Describe the sample space for the experiment.

Find the point of intersection of the lines 2x^(2)+xy+y^(2)-5x+3y+2=0

If the area of a triangle is 96 and the radii of the escribed circles are 8, 12, 24, then the greatest side of the triangle is

If (a + b)^(2) = c^(2) + ab " in a " Delta ABC , Sin^(4) B + Sin^(4) C = Sin^(2) Bsin^(2) C + 2Sin^(2) Csin^(2)A = 2Sin^(2) B then A =

A tower of x metres high, has a flagstaff at its top. The tower and the flagstaff subtend equal angles at a point distant ymetres from the foot of the tower. Then the length of the flagstaff in metres is

If R is the set of all real numbers, what do the cartesian products R xx R and R xx R xx R represent?

Find the mean deviation using arithmetic mean from the following table:

The polynomial p(x)is such that for any polynomial q(x) we have p (q( x) ) = q(p (x) )then p(x) is

If m^(th), n^(th) and p^(th) terms of an A.P and G.P be equal and be respectively x,y, z then………......................................................a ) x^(y).y^(z).z^(x) =x^(z).Y^(x).z^(y)b ) (x-y)^(x).(y-z)^(y)= (z-x)^(z)c )(x-y)^(z) (y-z)^(x)= (z-x)^(y)d ) None of these

Find dy/dx if x=acos^(3)t,y=asin^(3)t.

Write downthe slopes of the lines joining L(-p, q) and M(r, s)

By the principle of mathematical induction , prove that , for n in NN cos alpha + cos (alpha + beta)+cos (alpha + 2 beta) + .....+ cos (alpha +(n-1)beta) = cos (alpha + ((n-1)beta)/(2)) xx (sin((nbeta)/(2)))/(sin(beta/2))

The point (-1,4,-2) lie in the octant

A cure is represented parametrically by the equation x=f(t)=a^(In(b^t)) and y=g(t)=b^(-In(a^t))a,b gt0 and a = ne 1, b ne 1wheret in R Which of the following is not a correct expression for (dy)/(dx) ?

A variable plane is at a constant distance p from the origin and meets the axes in A, B and C. The locus of the centroid of the triangle ABC is

The ratio in which the line joining the ponts (2,5,4) and (3,5,4) is divided by the YZ plane is

Match the following

A line cuts x-axis at A(7, 0) and y-axis at B(0, -5). A variable line PQ is drawn perpendicular to AB cutting x, y-axis at P and Q. If AQ, BP intersect in R, then locus of R is

Let f={(1,1),(2,3)(0,-1),(-1-3)} be a linear function from Z into Z. Find f(x) ?

If bara, barb, barc are non-coplanar, nonzero vectors and barr is any vector in space then [bara barb barc]barc+[barb barc bara]bara+[barc bara barb]barb=

A horse runs along with a speed of 20 km/hr. A lantern is at the centre of the circle. A fence is along the tangent to the circle at the point at which the horse starts. The speed with which the shadow of the horse moves along the fence at the moment when it covers 1/8 of the circle in km/hr is.

The set {x in R : 1 le x lt 2} can be written as "…………".

Express (13i)/(2-3i) in the form A + Bi

A box contains 10red marbles, 20 blue marbles and30 green marbles. 5 marbles are drawn at random. From the box, what is theprobability that i. all are blue? ii. at least one is green?

If two sides of a triangle lie along 3x^(2)-xy-2y^(2)=0 and its orthocentre is (2,1) then equation to third side is

A coin is tossed. If it shows a tail, we draw a balls from a box which contains 2 red and 3 black balls. If it shows head, we throw a die. Find the sample space for this experiment.

Assertion (A) : bara,barb,barc and bard are the position vectors of four coplanar points A, B, C, D. If abs(bard-bara)=abs(bard-barb) =abs(bard-barc), then D is the circumcentre of Delta ABC Reason ( R ) : In any triangle, the circumcentre is equidistant from the vertice. Then

Find the standard deviation of first n natural numbers.

x ^(2) + y^(2) = t + 1/t, x ^(4) + y^(4) = t ^(2) + (1)/( t ^(2)) implies x ^(3) y (dy)/(dx) =

IfA and B are twosets such that AsubB , then write B^(c)-A^(c) interms of A and B.

The straight line 5x + 4y =0 passes through the point of intersection of the straight lines x+2y - 10 = 0 and 2x + y +5=0. True or False.

Find the derivative of the function wrt x. cos ^(-1) (2x ^(2) -1)

Find the angle between the lines 2x + y + 4 = 0 and y - 3x = 7

Find the derivative of sin2x from the first principle.

(1+(1)/1)(1+(1)/(2))(1+(1)/(3))......(1+(1)/n) n(n+1)

If (xy) is a variable point on the line y=2x lying between the line 2(x+1)+y=0 and x+3(y-1)-0, then

Does the equation x^(2)+xy+y^(2)=0 represent a pair of lines?

Evaluate the following limits : Lim_(x to sqrt(2))(x^(4)-4)/(x^(2)+3xsqrt(2)-8)

Obtain equation of ellipse satisfying given conditions Eccentricity e = (2)/(3), length of the latus rectum = 5

If bara =bari -2barj-3bark,barb =2bari + barj-bark, barc = bari +3barj-2barkand baraxx(barbxxbarc)=pbari+1barj+rbark then p+q+r=

Let A=[(-1,1,1),(1,-1,1),(1,1,-1)] then |"Adj (Adj A)"|=

Show that the statement " If x is a real number such thatx^(2) +4x=0 thenx is 0 true by ( 1) Direct method (2) method of contradiction (3) Method of contrapositive

If bara" is perpendicular to " bari,barj & bark, " then find " bara.

Find the vertex, focus, directrix, latus rectum, equation of latus rectum, equation of axis and co-ordinates of ends of latus rectum for the following parabola : (i) y^(2)=20x , (ii)y^(2)=-8y (iii) x^(2)=16y , (iv) x^(2)=-8y (v) 2x^(2)=3y , (iv) 3y^(2)+4x=0

Given that alpha and beta are the roots of the equation x^(2)=x+7. (i) Prove that (a) (1)/(alpha)=(alpha-1)/(7) and(b) alpha^(3)=8alpha+7. (ii) Find the numerical value of (alpha)/(beta)+(beta)/(alpha).

If 0 le x le 2 piand |cos x| le sin x, then

To fill 12 vacancies there are 25 candidates of which 5 are from scheduled castes. If 3 of the vacanies are reserved for scheduled caste candidates while the rest are open to all, the number of ways in which the selection can be made is ""^5C_3 xx ""^22C_9.

Find the co-efficient of x^(5) in (x+3)^(8) ?

Find Delta y and dy for the following functions for the values of x and Delta x which are shown against each of the functions. y = cos (x), x = 60^(@) and Delta x = 1^(@)