14949 + Interview Questions in Maths in Class 11 Page 143 InterviewSolution

7101.	If bara= 2bari+barj-3bark, barb = bari-2barj+bark, barc = -bari+barj-4bark" and "bard=bari+barj+bark, then compute \|(bara xx barb)xx (barc xx bard)\|.
Answer» ANSWER :`5sqrt(114)`

Discussion

7102.	find the number of straight lines that are equally inclined to three-dimensional coordinate axes, is
Answer» ANSWER :8

Discussion

7103.	By using the concept of equation of a line, prove that the three points (3, 0), (-2, -2) and (8, 2) are collinear.
Answer» ANSWER :POINTS A, B and C are COLLINEAR .

Discussion

7104.	A balloon which always remains spherical on inflation is being inflated by pumping in 900 cubic centimeters of gas per second. Find the rate at which the radius of balloon increases when the radius in 15 cm.
Answer» ANSWER :`1/pi` cm/sec

Discussion

7105.	Write the middle term or terms in the expansion of (i) (x^(2) - (1)/(x) )^6
Answer» ANSWER :`=-20x^3`.

Discussion

7106.	Find the derivative of the w.r.to x. (log x) ^( tan x )
Answer» ANSWER :`(LOG X ) ^( TAN x) [ (tan x )/( x log x) + SEC ^(2) x. log (log x)]`

Discussion

7107.	Answer the equation: int(2x^(e)+(ae)^(x)-a^(-x)+e^(x))dx
Answer» Answer :`(2X^(e+1))/(e+1)+((AE)^(x))/(LOG(ae))+(a^(-x))/(loga)+e^(x)+C`

Discussion

7108.	If 2f (x)- 3f((1)/(x))= x^(2) (x ne 0) then f(2)= ……
Answer» `-(7)/(4)` `(5)/(2)` `-1` NONE of these Answer :A

Discussion

7109.	Construct the consumer price index number for 1988 on basis of 1998 from the following data:
Answer» ANSWER :`124.41`

Discussion

7110.	If the transformed equation of a curve is X^(2) - 2XY tan 2 alpha - Y^(2) = a^(2)when the axes are rotated through an angle alpha , then the original equation of the curve is
Answer» ANSWER :`X^(2) - y^(2) = a^(2) COS^(2) ALPHA`

Discussion

7111.	sqrt(3)sin x+cos x=8y-y^(2)-18, there 0 le xl le 4 pi , y in R then ______
Answer» `x = ( 4 pi)/( 3), (10 pi)/( 3), y = - 2, 4` `x = (2 pi)/( 3), (4 pi)/( 3), y =- 2, 4` `x = (5 pi)/( 3), (10 pi)/( 3), y = - 2, 4` `x = (4 pi)/( 3), (5 pi)/( 3), y = - 2, 4` Answer :A

Discussion

7112.	If m is the minimum value of f(x,y)=x^(2)-4x+y^(2)+6ywhen x and y are subjected to the restrictions 0lexle1and0leyle1,then the value of \|m\| is ____________
Answer» ANSWER :3

Discussion

7113.	Anil is entitled to a monthly payment which in each month is less by one tenth than it was a month before. Suppose he receives Rs. 5000 in the first month. Express-the sequence of monthly payments.as a G.P. Using it show that he cannot receive more than Rs. 50,000 in his life
Answer» SOLUTION :5.0004500405036E+15

Discussion

7114.	A(a,0) , B(-a,0) are two point . If a point P moves such that anglePAB - anglePBA = 2alpha then find the locus of P .
Answer» `X^(2)+y^(2)+2XY cot2alpha=a^(2)` `x^(2)-y^(2)+2xy TAN 2alpha=a^(2)` `x^(2)+y^(2)-2xy tan 2alpha=a^(2)` `x^(2)-y^(2)+2xy cot2alpha=a^(2)` ANSWER :D

Discussion

7115.	Compute (98)^5.
Answer» ANSWER :9039207968

Discussion

7116.	Write down the contrapositive of the following statements.: If all three sides of a triangle are equal, then the triangle is equilateral.
Answer» ANSWER :TRIANGLE is not EQUAL.

Discussion

7117.	"cos" (2pi)/(7)+"cos" (4pi)/(7)+"cos"(6pi)/(7)=
Answer» `(1)/(2)` `-(1)/(2)` 0 1 Answer :B

Discussion

7118.	If f(x) = \|x - 2\| and g(x) = f(f(x)), then sum_(r = 0)^(3) g'(2r - 1) is equal to
Answer» `0` `1` `-1` `2` ANSWER :A

Discussion

7119.	Find the median of the followingdata if the value of x = 4 ,x -4, 2x - 6, 3x-10 ,(x)/(2) - 1 , ( 3x)/( 2 x - 4) , x + 3, (x)/( 2), 2x + 7, 3x - 2, 2x -5
Answer» ANSWER :`2 . 5`

Discussion

7120.	Find the distance of the line 4x + 7y + 5 = 0from the point (1, 2) along the line 2x - y = 0.
Answer» ANSWER :`(23 SQRT 5)/18 ` UNITS

Discussion

7121.	Findlimit of the following if it exists: lim_(xto5)(e^(x)-e^(5))/(x-5)
Answer» ANSWER :`E^(5)`

Discussion

7122.	Combined equation of pair of lines passing through origin and inclined at 30^(@) and 60^(@) respectively with x-axis is
Answer» `SQRT(3)y^(2)-X^(2)=0` `y^(2)-sqrt(3)x^(2)=0` `sqrt(3)y^(2)+4xy- sqrt(3)x^(2)=0` `sqrt(3)y^(2)-4xy+sqrt(3)x^(2)=0` ANSWER :D

Discussion

7123.	If theta is the acute between the pair of lines x^(2)+3xy-4y^(2)=0 then sin theta=
Answer» `pi/6` `pi/3` `5/sqrt34` `3/sqrt34` ANSWER :C

Discussion

7124.	Find the distance between P (x_(1), y_(1)) "and " Q (x_(2), y_(2))when : (i) PQ is parallel to the y-axis, (ii) PQ is parallel to the x-axis.
Answer» ANSWER :`(i) \| y_(2) - y_(1)\|, (II) \|x_(2) - x_(1)\|`

Discussion

7125.	If cos x + cos y + cos z =0 = sin + sin y +sin zthen tan (x-y) =
Answer» `SQRT3` `-sqrt3` `(1)/(sqrt3)` `-(1)/(sqrt3)` ANSWER :B

Discussion

7126.	Find the derivative of the function from first principle sqrt (x +1)
Answer» ANSWER :`(1)/( 2sqrt (X +1 )) `

Discussion

7127.	ABC is a triangle in a plane with vertices A(2, 3, 5), B(-1, 3, 2) and C(lambda, 5, mu). If the median through A is equally inclined to the coordinate axes, then the value of (lambda^(3)+mu^(3)+5) is:
Answer» 1130 1348 1077 676 Answer :B

Discussion

7128.	Solve Inequality 6 le -3 (2x-4) lt 12
Answer» ANSWER :`(0,1]`

Discussion

7129.	Differentiate the following functions w.r.t. x. f(x) = (3x +4)/( 4x +3) (x ne (-3)/(4) )
Answer» ANSWER :`(7)/( (4X +3)^2)`

Discussion

7130.	Two cards are drawn at random from a packof 52 cards. Find the probability that they areboth Aces if the first card is not replaced
Answer» `(1)/(169)` `(1)/(221)` `(4)/(13)` `(3)/(13)` ANSWER :B

Discussion

7131.	Two ships leave a port at the same time . One goes 24km per hour in the directionN45^(@)E and other travels 32km per hour in the directionS 75 ^(@) E.thenthe distance between the ships at the end of 3 hours
Answer» ` 80.5` ` 86.5` ` 76.5` ` 40.5` ANSWER :B

Discussion

7132.	Fourcards are drawn at random from a pack of 52 playing cards , Find the probability of getting all face cards , (king , Queen , jack )
Answer» ANSWER :`(""^(12)C_(4))/(""^(52)C_(4))`

Discussion

7133.	Seven different letters are given. Then the numberof waysin which, wordsof 5 letterscanbe formedsuch that atleast one of the lettersis repeated is
Answer» <P>P(7,5) 14287 `7^(5)` `5^(7)` ANSWER :B

Discussion

7134.	Fine r if (i) ""^(5) P_(r) =2""^(6)P_(r-1) (ii)""^(5) P_(r) = ""^(6)P_(r-1)
Answer» ANSWER :4

Discussion

7135.	Evaluate : 8 cos ^(3) ""(pi)/(9)- 6cos ""(pi)/(9)
Answer» ANSWER :1

Discussion

7136.	From the price of shares X and Y below, find out which is more stable in value:
Answer» ANSWER :11.58, 1.90

Discussion

7137.	Find out which of the following sentences are statements and which are not ?JustifyHurrah! We have won the match.
Answer» SOLUTION :Not STATEMENT

Discussion

7138.	0 lt theta lt (pi)/(2) then the minimum value of sin^(3) theta + cosec^(3) theta is……
Answer» 2 1 0 Not possible Answer :A

Discussion

7139.	Find which in suitable for the blank space given below:\|veca.vecb\|……..\|veca\|\|vecb\|
Answer» `LE` `GE` `=` `GT` ANSWER :A

Discussion

7140.	"sin"pi/14" sin"(3pi)/14" sin"(5pi)/14" sin"(7pi)/5=
Answer» 1 `1//4` `1//8` `SQRT(2)//7` ANSWER :C

Discussion

7141.	Find the coordinates of a pointon y axiswhich are at a distance of 5sqrt(2) from the point P(3,-2,5)
Answer» ANSWER :(0,2) and (0,-6,0)

Discussion

7142.	If the area of triangle with vertices (2a,a) (a,a) and (a,2a) is 18 square units then find the circumcentre of the triangle.
Answer» ANSWER :(9,9)

Discussion

7143.	AM, GM, HM denote the Arithmetic mean, Geometric mean and Harmonic meanrespectively the relationship between this is:
Answer» `AM LT GM lt HM` `AM le GM le HM` `AM gt GM gt HM` `AM GE GM ge HM` Answer :d

Discussion

7144.	If omega is a cube root of unity, then 1+omega= …..
Answer» ANSWER :`-OMEGA^(2)`

Discussion

7145.	Physical independence of force is a consequence of
Answer» III LAW of MOTION I law II law All Solution : I law

Discussion

7146.	If (x^(4)+2x.i )-(3x^(2)-iy)=(3-5i)+(1+2iy) then find the real value of x and y.
Answer» ANSWER :When `x=2,y=3` and when `x=-2y,=(1)/(3)`

Discussion

7147.	If f(x)=x^(11)+x^(9)-x^(7)+x^(3)+1 and f(sin^(-1)(sin8))=alpha, alpha constant then f(tan^(-1)(Tan8)) is equal to
Answer» `ALPHA` `alpha-2` `alpha+2` `2-alpha` ANSWER :D

Discussion

7148.	Let L _(1) : (x -1)/( 1) = (y+1)/(2) = (z-2)/(2) L _(2) : x - 2y -1 =0 lamda y - z + 2pi : 2x + y-z =0 If the line L_(2) ies in the plane L _(3) then angle between the lines L _(1) , L_(2)
Answer» `pi//6` `pi//3` `COS ^(-1) ((7)/(sqrt35))` `pi/2` ANSWER :D

Discussion

7149.	If the axes are rotated through an angle 30^(0) about the origin then the transformed equation of x^(2) + 2 sqrt(3) xy - y^(2) = 2a^(2)is
Answer» `X^(2) +Y^(2) = a^(2)` `X^(2)-Y^(2)=a^(2)` `X^(2)+Y^(2)=2A^(2)` `X^(2)-Y^(2)=2a^(2)` ANSWER :B

Discussion

7150.	If [.] denotes the greatest integer function, then find the value of [sin^(-1)[x^(2)+1/2]+cos^(-1)[x^(2)-1/2]]
Answer» 1 2 3 4 Answer :C

Discussion

Explore topic-wise InterviewSolutions in .

If bara= 2bari+barj-3bark, barb = bari-2barj+bark, barc = -bari+barj-4bark" and "bard=bari+barj+bark, then compute |(bara xx barb)xx (barc xx bard)|.

find the number of straight lines that are equally inclined to three-dimensional coordinate axes, is

By using the concept of equation of a line, prove that the three points (3, 0), (-2, -2) and (8, 2) are collinear.

A balloon which always remains spherical on inflation is being inflated by pumping in 900 cubic centimeters of gas per second. Find the rate at which the radius of balloon increases when the radius in 15 cm.

Write the middle term or terms in the expansion of (i) (x^(2) - (1)/(x) )^6

Find the derivative of the w.r.to x. (log x) ^( tan x )

Answer the equation: int(2x^(e)+(ae)^(x)-a^(-x)+e^(x))dx

If 2f (x)- 3f((1)/(x))= x^(2) (x ne 0) then f(2)= ……

Construct the consumer price index number for 1988 on basis of 1998 from the following data:

If the transformed equation of a curve is X^(2) - 2XY tan 2 alpha - Y^(2) = a^(2)when the axes are rotated through an angle alpha , then the original equation of the curve is

sqrt(3)sin x+cos x=8y-y^(2)-18, there 0 le xl le 4 pi , y in R then ______

If m is the minimum value of f(x,y)=x^(2)-4x+y^(2)+6ywhen x and y are subjected to the restrictions 0lexle1and0leyle1,then the value of |m| is ____________

Anil is entitled to a monthly payment which in each month is less by one tenth than it was a month before. Suppose he receives Rs. 5000 in the first month. Express-the sequence of monthly payments.as a G.P. Using it show that he cannot receive more than Rs. 50,000 in his life

A(a,0) , B(-a,0) are two point . If a point P moves such that anglePAB - anglePBA = 2alpha then find the locus of P .

Compute (98)^5.

Write down the contrapositive of the following statements.: If all three sides of a triangle are equal, then the triangle is equilateral.

"cos" (2pi)/(7)+"cos" (4pi)/(7)+"cos"(6pi)/(7)=

If f(x) = |x - 2| and g(x) = f(f(x)), then sum_(r = 0)^(3) g'(2r - 1) is equal to

Find the median of the followingdata if the value of x = 4 ,x -4, 2x - 6, 3x-10 ,(x)/(2) - 1 , ( 3x)/( 2 x - 4) , x + 3, (x)/( 2), 2x + 7, 3x - 2, 2x -5

Find the distance of the line 4x + 7y + 5 = 0from the point (1, 2) along the line 2x - y = 0.

Findlimit of the following if it exists: lim_(xto5)(e^(x)-e^(5))/(x-5)

Combined equation of pair of lines passing through origin and inclined at 30^(@) and 60^(@) respectively with x-axis is

If theta is the acute between the pair of lines x^(2)+3xy-4y^(2)=0 then sin theta=

Find the distance between P (x_(1), y_(1)) "and " Q (x_(2), y_(2))when : (i) PQ is parallel to the y-axis, (ii) PQ is parallel to the x-axis.

If cos x + cos y + cos z =0 = sin + sin y +sin zthen tan (x-y) =

Find the derivative of the function from first principle sqrt (x +1)

ABC is a triangle in a plane with vertices A(2, 3, 5), B(-1, 3, 2) and C(lambda, 5, mu). If the median through A is equally inclined to the coordinate axes, then the value of (lambda^(3)+mu^(3)+5) is:

Solve Inequality 6 le -3 (2x-4) lt 12

Differentiate the following functions w.r.t. x. f(x) = (3x +4)/( 4x +3) (x ne (-3)/(4) )

Two cards are drawn at random from a packof 52 cards. Find the probability that they areboth Aces if the first card is not replaced

Two ships leave a port at the same time . One goes 24km per hour in the directionN45^(@)E and other travels 32km per hour in the directionS 75 ^(@) E.thenthe distance between the ships at the end of 3 hours

Fourcards are drawn at random from a pack of 52 playing cards , Find the probability of getting all face cards , (king , Queen , jack )

Seven different letters are given. Then the numberof waysin which, wordsof 5 letterscanbe formedsuch that atleast one of the lettersis repeated is

Fine r if (i) ""^(5) P_(r) =2""^(6)P_(r-1) (ii)""^(5) P_(r) = ""^(6)P_(r-1)

Evaluate : 8 cos ^(3) ""(pi)/(9)- 6cos ""(pi)/(9)

From the price of shares X and Y below, find out which is more stable in value:

Find out which of the following sentences are statements and which are not ?JustifyHurrah! We have won the match.

0 lt theta lt (pi)/(2) then the minimum value of sin^(3) theta + cosec^(3) theta is……

Find which in suitable for the blank space given below:|veca.vecb|……..|veca||vecb|

"sin"pi/14" sin"(3pi)/14" sin"(5pi)/14" sin"(7pi)/5=

Find the coordinates of a pointon y axiswhich are at a distance of 5sqrt(2) from the point P(3,-2,5)

If the area of triangle with vertices (2a,a) (a,a) and (a,2a) is 18 square units then find the circumcentre of the triangle.

AM, GM, HM denote the Arithmetic mean, Geometric mean and Harmonic meanrespectively the relationship between this is:

If omega is a cube root of unity, then 1+omega= …..

Physical independence of force is a consequence of

If (x^(4)+2x.i )-(3x^(2)-iy)=(3-5i)+(1+2iy) then find the real value of x and y.

If f(x)=x^(11)+x^(9)-x^(7)+x^(3)+1 and f(sin^(-1)(sin8))=alpha, alpha constant then f(tan^(-1)(Tan8)) is equal to

Let L _(1) : (x -1)/( 1) = (y+1)/(2) = (z-2)/(2) L _(2) : x - 2y -1 =0 lamda y - z + 2pi : 2x + y-z =0 If the line L_(2) ies in the plane L _(3) then angle between the lines L _(1) , L_(2)

If the axes are rotated through an angle 30^(0) about the origin then the transformed equation of x^(2) + 2 sqrt(3) xy - y^(2) = 2a^(2)is

If [.] denotes the greatest integer function, then find the value of [sin^(-1)[x^(2)+1/2]+cos^(-1)[x^(2)-1/2]]