14949 + Interview Questions in Maths in Class 11 Page 127 InterviewSolution

6301.	If x=r cos alpha cos betacos gamma , y= cos alpha cos beta sin gamma , z= r sin alpha cos beta , mu = r sin beta " then " x^(2)+y^(2) + z^(2)+mu^(2)=
Answer» R 2r `r^(2)` `4r^(2)` ANSWER :C

Discussion

6302.	How many diagnals are there in a polygen of (i) 8 sides (ii) 10 sides?
Answer» ANSWER :` ""^(8) C _2- 8= 20 ` ` ""^(10) C_2 - 10 =35`

Discussion

6303.	If 2^((2pi)/(Sin^(-1)x))-2(a+2)2^(pi/(Sin^(-1)x))+8a lt 0 for at least one real x then
Answer» `1/8 LE a lt 2` `a lt 2` `a in R-{2}` `a in [0,1/8) CUP (2, INFTY)` Answer :D

Discussion

6304.	Write the following statements in the form of "if -then". (i) you get a job implies your credibility are good. (ii) a quadrilateral is a prallelogram if its diagonals biset each other. (iii) to get a grade in the class, it is necessary that you do all the exercise of the book.
Answer» Solution :(3)(i) if you get a JOB, then your CREDIBILITY are good. (ii) if diagonals of a quadrilateral bisect each other, then it is a PARALLELOGRAM. (iii) if you get A grade in the CLASS, then you do all the exercises in the book.

Discussion

6305.	Given the sets A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8}, which of the following may be considered as universal set (s) for all the three sets A, B and {0, 1, 2, 3, 4, 5, 6}
Answer» ANSWER :III

Discussion

6306.	Factorize:\|(p,p^(2),qr),(q,q^(2),rp),(r,r^(2),pq)\|
Answer» ANSWER :`DELTA=(qp+rp+pq)(p-q)(q-r)(r-p)`

Discussion

6307.	Statement: I sin^(-1)x=x has only one solution Statement II: cos^(-1)x=x has only one solution which of the above is true?
Answer» Only I Only II Both I and II Neighter I nor II Answer :C

Discussion

6308.	If the angles alpha , beta , gamma of a trianlge satisfy the relation, sin ((alpha+ beta)/(2)) + sin ((alpha - gamma)/( 2)) + sin ((3 alpha )/(2)) = 3/2, then Triangle is
Answer» ACUTE angled RIGHT angled but not isosceles isosceles isosceles right angled Answer :C

Discussion

6309.	Equation of the diameter of the circle x^(2) +y^(2) - 2x + 4y = 0 which passes through the origin is
Answer» `X + 2Y = 0 ` `x - 2y = 0 ` `2x + y = 0 ` `2x - y = 0 ` ANSWER :C

Discussion

6310.	If the angles alpha , beta , gamma of a trianlge satisfy the relation, sin ((alpha+ beta)/(2)) + sin ((alpha - gamma)/( 2)) + sin ((3 alpha )/(2)) = 3/2, then The measure of the smallest angle of the triangle is
Answer» `30^(@)` `40^(@)` `45^(@)` `50^(@)` ANSWER :B

Discussion

6311.	Find the coordinates of the points which divide the line joining the points (2,-4,3), (-4,5,-6) in the ratio (i) 1: 4 (ii) 2:1.
Answer» Answer :`(i) (4, -7, 6) (ii) -2,2,-3)`

Discussion

6312.	Let f(x) be a cubic polynomial which has local maximum at x=-1 and f(x) has a local minimum at x=1 , If f(-1) =10 and f(3) =-22, then one fourth of the distance between its two horizontal tangents is
Answer» ANSWER :8

Discussion

6313.	Point R (h, k) divides a line segment between the axes in the ratio 1:2 Find equation of the line.
Answer» ANSWER :`2KX + HY = 3KH`

Discussion

6314.	Examine the continuity of the following: \|x+2\|+\|x-1\|
Answer» ANSWER :`X in R`

Discussion

6315.	Compute a price index for the following by (i) simple aggregate and (ii ) average of price relative method.
Answer» ANSWER :(a) `117.143` (B) `122.92`

Discussion

6316.	If f(x)=x sin x then f'(pi/2) = ……
Answer» ANSWER :`(1+0=1)`

Discussion

6317.	Four sides of a quadrilateral are given by the equation xy(x-2)(y-3)=0, then the equation of the line parallel to x-4y=0that divides the quadrilateral into two equal parts is
Answer» `x-4y+5=0` `x-4y-5=0` `x+4y+1=0` `x-4y-1=0` ANSWER :A

Discussion

6318.	If the points A(k,2k) B(2k,3k) C(3,1) are collinear then k = ......... .
Answer» ANSWER :`-2`

Discussion

6319.	A man deposited Rs 10000 in a bank at the rate of 5% simple interest annually. Find the amount in 15^(th)year since he deposited the amount and also calculate the total amount after 20 years.
Answer» ANSWER :RS 17000; 20,000

Discussion

6320.	The sum of the solutionsof the equation tan x, tan 4 x =1 for0 lt x lt pi is
Answer» `10 PI` `(3 pi)/(2)` `(5 pi)/(2)` `2 pi` Answer :D

Discussion

6321.	Calculate Speraman's Rank Correlation for the following data and interpret the result
Answer» ANSWER :`0.81`

Discussion

6322.	Observe the following statements Assertion (A): (a-b) (vec(p) xx vec(q)) + (b-c) vec(p) + (c-a) vec(q)= vec(0) then a=b=c Reason (R ): The non zero vectors vec(p), vec(q), vec(p) xx vec(q) are always linearly independent
Answer» A is true, R is false A is false, R is true A is true, R is true `R rArr A` A is true, R is true `R CANCEL(rArr) A` Answer :C

Discussion

6323.	…….is the equation of ellipse with eccentricity e = (2)/(3). Length of latus rectum is 5 and centre of origin.
Answer» Answer :`(4x^(2))/(81) + (4Y^(2))/(45) = 1`, is REQUIRED ellipse.

Discussion

6324.	Leta , b, in R , (a ne 0). If the function defined asf(x) ={{:((2x^(2))/(a) , 0 le x lt 1),(a , 1 le x lt sqrt(2)),((2b^(2 ) - 4b)/(x^(3) ),sqrt(2) le x lt oo):} iscontinuous in the interval[0 ,oo), then an ordered pair (a,b) is :
Answer» `(- sqrt(2), 1- sqrt(3))` `(sqrt(2, -1 + sqrt(3))` `(sqrt(2), 1- sqrt(3))` `(-sqrt(2), 1 + sqrt(3))` ANSWER :C

Discussion

6325.	Simplify : (1)/(i)
Answer» ANSWER :`-i`

Discussion

6326.	Solve the following equations and write general solutions2sin^(2) theta = 3 cos theta
Answer» ANSWER :`2NPI PM(PI)/(3)`

Discussion

6327.	Find the mean deviation about the median for the data :
Answer» ANSWER :5.1

Discussion

6328.	Find the mean deviation about the median for the data :
Answer» ANSWER :3.23

Discussion

6329.	If f(x)=(sin^(2)x-1)^(n), then x=(pi)/(2) is a point of
Answer» LOCAL MAXIMUM , if N is odd local MINIMUM , if n is odd local maximum , if n is even local minimum , if n is even Answer :A::D

Discussion

6330.	Find the absoloute extremum of f(x) = 4x - (x^(2))/(2) on [-2, (9)/(2)].
Answer» Answer :Abosolute MINIMUM= -10, Absolute MAXIMUM= 8

Discussion

6331.	Find what the following equation becomes when origin is shifted of the point (1,1). (ii) xy-y^(2) - x+y=0
Answer» ANSWER :`xy-x-y+1=0`

Discussion

6332.	The sum of first three terms of a G.P. is to the sum of the first six terms as 125:152. Find the common ratio of the G.P.
Answer» ANSWER :`(3)/(5)`

Discussion

6333.	The point of intersection of the line ( x-1)/( 3) = (y+2)/( 4) = (z-3)/(-2) andplane 2x - y + 3z -1=0 is
Answer» `(10, -10 , 3)` `(10, 10-3)` `(-10, 10, 3)` `(-10, -10, -3)` ANSWER :B

Discussion

6334.	A bag contains 20 coloured balls . 8 are red , 6 are blue ,3 are green ,2 are white and 1 is brown. A ball is chosen at random from the bag . Whatis the probability that ball chosen is :not blue
Answer» ANSWER :`(14)/(20)`

Discussion

6335.	A bag contains 20 coloured balls . 8 are red , 6 are blue ,3 are green ,2 are white and 1 is brown. A ball is chosen at random from the bag . Whatis the probability that ball chosen is :blue
Answer» ANSWER :`(6)/(20)`

Discussion

6336.	Abag contains 20 coloured balls . 8 are red , 6 are blue ,3 are green ,2 are white and 1 is brown. A ball is chosen at random from the bag . Whatis the probability that ball chosen is :not brown
Answer» ANSWER :`(19)/(20)`

Discussion

6337.	A bag contains 20 coloured balls . 8 are red , 6 are blue ,3 are green ,2 are white and 1 is brown. A ball is chosen at random from the bag . Whatis the probability that ball chosen is :brown
Answer» ANSWER :`(1)/(20)`

Discussion

6338.	A bag contains 20 coloured balls . 8 are red , 6 are blue ,3 are green ,2 are white and 1 is brown. A ball is chosen at random from the bag . Whatis the probability that ball chosen is :blue or red
Answer» ANSWER :`(14)/(20)`

Discussion

6339.	Abag contains 20 coloured balls . 8 are red , 6 are blue ,3 are green ,2 are white and 1 is brown. A ball is chosen at random from the bag . Whatis the probability that ball chosen is :green or white or brown ?
Answer» ANSWER :`(6)/(20)`

Discussion

6340.	Abag contains 20 coloured balls . 8 are red , 6 are blue ,3 are green ,2 are white and 1 is brown. A ball is chosen at random from the bag . Whatis the probability that ball chosen is :red or green
Answer» ANSWER :`(11)/(20)`

Discussion

6341.	Make correct statements by filling in the symbols ⊂ or ⊄ in the blank spaces : { 2, 3, 4 } . . . { 1, 2, 3, 4,5 }
Answer» ANSWER :`⊂`

Discussion

6342.	If the position vectors of A, B are 2bar(i)-9bar(j)-4bar(k), 6bar(i)-3bar(j)+8bar(k) then the unit vector in the direction of vec(AB) is
Answer» `bar(R)=t(4bar(i)-6bar(j)+8BAR(k))` `bar(r)=t(4bar(i)-2bar(k))` `bar(r)=t(2bar(i)+3BAR(j)-6bar(k))` `bar(r)=t(6bar(i)-3bar(j)+2bar(k))` Answer :B

Discussion

6343.	Write the negation of each of the following statements. All pets are mammals.
Answer» ANSWER :some PETS are not MAMMALS

Discussion

6344.	If vec(a), vec(b) are unit vectors satisfying (5vec(a) + 3vec(b)) xx (3vec(a) -7vec(b))=vec(0), then (vec(a), vec(b)) is
Answer» `(pi)/(2)` `(pi)/(3)` `(pi)/(6)` `0 or pi` ANSWER :D

Discussion

6345.	If the transformed equation of curve is X^(2)+2Y^(2)+16=0 when the axes are translated to the point (-1,2) then find the original equation of the curve.
Answer» ANSWER :`X^(2)+2Y^(2)+2x-8y+25=0`

Discussion

6346.	A triangle of area 24 sq. units is formed by a straight line with the coordinate axes in the first quadrant. Find the equation of the straight line, if it passes through (3,4).
Answer» ANSWER :`x/6+y/8=1`

Discussion

6347.	If O is the origin and OP,OQ are the tangents from the origin to the circle x^2+y^2-6x+4y=8=0, then circum center of the triangle OPQis
Answer» (3,-2) `(3/2,-1)` `(3/4,-1/2)` `(-3/2,1)` ANSWER :B

Discussion

6348.	A parabola reflector is 9 cm deep and its diameter is 24 cm. Find the distance of its focus from vertex.
Answer» ANSWER :4 CM

Discussion

6349.	The point of intersection of the line passing through bar(i)-2bar(j)-bar(k), 2bar(i)+3bar(j)+bar(k) andthe plane passing through 2bar(i)+bar(j)-3bar(k), 4bar(i)-bar(j)+2bar(k), 3bar(i)+bar(k)
Answer» `5/3i+4/3bar(J)+1/3bar(K)` `5/3bar(i)-4/3bar(j)-1/3bar(k)` `5/3bar(i)+4/3bar(j)-1/3bar(k)` `5/3bar(i)-4/3bar(j)+1/3bar(k)` ANSWER :A

Discussion

6350.	If n (A ) = 10 ,n(B ) = 6 and AcapBnephi then maximum value of n (B-A) ….. .
Answer» ANSWER :5

Discussion

Explore topic-wise InterviewSolutions in .

If x=r cos alpha cos betacos gamma , y= cos alpha cos beta sin gamma , z= r sin alpha cos beta , mu = r sin beta " then " x^(2)+y^(2) + z^(2)+mu^(2)=

How many diagnals are there in a polygen of (i) 8 sides (ii) 10 sides?

If 2^((2pi)/(Sin^(-1)x))-2(a+2)2^(pi/(Sin^(-1)x))+8a lt 0 for at least one real x then

Write the following statements in the form of "if -then". (i) you get a job implies your credibility are good. (ii) a quadrilateral is a prallelogram if its diagonals biset each other. (iii) to get a grade in the class, it is necessary that you do all the exercise of the book.

Given the sets A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8}, which of the following may be considered as universal set (s) for all the three sets A, B and {0, 1, 2, 3, 4, 5, 6}

Factorize:|(p,p^(2),qr),(q,q^(2),rp),(r,r^(2),pq)|

Statement: I sin^(-1)x=x has only one solution Statement II: cos^(-1)x=x has only one solution which of the above is true?

If the angles alpha , beta , gamma of a trianlge satisfy the relation, sin ((alpha+ beta)/(2)) + sin ((alpha - gamma)/( 2)) + sin ((3 alpha )/(2)) = 3/2, then Triangle is

Equation of the diameter of the circle x^(2) +y^(2) - 2x + 4y = 0 which passes through the origin is

If the angles alpha , beta , gamma of a trianlge satisfy the relation, sin ((alpha+ beta)/(2)) + sin ((alpha - gamma)/( 2)) + sin ((3 alpha )/(2)) = 3/2, then The measure of the smallest angle of the triangle is

Find the coordinates of the points which divide the line joining the points (2,-4,3), (-4,5,-6) in the ratio (i) 1: 4 (ii) 2:1.

Let f(x) be a cubic polynomial which has local maximum at x=-1 and f(x) has a local minimum at x=1 , If f(-1) =10 and f(3) =-22, then one fourth of the distance between its two horizontal tangents is

Point R (h, k) divides a line segment between the axes in the ratio 1:2 Find equation of the line.

Examine the continuity of the following: |x+2|+|x-1|

Compute a price index for the following by (i) simple aggregate and (ii ) average of price relative method.

If f(x)=x sin x then f'(pi/2) = ……

Four sides of a quadrilateral are given by the equation xy(x-2)(y-3)=0, then the equation of the line parallel to x-4y=0that divides the quadrilateral into two equal parts is

If the points A(k,2k) B(2k,3k) C(3,1) are collinear then k = ......... .

A man deposited Rs 10000 in a bank at the rate of 5% simple interest annually. Find the amount in 15^(th)year since he deposited the amount and also calculate the total amount after 20 years.

The sum of the solutionsof the equation tan x, tan 4 x =1 for0 lt x lt pi is

Calculate Speraman's Rank Correlation for the following data and interpret the result

Observe the following statements Assertion (A): (a-b) (vec(p) xx vec(q)) + (b-c) vec(p) + (c-a) vec(q)= vec(0) then a=b=c Reason (R ): The non zero vectors vec(p), vec(q), vec(p) xx vec(q) are always linearly independent

…….is the equation of ellipse with eccentricity e = (2)/(3). Length of latus rectum is 5 and centre of origin.

Leta , b, in R , (a ne 0). If the function defined asf(x) ={{:((2x^(2))/(a) , 0 le x lt 1),(a , 1 le x lt sqrt(2)),((2b^(2 ) - 4b)/(x^(3) ),sqrt(2) le x lt oo):} iscontinuous in the interval[0 ,oo), then an ordered pair (a,b) is :

Simplify : (1)/(i)

Solve the following equations and write general solutions2sin^(2) theta = 3 cos theta

Find the mean deviation about the median for the data :

Find the mean deviation about the median for the data :

If f(x)=(sin^(2)x-1)^(n), then x=(pi)/(2) is a point of

Find the absoloute extremum of f(x) = 4x - (x^(2))/(2) on [-2, (9)/(2)].

Find what the following equation becomes when origin is shifted of the point (1,1). (ii) xy-y^(2) - x+y=0

The sum of first three terms of a G.P. is to the sum of the first six terms as 125:152. Find the common ratio of the G.P.

The point of intersection of the line ( x-1)/( 3) = (y+2)/( 4) = (z-3)/(-2) andplane 2x - y + 3z -1=0 is

A bag contains 20 coloured balls . 8 are red , 6 are blue ,3 are green ,2 are white and 1 is brown. A ball is chosen at random from the bag . Whatis the probability that ball chosen is :not blue

A bag contains 20 coloured balls . 8 are red , 6 are blue ,3 are green ,2 are white and 1 is brown. A ball is chosen at random from the bag . Whatis the probability that ball chosen is :blue

Abag contains 20 coloured balls . 8 are red , 6 are blue ,3 are green ,2 are white and 1 is brown. A ball is chosen at random from the bag . Whatis the probability that ball chosen is :not brown

A bag contains 20 coloured balls . 8 are red , 6 are blue ,3 are green ,2 are white and 1 is brown. A ball is chosen at random from the bag . Whatis the probability that ball chosen is :brown

A bag contains 20 coloured balls . 8 are red , 6 are blue ,3 are green ,2 are white and 1 is brown. A ball is chosen at random from the bag . Whatis the probability that ball chosen is :blue or red

Abag contains 20 coloured balls . 8 are red , 6 are blue ,3 are green ,2 are white and 1 is brown. A ball is chosen at random from the bag . Whatis the probability that ball chosen is :green or white or brown ?

Abag contains 20 coloured balls . 8 are red , 6 are blue ,3 are green ,2 are white and 1 is brown. A ball is chosen at random from the bag . Whatis the probability that ball chosen is :red or green

Make correct statements by filling in the symbols ⊂ or ⊄ in the blank spaces : { 2, 3, 4 } . . . { 1, 2, 3, 4,5 }

If the position vectors of A, B are 2bar(i)-9bar(j)-4bar(k), 6bar(i)-3bar(j)+8bar(k) then the unit vector in the direction of vec(AB) is

Write the negation of each of the following statements. All pets are mammals.

If vec(a), vec(b) are unit vectors satisfying (5vec(a) + 3vec(b)) xx (3vec(a) -7vec(b))=vec(0), then (vec(a), vec(b)) is

If the transformed equation of curve is X^(2)+2Y^(2)+16=0 when the axes are translated to the point (-1,2) then find the original equation of the curve.

A triangle of area 24 sq. units is formed by a straight line with the coordinate axes in the first quadrant. Find the equation of the straight line, if it passes through (3,4).

If O is the origin and OP,OQ are the tangents from the origin to the circle x^2+y^2-6x+4y=8=0, then circum center of the triangle OPQis

A parabola reflector is 9 cm deep and its diameter is 24 cm. Find the distance of its focus from vertex.

The point of intersection of the line passing through bar(i)-2bar(j)-bar(k), 2bar(i)+3bar(j)+bar(k) andthe plane passing through 2bar(i)+bar(j)-3bar(k), 4bar(i)-bar(j)+2bar(k), 3bar(i)+bar(k)

If n (A ) = 10 ,n(B ) = 6 and AcapBnephi then maximum value of n (B-A) ….. .