14949 + Interview Questions in Maths in Class 11 Page 93 InterviewSolution

4601.	Solve the following equations and write general solutions 4 cos theta. Cos 2 theta.cos 3 theta = 1 in (0, pi)
Answer» ANSWER :`{(pi)/(8),(pi)/(3),(3pi)/(8),(5pi)/(8),(2PI)/(3),(7pi)/(8)}`

Discussion

4602.	If bara, barb, barc, bard, bare are co-planar vectors then {(baraxxbarb)xx(barcxxbard)}xxbare=
Answer» `BAR0` `(BARAXXBARB)` `(baraxxbarc)` `(baraxxbard)` ANSWER :A

Discussion

4603.	If A = { 3, 5, 7, 9, 11 }, B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}, find A ∩ B
Answer» ANSWER :`{ 7, 9, 11 }`

Discussion

4604.	Given that a, b, c are the sides of Delta ABC which is right angled at vertex C, then the minimum value of ((c )/(a)+(c )/(b))^(2) is
Answer» 0 8 `2sqrt(2)` 2 Answer :B

Discussion

4605.	Find the derivative of the following functions from first principle. (1)/(x^(2))
Answer» ANSWER :`(-2)/(X^(3))`

Discussion

4606.	Let P(x)=a_0+a_1x+a_2x^2+...+a_nx^n.If\|P(x)\|le\|e^(x-1)-1,\|AAxge0, then the maximum value of \|a_1+2a_2+3a_3+..+na_n\|
Answer» `1/n` 1 n e Answer :B

Discussion

4607.	Tan ((pi)/(4)+theta).Tan((3pi)/(4)+theta)=
Answer» `npipm(PI)/(6)` `NPI-(pi)/(6)` `2npipm(pi)/(6)` `2NPI-(pi)/(6)` ANSWER :A

Discussion

4608.	If the angle between the line x = (y -1)/(2) =(z-3)/(lamda) and the plane x + 2y + 3z = 4 iscos ^(-1) (sqrt (5 //14))then lamda =
Answer» `3/2` `5/3` `2/3` `2/5` ANSWER :C

Discussion

4609.	Given that P(3,2,-4) Q(5,4-6) and R(9,8,-10) are collinear find the ratioin whichQ divides PR
Answer» ANSWER :`1:2`

Discussion

4610.	Prove that usingthe Mathematicalinductionsin ( alpha ) + sin ( alpha + pi/6) + sin ( alpha + ( 2pi)/6) + ..+ sin ( alpha + ((n-1)pi)/6) = ( sin [ alpha +((n-1)pi)/12] xx sin ( (npi)/12))/(sin (pi/12))
Answer» <P> ANSWER :p( K +1)

Discussion

4611.	Use inductionto provethat10^(n) + 3 xx 4^(n +2) +5 is divisibleby 9for all naturalnumbers n .
Answer» ANSWER :9

Discussion

4612.	Match the following
Answer» ANSWER :`A-s, B-r, C-p, D-q`

Discussion

4613.	Match the following
Answer» ANSWER :`A-r, B-p, C-s, D-q`

Discussion

4614.	Iff(x) = (1)/(1-x) " and " f^(n)= fofofo…. Of (nf's) then find the point of discontinuity off^(3n)(x).
Answer» ANSWER :DISCONTINUOUS at x=0, x=1

Discussion

4615.	Find the value of x for which x +9,x-6, 4 are the first three terms of a geometrical progression and calculate the fourth term of progression in this case
Answer» ANSWER :x=0 ,16 when x =0 `t_(4) - 2(2)/(3)` when x =16 , `t_(4) = 1 (3)/(5)`

Discussion

4616.	If u = sqrt ( a ^(2) cos ^(2) theta + b ^(2) sin ^(2) theta ) + sqrt (a ^(2) sin ^(2) theta + b ^(2) cos ^(2) theta ,) then the difference between the maximumand minimum value so u ^(2) is given by
Answer» `2 (a ^(2) +B ^(2))` `2 SQRT ( a ^(2) +b ^(2))` `(a + b) ^(2)` `(a-b) ^(2)` ANSWER :D

Discussion

4617.	Normal form of the line x+y+sqrt(2)=0 is
Answer» `x"cos"(PI)/4+y"sin"(pi)/4=1` `"cos"(3pi)/4+y"sin"(3pi)/4=1` `x"cos"(5pi)/4+y"sin"(5pi)/4=1` `x"cos"(7pi)/4+y"sin"(7pi)/4=1` ANSWER :C

Discussion

4618.	Prove that 3 sin ""pi/6 sec ""pi/3 -4 sin ""(5pi)/(6) cot"" (pi)/(4) =1
Answer» ANSWER :`=2-4 XX 1/2 =1 =R.H.S.`

Discussion

4619.	The slope of a line is double of the slope of another line. Iftangent of the angle between them (1)/(3), find the slopes of the lines.
Answer» ANSWER :1 and 2, or `1/2` and 1, or`-1 " and " -2`, or `- 1/2" and " -1`

Discussion

4620.	How manypermutations can be made out of the letters of the word'TRIANGLE '? How manyof these will begin with T and end with E ?
Answer» ANSWER :` 8! =40320 , ""^(6)P_6=6! =720`

Discussion

4621.	How many 2- digits numbers can be formed from the digits 8,1,3,5 and 4 assuming repetition of digits is allowed?
Answer» ANSWER :` 25 `

Discussion

4622.	The possible solutions of \|cot x\| = cot x + (1)/( sin x) ., xin [ 0 , 3 pi] is equal to
Answer» `(2PI)/3` `2pi` `(8pi)/3` `(PI)/3` ANSWER :A::C

Discussion

4623.	By the principle of mathematical induction , prove that forn ge 1
Answer» ANSWER :` RARR cos ALPHA + cos beta + cos gamma - 0 " and " SIN alpha + sin beta + sin gamma = 0 `

Discussion

4624.	Illustrate and explain the set of points z in the Argand diagram, which represents \|z- z_(1)\| le 3 where z_(1)= 3-2i
Answer» Answer :`X^(2) + y^(2)- 6x + 4y + 4 le 0`, all points inside and on this circle whose CENTRE is `(3, -2)` and RADIUS is 3

Discussion

4625.	sec^(-1)((2sqrt(2))/(1+sqrt(3)))=
Answer» `(PI)/12` `(pi)/3` `(3pi)/3` `(pi)/6` Answer :A

Discussion

4626.	Which of the following pairs of sets are equal? Justify your answer. (i) X, the set of letters in “ALLOY” and B, the set of letters in “LOYAL”.
Answer» ANSWER :B

Discussion

4627.	(r+r_(1))"tan"(B-C)/(2)+(r+r_(2))"tan"(C-A)/(2)+(r+r_(3))"tan"(A-B)/(2)=
Answer» 2s s `DELTA` 0 Answer :D

Discussion

4628.	The statement: If x^(2) is not even, then x is not eve is converse of the statement…………
Answer» If `X^(2)` is ODD, then x is EVEN. If x is not even, then `x^(2)` is not even If x is VEN then `x^(2)` is even If x is odd, then `x^(2)` is even Answer :B

Discussion

4629.	Consider the points P (2,4) and Q (-2,5) Find the mid point of PQ Hence, find the equation of the perpendicular bisector of PQ
Answer» SOLUTION :`(0,9/2), 8X - 2Y + 9 = 0`

Discussion

4630.	Find the component statements of the following compound statements: 0 is less than every positive integer and every negative integer.
Answer» ANSWER :p: positive INTEGER. q: NEGATIVE integer.

Discussion

4631.	From a group of 2 men and 3 women , two persons are selected . Describe the sample space of the experiment , if E is the event in which one man and one women are selected , then which are the cases favourable to E?
Answer» ANSWER :`S={M1M2,MW1,M1W2,M1W3,M2W1,M2W2,M2W3,W1W2,W2W3,W3W1}` `E={M1W1,M1W2,M1W3,M2W1,M2W2,M2W3}`

Discussion

4632.	State the equation of the line which has the y-intercept -1 and is parallel to y=5x+7
Answer» ANSWER : `y=5x-1`

Discussion

4633.	Calculate Mode for the following data
Answer» ANSWER :`12.35`

Discussion

4634.	The minor axis of the ellipse having eccentricity is (1)/(2) and vertices(4, 0) and (10, 0) is x = k, then value of k is
Answer» 9 `-7` 7 `-9` SOLUTION :N/A

Discussion

4635.	A lattice point in a plane is a point for which both coordinate are integers. The number of lattice points inside the triangle whose sides are x=0, y=0 and 9x+223y=2007 is
Answer» 198 173 99 888 Answer :D

Discussion

4636.	(Tan^(-1)x)^(2)+(Cos^(-1)x)^(2)=5pi^(2)//8rArrx=
Answer» `-1` 1 0 2 Answer :A

Discussion

4637.	Evaluate sin^(2)((pi)/(8)+(theta)/(2))-sin^(2)((pi)/(8)-(theta)/(2))
Answer» ANSWER :`(1)/(sqrt(2))SIN THETA`

Discussion

4638.	If f(x + 1/x ) = x^(3)+ (1)/(x^(3)) -4 (x^(2)+1/x^(2))+13 then the value of f(2+sqrt(3))=
Answer» 9 10 11 12 Answer :A

Discussion

4639.	If barp is non- · zero vector such that barp. bara= barp. barb = 0 and barp xx barc = bar0 then
Answer» `[BARABARBBARC]=0` `baraxx(BARBXXBARC)=BAR0` `(baraxxbarb)xxbarcbar0` `(baraxxbarc)xxbarb=bar0` Answer :C

Discussion

4640.	Count the number of three - digitnumbers whichcan be formed from the digits 2,4,6,8, if (i) repetitions of digits is allowed ? (ii) repetitionsof digits is notallowed ?
Answer» ANSWER :(i) 125, (II) 60.

Discussion

4641.	If the image of the point (-1, 3, 4) in the pane x - 2y =0 is (x _(1) , y _(1) , z _(1)) then z_(1) =
Answer» 1 2 3 4 Answer :D

Discussion

4642.	lim_(xrarr0)(sin(picos^2x))/x^2 = ….. .
Answer» ANSWER :`PI`

Discussion

4643.	The value of sum_(k=1)^(100) sin(kx) cos(101-k)x is equal to:
Answer» `(101)/(2)SIN(101x)` `99 sin (101 X)` `50 sin(101 x)` `100 sin (101 x)` ANSWER :B

Discussion

4644.	Observe the following statements : Assertion (A) : Three vectors are coplanar if one of them is expressible as a linear combination of the other two. Reason (R) : Any three coplanar vectors are linearly dependent. Then which of the following is true?
Answer» Both A and R are TRUE and R is the correct explanation of A. Both A and R are true but R ISNOT the correct explanation of A. A is true, but R is FALSE. A is false, but R is true. Answer :B

Discussion

4645.	Assertion If D is the midpoint of the side BC of a triangle ABC then vecAB+vecAC=2vecAD.Reason: If veca and vecb are two position vector of A and B , then the position vector of midpoint of AB in (veca+vecb)/(2)
Answer» Assertion is DIRECT APPLICATION of Reason. Assertion is not derived from Reason Reason is TRUE but Assertion is not True. Assertion IMPLIES Reason. Answer :A

Discussion

4646.	Equation of the line passing through the point (-4, 3) andthe portion of the line intercepted between the axes which is divided internally in the ratio 5:3 by this point, is
Answer» `9X + 20Y +96=0` `20x+9y+96=0` `9x-20y +96=0` NONE of these ANSWER :C

Discussion

4647.	Number of solutionsof the equation of the equation tanx + tan 2 x + tan 3 x = tan 3 x = tan x tan 2x tan 3 x, x in [ 0 , pi ]is
Answer» `PI/6, (2pi)/3, pi` `pi/3, (2pi)/3, pi` `(pi)/3, pi/2 , 2pi` `pi/2, (3PI)/2,pi` ANSWER :B

Discussion

4648.	The perpendicular distance from the origin to a line L is 7 and the line L makes an anlge of 150^(@) with the +ve direction of y-axis and makes negative intercept on x-axis. Then the equation of the line is
Answer» `SQRT(3)x+y=14` `sqrt(3)x-y=-14` `3x-y=14` `3x+y=14` ANSWER :B

Discussion

4649.	Write the negation of the following statements: r: All birds have wings.
Answer» ANSWER :WITHOUT WINGS.

Discussion

4650.	If the lines (x-2)/(1) = (y-3)/(1) = (z-4)/(lamda ) and (x-1)/(lamda ) = (y-4)/(2) = ( z -5)/(1) intersect, then
Answer» `lamda = -1` `lamda =2` `lamda = -3` `lamda = 0` ANSWER :A::D

Discussion

Explore topic-wise InterviewSolutions in .

Solve the following equations and write general solutions 4 cos theta. Cos 2 theta.cos 3 theta = 1 in (0, pi)

If bara, barb, barc, bard, bare are co-planar vectors then {(baraxxbarb)xx(barcxxbard)}xxbare=

If A = { 3, 5, 7, 9, 11 }, B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}, find A ∩ B

Given that a, b, c are the sides of Delta ABC which is right angled at vertex C, then the minimum value of ((c )/(a)+(c )/(b))^(2) is

Find the derivative of the following functions from first principle. (1)/(x^(2))

Let P(x)=a_0+a_1x+a_2x^2+...+a_nx^n.If|P(x)|le|e^(x-1)-1,|AAxge0, then the maximum value of |a_1+2a_2+3a_3+..+na_n|

Tan ((pi)/(4)+theta).Tan((3pi)/(4)+theta)=

If the angle between the line x = (y -1)/(2) =(z-3)/(lamda) and the plane x + 2y + 3z = 4 iscos ^(-1) (sqrt (5 //14))then lamda =

Given that P(3,2,-4) Q(5,4-6) and R(9,8,-10) are collinear find the ratioin whichQ divides PR

Prove that usingthe Mathematicalinductionsin ( alpha ) + sin ( alpha + pi/6) + sin ( alpha + ( 2pi)/6) + ..+ sin ( alpha + ((n-1)pi)/6) = ( sin [ alpha +((n-1)pi)/12] xx sin ( (npi)/12))/(sin (pi/12))

Use inductionto provethat10^(n) + 3 xx 4^(n +2) +5 is divisibleby 9for all naturalnumbers n .

Match the following

Match the following

Iff(x) = (1)/(1-x) " and " f^(n)= fofofo…. Of (nf's) then find the point of discontinuity off^(3n)(x).

Find the value of x for which x +9,x-6, 4 are the first three terms of a geometrical progression and calculate the fourth term of progression in this case

If u = sqrt ( a ^(2) cos ^(2) theta + b ^(2) sin ^(2) theta ) + sqrt (a ^(2) sin ^(2) theta + b ^(2) cos ^(2) theta ,) then the difference between the maximumand minimum value so u ^(2) is given by

Normal form of the line x+y+sqrt(2)=0 is

Prove that 3 sin ""pi/6 sec ""pi/3 -4 sin ""(5pi)/(6) cot"" (pi)/(4) =1

The slope of a line is double of the slope of another line. Iftangent of the angle between them (1)/(3), find the slopes of the lines.

How manypermutations can be made out of the letters of the word'TRIANGLE '? How manyof these will begin with T and end with E ?

How many 2- digits numbers can be formed from the digits 8,1,3,5 and 4 assuming repetition of digits is allowed?

The possible solutions of |cot x| = cot x + (1)/( sin x) ., xin [ 0 , 3 pi] is equal to

By the principle of mathematical induction , prove that forn ge 1

Illustrate and explain the set of points z in the Argand diagram, which represents |z- z_(1)| le 3 where z_(1)= 3-2i

sec^(-1)((2sqrt(2))/(1+sqrt(3)))=

Which of the following pairs of sets are equal? Justify your answer. (i) X, the set of letters in “ALLOY” and B, the set of letters in “LOYAL”.

(r+r_(1))"tan"(B-C)/(2)+(r+r_(2))"tan"(C-A)/(2)+(r+r_(3))"tan"(A-B)/(2)=

The statement: If x^(2) is not even, then x is not eve is converse of the statement…………

Consider the points P (2,4) and Q (-2,5) Find the mid point of PQ Hence, find the equation of the perpendicular bisector of PQ

Find the component statements of the following compound statements: 0 is less than every positive integer and every negative integer.

From a group of 2 men and 3 women , two persons are selected . Describe the sample space of the experiment , if E is the event in which one man and one women are selected , then which are the cases favourable to E?

State the equation of the line which has the y-intercept -1 and is parallel to y=5x+7

Calculate Mode for the following data

The minor axis of the ellipse having eccentricity is (1)/(2) and vertices(4, 0) and (10, 0) is x = k, then value of k is

A lattice point in a plane is a point for which both coordinate are integers. The number of lattice points inside the triangle whose sides are x=0, y=0 and 9x+223y=2007 is

(Tan^(-1)x)^(2)+(Cos^(-1)x)^(2)=5pi^(2)//8rArrx=

Evaluate sin^(2)((pi)/(8)+(theta)/(2))-sin^(2)((pi)/(8)-(theta)/(2))

If f(x + 1/x ) = x^(3)+ (1)/(x^(3)) -4 (x^(2)+1/x^(2))+13 then the value of f(2+sqrt(3))=

If barp is non- · zero vector such that barp. bara= barp. barb = 0 and barp xx barc = bar0 then

Count the number of three - digitnumbers whichcan be formed from the digits 2,4,6,8, if (i) repetitions of digits is allowed ? (ii) repetitionsof digits is notallowed ?

If the image of the point (-1, 3, 4) in the pane x - 2y =0 is (x _(1) , y _(1) , z _(1)) then z_(1) =

lim_(xrarr0)(sin(picos^2x))/x^2 = ….. .

The value of sum_(k=1)^(100) sin(kx) cos(101-k)x is equal to:

Observe the following statements : Assertion (A) : Three vectors are coplanar if one of them is expressible as a linear combination of the other two. Reason (R) : Any three coplanar vectors are linearly dependent. Then which of the following is true?

Assertion If D is the midpoint of the side BC of a triangle ABC then vecAB+vecAC=2vecAD.Reason: If veca and vecb are two position vector of A and B , then the position vector of midpoint of AB in (veca+vecb)/(2)

Equation of the line passing through the point (-4, 3) andthe portion of the line intercepted between the axes which is divided internally in the ratio 5:3 by this point, is

Number of solutionsof the equation of the equation tanx + tan 2 x + tan 3 x = tan 3 x = tan x tan 2x tan 3 x, x in [ 0 , pi ]is

The perpendicular distance from the origin to a line L is 7 and the line L makes an anlge of 150^(@) with the +ve direction of y-axis and makes negative intercept on x-axis. Then the equation of the line is

Write the negation of the following statements: r: All birds have wings.

If the lines (x-2)/(1) = (y-3)/(1) = (z-4)/(lamda ) and (x-1)/(lamda ) = (y-4)/(2) = ( z -5)/(1) intersect, then