14949 + Interview Questions in Maths in Class 11 Page 41 InterviewSolution

2001.	Find the derivative of the function Iff(x) = tan ^(-1) ((5 tan ((x)/(2)) +4)/( 3))then show that f'(x) = (3)/(10 + 8 sin x )
Answer»

Discussion

2002.	Factorise x^2 - 6x + 8 into linear factors.
Answer» SOLUTION :`x^2 - 6X + 8 = (x-2)(x-4)`

Discussion

2003.	Find the modulus of the following complex numbers (3 +2i) (5-4i)
Answer» ANSWER :`sqrt533`

Discussion

2004.	A team of medical students doing their internship have to assist during surgeries at a city hospital. The probabilities of surgeries rated as very complex, complex, routine, simple or very simple are respectively, 0.15, 0.20, 0.31, 0.26, .08. Find the probabilities that a particular surgery will be rated (i) complex or very complex (ii) neither very complex nor very simple (iii) routine or complex (iv) routine or simple
Answer» ANSWER :(i) 0.35 (II) 0.77 (III) 0.51 (IV) 0.57

Discussion

2005.	Iftan theta + sin theta = m, tan theta - sin theta = n " then " (m^(2)-n^(2))^(2)=
Answer» 4mn 8mn 16 mn mn Answer :C

Discussion

2006.	Given that P (3,2,-4), Q(5,4,-6), R (9,8-10) are collinear, find the ratio in which Q divides PR.
Answer» ANSWER :`1:2`

Discussion

2007.	Find the equation of a circle circumscribing the triangle whose sides are 2x+y-3=0, 3x-y-7=0 and x-2y+1=0.
Answer» ANSWER :`X^(2)+y^(2)-5x-y+4=0`

Discussion

2008.	A ray of light passing through the point (8,3) and is reflected at (14,0) on x axis. Then the equationof the reflected ray
Answer» x+y=14 x-y=14 2y=x-14 3y=x-14 Answer :C

Discussion

2009.	When the radius of a sphere decreases from 3cm to 2.98cm then the approximate decrease in volume of sphere is
Answer» `0.002 picm^(3)` `0.72 PI CM^(3)` `0.72 picm^(3)` `0.008 pi cm^(3)` ANSWER :B

Discussion

2010.	Let A={9,10,11,12,13} and let f: A to N be defined by f(n)= the highest prime factor of n. Find the range of f.
Answer» ANSWER :`UL(13) XX 1`

Discussion

2011.	The minimum andmaximum values of1-8 sin^(2) x cos^(2) xare
Answer» `-1//4 ,1//4` `-4,4` `-1,1` `-1//8 ,1//8` ANSWER :4

Discussion

2012.	Calculate the standard deviation of the following distribution:
Answer» ANSWER :7.936

Discussion

2013.	A man running a race course notes that the sum of the distances from the two flag posts from him is always 10 m and the distances between the flag posts is 8 m. Find the equation of track traced by man.
Answer» ANSWER :`9X^(2)+25Y^(2)=225`

Discussion

2014.	Evaluate the following limits : Lim_(xto2) (sin(e^(x-2)-1))/(log(x-1))
Answer» ANSWER :`1 XX1 xx1 = 1 `

Discussion

2015.	Differentiate the following w.r.t. x or t or u as the case may be: 10. z= (u)/( u^(2) +1)
Answer» ANSWER :`(DZ)/( DU) = (1- u^2)/( (u^2 +1)^2)`

Discussion

2016.	Find the locus of the foot of the perpendicular from the orign to a variable straighht line which always passes through the fixed point (a,b).
Answer» ANSWER :`X^(2)+y^(2)-ax-by=0`

Discussion

2017.	The negation of the statement p: A circle is an ellipse is ………
Answer» An ELLIPSE is an CIRCLE. An ellipse is not a circle A circle is not an ellipse A circle is an ellipse Answer :C

Discussion

2018.	If r=x+y+z and tan^(-1)sqrt((xr)/(yz))+tan^(-1)sqrt((yr)/(zx))+tan^(-1)sqrt((zr)/(xy))=kpi then the value of k is
Answer» ANSWER :1

Discussion

2019.	vec(OA)= vec(a), vec(OB)= 10vec(a) + 2vec(b), vec(OC)= vec(b) where O, A, C are non-collinear points. Let 'p' denote area of quadrilateral OABC, 'q' denote area of parallelogram with OA, OC as adjacent sides, then (p)/(q)=
Answer» 2 4 6 8 Answer :C

Discussion

2020.	Let the sequence a_(n) be defined as follows: a_(1)= 1, a_(n)= a_(n-1) + 2 " for " n ge 2. Find first five terms and write corresponding series.
Answer» ANSWER :1,3,5,7 and 9

Discussion

2021.	Find the equation of the line passing through the point (-4, 3)with slope 1/2.
Answer» ANSWER :`X - 2Y + 10 = 0 `

Discussion

2022.	What is theprobability of getting 3 white balls in a draw of 3 balls from a box containing 6 white and 4 red balls ?
Answer» ANSWER :`(""^(6)C_(3))/(""^(10)C_(3))=(1)/(6)`

Discussion

2023.	A point Rwith X coordinate 4 lie on the line segment joining the points P(2,-3,4) and Q(8,0,10) find the coordinates of the pont R
Answer» ANSWER :(4,-2,6)

Discussion

2024.	At any point on the curve (a)/(x^(2))+(b)/(y^(2))=1, then y-intercept made by the tangent is proportional to
Answer» SQUARE of the ABSCISSA CUBE of the abscissa Square of the ordinate Cube of the ordinate Answer :D

Discussion

2025.	If A=[(2,-1,2),(1,3,-4)] and B=[(1,-2),(-3,0),(5,4)] then verify that (AB)^(T)=B^(T)A^(T)
Answer» ANSWER :`B^(T)A^(T)`

Discussion

2026.	Iftan x lt 2 then
Answer» `x in (n PI + (pi)/(2), n pi - tan ^(-1) 2) n in Z` `x in ( n pi + (pi)/(4), n pi + tan^(-1) 2) n in Z` `x in ( n pi - (pi)/(2), n pi + tan^(-1) 2) n in Z` `x in (n pi - (pi)/( 4), n pi - tan^(-1) 2 ) n in Z` Answer :C

Discussion

2027.	Let f(x) be a function satisfying f(x+y) = f(x) f(y) for all x,y in N such that f(1) = 3 and sum_(x=1)^(n) f(x) = 120 . Then the vlaue of n is :
Answer» ANSWER :4

Discussion

2028.	The point (4,1) undergoes the following transformations successively (i) reflection about the line y = x (ii) translation through a distance 2 units along the positive direction of y-axis . Then find the final position of the point.
Answer» ANSWER :(1, 6)

Discussion

2029.	If 3sin x+4cosax =7 has at least one solution, then the possible values of a as
Answer» `(4M)/(4n+1)` `(2M)/(2n+1)` `(3M)/(2n+1)` `(2m)/(4n+1)` ANSWER :A

Discussion

2030.	Compute (i)(7!)/(5!) (ii) (12!)/((10!)(2!)
Answer» ANSWER :(i) 42, (II) 66

Discussion

2031.	If bara, barb, barc are the sides of a triangle ABC then [barabarb barc] =
Answer» 0 1 `-1` 2 Answer :A

Discussion

2032.	Which of the following sentences are statements? Justify Sum of opposite angles of a cyclic quadrilateral is 180^(@)
Answer» ANSWER :It is a STATEMENT

Discussion

2033.	The orthocentre of the triangle formed by (0,0),(5,-1),(-2,3) is
Answer» `(4,-7)` `(-4,7)` `(4,7)` `(-4,-7)` ANSWER :D

Discussion

2034.	Find the eccentricity, the coordinates of the foci, and the length of the latus rectum of the ellipse 2x^(2)+3y^(2)=1.
Answer» ANSWER :`1/sqrt(3), (pm1/sqrt(6), ), (2sqrt(2))/3`

Discussion

2035.	If f^(1)(x)=sin(logx)andy=f((2x+3)/(3-2x)) then (dy)/(dx) is
Answer» `sin(LOGX).(1)/(xlogx)` `12/((3-2x)^2)sin[LOG((2x+3)/(3-2x))]` `sin[log((2x+3)/(3-2x))]` `sin(logx)` ANSWER :B

Discussion

2036.	Statement 1 : If A is nxxn matrix then \|"adj(adj(adjA))\|=\|A\|^((n-1)^(3)) Statement 2 \|"adj A"\|=\|A\|^(n)
Answer» Statement - 1 is true, Statement -2 is true, Statement - 2 ISCORRECT explanation for Statement - 1 Statement - 1 is true, Statement -2 is true, Statement - 2 is not a correct explanation for Statement - 1 Statement - 1 is true, Statement -2 is false Statement -1 is false, Statement - 2 is true ANSWER :C

Discussion

2037.	If 3R=4r, then cosA+cosB+cosC=
Answer» 4 7 1 `(7)/(4)` ANSWER :D

Discussion

2038.	If : (csc alpha - cot alpha)(csc beta -cot beta)(csc gamma-cot gamma)=(csc alpha +cot alpha)(csc beta + cot beta)(csc gamma + cot gamma), then the value of each side is
Answer» 1 2 3 none of these Answer :A

Discussion

2039.	A relation R is defined on the set of N_(2) as follows : R: {(a,b): a,b in N and a=b^(2)} Check whether the following statements are true ? (i) For each a in N, (a,a) in R (ii) (a,b) in R and (b,c)in R, when a, b in N (iii) (a,b) in R and (b,c) in R rarr (a,c) in R, when a,b,c in N
Answer» ANSWER :(i) , (II), (III) all are FALSE

Discussion

2040.	Find the vertex, focus, and directrix of the following parabolas: y^(2)-2y+8x-23=0
Answer» ANSWER :LATUS rectum `-8`,vertex `(3,1)`, focus `(1,1)`,Axis `y-1`, DIRECTRIX `x-5`.

Discussion

2041.	Differentiate the following functions w.r.t. x: sin "" (x)/(2)
Answer» ANSWER :`(1)/(2) COS"" (X)/(2)`

Discussion

2042.	Let A ={ 2,4,6,8,10} . Determine the truth value of each of the following : EE x in A,xis a prime number.
Answer» ANSWER :TRUE

Discussion

2043.	If x = e ^(y+ e ^(y +...10oo)), x gt 0, then(dy)/(dx)is
Answer» `X/(1 + x)(x)/(1 + x)` `1/x` `(1 - x)/x` `(1 + x)/(x)` ANSWER :C

Discussion

2044.	The derivative of log \|sec x + tan x\| w.r.tx is
Answer» ANSWER :`SEC X`

Discussion

2045.	The solution of 2x+y+z=1,x-2y-3z=1,3x+2y+4z=5 is
Answer» 1,2,3 1,2,`-3` 1,`-3`,2 1,3,2 Answer :C

Discussion

2046.	If vec(a)= 3 vec(i)- vec(j)-2vec(k), vec(b)= 2vec(i) + 3vec(j) + vec(k), then (vec(a) + 2vec(b)) xx (2vec(a) - vec(b))=
Answer» `-25 vec(i) + 35 vec(J) -55vec(k)` `25 vec(i)-35 vec(j) + 55vec(k)` `25 vec(i) + 35vec(j)- 55vec(k)` `-25vec(i) -35vec(j)-55vec(k)` ANSWER :A

Discussion

2047.	Reduce the following equations to the normal form and find the values of p and alpha. 3x+4y+10=0 (use tables).
Answer» ANSWER : `X"COS"233^(@)8'+y"SIN"233^(@)8'=2`

Discussion

2048.	If the vectors lambda bar(i)-3bar(j)+5bar(k), and 2lambdabar(i)-lambda(j)-bar(k), are perpendicular to each other find lambda.
Answer» ANSWER :`-5/2 and 1 ;`

Discussion

2049.	Lagrange's mean value theorem cannot be applied for
Answer» `F(x) = LOG x` in [1,e] f(x) =` x- ( 1)/(x) ` in [ 1,3] `f(x) = sqrt( x^(2) - 4)` in [2,4] f(x) = `\|x \|` in [ -1,2] ANSWER :D

Discussion

2050.	IfC = 60 ^(@)" then "= ( b)/( c^(2) -a^(2)) + ( a) /(c^(2)- b^(2)) =
Answer» `-1` ` 1` ` 0` `2` ANSWER :C

Discussion

Explore topic-wise InterviewSolutions in .

Find the derivative of the function Iff(x) = tan ^(-1) ((5 tan ((x)/(2)) +4)/( 3))then show that f'(x) = (3)/(10 + 8 sin x )

Factorise x^2 - 6x + 8 into linear factors.

Find the modulus of the following complex numbers (3 +2i) (5-4i)

Iftan theta + sin theta = m, tan theta - sin theta = n " then " (m^(2)-n^(2))^(2)=

Given that P (3,2,-4), Q(5,4,-6), R (9,8-10) are collinear, find the ratio in which Q divides PR.

Find the equation of a circle circumscribing the triangle whose sides are 2x+y-3=0, 3x-y-7=0 and x-2y+1=0.

A ray of light passing through the point (8,3) and is reflected at (14,0) on x axis. Then the equationof the reflected ray

When the radius of a sphere decreases from 3cm to 2.98cm then the approximate decrease in volume of sphere is

Let A={9,10,11,12,13} and let f: A to N be defined by f(n)= the highest prime factor of n. Find the range of f.

The minimum andmaximum values of1-8 sin^(2) x cos^(2) xare

Calculate the standard deviation of the following distribution:

A man running a race course notes that the sum of the distances from the two flag posts from him is always 10 m and the distances between the flag posts is 8 m. Find the equation of track traced by man.

Evaluate the following limits : Lim_(xto2) (sin(e^(x-2)-1))/(log(x-1))

Differentiate the following w.r.t. x or t or u as the case may be: 10. z= (u)/( u^(2) +1)

Find the locus of the foot of the perpendicular from the orign to a variable straighht line which always passes through the fixed point (a,b).

The negation of the statement p: A circle is an ellipse is ………

If r=x+y+z and tan^(-1)sqrt((xr)/(yz))+tan^(-1)sqrt((yr)/(zx))+tan^(-1)sqrt((zr)/(xy))=kpi then the value of k is

vec(OA)= vec(a), vec(OB)= 10vec(a) + 2vec(b), vec(OC)= vec(b) where O, A, C are non-collinear points. Let 'p' denote area of quadrilateral OABC, 'q' denote area of parallelogram with OA, OC as adjacent sides, then (p)/(q)=

Let the sequence a_(n) be defined as follows: a_(1)= 1, a_(n)= a_(n-1) + 2 " for " n ge 2. Find first five terms and write corresponding series.

Find the equation of the line passing through the point (-4, 3)with slope 1/2.

What is theprobability of getting 3 white balls in a draw of 3 balls from a box containing 6 white and 4 red balls ?

A point Rwith X coordinate 4 lie on the line segment joining the points P(2,-3,4) and Q(8,0,10) find the coordinates of the pont R

At any point on the curve (a)/(x^(2))+(b)/(y^(2))=1, then y-intercept made by the tangent is proportional to

If A=[(2,-1,2),(1,3,-4)] and B=[(1,-2),(-3,0),(5,4)] then verify that (AB)^(T)=B^(T)A^(T)

Iftan x lt 2 then

Let f(x) be a function satisfying f(x+y) = f(x) f(y) for all x,y in N such that f(1) = 3 and sum_(x=1)^(n) f(x) = 120 . Then the vlaue of n is :

The point (4,1) undergoes the following transformations successively (i) reflection about the line y = x (ii) translation through a distance 2 units along the positive direction of y-axis . Then find the final position of the point.

If 3sin x+4cosax =7 has at least one solution, then the possible values of a as

Compute (i)(7!)/(5!) (ii) (12!)/((10!)(2!)

If bara, barb, barc are the sides of a triangle ABC then [barabarb barc] =

Which of the following sentences are statements? Justify Sum of opposite angles of a cyclic quadrilateral is 180^(@)

The orthocentre of the triangle formed by (0,0),(5,-1),(-2,3) is

Find the eccentricity, the coordinates of the foci, and the length of the latus rectum of the ellipse 2x^(2)+3y^(2)=1.

If f^(1)(x)=sin(logx)andy=f((2x+3)/(3-2x)) then (dy)/(dx) is

Statement 1 : If A is nxxn matrix then |"adj(adj(adjA))|=|A|^((n-1)^(3)) Statement 2 |"adj A"|=|A|^(n)

If 3R=4r, then cosA+cosB+cosC=

If : (csc alpha - cot alpha)(csc beta -cot beta)(csc gamma-cot gamma)=(csc alpha +cot alpha)(csc beta + cot beta)(csc gamma + cot gamma), then the value of each side is

A relation R is defined on the set of N_(2) as follows : R: {(a,b): a,b in N and a=b^(2)} Check whether the following statements are true ? (i) For each a in N, (a,a) in R (ii) (a,b) in R and (b,c)in R, when a, b in N (iii) (a,b) in R and (b,c) in R rarr (a,c) in R, when a,b,c in N

Find the vertex, focus, and directrix of the following parabolas: y^(2)-2y+8x-23=0

Differentiate the following functions w.r.t. x: sin "" (x)/(2)

Let A ={ 2,4,6,8,10} . Determine the truth value of each of the following : EE x in A,xis a prime number.

If x = e ^(y+ e ^(y +...10oo)), x gt 0, then(dy)/(dx)is

The derivative of log |sec x + tan x| w.r.tx is

The solution of 2x+y+z=1,x-2y-3z=1,3x+2y+4z=5 is

If vec(a)= 3 vec(i)- vec(j)-2vec(k), vec(b)= 2vec(i) + 3vec(j) + vec(k), then (vec(a) + 2vec(b)) xx (2vec(a) - vec(b))=

Reduce the following equations to the normal form and find the values of p and alpha. 3x+4y+10=0 (use tables).

If the vectors lambda bar(i)-3bar(j)+5bar(k), and 2lambdabar(i)-lambda(j)-bar(k), are perpendicular to each other find lambda.

Lagrange's mean value theorem cannot be applied for

IfC = 60 ^(@)" then "= ( b)/( c^(2) -a^(2)) + ( a) /(c^(2)- b^(2)) =