14949 + Interview Questions in Maths in Class 11 Page 240 InterviewSolution

11951.	Find the component statements of the following compound statements and check whether they are true or false. 100 is divisible by 3, 11 and 5.
Answer» ANSWER :100 is DIVISIBLE by 3,100 is divisible by 11 and 100 is divisible by 5 (False).

Discussion

11952.	Find the component statements of the following compound statements and check whether they are true or false. Number 3 is prime or it is odd.
Answer» ANSWER :NUMBER 3 is prime; number 3 is odd (TRUE).

Discussion

11953.	A line passes through (2,2) and is perpendicular to the line 3x + y=3. Its y-intercept is
Answer» `(1)/(3)` `(2)/(3)` `1` `(4)/(3)` ANSWER :D

Discussion

11954.	Minimum value of y = 256 sin^(2) x + 324 cosec^(2) x AA x in R is
Answer» 432 504 576 776 Answer :C

Discussion

11955.	Evaluate the following limits : Lim_( xto 0) (a^(sin x) - 1)/(sin x)
Answer» ANSWER :LOG a

Discussion

11956.	Find the value of cos^(2)45^(@)-sin^(2)15^(@)
Answer» ANSWER :`(SQRT(3))/(4)`

Discussion

11957.	Find the value of :""^(5) C _2
Answer» ANSWER :` 10 `

Discussion

11958.	Find the constant k so that the planes x-2y+kz=0 and 2x+5y-z=0 are at right angles. Find the equation of the plane through (1, -1, 1) and perpendicular to these planes.
Answer» ANSWER :`k=-8,42x-15y+9z-48=0`

Discussion

11959.	baraxx(barbxxbarc)+barbxx(barcxxbara)+barcxx(baraxxbarb)=
Answer» 0 `BAR0` 1 `baraxxbarbxxbarc` ANSWER :B

Discussion

11960.	Find r if .^(5)P_(r )=2 .^(6)P_(r-1)
Answer» ANSWER :3

Discussion

11961.	Find equation of the line passes from point of intersection of lines x+2y-3 =0 and 4x-y+7=0. Whose is parallel to line 5x+4y-20=0.
Answer» ANSWER :`15x+12y-7=0` which is REQUIRED EQUATION.

Discussion

11962.	If Cos^(-1)lamda+Cos^(-1)mu+Cos^(-1)V=3pi then lamda mu+muV+Vlamda=
Answer» 1)`3` 2)`0` 3)`3//4` 4)`-3` Answer :A

Discussion

11963.	A and B are two fixed points and if the vertex 'C' of DeltaABC moves such that cot A + cot B =k, then show that locus of 'C' is a line parallel to AB.
Answer» a line PERPENDICULAR AB a line parallel to AB a parabola not a straight line Answer :B

Discussion

11964.	A straight line whose inclination with the positive direction of the X-axis measured in the anti-clockwise sense is pi//3 makes positive intercept on the Y-axis. If the straight lie is at a distance of 4 from the origin, find its equation.
Answer» ANSWER :`SQRT(3)x-y+8=0`

Discussion

11965.	Intersecting the y-axis at a distance of 2 units above the origin and making an angle of 30^(@) with positive direction of the x-axis.
Answer» ANSWER :`X - SQRT3 y + 2 sqrt3 = 0 `

Discussion

11966.	State and prove any one of the Napier's formulae.
Answer» ANSWER :` (A-B)/(2) = LHS `

Discussion

11967.	Expand using Binomial Theorem (1+ x/2 - 2/x)^4 , x!= 0.
Answer» ANSWER :`16/x + 8/(x^2) - 32/(x^3) + 16/(x^4) - 4x + (x^2)/2 + (x^3)/2 + (x^4)/16 - 5`

Discussion

11968.	Ifr_1 = 36,r_2 = 18 r_3 = 12then the area ofDelta ABCis
Answer» ` 316` ` 216` ` 136` ` 116` Answer :B

Discussion

11969.	Find lim_(xto1)f(x), where f(x)={{:(x^(2)-1","xle1),(-x^(2)-1","xgt1):}
Answer» ANSWER :LIMIT does not EXIST at `X = 1`

Discussion

11970.	Show that the area of the triangle formed by the lines y= m_(1) x + c_(1) , y= m_(2) x + c_(2)and x = 0 is ((c_1 - c_2)^2)/( 2\| m_1 - m_2 \| ).
Answer» ANSWER :`((c_(2) - c_(1))^(2))/(2\|m_(1) - m_(2)\|)`

Discussion

11971.	Assertion (A): cos 1 le cos2 Reason (R) : In (0,pi) cosx is decreasing function
Answer» A is true, r is true and R is CORRECT explanation of A A is true, R is true and R is not correct explanation of A A is tre, R is false A is false, R is true Answer :D

Discussion

11972.	Given x + sin y = 2009 , x + 2009 cosy = 2 2008,where yin [0, (pi)/(2)] , then \|x = y \| = Where [*]represents the greatest integer function
Answer» 2008 2009 2100 2010 Answer :B

Discussion

11973.	Find the probility of getting a sum as 6 when two dice are thrown simultaneously .
Answer» ANSWER :`(5)/(36)`

Discussion

11974.	If p(x) is a polynomial such that p(x^2+1)={p(x)}^2+1 and p(0)=0 then p^1(0) is equal to
Answer» -1 0 1 2 Answer :C

Discussion

11975.	Solve sin 2 theta = (sqrt(5) -1)/(4)
Answer» ANSWER :`(N pi)/(2) +(-1)^(n)(pi)/(20), n in Z`

Discussion

11976.	Find the d.c's of a line that makes equal angles with the axes, and find number of such lines.
Answer» Answer :`(pm(1)/(SQRT(3)),pm(1)/(sqrt(3))pm(1)/(sqrt(3))),4`

Discussion

11977.	A computer while calculating the correlation coefficient between the variables x and y obtained the followingresults :n=25,sumx_(i)=125,sumy_(i)=100,sumx_(i)^(2)=650,sumy_(i)^(2)=460,sumx_(i)y_(i)=508 It washoweverlater discovered at the time of checking that it has copied down two pairs of obervations as (6,14) and (8,6) where as values were (8,12) and (6,8).Calculate the correct correlation coefficient of x and y.
Answer» ANSWER :0.667

Discussion

11978.	Differentiate the following functions w.r.t. x: cos 8x
Answer» ANSWER :`-8 SIN 8X`

Discussion

11979.	Let 10 vertical poles standing at equal distances on a straight line, substend the same angle of elevation alpha at a point O on this line and all the poles are on the same side of O. If the height of the longest pole is 'h' and the distance of he foot of the smallest pole from O is 'a', then the distance between two consecutive poles is
Answer» `(hsinalpha+acosalpha)/(9sinalpha)` `(hcosalpha-asinalpha)/(9cosalpha)` `(hcosalpha-asinalpha)/(9sinalpha)` `(hsinalpha+acosalpha)/(9cosalpha)` ANSWER :C

Discussion

11980.	If vec(OA)= (1, 2, -5), vec(OB)= (-2, 2,1), vec(OC)= (4, 3, -1) then perpendicular distance from 'C' to the line AB is
Answer» `sqrt19` `sqrt21` `sqrt23` `sqrt25` ANSWER :B

Discussion

11981.	Show that the following equations represents a pair of parallel lines and also find the distance between them. 9x^(2)-6xy+y^(2)+18x-6y+8=0
Answer» ANSWER :SQRT((2)/(5))`

Discussion

11982.	Prove that (cos3A + sin3A)/(cosA - sin A) = 1+ 2sin 2A.
Answer» ANSWER :`2+sqrt3`

Discussion

11983.	Which of the following sentences are statements? Give reasons for your answer The product of (-1) and 8 is 8.
Answer» Answer :This sentence is false as the PRODUCT is `(-8)`. THEREFORE, it is a statement.

Discussion

11984.	A cubic f(x)=ax^(3)+bx^(2)+cx+d vanishes at x=-2 and has relative maximum/minimum at x=-1 and x=1//3andifint_(1)^(1)f(x)dx=(14)/(3)The value of 'd' is
Answer» 5 2 0 `-4` ANSWER :B

Discussion

11985.	A cubic f(x)=ax^(3)+bx^(2)+cx+d vanishes at x=-2 and has relative maximum/minimum at x=- 1 and x=1//3 if int_(-1)^(1)f(x)dx=(14)/(3) f(x) decreases in the interval
Answer» `((-1)/(3),1)` `((-1)/(3),-1)` `(-1,(-1)/(3))` `(1,(3)/(2))` ANSWER :C

Discussion

11986.	If 0ltxlt1 then sqrt(1+x^(2))[{xcos(cot^(-1)x)+sin(cot^(-1)x)}^(2)-1]^(1/2) is equal ot
Answer» `X/(SQRT(1+x^(2)))` `x` `xsqrt(1+x^(2))` `sqrt(1+x^(2))` ANSWER :C

Discussion

11987.	A cubic f(x)=ax^(3)+bx^(2)+cx+d vanishes at x=-2 and has relative maximum/minimum at x=- 1 and x=1//3 if int_(-1)^(1)f(x)dx=(14)/(3) The value of 'c' is
Answer» `-2` `-1` 0 2 Answer :B

Discussion

11988.	If cosA+cosB+cosC=0=sinA+sinB+sinC then cos^(2)((A-B)/2)=
Answer» `1//2` `1//4` `3//4` 1 Answer :B

Discussion

11989.	A Force vec(F)= 2vec(i) - lamda vec(j) + 5vec(k) is applied at the point A(1,2,5). If its moment about the point (-1, -2, 3) is 16 vec(i)-6 vec(j) + 2lamda vec(k), then lamda=
Answer» 1 2 `-1` `-2` ANSWER :D

Discussion

11990.	The plane x =0, x =a, y =0, y =a , z = and z =afrom a
Answer» parallelopiped RECTANGULAR parallelopiped with DISTANCT edges Cube Tetrahedron ANSWER :C

Discussion

11991.	The product of first three terms of a G.P. is 1000. If we add 6 to its second term and 7 to its third term, the resulting three terms form an A.P. Find the terms of the G.P.
Answer» ANSWER :20,10,5,10,20

Discussion

11992.	(1+x-2x^(2))^(6)=1+a_(1),x+a_(2)x^(2)+….+a_(12)^(12)then the value of a_(2) +a_(4)+a_(6)+….+a_(12)=………
Answer» 32 63 64 31 Answer :D

Discussion

11993.	If A is 4xx4 matrix and \|2A\|=64,B="Adj A" then \|"Adj B"\|=
Answer» `2^(9)` `2^(18)` `2^(36)` `2^(6)` ANSWER :B

Discussion

11994.	A ray of light passing through the point (1,2) reflects on the X -axis at point A and the reflected ray passes through the point (5,3). Find the coordinates of A.
Answer» Answer :COORDINATES of POINT A `= ((13)/( 5) , 0)`

Discussion

11995.	In triangle ABC, if sinA cos B=1/4and 3 tanA = tanB, then cot^(2)A is equal to
Answer» 2 3 4 5 Answer :B

Discussion

11996.	Radius of the parametric equation represented by x = 2a ((1- t ^(2))/(1+t ^(2))),y = (4at)/(1+t ^(2))is
Answer» a `a ^(2)` `3A` `2A` ANSWER :D

Discussion

11997.	If alpha and beta aretwo different solutions lying between -(pi)/(2) and (pi)/(2) of the equation 2tan theta+sectheta=2 then tanalpha+tanbeta =
Answer» 0 1 `4//3` `8//3` ANSWER :D

Discussion

11998.	Let 'f' be a non-zero real valued continuous function satisfyingf(x + y) = f(x), f(y) . f(y) for allx, y in Riff(2) = 9 , then f(6) =
Answer» `3^(2)` `3^(6)` `3^(4)` `3^(3)` ANSWER :B

Discussion

11999.	Which of the following is not the value of sin 27^(@) - cos 27^(@)?
Answer» `- (sqrt ( 3 - SQRT5))/( 2)` `- (sqrt ( 5 - sqrt5))/(2)` `- (sqrt5 - 1)/(2 sqrt2)` none of these Answer :A

Discussion

12000.	lim_(xrarr-1)(x^7+1)/(x^8-1) = ….. .
Answer» ANSWER :`7/(-8)`

Discussion

Explore topic-wise InterviewSolutions in .

Find the component statements of the following compound statements and check whether they are true or false. 100 is divisible by 3, 11 and 5.

Find the component statements of the following compound statements and check whether they are true or false. Number 3 is prime or it is odd.

A line passes through (2,2) and is perpendicular to the line 3x + y=3. Its y-intercept is

Minimum value of y = 256 sin^(2) x + 324 cosec^(2) x AA x in R is

Evaluate the following limits : Lim_( xto 0) (a^(sin x) - 1)/(sin x)

Find the value of cos^(2)45^(@)-sin^(2)15^(@)

Find the value of :""^(5) C _2

Find the constant k so that the planes x-2y+kz=0 and 2x+5y-z=0 are at right angles. Find the equation of the plane through (1, -1, 1) and perpendicular to these planes.

baraxx(barbxxbarc)+barbxx(barcxxbara)+barcxx(baraxxbarb)=

Find r if .^(5)P_(r )=2 .^(6)P_(r-1)

Find equation of the line passes from point of intersection of lines x+2y-3 =0 and 4x-y+7=0. Whose is parallel to line 5x+4y-20=0.

If Cos^(-1)lamda+Cos^(-1)mu+Cos^(-1)V=3pi then lamda mu+muV+Vlamda=

A and B are two fixed points and if the vertex 'C' of DeltaABC moves such that cot A + cot B =k, then show that locus of 'C' is a line parallel to AB.

A straight line whose inclination with the positive direction of the X-axis measured in the anti-clockwise sense is pi//3 makes positive intercept on the Y-axis. If the straight lie is at a distance of 4 from the origin, find its equation.

Intersecting the y-axis at a distance of 2 units above the origin and making an angle of 30^(@) with positive direction of the x-axis.

State and prove any one of the Napier's formulae.

Expand using Binomial Theorem (1+ x/2 - 2/x)^4 , x!= 0.

Ifr_1 = 36,r_2 = 18 r_3 = 12then the area ofDelta ABCis

Find lim_(xto1)f(x), where f(x)={{:(x^(2)-1","xle1),(-x^(2)-1","xgt1):}

Show that the area of the triangle formed by the lines y= m_(1) x + c_(1) , y= m_(2) x + c_(2)and x = 0 is ((c_1 - c_2)^2)/( 2| m_1 - m_2 | ).

Assertion (A): cos 1 le cos2 Reason (R) : In (0,pi) cosx is decreasing function

Given x + sin y = 2009 , x + 2009 cosy = 2 2008,where yin [0, (pi)/(2)] , then |x = y | = Where [*]represents the greatest integer function

Find the probility of getting a sum as 6 when two dice are thrown simultaneously .

If p(x) is a polynomial such that p(x^2+1)={p(x)}^2+1 and p(0)=0 then p^1(0) is equal to

Solve sin 2 theta = (sqrt(5) -1)/(4)

Find the d.c's of a line that makes equal angles with the axes, and find number of such lines.

Differentiate the following functions w.r.t. x: cos 8x

If vec(OA)= (1, 2, -5), vec(OB)= (-2, 2,1), vec(OC)= (4, 3, -1) then perpendicular distance from 'C' to the line AB is

Show that the following equations represents a pair of parallel lines and also find the distance between them. 9x^(2)-6xy+y^(2)+18x-6y+8=0

Prove that (cos3A + sin3A)/(cosA - sin A) = 1+ 2sin 2A.

Which of the following sentences are statements? Give reasons for your answer The product of (-1) and 8 is 8.

A cubic f(x)=ax^(3)+bx^(2)+cx+d vanishes at x=-2 and has relative maximum/minimum at x=-1 and x=1//3andifint_(1)^(1)f(x)dx=(14)/(3)The value of 'd' is

A cubic f(x)=ax^(3)+bx^(2)+cx+d vanishes at x=-2 and has relative maximum/minimum at x=- 1 and x=1//3 if int_(-1)^(1)f(x)dx=(14)/(3) f(x) decreases in the interval

If 0ltxlt1 then sqrt(1+x^(2))[{xcos(cot^(-1)x)+sin(cot^(-1)x)}^(2)-1]^(1/2) is equal ot

A cubic f(x)=ax^(3)+bx^(2)+cx+d vanishes at x=-2 and has relative maximum/minimum at x=- 1 and x=1//3 if int_(-1)^(1)f(x)dx=(14)/(3) The value of 'c' is

If cosA+cosB+cosC=0=sinA+sinB+sinC then cos^(2)((A-B)/2)=

A Force vec(F)= 2vec(i) - lamda vec(j) + 5vec(k) is applied at the point A(1,2,5). If its moment about the point (-1, -2, 3) is 16 vec(i)-6 vec(j) + 2lamda vec(k), then lamda=

The plane x =0, x =a, y =0, y =a , z = and z =afrom a

The product of first three terms of a G.P. is 1000. If we add 6 to its second term and 7 to its third term, the resulting three terms form an A.P. Find the terms of the G.P.

(1+x-2x^(2))^(6)=1+a_(1),x+a_(2)x^(2)+….+a_(12)^(12)then the value of a_(2) +a_(4)+a_(6)+….+a_(12)=………

If A is 4xx4 matrix and |2A|=64,B="Adj A" then |"Adj B"|=

A ray of light passing through the point (1,2) reflects on the X -axis at point A and the reflected ray passes through the point (5,3). Find the coordinates of A.

In triangle ABC, if sinA cos B=1/4and 3 tanA = tanB, then cot^(2)A is equal to

Radius of the parametric equation represented by x = 2a ((1- t ^(2))/(1+t ^(2))),y = (4at)/(1+t ^(2))is

If alpha and beta aretwo different solutions lying between -(pi)/(2) and (pi)/(2) of the equation 2tan theta+sectheta=2 then tanalpha+tanbeta =

Let 'f' be a non-zero real valued continuous function satisfyingf(x + y) = f(x), f(y) . f(y) for allx, y in Riff(2) = 9 , then f(6) =

Which of the following is not the value of sin 27^(@) - cos 27^(@)?

lim_(xrarr-1)(x^7+1)/(x^8-1) = ….. .