14949 + Interview Questions in Maths in Class 11 Page 75 InterviewSolution

3701.	Equation of directrix of Conic x^(2) + 2x - y^(2) + 5 = 0 is …….
Answer» `x = pm 1` `x = pm 2` `y = pm SQRT(2)` `y = pm sqrt(3)` ANSWER :C

Discussion

3702.	If the rate of change in the area of a circle is it pi sq. cm/sec, then find the rate of change in the radius of the circle when the radius is 10cm.
Answer» ANSWER :0.06 cm/sec

Discussion

3703.	Find the condition that sec^2theta=(4xy)/((x+y)^2) is true.
Answer» `X + y != 0` `x = y, x != 0` x = y `x !=0, y !=0` ANSWER :B

Discussion

3704.	Let f(x)=3x^(10)-7x+5x-21x^(3)+3x^(2)-7, then the value of underset(h to 0)(Lt)(f(1-h)f(1))/(h^(3)+3h) is
Answer» `-(50)/(3)` `(22)/(3)` 13 `(53)/(3)` ANSWER :D

Discussion

3705.	nth tern of some sequence are given below. Which term can be the n th term of an AP?
Answer» `a_n=n(n+1)` `a_n=2+5n` `a_n=2^n+2` `a_n=n^2+n+1` ANSWER :B

Discussion

3706.	The value of
Answer» `(1)/(2)` 1 0 2 Answer :D

Discussion

3707.	The sum of two positive numbers is 48. The numbers so that the sum of their squares is a minimum are
Answer» 36,12 32,16 24,24 22,26 Answer :C

Discussion

3708.	If the normal to the curve y=f(x) at (1, 2) make an angle (3pi)/(4) with positive X-axis, then f'(1)=
Answer» `-1` 1 `-3//4` `(4//3)` ANSWER :B

Discussion

3709.	If x_(1)=2tan^(-1)((1+x)/(1-x)), x_(2)=sin^(-1)((1-x^(2))/(1+x^(2)))," where "x in (0, 1)," then "x_(1)+x_(2) is equal to
Answer» 0 `2PI` `PI` NONE of these Answer :C

Discussion

3710.	Differentiate the following function w.r.t. x. tan (5x + 7)
Answer» Answer :`5 SEC^(2) (5X +7)`

Discussion

3711.	The table shows the averages prices of coffee, sugar and milk in 1979 and 1980, and the weights used to calculate the cost of making a cup of coffee, C:alculate, correct to one decimal place, the index number for the cost of a cup of coffee in 1980 using. (i) weighted price relatives, (ii) weighted aggregates taking the index number for 1979 as 100 in each case.
Answer» ANSWER :(i) `159.3` (II) `136.8`

Discussion

3712.	lim_(xrarr0)(e^(sinx)-1)/x
Answer» ANSWER :1

Discussion

3713.	A flag staff stands vertically on a pillar. The height of the flag staff being double the height ofthe pillar. A man on the ground at a distance finds both pillar and the flag staff subtends equal angle 'theta' at his eye then theta =
Answer» `pi/12` `pi/8` `pi/10` `pi/6` ANSWER :D

Discussion

3714.	(i) Find the equation of a line passing through the points (a,b) and (ab,b^(2)). (ii) The vertices of DeltaABC are A(2,5), B(3,2) and C(5,6). Find the equation of the bisector of /_A.
Answer» ANSWER :`(i) bx-ay=0` `(II) x+2y=12`

Discussion

3715.	Let ABC be an isosceles triangle with base BC. If 'r'is the radius of the circle inscribed in triangle ABC and r_(1)is the radius of the circle escribed opposite to the angle A, then the product r_(1)rcan be equal to
Answer» `R^(2)SIN^(2)A` `R^(2)sin^(2)2B` `(1)/(2)a^(2)` `(a^(2))/(4)` Answer :B::C

Discussion

3716.	Each side of an equilateral triangle expands at the rate of 2 cm/sec. The rate of increase of its area when each side is 10 cm is (in cm^2/sec)
Answer» `10sqrt(2)` sq.cms/sec `10sqrt(3)` sq.cms/sec 10 sq.cms/sec 5 sq.cms/sec Answer :B

Discussion

3717.	Find the point to which the origin has to be shifted to eliminate x and yterms in the equation 14x^(2) - 4xy + 11y^(2) - 36x + 48y + 41 = 0
Answer» ANSWER :We GET a = 14, b = 11, c = 41, f = 24, g = -18, h = - 2

Discussion

3718.	If the point (3,-2) is transformed to (-2,1) which the origin is shifted to P, then P=
Answer» <P> ANSWER :`:. P = (5, -3)`

Discussion

3719.	Find the equation of a line that cuts off equal intercepts on the coordinate axes and passes through the point (2, 3).
Answer» ANSWER :`x+y-5=0`

Discussion

3720.	If cos theta- sin theta=(1)/(5), theta lt theta lt (pi)/(2) then match the following:
Answer» 1-,a 2-B,3-c,4-d 1-b, 2-c, 3-d, d,4-b 1-c,2-d, 3-a, 4-b 1-d, 2-a, a,3-b, 4-c Answer :B

Discussion

3721.	Find the centre and radius of the circle 2x^(2) + 2y^(2) - x = 0
Answer» ANSWER :`1/4`

Discussion

3722.	If 4,5 are twosides of a triangleand includedangle60 ^(@),then itsarea is
Answer» ` 3SQRT3` ` 2SQRT3` ` 4 sqrt3 ` ` 5 sqrt3` ANSWER :D

Discussion

3723.	If U={1,2,3....9},A={1,3,5,7,9} and B={2,3,5,7}, then show that (i) (A cupB)'=A'capB' (ii) (AcapB)'=A'cupB'.
Answer»

Discussion

3724.	Find the domains of the following functions f(x) = log\|x\|
Answer» ANSWER :`R - { 0 }`

Discussion

3725.	bar(a), bar(b), bar(c) are three vectors of which every pair is non-collinear. If the vectors bar(a)+2bar(b) and bar(b)+3bar(c) are collinear with bar(c) and bar(a) respectively, then bar(a)+2bar(b)+6bar(c)=
Answer» `BAR(a)` `bar(B)` `bar(C)` `bar(0)` ANSWER :D

Discussion

3726.	Given z_(1)=1 -i, z_(2)= -2 + 4i, calculate the values of a and b if a + bi= (z_(1)z_(2))/(z_(1))
Answer» ANSWER :a=4, b=2

Discussion

3727.	Value of 'c' of Rolle's theorem for f(x) = {:{ (x^(2) + 1,"when "0lexle1),(3 - x,"when "1lexle2):}
Answer» 1 0 `-1` does not exists Answer :D

Discussion

3728.	Let f : R to Rbe defined, by {{:(k-2x,"if"" "x le -1),(2x+3,"if" " "xgt -1):} If f has a local minimum at x=-1 , then a possible value of k is
Answer» 1 0 `-1/2` -1 Answer :D

Discussion

3729.	One urn contains two black balls (labelled B_(1) and B_(2) ) and one white ball. A second urn contains one black ball and two white balls (labelled W_(1), and W_(2) ). Suppose the following experiment is performed. One of the two urns is chosen at random. Next a ball is randomly chosen from the urn. Then a second ball is chosen at random from the same urn without replacing the first ball. (i) Write the sample space showing all possible outcomes (ii) What is the probability that two black balls are chosen ? (iii) What is the probability that two balls of opposite colour are chosen ?
Answer» ANSWER :(i) 12 (ii) `(1)/(6)` (iii) `(2)/(3)`

Discussion

3730.	r ( cot "" ( B)/(2)+ cot "" ( C) /(2)) =
Answer» `a ` `B ` ` C ` ` 0` ANSWER :A

Discussion

3731.	If 0lt theta ltpi and 81^(sin^(2))+81^(cos^(2)theta)=30, then theta is
Answer» `30^(@)` `60^(@)` `120^(@)` `150^(@)` Answer :A::B::C::D

Discussion

3732.	A card is drawn from a pack of cards . Findthe probability that it is an ace
Answer» ANSWER :`=(1)/(13)`.

Discussion

3733.	matchthe following
Answer» `X^(-x)` `2/(1+x^(2))` `(-2X)/(1+x^(2)^(2))` x Answer :C

Discussion

3734.	Differentiate from first principles: 5. sqrt( x+1), x gt -1
Answer» ANSWER :`(1)/( 2 SQRT(X +1) )`

Discussion

3735.	The value of cos^(2)48^(@)-sin^(2)12^(@) is
Answer» `(sqrt(5)+1)/(8)` `(sqrt(5)-1)/(8)` `(sqrt(5)+1)/(5)` `(sqrt(5)+1)/(2sqrt(2))` ANSWER :A

Discussion

3736.	A= {x : x in N, x^(2)+4=0} then,
Answer» `A= {-2, 2}` `A= {2}` `A= PHI` `A= {phi}` ANSWER :C

Discussion

3737.	A farm house uses atleast 800 kg of special food daily. The special food is a mixture of corn and soyabean with the following compositions The dietary requirements of the special food stipulate atleast 30% protein and at most 5% fibre. Determine the daily minimum cost of the food mix.
Answer» ANSWER :RS 11294

Discussion

3738.	Let 'f' be an injective mapping with domain {x,y,z} and range {1,2,3} such that exactly one of the following statements is correct and the remaining are false f(x)=1, f(y) != 1, f(z) != 2,then f^(-1)(1)=
Answer» x y z 2 Answer :B

Discussion

3739.	Out of 80studentsin a class , 30 passedin Mathematices , 20 in Electronics and 10in both. Ifone students is selectedat random . The probabilitythat thehas passedin noneof the subjectin
Answer» `(3)/(5)` `(1)/(4)` `(3)/(2)` `(1)/(4)` Answer :D

Discussion

3740.	If the straight line through the point P(3,4) makes an angle pi//6 with the x-axis in the positive direction and meets the line 3x+5y+1=0 at Q the length PQ is
Answer» `30` `30(SQRT(3)-1)` `sqrt(3)-1` `30(3sqrt(3)-5)` ANSWER :D

Discussion

3741.	Find the value of tan(22^(@)30').
Answer» ANSWER :`(1)/(SQRT(2)+1)`

Discussion

3742.	Write the negation of the following statements: sqrt2 is not a complex number
Answer» ANSWER :`SQRT2` is a COMPLEX NUMBER

Discussion

3743.	Find the equation of tangents to the ellipse 4x^(2)+5y^(2)=20 which are perpendicular to the line 3x+2y-5=0
Answer» ANSWER :`2x-3y+2sqrt(14)=0`

Discussion

3744.	If f(x) = (cos x + i sin x)(cos 3x + i sin 3x) ….(cos (2n - 1)x + i(sin(2n - 1)x), then f^(11)(x) is
Answer» `N^2f(X) ` `-n^(4)F(x)` `-n^2f(x)` `n^4f(x)` Answer :B

Discussion

3745.	(cos^(3)21^(@)+cos^(3)39^(@))/(cos21^(@)+cos39^(@))=
Answer» `3//2` `2//3` `3//4` `4//3` ANSWER :C

Discussion

3746.	AA n in N, 7.5^(2n ) + 12.6^(n) is divisible by
Answer» `13` `19` `247` `26` ANSWER :B

Discussion

3747.	Find the number of terms in the expansion of the following : (2x+1/y)^(7)+(2x-1/y)^(7)
Answer» ANSWER :4

Discussion

3748.	The period of the function f(x) = [6x+7] + cos pi x- 6x, where [.] denotes the greatest integer function, is
Answer» `3` `2pi` `2` `PI` ANSWER :C

Discussion

3749.	Find the equation of a line passing through the point of intersection of the lines 5x+y-3=0 and x+3y+1=0 and made equal angles from the co-ordinates axes.
Answer» ANSWER :`7x+7y-1=0`, `7x-7y-9=0`

Discussion

3750.	There are n letters and n addressed envelopes . If the letters are placed in the envelopes at random , what is the probability that all the letters are not placed in the right evelope ?
Answer» ANSWER :`1-(1)/(N!)`

Discussion

Explore topic-wise InterviewSolutions in .

Equation of directrix of Conic x^(2) + 2x - y^(2) + 5 = 0 is …….

If the rate of change in the area of a circle is it pi sq. cm/sec, then find the rate of change in the radius of the circle when the radius is 10cm.

Find the condition that sec^2theta=(4xy)/((x+y)^2) is true.

Let f(x)=3x^(10)-7x+5x-21x^(3)+3x^(2)-7, then the value of underset(h to 0)(Lt)(f(1-h)f(1))/(h^(3)+3h) is

nth tern of some sequence are given below. Which term can be the n th term of an AP?

The value of

The sum of two positive numbers is 48. The numbers so that the sum of their squares is a minimum are

If the normal to the curve y=f(x) at (1, 2) make an angle (3pi)/(4) with positive X-axis, then f'(1)=

If x_(1)=2tan^(-1)((1+x)/(1-x)), x_(2)=sin^(-1)((1-x^(2))/(1+x^(2)))," where "x in (0, 1)," then "x_(1)+x_(2) is equal to

Differentiate the following function w.r.t. x. tan (5x + 7)

lim_(xrarr0)(e^(sinx)-1)/x

A flag staff stands vertically on a pillar. The height of the flag staff being double the height ofthe pillar. A man on the ground at a distance finds both pillar and the flag staff subtends equal angle 'theta' at his eye then theta =

(i) Find the equation of a line passing through the points (a,b) and (ab,b^(2)). (ii) The vertices of DeltaABC are A(2,5), B(3,2) and C(5,6). Find the equation of the bisector of /_A.

Let ABC be an isosceles triangle with base BC. If 'r'is the radius of the circle inscribed in triangle ABC and r_(1)is the radius of the circle escribed opposite to the angle A, then the product r_(1)rcan be equal to

Each side of an equilateral triangle expands at the rate of 2 cm/sec. The rate of increase of its area when each side is 10 cm is (in cm^2/sec)

Find the point to which the origin has to be shifted to eliminate x and yterms in the equation 14x^(2) - 4xy + 11y^(2) - 36x + 48y + 41 = 0

If the point (3,-2) is transformed to (-2,1) which the origin is shifted to P, then P=

Find the equation of a line that cuts off equal intercepts on the coordinate axes and passes through the point (2, 3).

If cos theta- sin theta=(1)/(5), theta lt theta lt (pi)/(2) then match the following:

Find the centre and radius of the circle 2x^(2) + 2y^(2) - x = 0

If 4,5 are twosides of a triangleand includedangle60 ^(@),then itsarea is

If U={1,2,3....9},A={1,3,5,7,9} and B={2,3,5,7}, then show that (i) (A cupB)'=A'capB' (ii) (AcapB)'=A'cupB'.

Find the domains of the following functions f(x) = log|x|

bar(a), bar(b), bar(c) are three vectors of which every pair is non-collinear. If the vectors bar(a)+2bar(b) and bar(b)+3bar(c) are collinear with bar(c) and bar(a) respectively, then bar(a)+2bar(b)+6bar(c)=

Given z_(1)=1 -i, z_(2)= -2 + 4i, calculate the values of a and b if a + bi= (z_(1)z_(2))/(z_(1))

Value of 'c' of Rolle's theorem for f(x) = {:{ (x^(2) + 1,"when "0lexle1),(3 - x,"when "1lexle2):}

Let f : R to Rbe defined, by {{:(k-2x,"if"" "x le -1),(2x+3,"if" " "xgt -1):} If f has a local minimum at x=-1 , then a possible value of k is

r ( cot "" ( B)/(2)+ cot "" ( C) /(2)) =

If 0lt theta ltpi and 81^(sin^(2))+81^(cos^(2)theta)=30, then theta is

A card is drawn from a pack of cards . Findthe probability that it is an ace

matchthe following

Differentiate from first principles: 5. sqrt( x+1), x gt -1

The value of cos^(2)48^(@)-sin^(2)12^(@) is

A= {x : x in N, x^(2)+4=0} then,

A farm house uses atleast 800 kg of special food daily. The special food is a mixture of corn and soyabean with the following compositions The dietary requirements of the special food stipulate atleast 30% protein and at most 5% fibre. Determine the daily minimum cost of the food mix.

Let 'f' be an injective mapping with domain {x,y,z} and range {1,2,3} such that exactly one of the following statements is correct and the remaining are false f(x)=1, f(y) != 1, f(z) != 2,then f^(-1)(1)=

Out of 80studentsin a class , 30 passedin Mathematices , 20 in Electronics and 10in both. Ifone students is selectedat random . The probabilitythat thehas passedin noneof the subjectin

If the straight line through the point P(3,4) makes an angle pi//6 with the x-axis in the positive direction and meets the line 3x+5y+1=0 at Q the length PQ is

Find the value of tan(22^(@)30').

Write the negation of the following statements: sqrt2 is not a complex number

Find the equation of tangents to the ellipse 4x^(2)+5y^(2)=20 which are perpendicular to the line 3x+2y-5=0

If f(x) = (cos x + i sin x)(cos 3x + i sin 3x) ….(cos (2n - 1)x + i(sin(2n - 1)x), then f^(11)(x) is

(cos^(3)21^(@)+cos^(3)39^(@))/(cos21^(@)+cos39^(@))=

AA n in N, 7.5^(2n ) + 12.6^(n) is divisible by

Find the number of terms in the expansion of the following : (2x+1/y)^(7)+(2x-1/y)^(7)

The period of the function f(x) = [6x+7] + cos pi x- 6x, where [.] denotes the greatest integer function, is

Find the equation of a line passing through the point of intersection of the lines 5x+y-3=0 and x+3y+1=0 and made equal angles from the co-ordinates axes.

There are n letters and n addressed envelopes . If the letters are placed in the envelopes at random , what is the probability that all the letters are not placed in the right evelope ?