14949 + Interview Questions in Maths in Class 11 Page 280 InterviewSolution

13951.	length of latus rectum of parabola y^2=4axwhich passes from (3,2) is ........... .
Answer» ANSWER :`4/3`

Discussion

13952.	If the focal distance of one ed of minor axis of an ellipse is k and distance betwnn foci is 2h then find the equation of the ellipse.
Answer» Answer :`(X^(2))/(K^(2))+(y^(2))/(K^(2)-H^(2))=1`

Discussion

13953.	Let y=(x+3) /( x).Find the instantaneous rate of change of y with respect to x at x = 3.
Answer» ANSWER :`=2X +3 - (3)/(x^2)`

Discussion

13954.	Prove that the equation of the parabola whose vertex and focus lie on x-axis at distances 'a' and 'b' from origin (bgta), is y^(2)=4(b-a)(x-a).
Answer»

Discussion

13955.	An analysis of monthly wages paid to workers in two firms A and B, belonging to the same industry, gives the following results: {:(,"Firm A","Firm B"),("No. of wage earners",586,648),("Mean of monthly wages","Rs 5253","Rs 5253"),("Variance of the distribution",100,121):} (i) Which firm A or B pays larger amount as monthly wages? (ii) Which firm, A or B, shows greater variability in individual wages?
Answer» ANSWER :(i) B, (II) B

Discussion

13956.	Reduce the following equations into slope - intercept form and find their slopes and the y-intercepts. (i) x + 7y = 0 , "" (ii) 6x + 3y - 5 = 0 , "" (iii) y = 0
Answer» Answer :`(i) y = - 1/7 x + 0 , - 1/7 , 0; (ii) y = - 2X + 5/3, -2 , 5/3; (iii) y = 0x + 0, 0, 0`

Discussion

13957.	If the 3^(rd) term in expansion (x+x^(log)10^(x))^(5) " is " 10^(6) then the value of x is ………..
Answer» 10 11 12 20 Answer :A

Discussion

13958.	If 4^(1+x)+4^(1-x)=10, find x.
Answer» ANSWER :`-1impliesx=(1)/(2),-(1)/(2)`.

Discussion

13959.	If Cos^(-1)x-Cos^(-1)(y/2)=alpha" then "4x^(2)-4xycosalpha+y^(2)=
Answer» `-4sin^(2)alpha` `4sin^(2)alpha` 4 `2 sin 2ALPHA` ANSWER :B

Discussion

13960.	cos(alpha-beta)=1 and cos(alpha+beta)=1//e, where alpha, beta in [-pi, pi]. Number of pairs of alpha, beta which satisfy both the equations
Answer» 0 1 2 4 Answer :D

Discussion

13961.	A card is drawn from a well shuffled pack of 52 cards . Findthe probability of 3 of heart or diamond.
Answer» ANSWER :`(2)/(52),i.e,(1)/(26)`

Discussion

13962.	If the letters of the word 'RACHIT' are arranged in all possible ways as listed in dictionary. Then, what is the rank of the word 'RACHIT' ?
Answer» ANSWER :481

Discussion

13963.	Simplify: i^(23)
Answer» ANSWER :`-i`

Discussion

13964.	IfDelta ABCis such thatangle A = 90 ^(@) , angle B ne angle C " then " ( b^(2) + c^(2))/( b^(2) - c^(2)) sin ( B- C)=
Answer» `(1)/(3) ` ` (1)/(2)` `1` ` ( 3)/(2)` ANSWER :C

Discussion

13965.	If in a triangle ABC, r_(1)=2, r_(2)=3 and r_(3) =6 then b=
Answer» 1 2 3 4 Answer :D

Discussion

13966.	If sintheta+costheta=1, then find the general value of theta.
Answer» Answer :`THEREFORE theta=npi+(-1)^(N)(pi)/(4)-(pi)/(4);ninZ`

Discussion

13967.	2.4 + 4.7 + 6.10+ …. upto (n-1) terms=
Answer» `2n^(3) + 2n^(2)` `(1)/( 6) (n^(3) + 3n^(2) + 1)` `2n^(3) + 2n` `2n^(3) - 2n^(2)` ANSWER :D

Discussion

13968.	Let z_(1) =2-i, z_(2) =-2 + i, Find (Re(z_(1)z_(2))/barz_(1))
Answer» ANSWER :`-2/5`

Discussion

13969.	If X= { a, b, c, d } and Y = { f, b, d, g}, find X ∩ Y
Answer» ANSWER :`{ B , d}`

Discussion

13970.	If X= { a, b, c, d } and Y = { f, b, d, g}, find X – Y
Answer» ANSWER :`{ a, C }`

Discussion

13971.	If the sum of the distances of a moving point in a plane from the axes is 1, then find the locus of the point. Thinking Process : Given that \|x\| + \| y\| =1 which gives four sides of a square.
Answer» ANSWER :LOCUS of POINT is SQUARE.

Discussion

13972.	Show that the following vectors are co-planar(ii) 5hati+6hatj+7hatk,7hati-8hatj+9hatk,-3hati+20hatj+5hatk.
Answer» Answer :` rArr 7 = 7 ` Which SATISFIES the (3) equation . THUS , ONE vector is a linear COMBINATION of other TWO vectors . Hence , the given vectors are co-planar

Discussion

13973.	If sin^(-1)(x)-cos^(-1)(x)=sin^-1(x-1) then x=
Answer» `0,1//2` `-1,1//2` `1,-1//2` `1//2,1` ANSWER :A

Discussion

13974.	Find the modulus of the complex number (1/(1-2i)+3/(1+i)) ((3+4i)/(2-4i))
Answer» ANSWER :`SQRT(41/8)`

Discussion

13975.	In triangle ABC//a(b^(2)+c^(2))cosA+b(c^(2)+a^(2))(cosB+c(a^(2)+b^(2))cosC=
Answer» `2ABC^(2)` `2a^(2)bc` `3abc` `2AB^(2)C` Answer :C

Discussion

13976.	Let bara=2bari+barj-2bark,barb=bari+barj. If barc is a vector such that bara.barc=abs(barc),abs(barc-bara)=2sqrt2 and the angle between (baraxxbarb) and barc is 30^(@), then abs((baraxxbarb)xxbarc)=
Answer» `2/3` `3/2` 2 3 Answer :B

Discussion

13977.	Consider the following statement : p : I shall pass, q : I study, then write the verbal translation of the symbolic representation p hArr q.
Answer» ANSWER :"I SHALL PASS IFF I STUDY."

Discussion

13978.	Find the derivative of v = cos [log(cotx)]
Answer» ANSWER :`2 cosec 2X sin (log (COT X ))`

Discussion

13979.	Find the value of p so that the three lines 3x + y-2=0, px+2y-3 =0 and 2x-y -3 =0 may intersect at one point.
Answer» ANSWER :`p=5`

Discussion

13980.	Find the equation of the parabola whose vertex is at (0,0) and the focus is at (0,a).
Answer» ANSWER :`X^(2)-4A(a-y)`

Discussion

13981.	Which of the following is/are true ?
Answer» `(dy)/(dx) ` for `y = SIN^(-1)(cosx) ` where `X in (0,pi)` , is - 1 `(dy)/(dx) ` for `y = sin^(-1)(cosx) ` where `x in (pi,2pi)` , is - 1 `(dy)/(dx) ` for `y = cos^(-1)(cosx) ` where `x in (-pi/2,pi/2)` is -1 `(dy)/(dx) ` for `y = cos^(-1)(cosx) ` where `x in (pi/2,(3pi)/2)` is -1 ANSWER :A::B::C

Discussion

13982.	1/(sin10^(@))-sqrt3/(cos10^(@))=
Answer» 4 `-4` 2 `-2` ANSWER :A

Discussion

13983.	Let g(x) = ax+b, where a lt 0 and g is defined from [1,3] onto [0,2] then prove that cot(cos^(-1)(abs(sinx)+abs(cosx))+sin^(-1)(-abs(cosx)+abs(sinx)))=
Answer» `g(1)` `g(3)` `g(2)` `g(0)` Answer :B

Discussion

13984.	Write the converse of the following statements: If you a do all the exercises in the book, you get an A grade in the class.
Answer» ANSWER :If you get an an grade in a class, then you have DONE all the exercises of the BOOK.

Discussion

13985.	Graph of the function f : R rarr R,f(x)=3x+5 is …. .
Answer» ANSWER :STRAIGHT LINE

Discussion

13986.	The square of the distance of the point of intersection of the line 6x^2-5xy-6y^2+x+5y+1=0 from the origin is
Answer» `74//169` `85//169` `74/185` `2//13` ANSWER :D

Discussion

13987.	An obserever finds that the angular elevation of a tower is theta.On advancing a metres towards the tower the elevation is 45^(@) and an advancing 'b' metres nearer the elevation is 90^(@)-theta then the height of the tower in metres is
Answer» `(AB)/(a+B)` `(ab)/(a-b)` `(2AB)/(a+b)` `(2ab)/(a-b)` ANSWER :B

Discussion

13988.	For x != 0, 1, define f_(1)(x)=x, f_(2)(x)=1/x, f_(3)(x)=1-x, f(5) (x)=(x-1)//x, f_(6)(x)=x//(x-1) This family of functions is closed under composition that is , the composition of any two of these functions is again one of these. Let G be a function such that GOf_(3)=f_(6). Then G is equal to
Answer» `f_(5)` `f_(4)` `f_(3)` `f_(2)` Answer :A

Discussion

13989.	For x != 0, 1, define f_(1)(x)=x, f_(2)(x)=1/x, f_(3)(x)=1-x, f(5) (x)=(x-1)//x, f_(6)(x)=x//(x-1) This family of functions is closed under composition that is , the composition of any two of these functions is again one of these. Let H be a function such that f_(4)OH=f_(5). Then H is equal to
Answer» `f_(1)` `f_(2)` `f_(3)` `f_(4)` Answer :D

Discussion

13990.	A sphere of radius 'a' subtends an angle 60^(@) at a point P. Then the distance of P from the centre of the sphere is.
Answer» ` 6 cm ` ` 2 cm ` ` 8 cm ` ` 4 cm ` ANSWER :C

Discussion

13991.	Find the derivative of the w.r.t.x log (( sqrt (e ^(x) +1 )-1)/( sqrt (e ^(x) + 1 )+1))
Answer» ANSWER :`(1)/( SQRT (1 + E ^(X)))`

Discussion

13992.	Evaluate the following limits : Lim_( xto 4) (3 - sqrt(5+x))/(x-4)
Answer» ANSWER :`-1/6`

Discussion

13993.	Using contrapositive method prove that if n^(2) is an even integer, then n is also an even integers.
Answer» ANSWER :EVEN NUMBER.

Discussion

13994.	Let A={x:x inZ^(+)}, B= {x:x is a multiple of 3, inZ}, C={x:xis a negative integer} , D= {x:x is an odd integer}. Find : (i) AcapB(ii)BcapC (iii) CcapD (iv) AcapC(v) AcapD (vi) BcapD.
Answer» Answer :(i) `{3n:N INZ^(+)}` (ii) {3n : n is a negative integer} (iii) `{-1,-3,-5,-7,…}` (iv) `phi` (V) {1,3,5,7,…..} (vi) {…, -15,-9,-3,9,15}.

Discussion

13995.	For 0 lt x le pi, sinh^(-1) (cotx)=
Answer» 1)`LOG("cot"(x)/(2))` `2)log("TAN"(x)/(2))` 3)`log(1+cotx)` 4)`log(1+tanx)` ANSWER :A

Discussion

13996.	Let R be a relation from N to N defined by R={(a,b): a, b in N and a=b^(2)). Are the following true? (i) (a,a) in R," for all " a in N (ii) (a,b) in R," implies "(b,a) in R (iii) (a,b) in R, (b,c) in R" implies "(a,c) in R. Justify your answer in each case.
Answer» ANSWER :not TRUE

Discussion

13997.	One card is draw from a pack of 52 cards being equally likely to be drawn . Findthe probability ofthe card drawn to be either red or a king .
Answer» ANSWER :`(28)/(52),i.e,(7)/(13)`

Discussion

13998.	One card is draw from a pack of 52 cards being equally likely to be drawn . Findthe probability ofthe card drawn to be redanda king
Answer» ANSWER :`(2)/(52),i.e,(1)/(26)`

Discussion

13999.	One card is draw from a pack of 52 cards being equally likely to be drawn . Findthe probability ofthe card drawn to be a king
Answer» ANSWER :`(4)/(52),i.e,(1)/(13)`

Discussion

14000.	One card is draw from a pack of 52 cards being equally likely to be drawn . Findthe probability ofthe card to be red
Answer» ANSWER :`(26)/(52),i.e,(1)/(2)`

Discussion

Explore topic-wise InterviewSolutions in .

length of latus rectum of parabola y^2=4axwhich passes from (3,2) is ........... .

If the focal distance of one ed of minor axis of an ellipse is k and distance betwnn foci is 2h then find the equation of the ellipse.

Let y=(x+3) /( x).Find the instantaneous rate of change of y with respect to x at x = 3.

Prove that the equation of the parabola whose vertex and focus lie on x-axis at distances 'a' and 'b' from origin (bgta), is y^(2)=4(b-a)(x-a).

Reduce the following equations into slope - intercept form and find their slopes and the y-intercepts. (i) x + 7y = 0 , "" (ii) 6x + 3y - 5 = 0 , "" (iii) y = 0

If the 3^(rd) term in expansion (x+x^(log)10^(x))^(5) " is " 10^(6) then the value of x is ………..

If 4^(1+x)+4^(1-x)=10, find x.

If Cos^(-1)x-Cos^(-1)(y/2)=alpha" then "4x^(2)-4xycosalpha+y^(2)=

cos(alpha-beta)=1 and cos(alpha+beta)=1//e, where alpha, beta in [-pi, pi]. Number of pairs of alpha, beta which satisfy both the equations

A card is drawn from a well shuffled pack of 52 cards . Findthe probability of 3 of heart or diamond.

If the letters of the word 'RACHIT' are arranged in all possible ways as listed in dictionary. Then, what is the rank of the word 'RACHIT' ?

Simplify: i^(23)

IfDelta ABCis such thatangle A = 90 ^(@) , angle B ne angle C " then " ( b^(2) + c^(2))/( b^(2) - c^(2)) sin ( B- C)=

If in a triangle ABC, r_(1)=2, r_(2)=3 and r_(3) =6 then b=

If sintheta+costheta=1, then find the general value of theta.

2.4 + 4.7 + 6.10+ …. upto (n-1) terms=

Let z_(1) =2-i, z_(2) =-2 + i, Find (Re(z_(1)z_(2))/barz_(1))

If X= { a, b, c, d } and Y = { f, b, d, g}, find X ∩ Y

If X= { a, b, c, d } and Y = { f, b, d, g}, find X – Y

If the sum of the distances of a moving point in a plane from the axes is 1, then find the locus of the point. Thinking Process : Given that |x| + | y| =1 which gives four sides of a square.

Show that the following vectors are co-planar(ii) 5hati+6hatj+7hatk,7hati-8hatj+9hatk,-3hati+20hatj+5hatk.

If sin^(-1)(x)-cos^(-1)(x)=sin^-1(x-1) then x=

Find the modulus of the complex number (1/(1-2i)+3/(1+i)) ((3+4i)/(2-4i))

In triangle ABC//a(b^(2)+c^(2))cosA+b(c^(2)+a^(2))(cosB+c(a^(2)+b^(2))cosC=

Let bara=2bari+barj-2bark,barb=bari+barj. If barc is a vector such that bara.barc=abs(barc),abs(barc-bara)=2sqrt2 and the angle between (baraxxbarb) and barc is 30^(@), then abs((baraxxbarb)xxbarc)=

Consider the following statement : p : I shall pass, q : I study, then write the verbal translation of the symbolic representation p hArr q.

Find the derivative of v = cos [log(cotx)]

Find the value of p so that the three lines 3x + y-2=0, px+2y-3 =0 and 2x-y -3 =0 may intersect at one point.

Find the equation of the parabola whose vertex is at (0,0) and the focus is at (0,a).

Which of the following is/are true ?

1/(sin10^(@))-sqrt3/(cos10^(@))=

Let g(x) = ax+b, where a lt 0 and g is defined from [1,3] onto [0,2] then prove that cot(cos^(-1)(abs(sinx)+abs(cosx))+sin^(-1)(-abs(cosx)+abs(sinx)))=

Write the converse of the following statements: If you a do all the exercises in the book, you get an A grade in the class.

Graph of the function f : R rarr R,f(x)=3x+5 is …. .

The square of the distance of the point of intersection of the line 6x^2-5xy-6y^2+x+5y+1=0 from the origin is

An obserever finds that the angular elevation of a tower is theta.On advancing a metres towards the tower the elevation is 45^(@) and an advancing 'b' metres nearer the elevation is 90^(@)-theta then the height of the tower in metres is

For x != 0, 1, define f_(1)(x)=x, f_(2)(x)=1/x, f_(3)(x)=1-x, f(5) (x)=(x-1)//x, f_(6)(x)=x//(x-1) This family of functions is closed under composition that is , the composition of any two of these functions is again one of these. Let G be a function such that GOf_(3)=f_(6). Then G is equal to

For x != 0, 1, define f_(1)(x)=x, f_(2)(x)=1/x, f_(3)(x)=1-x, f(5) (x)=(x-1)//x, f_(6)(x)=x//(x-1) This family of functions is closed under composition that is , the composition of any two of these functions is again one of these. Let H be a function such that f_(4)OH=f_(5). Then H is equal to

A sphere of radius 'a' subtends an angle 60^(@) at a point P. Then the distance of P from the centre of the sphere is.

Find the derivative of the w.r.t.x log (( sqrt (e ^(x) +1 )-1)/( sqrt (e ^(x) + 1 )+1))

Evaluate the following limits : Lim_( xto 4) (3 - sqrt(5+x))/(x-4)

Using contrapositive method prove that if n^(2) is an even integer, then n is also an even integers.

Let A={x:x inZ^(+)}, B= {x:x is a multiple of 3, inZ}, C={x:xis a negative integer} , D= {x:x is an odd integer}. Find : (i) AcapB(ii)BcapC (iii) CcapD (iv) AcapC(v) AcapD (vi) BcapD.

For 0 lt x le pi, sinh^(-1) (cotx)=

Let R be a relation from N to N defined by R={(a,b): a, b in N and a=b^(2)). Are the following true? (i) (a,a) in R," for all " a in N (ii) (a,b) in R," implies "(b,a) in R (iii) (a,b) in R, (b,c) in R" implies "(a,c) in R. Justify your answer in each case.

One card is draw from a pack of 52 cards being equally likely to be drawn . Findthe probability ofthe card drawn to be either red or a king .

One card is draw from a pack of 52 cards being equally likely to be drawn . Findthe probability ofthe card drawn to be redanda king

One card is draw from a pack of 52 cards being equally likely to be drawn . Findthe probability ofthe card drawn to be a king

One card is draw from a pack of 52 cards being equally likely to be drawn . Findthe probability ofthe card to be red