28278 + Interview Questions in Maths in Class 12 Page 129 InterviewSolution

6401.	If A,B,C are 3 points on a parabola , Delta _1, Delta_2are the areas of triangles is formed by the points A, B,C and the tangents at A, B, C . IfDelta_1, Delta _2are the roots of px^(2) +qx +r=0then condition is
Answer» `9Q^(2) =2pr` ` 9pr= 2q^(2) ` ` 9p^(2) = 2qr` ` 2P^(2) =9qr ` Answer :B

Discussion

6402.	A six faced dice is thrown a dozen times. Probability that six is not obtained even one is
Answer» `((5)/(6))^(12)` `((5)/(6))^(11)` `((1)/(6))^(12)` NONE of these Answer :A

Discussion

6403.	int_(0)^(pi//2)(200 sin x + 100 cos x)/(sin x + cos x) dx =
Answer» `50pi` `25 PI` `75 pi` `150 pi` ANSWER :C

Discussion

6404.	1 +(2^3)/(1!) x + (3^3)/(2!) x^2 + ....oo=
Answer» `(x^3+6X^(2) -7x -1)e^(x)` `(x^3+6x^(2) +7x -1)e^(x)` `(x^3+7x^(2) -6x +1)e^(x)` `(x^3+x^(2) -2x -1)e^(x)` ANSWER :B

Discussion

6405.	Find thevalues of the following : tan""^(-1)(1)+"cos"^(-1)-1/2+""sin"^(-1)-1/2
Answer» ANSWER :`(3PI)/4`

Discussion

6406.	Which of the following order is CORRECT according to given property ?
Answer» N-N GT P-P : BOND strength H-H gt F-F : Bond energy `2p_pi-3p_pi gt 2p_pi-2p_pi` : EFFECTIVE `PI`-bond 4f gt 7s : Energy of subshell

Discussion

6407.	Consider the graph ofy = f(x) as shown in the following figure. (i) Find the sumof the roots of the equation f (x) = 0. (ii) Find the product of the roots of the equation f(x) = 4. (iii) Find the absolute value of the difference of the roots of theequationf(x) = x+2 .
Answer» Solution : (i) Roots of theequation f(x) = 0 OCCUR where thegraph of y = f(x) and y = 0 INTERSECT. From the diagram, the points of intersection ofintersectionare x =- 2 and x= 1. HENCE sum of the roots is - 1. (ii) Roots of the equation f(x) = 4 occur where thegraph of y = f(x) and y = 4 intersect. From thediagram, the points of intersection are x =- 3 and x = 2. Hence the PRODUCT of theroots is -6. (iii) Roots of the equation f(x) = x+2 occur where the graph of y = f(x) and y = x+2 intersect. From thediagram, the points of intersection are x =- 2 and x = 2. Hence the difference of the roots is 4.

Discussion

6408.	If the vectors a, b and c are coplanar, then \|(a,b,c),(a.a,a.b,a.c),(b.a,b.b,b.c)\| is equal to
Answer» 1 0 `-1` None of these Solution :Since a, b and c are COPLANAR, there must EXIST three scalars x,y and z not all zero such that `ax+yb+zc=0""…(i)` ON multiplyaing both sids of Eq (i) by a and b respectively we get `xaa+ya.b+za.c =0:""…(II)` `ab.a+yb.b+zb.c=0""...(iii)` On eliminating x,y and z from Eqs, (i), (ii) and (iii), we get `\|{:(a,b,c),(a.a., a.b.,b.c),(b.a, a.b, b.c):}\|=0`

Discussion

6409.	The probability that a number selected at random from theset of number {1,2,3,…100) is a cube ,is
Answer» `(1)/(25)` `(2)/(25)` `(3)/(25)` `(4)/(25)` ANSWER :A

Discussion

6410.	Prove that the orthocentre of the triangle formed by any three tangents to a parabola lies on the directrixof the parabola
Answer» Answer :the orthocenter of the triangle `PQR`, with abscissa as `-a`, LIES on the DIRECTRIX of the PARABOLA.

Discussion

6411.	Solution of the differential equation (2sin((y)/(x))+2xtan((y)/(x))-ycos((y)/(x))-ysec^(2)((y)/(x)))dx+(xcos((y)/(x))+xsec^(2)((y)/(x)))dy=0
Answer» `X^(2)(SIN((y)/(x))-tan((y)/(x)))=c` `-x^(2)(sin((y)/(x))+tan((y)/(x)))=c` `x^(2)(sin((y)/(x))+tan((y)/(x)))=c` `-x^(2)(sin((y)/(x))-tan((y)/(x)))=c` ANSWER :C

Discussion

6412.	Integrate the function (x^(2))/(sqrt(x^(6)+a^(6)))
Answer» ANSWER :`1/3logabs(X^(3)+SQRT(x^(6)+a^(6)))+C`

Discussion

6413.	Fill int the blanks choosing correct answer from the bracket. If sinA = sinB and b = 1/2 then a = _____.
Answer» 2 1/2 1 Answer :B

Discussion

6414.	The solution of differential equation : x(dy)/(dx)+2y=x^2 is :
Answer» `y= (X^(4) + C)/(4X^(2))` `y= (x^(4) +C)/(x^(2))` `y= (x^(2))/(4) + C` `y= (x^(2) C)/(4x^(2))` ANSWER :A

Discussion

6415.	Find the equation and length of the common chord of the two circles S=x^2+y^2+3x+5y+4=0 and S=x^2+y^2+5x+3y+4=0
Answer» ANSWER :x-y=0,9/sqrt2

Discussion

6416.	If the magnitude of the coefficient of x^(7) in the expansion of (ax^(2) + (1)/(bx) )^(8), where a, b are positive numbers,is equal to the magnitude of the coefficient of x^(-7) in the expansion of (ax+(1)/(bx^(2)))^(8), then a and b are connected by the relation
Answer» `AB=1` `ab=2` `a^(2) b=1` `ab^(2) =2` ANSWER :A

Discussion

6417.	If I_(n)=int_(0)^(pi)x^(n). sin x dx then the value of I_(5)+20I_(3)=
Answer» `((PI)/(2))^(5)` `5(pi)^(5)` `pi^(5)` 0 Answer :3

Discussion

6418.	Prove that if the lines x = ay + b, z = cy + d and x = a'y + b', z = c'y + d' are perpendiclar to each other aa' + cc' + 1 = 0.
Answer» `ac_1 + a_1 c = 1` `"aa"_1 + "cc"_1 + 1 = 0` `bc_1 + b_1c + 1 =0` NONE of these Answer :B

Discussion

6419.	The tangent to y^(2)=axmakes an angle 45^(@) with x-axis . Then its point of contact is
Answer» A.P. G.P. H.P. none Answer :B

Discussion

6420.	Figure shows .................
Answer» Solution :ACCELERATION of bot, `a_(B)=50/250=1/5 m//s^(2)` `v_(b)=0+1/5xx5=1 m//s` Acceleration of BOX, `a_("box")=50/500=1/10 m//s^(2)` `v_("box")=0+1/10xx5=0.5 m//s` `v_(b)," box"=1-(-0.5)` `=1.5 m//s`.

Discussion

6421.	Differentiate x^(sinx) , x gt 0 with respect to x.
Answer» ANSWER :`(DY)/(DX)= X^(SINX)[(sinx)/(x)+logx.cosx]`

Discussion

6422.	If x = y and x + y = 10, then 2x + y =
Answer» 3 15 18 24 Answer :B

Discussion

6423.	Find the number of ways to arrange 8 persons around circular table if two specified persons wish to sit together
Answer» ANSWER :1440

Discussion

6424.	(b xx c) xx (c xx a) =
Answer» [a B C] c [a b c] b [a b c] a `a XX (b xx c)` ANSWER :A

Discussion

6425.	Definite integration as the limit of a sum : lim_(ntooo)(1)/(n)+(1)/(n+1)+(1)/(n+2)+.......+(1)/(2n)
Answer» 0 `log_(E)4` `log_(e)3` `log_(e)2` Answer :D

Discussion

6426.	If f(x) = underset(nrarroo)lime^(xtan(1//n)log(l//n),andint(f(x))/(3sqrt(sin^(11)xcosx))dx=g(x)+C (C being the constant of intergrtion), then.
Answer» `g(pi//4) = 3//2` g(x) is continuous for all `x in R` `g(pi//4) = - 15//8` `g(pi//4)= 1//2` ANSWER :C

Discussion

6427.	lf baru and barv are any two vectors, then : ((1-baru.barv)^(2)+(baru+barv+baruxxbarv)^(2))/(1+v^(2))=
Answer» 0 `1+u^(2)` `baru.barv` `(baru+barv)^(2)` ANSWER :B

Discussion

6428.	Find gof and fog , if f (x) = \|x\| and g(x) = \|5x-2\|.
Answer» SOLUTION :N/A

Discussion

6429.	The least positive integral value of n for which ((1-i)/(1+i))^(2n) = 1 is
Answer» only I is TRUE only II is true both I and II are true NEITHER I nor II are true ANSWER :C

Discussion

6430.	sin^(4)frac(pi)(8) + sin^(4) frac(2pi)8 + sin^(4) frac(3pi)8+sin^(4) frac(4pi)(8) +sin^(4)frac(5pi)(8) + sin^(4) frac(6pi)8 + sin^(4) frac(7pi)(8)=
Answer» A `3/2` B`5/2` C3 D`7/2` ANSWER :C

Discussion

6431.	if siny=xsin(a+y) then show that dy/dx=sin^(2)(a+y)/(sina).
Answer» ANSWER :`(SIN^(2)(a+y))/(SINA)`

Discussion

6432.	Find the number of possible common tangent that exits for the following pairs of circle. (a)x^(2) + y ^(2) -4x -2y +1= 0, x^(2) +y^(2) -6x -4y +4=0 (b)x^(2) + y ^(2)-4 x + 2y -4=0 , x^(2) + y ^(2)+ 2x - 6y + 6=0
Answer» ANSWER :` therefore ` NUMBER of common tangents of (1) & (2) = 3

Discussion

6433.	A stone thrown upwards has its equation of motion S=490t-4.9t^2. Then the maximum height reached by it is
Answer» 24500 12500 12250 25400 Answer :C

Discussion

6434.	Examine the continuity of the following functions at indicated points.f(x)={(frac{[x]}{x}ifxne0 at x=0),(0 if x=0):}
Answer» SOLUTION :f(0)=0 L.H.L `=lim_(hto0)\|-h\|/(-h)` `=lim_(hto0)h/-h=-1` `R.H.L==lim_(hto0)\|h\|/h` `=lim_(hto0)h/h=1` As L.H.L. ne R.H.L. ne f(0)` `therefore` f is DISCONTINUOUS at x=0

Discussion

6435.	Differentiate w.r.t.x the function in Exercises 1 to 11. cos( a cos x+ b sin x), for some constant a and b.
Answer» ANSWER :`(a SIN X -B COS x)sin (a cos x+b sin x)`

Discussion

6436.	Which of the correct order for a given number alpha, alpha gt 1
Answer» `log_(2)ALPHA LT log_(3)alpha lt log_(e)alpha lt log_(10)alpha` `log_(10)alpha lt log_(3)alpha lt log_(e)alpha lt log_(2) alpha` `log_(10)alpha lt log_(e)alpha lt log_(2) alpha lt log_(3)alpha ` `log_(3) alpha lt log_(e) alpha lt log_(2) alpha lt log_(10)alpha` Answer :B

Discussion

6437.	The equation of the tangent to the parabola y^(2)=4x at the end of the latus rectum in the fourth quadrant is
Answer» X-y+2 =0 x - y + 4=0 x+y+2=0 x+y+4=0 Answer :C

Discussion

6438.	ABCD is a parallelogram. Equations of overset(" "harr)(AB) and overset(" "harr)(AD)are 4x+5y=0, 7x+2y=0 and the equation of the diagonal overset(" "harr)(BD)is 11x+7y=9. Then the equation of overset(" "harr)(AC) is
Answer» `x=y` `x+y=0` `7x-11y=0` `7x+11y=0` ANSWER :A

Discussion

6439.	A polygobn has 44 diagonals .The number of the sides is
Answer» 10 11 12 13 Answer :B

Discussion

6440.	Let f(x) = [x]and g(x) = x - [x], then which of the following functions is the zero function ?
Answer» (f+g) (X) (FG) (x) (f-g) (x) (FOG) (x) ANSWER :D

Discussion

6441.	A kite is flying with the string inclined at 75^(@) to the horizon. If the length of the string is 25 m, the height of the kite is
Answer» `(25//2) (sqrt(3) - 1)^(2)` `(25//4) (sqrt(3) + 1) sqrt(2)` `(25//2) (sqrt(3) + 1)^(2)` `(25//2) (sqrt(6) + sqrt(2))` Answer :B

Discussion

6442.	If bar(a) = 3 overset(^)(i) + 2 overset(^)(j), bar(b) = 2 overset(^)(i) + 2 overset(^)(j) + overset(^)(k) , bar(c ) = 5 overset(^)(i) - overset(^)(j) + overset(^)(k) then the unit vectorbar(a) + bar(b) + bar(c ) 1 in opposite direction is
Answer» `OVERSET(^)(i)` `-overset(^)(i)` `-overset(^)(J)` `overset(^)(j)` ANSWER :C

Discussion

6443.	Evaluate the following integrals int(e^(x)(x+1))/((x+2))dx
Answer» ANSWER :`(E^(X))/(x+2)+C`

Discussion

6444.	Find the shortest distance between the linesvecr=(lambda-1)hati+(lambda+1)hatj-(1+lambda)hatk and (vecr=(1-mu)hati+(2mu-1)hatj+(mu+2)hatk.
Answer» ANSWER :`(5)/(SQRT2)`

Discussion

6445.	If ane1,bne-1,cne-1 and the system of equations, x=a(y+z),y=b(z+x),z=c(x+y) has a non-trivial solution, then.
Answer» `a/(a+1)+B/(b+1)+C/(c+1)=0` `a/(a+1)+b/(b+1)+c/(c+1)=1` `(ABC)/((a+1)(b+1)(c+1))=1` `(a+b+c)/((a+1)(b+1)(c+1))=2` Answer :B

Discussion

6446.	I : The image of the point (2, 1) with respect to the line x+1=0 is (-4, 1). II. If the point (1, 2) is reflected through origin and then through the line x = y then the new coordinates of the point are (-2, -1).
Answer» only I is TRUE only II is true both I and II are true NEITHER I nor II are true ANSWER :C

Discussion

6447.	If the function g(x) is defined by g(x)= (x^(200))/(200) + (x^(199))/(199)+ …..+ (x^(2))/(2)+ x + 5, then g'(0)=________
Answer» 1)5 2)100 3)200 4)1 Answer :D

Discussion

6448.	If \|x\|lt1 and y=x-(x^(2))/(2)+(x^(3))/(3)-(x^(4))/(4)+..., then x =
Answer» `y+(y^(2))/(2!)+(y^(3))/(3!)+…OO` `y-(y^(2))/(2)+(y^(3))/(3)-….oo` `y-(y^(2))/(2!)+(y^(3))/(3!)+…oo` `y-(y^(2))/(2!)+(y^(3))/(3!)- ….. oo` ANSWER :A

Discussion

6449.	A bag contains 8 red and 7 black balls . Two balls are drawn at random . Probability that both the balls are of the same color is
Answer» `14/15` `11/15` `7/15` `4/15` ANSWER :C

Discussion

6450.	Differentiate tan^(-1) e^(2x)
Answer» SOLUTION :`y = TAN^(-1) (e^(2x)) dy/dx = 1/(1+(e^(2x)^)^2) cdot d/dx(e^(2x)) = 1/(1+e^(4X)).2E^(2x) ={2e^(2x)}/(1+e^(4x))`

Discussion

Explore topic-wise InterviewSolutions in .

If A,B,C are 3 points on a parabola , Delta _1, Delta_2are the areas of triangles is formed by the points A, B,C and the tangents at A, B, C . IfDelta_1, Delta _2are the roots of px^(2) +qx +r=0then condition is

A six faced dice is thrown a dozen times. Probability that six is not obtained even one is

int_(0)^(pi//2)(200 sin x + 100 cos x)/(sin x + cos x) dx =

1 +(2^3)/(1!) x + (3^3)/(2!) x^2 + ....oo=

Find thevalues of the following : tan""^(-1)(1)+"cos"^(-1)-1/2+""sin"^(-1)-1/2

Which of the following order is CORRECT according to given property ?

Consider the graph ofy = f(x) as shown in the following figure. (i) Find the sumof the roots of the equation f (x) = 0. (ii) Find the product of the roots of the equation f(x) = 4. (iii) Find the absolute value of the difference of the roots of theequationf(x) = x+2 .

If the vectors a, b and c are coplanar, then |(a,b,c),(a.a,a.b,a.c),(b.a,b.b,b.c)| is equal to

The probability that a number selected at random from theset of number {1,2,3,…100) is a cube ,is

Prove that the orthocentre of the triangle formed by any three tangents to a parabola lies on the directrixof the parabola

Solution of the differential equation (2sin((y)/(x))+2xtan((y)/(x))-ycos((y)/(x))-ysec^(2)((y)/(x)))dx+(xcos((y)/(x))+xsec^(2)((y)/(x)))dy=0

Integrate the function (x^(2))/(sqrt(x^(6)+a^(6)))

Fill int the blanks choosing correct answer from the bracket. If sinA = sinB and b = 1/2 then a = _____.

The solution of differential equation : x(dy)/(dx)+2y=x^2 is :

Find the equation and length of the common chord of the two circles S=x^2+y^2+3x+5y+4=0 and S=x^2+y^2+5x+3y+4=0

If the magnitude of the coefficient of x^(7) in the expansion of (ax^(2) + (1)/(bx) )^(8), where a, b are positive numbers,is equal to the magnitude of the coefficient of x^(-7) in the expansion of (ax+(1)/(bx^(2)))^(8), then a and b are connected by the relation

If I_(n)=int_(0)^(pi)x^(n). sin x dx then the value of I_(5)+20I_(3)=

Prove that if the lines x = ay + b, z = cy + d and x = a'y + b', z = c'y + d' are perpendiclar to each other aa' + cc' + 1 = 0.

The tangent to y^(2)=axmakes an angle 45^(@) with x-axis . Then its point of contact is

Figure shows .................

Differentiate x^(sinx) , x gt 0 with respect to x.

If x = y and x + y = 10, then 2x + y =

Find the number of ways to arrange 8 persons around circular table if two specified persons wish to sit together

(b xx c) xx (c xx a) =

Definite integration as the limit of a sum : lim_(ntooo)(1)/(n)+(1)/(n+1)+(1)/(n+2)+.......+(1)/(2n)

If f(x) = underset(nrarroo)lime^(xtan(1//n)log(l//n),andint(f(x))/(3sqrt(sin^(11)xcosx))dx=g(x)+C (C being the constant of intergrtion), then.

lf baru and barv are any two vectors, then : ((1-baru.barv)^(2)+(baru+barv+baruxxbarv)^(2))/(1+v^(2))=

Find gof and fog , if f (x) = |x| and g(x) = |5x-2|.

The least positive integral value of n for which ((1-i)/(1+i))^(2n) = 1 is

sin^(4)frac(pi)(8) + sin^(4) frac(2pi)8 + sin^(4) frac(3pi)8+sin^(4) frac(4pi)(8) +sin^(4)frac(5pi)(8) + sin^(4) frac(6pi)8 + sin^(4) frac(7pi)(8)=

if siny=xsin(a+y) then show that dy/dx=sin^(2)(a+y)/(sina).

Find the number of possible common tangent that exits for the following pairs of circle. (a)x^(2) + y ^(2) -4x -2y +1= 0, x^(2) +y^(2) -6x -4y +4=0 (b)x^(2) + y ^(2)-4 x + 2y -4=0 , x^(2) + y ^(2)+ 2x - 6y + 6=0

A stone thrown upwards has its equation of motion S=490t-4.9t^2. Then the maximum height reached by it is

Examine the continuity of the following functions at indicated points.f(x)={(frac{[x]}{x}ifxne0 at x=0),(0 if x=0):}

Differentiate w.r.t.x the function in Exercises 1 to 11. cos( a cos x+ b sin x), for some constant a and b.

Which of the correct order for a given number alpha, alpha gt 1

The equation of the tangent to the parabola y^(2)=4x at the end of the latus rectum in the fourth quadrant is

ABCD is a parallelogram. Equations of overset(" "harr)(AB) and overset(" "harr)(AD)are 4x+5y=0, 7x+2y=0 and the equation of the diagonal overset(" "harr)(BD)is 11x+7y=9. Then the equation of overset(" "harr)(AC) is

A polygobn has 44 diagonals .The number of the sides is

Let f(x) = [x]and g(x) = x - [x], then which of the following functions is the zero function ?

A kite is flying with the string inclined at 75^(@) to the horizon. If the length of the string is 25 m, the height of the kite is

If bar(a) = 3 overset(^)(i) + 2 overset(^)(j), bar(b) = 2 overset(^)(i) + 2 overset(^)(j) + overset(^)(k) , bar(c ) = 5 overset(^)(i) - overset(^)(j) + overset(^)(k) then the unit vectorbar(a) + bar(b) + bar(c ) 1 in opposite direction is

Evaluate the following integrals int(e^(x)(x+1))/((x+2))dx

Find the shortest distance between the linesvecr=(lambda-1)hati+(lambda+1)hatj-(1+lambda)hatk and (vecr=(1-mu)hati+(2mu-1)hatj+(mu+2)hatk.

If ane1,bne-1,cne-1 and the system of equations, x=a(y+z),y=b(z+x),z=c(x+y) has a non-trivial solution, then.

I : The image of the point (2, 1) with respect to the line x+1=0 is (-4, 1). II. If the point (1, 2) is reflected through origin and then through the line x = y then the new coordinates of the point are (-2, -1).

If the function g(x) is defined by g(x)= (x^(200))/(200) + (x^(199))/(199)+ …..+ (x^(2))/(2)+ x + 5, then g'(0)=________

If |x|lt1 and y=x-(x^(2))/(2)+(x^(3))/(3)-(x^(4))/(4)+..., then x =

A bag contains 8 red and 7 black balls . Two balls are drawn at random . Probability that both the balls are of the same color is

Differentiate tan^(-1) e^(2x)