28278 + Interview Questions in Maths in Class 12 Page 561 InterviewSolution

28001.	Definite integration as the limit of a sum : lim_(ntooo)[(1)/(n)+(n^(2))/((n+1)^(3))+(n^(2))/((n+2)^(3))+.........+(1)/(8n)]=........
Answer» `(3)/(8)` `(1)/(8)` `(1)/(3)` `(8)/(3)` ANSWER :A

Discussion

28002.	The value of the integral int _(0) ^(1) x cot ^(-1) (1- x ^(2) + 4x ^(4)) dx is equal to (pi)/(4) - (k)/(2) ln 2, (natural log ln) then k is
Answer» ANSWER :1

Discussion

28003.	Write down the first three terms is the following expansions(8 - 5x)^(2//3)
Answer» ANSWER :`4, - 5/3x, (-25)/(144) x^2`

Discussion

28004.	If 2, 3, 5 are the rootsof ax^(3) + bx^(2) + cx + d = 0 then the roots of ax sqrt(x) + bx + c sqrt(x) + d = 0 are
Answer» `2, 3, 5 ` `4, 6, 10 ` 4, 9, 25 `SQRT(2), sqrt(3), sqrt(5)` ANSWER :3

Discussion

28005.	If therootsof theequationx^3 -9x^2 + 23x-15=0are inA.Pthencommondifferenceof thatA.Pis
Answer» 3 1 2 4 Answer :C

Discussion

28006.	Let y = f(x) be a differentiable function, AA x in R and satisfies, f(x) = x+ int_(0)^(1)x^(2)z f(z) dz + int_(0)^(1)x z^(2) f(z) dz, then
Answer» `f(X) = (20 x)/(119)(2 + 9x)` `f(x) = (20X)/(119)(4 + 9x)` `f(x) = (10x)/(119) (4 + 9x)` `f(x) = (5x)/(119)(4 + 9x)` ANSWER :B

Discussion

28007.	Find the 5th term of the extension (2a+b)^8
Answer»

Discussion

28008.	Carbon and oxygen combine to form two oxides, carbon monoxide and carbon dioxide in which the ratio of the weights of carbon and oxygen is respectively 12 : 16 and 12 : 32. These figures illustrate the :-
Answer» Law of MULTIPLE proportions Law of RECIPROCAL proportions Law of CONSERVATION of mass Law of constant proportions Answer :A

Discussion

28009.	From the point P(2, 3) tangents PA,PB are drawn to the circle x^2+y^2-6x+8y-1=0. The equation to the line joining the mid points of PA and PB is
Answer» x-7y+7=0 x+7y-5=0 x+7y+5=0 x-7y+5=0 ANSWER :A

Discussion

28010.	lim_(x to 0) ((1+x^2)^(1//3) - (1-2x)^(1//4))/ (x+x^2) is
Answer» 2 `1//2` `3//2` cannot be DETERMINED ANSWER :B

Discussion

28011.	There are n black balls and 2 red balls in a bag. One by one balls are drawn from the bag X wins as soon as 2 black balls are drawn and Y wins as soon as 2 red balls are drawn. The game continuous until one of 2 wins. Let X(n) and Y(n) denotes the probability that X and Y wins respectively. The value of lim_(n+prop) (X(2).X(3).X(4)...(n)) is
Answer» `1//3` `1//10` `1//5` `1//20`. ANSWER :B

Discussion

28012.	There are n black balls and 2 red balls in a bag. One by one balls are drawn from the bag X wins as soon as 2 black balls are drawn and Y wins as soon as 2 red balls are drawn. The game continuous until one of 2 wins. Let X(n) and Y(n) denotes the probability that X and Y wins respectively. The value of lim_(n to prop) (Y(1)+Y(2)+Y(3)+......+(n)) is
Answer» `1//3` `1//2` 2 3 Answer :D

Discussion

28013.	Solve the equation z^3=i
Answer» Solution :`Z^3=i=COS((3pi)/2)+ISIN((3pi)/2)` `=cos(2kpi+PI/2)+isin (2kpi+pi/2)` `=cos(pi(4k+1))/2 +sin(pi(4k+1))/2` `:.z=[cos((4k+1))/2+isin((4k+1)pi)/2]^(1/3) `=cos((4k+1)pi)/6+isin((4k+1)pi)/6` `"where" k=0,1,2.`

Discussion

28014.	There are n black balls and 2 red balls in a bag. One by one balls are drawn from the bag X wins as soon as 2 black balls are drawn and Y wins as soon as 2 red balls are drawn. The game continuous until one of 2 wins. Let X(n) and Y(n) denotes the probability that X and Y wins respectively. Then the value of Y(n) is '
Answer» `(1)/((N+1)(n+2))` `(6)/((n+1)(n+2))` `(6)/(n(n+1(n+2))` `(1)/(n(n+1)(n+2))`. ANSWER :B

Discussion

28015.	The volume of solid generated by revolving about the y-axisthe figure bounded by the parabola y=x^(2)andx=y^(2) is
Answer» `(21)/(5)pi` `(24)/(5)pi` `(2)/(15)pi` `(5)/(24)pi` SOLUTION :`V= int _(0)^(1) pi X^(2)dy` `=\|pi int _(0)^(1) (y^(4)-y)dy\|` `=\| pi [(y^(5))/(5)-(y^(2))/(2)]_(0)^(1)\|` `=\| pi [(1)/(5)-(1)/(3)]\|` `=\|(-2pi)/(15)\|=(2pi)/(15)`

Discussion

28016.	The statement ~prarr(qrarrp) is equivalent to
Answer» `prarr(PRARRQ)` `prarr(p vv Q)` `q rarrp` `q RARR (prarrq)` Answer :C

Discussion

28017.	int (dx)/(cos (x -a) cos (x-b) )= (1)/(p) log q, then (p, q)=
Answer» `SIN (B-a) (sec (X-a) )/(sec (x-b))` `sin (a-b) (cos (x-a) )/(cos (x-b))` `sin (b+a) (sec (x-a))/(sec (x -b))` `sin (a-b) (sec (x-a))/(sec (x-b))` Answer :A

Discussion

28018.	If the equations of the perpendicular bisectors of the sides AB and AC of a Delta ABC are x - y + 5 = 0 and x + 2y =0 respectively and if A is (1,-2), then the equation of the perpendicular bisector of the side BC is
Answer» 3X + 3Y + 5 = 0 9x - 23y + 40 =0 6x + 15y = 5 23x - 14y + 100 = 0 Answer :D

Discussion

28019.	A bag contains 2 white and 2 black balls. A ball is drawn at random. If it is white, it is not replaced in to the bag otherwise it is replaced along with another ball of the same colour. The process is repeated. Find the probability that the third ball drawn is black.
Answer» ANSWER :`(23)/(30)`

Discussion

28020.	If M_(1),M_(2),M_(3) "and" M_(4), are respectively the magnitudes of the vectors a_(1)=2hati-hatj+hatk, a_(2)=-3hati-4hatj-4hatk, a_(3)=-hati+hatj-hatk, a_(4)=-hati+3hatj+hatk, then the correct order of M_(1),M_(2),M_(3) "and" M_(4)is
Answer» `M_(3)ltM_(1)ltM_(4)ltM_(2)` `M_(3)ltM_(1)ltM_(2)ltM_(4)` `M_(3)ltM_(4)ltM_(1)ltM_(2)` `M_(3)ltM_(4)ltM_(2)ltM_(1)` Answer :A

Discussion

28021.	Find the value of(1 + (1)/( 3 ^(2)) + (1)/( 5 ^(2)) + ...+ (1)/( 997 ^(2)) + (1)/(1002 ^(2)) - (1)/( 1004^(2)) -(1)/( 1006 ^(2)) -...- (1)/( 2000 ^(2)))/(1 + (1)/(2 ^(2)) + (1)/( 3 ^(2)) + (1)/( 4^(2)) + .....+ (1)/(999 ^(2)) + (1)/(1000 ^(2)))
Answer» ANSWER :`3/4`

Discussion

28022.	AB is a diameter of a circle and C is any point on the circle. Show that the area of Delta ABC is maximum, when it is isosceles.
Answer» ANSWER :`x=y=sqrt(2)R`

Discussion

28023.	If OB is the semi-minor axis of an ellipse , F_1 and F_2 are its foci and the angle between F_1B and F_2Bis a right angle , then the square of the eccentricity of the ellipse is
Answer» `(1)/(2) ` ` ( 1)/(SQRT2) ` `( 1)/(2sqrt2) ` `( 1)/(4)` ANSWER :A

Discussion

28024.	Evaluate the following integrals int(dx)/(x^2-5)
Answer» SOLUTION :`int(DX)/(x^2-5)=int(dx)/((x-sqrt5)(x-sqrt5))` `(1/(2sqrt5))int{(1/(x-sqrt5)-(1/(x+sqrt5)}` `(1/(2sqrt5))Inabs((x-sqrt5)/(x+sqrt5))+C``

Discussion

28025.	In triangleABC, (tan((B)/(2))-tan((C)/(2)))/ (tan((B)/(2))+tan((C)/(2)))=
Answer» `(b-C)/(2A)` `(c-d)/(2a)` `(b-c)/(a)` `(c-b)/(a)` ANSWER :C

Discussion

28026.	Find the values of k so that the function f is continuous at the indicated point. f(x)={{:(kx+1," if "x le pi),(cos x," if "x gt pi):}" at "x= pi.
Answer» ANSWER :`K=(-2)/(PI)`.

Discussion

28027.	Find the values of k so that the function f is continuous at the indicated point. f(x)={{:(kx^(2)," if "x le2),(3," if "x gt 2):}" at "x= 2.
Answer» ANSWER :`K=(3)/(4)`

Discussion

28028.	Find the values of k so that the function f is continuous at the indicated point. f(x)={{:((k cos x)/(pi -2x)," if "x ne (pi)/(2)),(3," if "x= (pi)/(2)):}" at "x=(pi)/(2).
Answer» ANSWER :`k=6`

Discussion

28029.	z = 30x - 30y + 1800 is a objective function. The corner points of the feasible region are (15, 0), (15, 15), (10, 20), (0, 20) and (0, 15). z has the minimum value at …….. point.
Answer» (0, 20) (0, 15) (15, 0) (10, 20) ANSWER :A

Discussion

28030.	Statement 1: The line x-2y =2 meets the parabola y^(2) +2x=0only at the point(-2,-2) Statement 2:The liney= mx -1//2m (m ne 0 )is a tangent to the parabola , y ^(2)=-2xat the point (-( 1)/( 2m ^(2)), ( 1)/(m))
Answer» STATEMENT 1 and Statement 2 are both false Statement 1 and Statement 2 are both TRUE Statement 1 is true and Statement 2 is false Statement 1 is false and statement 2 is true. Answer :A

Discussion

28031.	A number is chosen from the first 100 natural numbers. Find the probability that it is a multiple of 4 or 6.
Answer» ANSWER :`(33)/(100)`

Discussion

28032.	Find :int(sqrtx+1/sqrtx)dx.
Answer» `1/3x^(1/3)+2X^(1/2)+C` `2/3x^(1/3)+1/2x^(2)+C` `2/3x^(3/2)+2x^(1/2)+C` `3/2x^(3/2)+1/2x^(1/2)+C` ANSWER :C

Discussion

28033.	The value of theta satisfying the given equation costheta+sqrt(3)sintheta=2, is
Answer» `(PI)/(3)` `(5pi)/(3)` `(2PI)/(3)` `(4pi)/(3)` ANSWER :A

Discussion

28034.	Let f(x) =x^3+ax^2+bx+5 sin ^2x be an increasing function on the set R. Then a and b satisfy
Answer» `a^2-3b-15gt0` `a^2-2b+15 GT0` `a^2-3b+15lt0` `a GT 0 and B gt 0` ANSWER :C

Discussion

28035.	Each term of a sequence is the sum of its preceding two terms from the third term onwards. The second term of the sequence is -1 and the 10th term is 29. The first term is "_________"
Answer» ANSWER :3

Discussion

28036.	Find the range of each of the following function: f(x)=cos^(-1)(((x-1)(x+5))/(x(x-2)(x-3)))
Answer» SOLUTION :NA

Discussion

28037.	If (x^(2)-5x+7)/(x-1)^(3)=A/(x-1)+B/(x-1)^(2)+C/(x-1)^(3) " then " A+B-C=
Answer» 5 3 0 -5 Answer :D

Discussion

28038.	Find the values of k so that the function f is continuous at the indicated point. f(x)={{:(kx+1," if "x le 5),(3x-5," if "x gt 5):}" at "x= 5.
Answer» ANSWER :`K=(9)/(5)`

Discussion

28039.	Consider the equation\|2x\|-\|x-4\|=x+4 Total number of prime numbers less than 20 satisfying the equation is
Answer» 3 4 5 6 Answer :D

Discussion

28040.	If x=a(gt0) divides the area bounded by X-axis, part of the curve y=1+(8)/(x^(2)) and the ordinates x = 2, x = 4 into equal parts then a =
Answer» 2 `SQRT(2)` `(1)/(sqrt(2))` `2sqrt(2)` ANSWER :D

Discussion

28041.	If f(x)=3x^(2)+15x+5, then the approximate value of f(3.02) is ……….
Answer» `47.66` `57.66` `67.66` `77.66` ANSWER :D

Discussion

28042.	The value of c for which P(x=k)=ck^(2) can serve as the probabilitydistribution function of a random variable X that takes values 0, 1, 2, 3, 4 is
Answer» `(1)/(10)` `(1)/(15)` `(1)/(20)` `(1)/(30)` Answer :D

Discussion

28043.	If A and B are symmetric matrices of the same order , then (AB-BA)is a :
Answer» ANSWER :AB

Discussion

28044.	If (5,12), (24,7) are the foci of the hyperbola passing through origin, then its eccentricity is
Answer» `(13)/(5)` `SQRT(386)/(13)` `sqrt(386)/(25)` `sqrt(386)/(12)` Answer :D

Discussion

28045.	Find the centre and radius of the following circles: x^(2)+y^(2)-2x+4y-4=0 and 2x^(2)+2y^(2)+16x-28y+32=0. Also find the ratio of their diameters.
Answer» ANSWER :`3:7`

Discussion

28046.	Evaluate int cot^(5) x dx
Answer» ANSWER :`-(COT^(4))/(4)+(cot^(2))/(2)+log\|sinx\|+c`

Discussion

28047.	Prove that \|{:(a+1,1,1),(1,b+1,1),(1,1,c+1):}\|=abc(1/a+1/b+1/c+1)
Answer» ANSWER :`ABC(1/a+1/b+1/c+1)`

Discussion

28048.	Find the derivative of the following functions with respect to x sin [cos(x^(2))]
Answer» Answer :`-2x sin X^(2) COS (cos x^(2))`

Discussion

28049.	If no one in a group of friends has more than $75, what is the smallest number of people who could be in the group if the group purchease a flat - screen TV that costs $1,100?
Answer» ANSWER :15

Discussion

28050.	If sinx+co secx+tany=4 whre x and y in[0,(pi)/(2)] then tan""(y)/(2) is a root of the equation.
Answer» `a^(2)+2alpha+1=0` `a^(2)+2a=0` `2a^(2)-2a-1=0` `a^(2)-alpha-1=0` Solution :`TAN A-tanB=(1)/(2)` `rArr(TANA)/(1)=(COTB)/(2)=gamma`(SAY) `rArr tan A=gamma` and `tan B=(1)/(2lambda)` `therefore (5-3cos 2A)(5-3cos2B)` `=[5-(3(1-lambda^(2)))/((1+lambda^(2)))]xx[5-(3(1-(1)/(4lambda^(2))))/((1+(1)/(4lambda^(2))))]`

Discussion

Explore topic-wise InterviewSolutions in .

Definite integration as the limit of a sum : lim_(ntooo)[(1)/(n)+(n^(2))/((n+1)^(3))+(n^(2))/((n+2)^(3))+.........+(1)/(8n)]=........

The value of the integral int _(0) ^(1) x cot ^(-1) (1- x ^(2) + 4x ^(4)) dx is equal to (pi)/(4) - (k)/(2) ln 2, (natural log ln) then k is

Write down the first three terms is the following expansions(8 - 5x)^(2//3)

If 2, 3, 5 are the rootsof ax^(3) + bx^(2) + cx + d = 0 then the roots of ax sqrt(x) + bx + c sqrt(x) + d = 0 are

If therootsof theequationx^3 -9x^2 + 23x-15=0are inA.Pthencommondifferenceof thatA.Pis

Let y = f(x) be a differentiable function, AA x in R and satisfies, f(x) = x+ int_(0)^(1)x^(2)z f(z) dz + int_(0)^(1)x z^(2) f(z) dz, then

Find the 5th term of the extension (2a+b)^8

Carbon and oxygen combine to form two oxides, carbon monoxide and carbon dioxide in which the ratio of the weights of carbon and oxygen is respectively 12 : 16 and 12 : 32. These figures illustrate the :-

From the point P(2, 3) tangents PA,PB are drawn to the circle x^2+y^2-6x+8y-1=0. The equation to the line joining the mid points of PA and PB is

lim_(x to 0) ((1+x^2)^(1//3) - (1-2x)^(1//4))/ (x+x^2) is

Solve the equation z^3=i

The volume of solid generated by revolving about the y-axisthe figure bounded by the parabola y=x^(2)andx=y^(2) is

The statement ~prarr(qrarrp) is equivalent to

int (dx)/(cos (x -a) cos (x-b) )= (1)/(p) log q, then (p, q)=

If the equations of the perpendicular bisectors of the sides AB and AC of a Delta ABC are x - y + 5 = 0 and x + 2y =0 respectively and if A is (1,-2), then the equation of the perpendicular bisector of the side BC is

A bag contains 2 white and 2 black balls. A ball is drawn at random. If it is white, it is not replaced in to the bag otherwise it is replaced along with another ball of the same colour. The process is repeated. Find the probability that the third ball drawn is black.

If M_(1),M_(2),M_(3) "and" M_(4), are respectively the magnitudes of the vectors a_(1)=2hati-hatj+hatk, a_(2)=-3hati-4hatj-4hatk, a_(3)=-hati+hatj-hatk, a_(4)=-hati+3hatj+hatk, then the correct order of M_(1),M_(2),M_(3) "and" M_(4)is

Find the value of(1 + (1)/( 3 ^(2)) + (1)/( 5 ^(2)) + ...+ (1)/( 997 ^(2)) + (1)/(1002 ^(2)) - (1)/( 1004^(2)) -(1)/( 1006 ^(2)) -...- (1)/( 2000 ^(2)))/(1 + (1)/(2 ^(2)) + (1)/( 3 ^(2)) + (1)/( 4^(2)) + .....+ (1)/(999 ^(2)) + (1)/(1000 ^(2)))

AB is a diameter of a circle and C is any point on the circle. Show that the area of Delta ABC is maximum, when it is isosceles.

If OB is the semi-minor axis of an ellipse , F_1 and F_2 are its foci and the angle between F_1B and F_2Bis a right angle , then the square of the eccentricity of the ellipse is

Evaluate the following integrals int(dx)/(x^2-5)

In triangleABC, (tan((B)/(2))-tan((C)/(2)))/ (tan((B)/(2))+tan((C)/(2)))=

Find the values of k so that the function f is continuous at the indicated point. f(x)={{:(kx+1," if "x le pi),(cos x," if "x gt pi):}" at "x= pi.

Find the values of k so that the function f is continuous at the indicated point. f(x)={{:(kx^(2)," if "x le2),(3," if "x gt 2):}" at "x= 2.

Find the values of k so that the function f is continuous at the indicated point. f(x)={{:((k cos x)/(pi -2x)," if "x ne (pi)/(2)),(3," if "x= (pi)/(2)):}" at "x=(pi)/(2).

z = 30x - 30y + 1800 is a objective function. The corner points of the feasible region are (15, 0), (15, 15), (10, 20), (0, 20) and (0, 15). z has the minimum value at …….. point.

Statement 1: The line x-2y =2 meets the parabola y^(2) +2x=0only at the point(-2,-2) Statement 2:The liney= mx -1//2m (m ne 0 )is a tangent to the parabola , y ^(2)=-2xat the point (-( 1)/( 2m ^(2)), ( 1)/(m))

A number is chosen from the first 100 natural numbers. Find the probability that it is a multiple of 4 or 6.

Find :int(sqrtx+1/sqrtx)dx.

The value of theta satisfying the given equation costheta+sqrt(3)sintheta=2, is

Let f(x) =x^3+ax^2+bx+5 sin ^2x be an increasing function on the set R. Then a and b satisfy

Each term of a sequence is the sum of its preceding two terms from the third term onwards. The second term of the sequence is -1 and the 10th term is 29. The first term is "_________"

Find the range of each of the following function: f(x)=cos^(-1)(((x-1)(x+5))/(x(x-2)(x-3)))

If (x^(2)-5x+7)/(x-1)^(3)=A/(x-1)+B/(x-1)^(2)+C/(x-1)^(3) " then " A+B-C=

Find the values of k so that the function f is continuous at the indicated point. f(x)={{:(kx+1," if "x le 5),(3x-5," if "x gt 5):}" at "x= 5.

Consider the equation|2x|-|x-4|=x+4 Total number of prime numbers less than 20 satisfying the equation is

If x=a(gt0) divides the area bounded by X-axis, part of the curve y=1+(8)/(x^(2)) and the ordinates x = 2, x = 4 into equal parts then a =

If f(x)=3x^(2)+15x+5, then the approximate value of f(3.02) is ……….

The value of c for which P(x=k)=ck^(2) can serve as the probabilitydistribution function of a random variable X that takes values 0, 1, 2, 3, 4 is

If A and B are symmetric matrices of the same order , then (AB-BA)is a :

If (5,12), (24,7) are the foci of the hyperbola passing through origin, then its eccentricity is

Find the centre and radius of the following circles: x^(2)+y^(2)-2x+4y-4=0 and 2x^(2)+2y^(2)+16x-28y+32=0. Also find the ratio of their diameters.

Evaluate int cot^(5) x dx

Prove that |{:(a+1,1,1),(1,b+1,1),(1,1,c+1):}|=abc(1/a+1/b+1/c+1)

Find the derivative of the following functions with respect to x sin [cos(x^(2))]

If no one in a group of friends has more than $75, what is the smallest number of people who could be in the group if the group purchease a flat - screen TV that costs $1,100?

If sinx+co secx+tany=4 whre x and y in[0,(pi)/(2)] then tan""(y)/(2) is a root of the equation.