28278 + Interview Questions in Maths in Class 12 Page 136 InterviewSolution

6751.	Solve (dy)/(dx) = (3x- y - 1)^(2)
Answer» ANSWER :`1/(SQRT(3)) TAN^(-1)((3x-y-1)/(sqrt(3)))= x+c`

Discussion

6752.	How many integer pairs (x,y) satisfy x^(2) + 4y^(2) -2xy -2x - 4y -8=0 ?
Answer» ANSWER :6

Discussion

6753.	Which of the following is equivalent to1 le \|x-2\| le 4 ?
Answer» `3 le x le 6` `x le 1 or x GE 3` `1le x le 3` `-2le x le 1 or3 le x le 6` Solution :Enter ABS `(x-2)` into `Y_(1)`, 1 into `Y_(2)`, and 4 into `Y_(3)`. An inspection of the graphs SHOWS that the values of x for which the graph of `Y_(1)` is betweenthe other two graphs are in two intervals. Choice E is the only answer choice having this configuration.

Discussion

6754.	The locus of Z satisfying \|z\| + \|z- 1\| = 3 is
Answer» a CIRCLE a pair of straight LINE an ELLIPSE a PARABOLA ANSWER :C

Discussion

6755.	Equation of a line passing through point (2, -1, 3) and parallel to line (2x-1)/(2)=(1-y)/(1)=(z)/(3) is
Answer» `(x-2)/(2)=(y+1)/(1)=(z-3)/(3)` `(x-2)/(1)=(y+1)/(1)=(z-3)/(3)` `(x-2)/(1)=(y+1)/(-1)=(z-3)/(3)` `(x+2)/(1)=(y-1)/(-1)=(z+3)/(3)` ANSWER :C

Discussion

6756.	From which of the following the distance of the point (1,2,3) is sqrt(10)?
Answer» Origin X-axis Y-axis Z-axis Answer :C

Discussion

6757.	If the total produce sales in July at Produce Stand P were $4,500, what were the approximate total fruit sales in December at Product Stand P?
Answer» `$2,100` `$2,200` `$2,300` Cannot be determined Answer :D

Discussion

6758.	a circular wheel with numbers 1 to 20 on its surface is rolled twice. What is the probability of getting two 13's ?
Answer» `(1)/(20)` `(1)/(40)` `(1)/(400)` `(1)/(200)` Answer :C

Discussion

6759.	Evaluate the definite integrals . underset(-pi//2)overset(pi//2)int (cosx)/(1+e^(x))dx
Answer» ANSWER :1

Discussion

6760.	If D=\|{:(2,3,1),(5,-1,2),(7,4,-1):}\| , performing R_(12(-1) on D then D will become ….
Answer» `\|{:(-1,3,1),(6,-1,2),(3,4,-1):}\|` `\|{:(2,1,1),(5,-6,2),(7,-3,-1):}\|` `\|{:(-3,4,-1),(5,-1,2),(7,4,-1):}\|` `\|{:(2,3,1),(3,-4,1),(7,4,-1):}\|` Answer :D

Discussion

6761.	If y=xlog(x/(2-3x))" for "0ltxlt2/3," then "(d^(2)y)/(dx^(2))" at "x=1/2 is
Answer» 4 16 32 2 Answer :C

Discussion

6762.	The points in which the line (x-1)/(1)=(y-1)/(-1)=(z+3)/(1) cuts the surface x^(2)+y^(2)+z^(2)-20=0
Answer» (0, 2, 4) (0, 1, -4) (4, -2, 0) (0,-2,-4) ANSWER :C

Discussion

6763.	A person standing at the junction (crossing) of two straight paths represented by the equations 2x-3y+4= 0 and 3x + 4y-5=0 wants to reach the path whose equation is 6x – 7y+8=0 in the least time. Find equation of the path that he should follow.
Answer» ANSWER :119x + 102y - 125 = 0

Discussion

6764.	"Let" f(x) =sqrtx "and" g(x) = 1 -x^2.Find natural domain of h(x) = 1-x.
Answer» SOLUTION :Domain of h(x) =1 -x is R.

Discussion

6765.	If f is continuous function then which of the following is correct:
Answer» `int_(-2)^(2) f(x) dx=int_(0)^(2)(f(x)-f(-x))dx` `int_(-3)^(5)2f(x)dx= int_(-6)^(10)f(x-1)dx` `int_(-3)^(5)f(x)dx=int_(-6)^(10)f((x)/(2))dx` `int_(-3)^(5)f(x)dx= int_(-2)^(6)f(x-1)dx` ANSWER :4

Discussion

6766.	CH_(2)=CH-CH_(2)-CH_(2)-C-=CH underset((1 eq))overset(HBr)toProduct is
Answer» `BrCH_(2)-CH_(2)-CH_(2)-CH_(2)-C-=CH` `CH_(2)=CH-CH_(2)-CH_(2)-CH=CH-Br` `CH_(2)=CH-CH_(2)-CH_(2)-UNDERSET(Br)underset(\|)C=CH_(2)` `CH_(3)-underset(Br)underset(\|)CH-CH_(2)-CH_(2)-C-=CH` Answer :D

Discussion

6767.	Write the direction ratios and direction cosines of the vectoroversetrarra=2overset^^i+3overset^^j-4overset^^k.
Answer» Solution :DIRECTION Ratios (2,3-4) `\|a\|=SQRT(4+9+16)=sqrt(29)` Direction COSINES` (2/sqrt(29),3/sqrt(29),-4/sqrt(29))`

Discussion

6768.	Match the following {:("I. Foot of the perpendicular from (3, 4) to the line " 3x-4y=18, (a) "(-7/5, -6/5)"), ("II. Image of (-3, 4) with respectto the origin" , (b) "(-1, -14)"), ("III. Image of (1, 2) with respect to "3x+4y-1=0, (c)"(6,0)"), ("IV. The reflection of (4, -13) in the line "5x+y+6=0, (d)"(3, -4)"):}
Answer» C, d, a, B c, b, d, a d, c, b, a a, b, c, d ANSWER :A

Discussion

6769.	A number is selected from the set of all 4 digited numbers and found that the sum of the 4 digits of the selected number is 33. Find the probabiltiy that the selected number is divisible by 4.
Answer» ANSWER :`(3)/(20)`

Discussion

6770.	Solve : x^3-15x^2+66x+80=0given that the roots as in AP.
Answer» ANSWER :2,5,8

Discussion

6771.	If A+B+C=0^(@) then sin A +sin B+sin C=
Answer» `4sin A//2sinB//2 sin C//2` `-4sinA//2 sinB//2 sin C//2` `4COS A//2 COS B//2 cos C//2` `-4cosA//2 cos B//2 cos C//2` ANSWER :B

Discussion

6772.	Find the optimal solutionof the aboveLPP and the maximumvalue of Z
Answer» ANSWER :C

Discussion

6773.	In a box there are 3 green and 7 white balls. Two balls are drawn from it without replacement. Find the probability of an event that selected second ball is green when selected first ball is also green.
Answer» ANSWER :`(2)/(9)`

Discussion

6774.	A circle touches a rectangle ABCD of side lengths 2a and 2b at M and N on sides AB and AD respectively , it also passes through the point C. If perpendicular distance of the line MN from points C is 6 cm.Then value of ab is ____
Answer»

Discussion

6775.	An ellipse having coordinate axes as its axes and semi major and semi minor of ellipse area a and b respectively whre a and b are middle terms of aseries a_(1), a_(2), a_(10) where a_(1i) a_(11-i)=5 sqrt(3) for all I from 1 to 10. also triangle FBF is an equilaterla triangle where B, F, F are one end of minor axis and foci of ellipse respectively. The equation of ellipse is
Answer» `(X^(2))/(10)+(2y^(2))/(15)=1` `(x^(2))/(10)+(y^(2))/(15)=1` `(x^(2))/(10)+(y^(2))/(15)=1` `(x^(2))/(10)+(y^(2))/(15)=1` ANSWER :A

Discussion

6776.	Leta functionf(x)bedefinded by f(x) =(x-\|x-1\|)/(x) whichof thefollowingis nottrue ?
Answer» Discontinuousat x=0 DISCONTINUOUS at x=1 Not DIFFERENTIABLE at x=0 Not differentiable at x=1 Answer :B

Discussion

6777.	Delta ABC be a triangle inscribed in a circle \|z\|=1 when B(Z_1), C(Z_2) are the vertices perpendicular from Ais drawn to BC which meet circle at P(Z). Then reflection of P(Z) through BC is
Answer» `("ZZ"_1 - Z_1 Z_2 + "ZZ"+_2)/(Z)` `("ZZ"_1 + Z_1 Z_2 + "ZZ"_2)/(2)` `("ZZ"_1 + Z_1 Z_2 + "ZZ"_3)/(Z)` 0 Answer :A

Discussion

6778.	Out of the following points, how many points are satisfied the inequality 2x-3y gt -5 ? (1, -1), (-1, 1), (1, -1), (-1, -1), (-2, 1), (2, -1), (-1, 2) and (-2, -1).
Answer» 3 5 6 4 Answer :B

Discussion

6779.	In triangle ABC, AB = AC and the length of median from B to the side AC is l. Find the cosine of angle A for which the area of triangle ABC is maximum.
Answer» ANSWER :`COS A = 4/5`

Discussion

6780.	For given vectors vec(a)=3hati+4hatj-5hatk and vec(b)=2hati+hatj find the unit vectors in the direction of the vector vec(a)+2vec(b).
Answer» Answer :`(7)/(SQRT(110))HATI+(6)/(sqrt(110))hatj-(5)/(sqrt(110))HATK`

Discussion

6781.	{:("Column A","A regurlar polygong of 24 sides is inscribed in a circle","Column B"),("The perimenter of the polygon",,"The circumference of the circle"):}
Answer» If column A is larger If column B is larger If the columns are EQUAL If there is not ENOUGH INFORMATION to decide Answer :B

Discussion

6782.	A new tetrahedron is formed by joining the centroids of the faces of a given tetrahedron OABC. Then the ratio of the volume of the new tetrahedron to that of the given tetrahedron is
Answer» `3/25` `1/27` `5/62` `1/162` ANSWER :B

Discussion

6783.	Find the area of the region bounded by the ellipse : (a) (x ^(2))/( 9) + (y ^(2))/(4) =1 (b) (i ) 16 x ^(2) + 9y ^(2) = 144 (ii) 4x ^(2) + 25 y ^(2) =1.
Answer» Answer :(a)` 6PI` sq. UNITS (B) (i) `12pi` sq. units (ii) `(PI)/(10)` sq. units

Discussion

6784.	If veca, vecb, vecc are three non - coplanar vector such that vecaxx(vecbxxvecc)=(vecb+vecc)/(sqrt2), then the angle between veca and vecb is ……………. .
Answer» 3pi/4 3pi `(PI)/(4)` `pi` ANSWER :B

Discussion

6785.	The number of triangles which are obtuse and which have the points (8,9),(8,16) and (20,25) as the feet of perpendiculars drawn from the vertices on the opposite sides is
Answer» 0 1 2 3 Solution :There EXIST exactly four triangles `ABC,APC,APB` and BPC satisfying the given conditions of which three triangles will be OBTUSE angle.

Discussion

6786.	A factory owner purchases two types of machines, Aand Bfor hisfactory. The requirements and the limitations for the machines are asfollows:MachineAreaoccupiedLabour forceDaily output(in units) A 1000\ m^2 12\ m e n 60 B 1200\ m^2 8\ m e n 40He has maximum area of 9000\ m^2available, and 72 skilled labourers who canoperate both the machines. How many machines of each type should he buy tomaximise the daily output?
Answer» ANSWER :X: 2 UNITS; Y : 6 uniys maximum revenue Rs. 760

Discussion

6787.	Find the equation of circle passing through each of the following three points. (3,4),(3,2),(1,4)
Answer» ANSWER :` X^(2) + y ^(2)-4X -6Y +11=0 `

Discussion

6788.	Whichof thefollowingfunctionis thricedifferentiableat x=0?
Answer» `f(x) =\|x^(3)\|` `f(x)=x^(3)\|x\|` `f(x)=\|x\|sin ^(3) x` `f(x) = x \|tan ^(3)x\|` ANSWER :B::C::D

Discussion

6789.	Coefficient of x^25 in the expansion of the expression sum_(r = 0)^50 ""^50C_r (2x - 3)^r (2-x)^(n-r)is :
Answer» `""^50C_25` `-""^50C_24` `-""^50C_25` None of these Solution :`sum_(R =0)^50 ""^50C_r (2x - 3)^r (2-x)^(N-r)` `= ""^50C_0 (2x - 3)^0 . (2-x)^n + ""^50C_1 (2x - 3)^1 (2-x)^(n-1) + ""^50C_2(2x - 3)^2 (2-x)^(n-2) + ……""^50C_50(2x - 3)^n` ` = (x - 1)^50 = ""^50C_0 x^50 - ""^50C_1 x^49 + …….` COEFFICIENT of `x^25` is`-""^50C_25` .

Discussion

6790.	The two variable vectors 3xhati+yhatj-3hatk and xhati-4yhatj+4hatk are orthogonal to each other, then the locus of (x, y) is
Answer» HYPERBOLA circle straight line ellipse Solution :Givenvectors areorthogonal ` (3xhati +yhatj-3hatk ).(xhati -4yhatj-4hatk)=0` `implies3x ^(2) -4Y^(2) -12=0` `implies (X^(2))/(4)-(y^(2))/(3)=1` HENCE. It represents a hyperbola.

Discussion

6791.	Find the mean deviation from the median of the observations 1, 2, 3, 4 ?
Answer» ANSWER :1

Discussion

6792.	Compute the following: [[a,b],[-b,a]]+[[a,b],[b,a]]
Answer» Solution :Given SUM=`[[a+a, b+b],[-b+b, a+a]]=[[2A, 2B],[0, 2a]]`

Discussion

6793.	Integrate the following functions (2cosx- 3sinx)/(6cosx +4sinx)
Answer» Solution :`(2cosx-3sinx)/(6cosx +4 SINX)` `(2cosx- 3sinx)/(2(2sinx +3cosx))` Let t = 2sinx +3cosx. Then dt = (2cosx-3sinx)dx therefore` INT (2cosx-3sinx)/(6cosx+4 sinx) dx` =`int 1/2 (dt)/t` =`1/2 log\|2sinx+3 cosx\|+c`

Discussion

6794.	Given that the events A and B are such that P(A)=1/2,P(AUB)=3/5 and P(B) =P.Find p if they are mutually exclusive
Answer» SOLUTION :SINCE A and B are mutually EXCLUSIVE,`P(ANNB)`=P(A)+P(B)`rArr`3/5=1/2+p`rArr`p=3/5-1/2=6-5/10

Discussion

6795.	If [(2,-3),(6,5)][(1,0),(2,3)]=[(-4,-9),(16,15)] Write the equation after applying elementary column transformation C_(2)rarrC_(2)+2C_(1)
Answer» ANSWER :`[(2,-3),(6,5)][(1,2),(2,7)]=[(-4,-17),(16,47)]`

Discussion

6796.	The quadrilateral by pairs of lines xy+x+y+1=0 ,xy+3x+4y+9=0 is
Answer» a RECTANGLE a SQUARE a parallelogram a RHOMBUS Answer :B

Discussion

6797.	A = The maximum value of 4x^(2) + 4x + 5 B = The maximum value of 8x-x^(2) C = The maximum value of -x^(2) + 4x-4 D = The maximum value of -7x^(2) + 100 then
Answer» `B LT D lt A lt C` `B lt C lt A lt D` `C lt A lt BLT D` `A lt D lt C lt B` ANSWER :C

Discussion

6798.	If the vectors 2hat(i)-hat(j)+hat(k),hat(i)+2hat(j)-3hat(k),3hat(i)+ahat(j)+5hat(k) are coplanar, then a =
Answer» -2 -3 -4 2 Answer :C

Discussion

6799.	Let 'S' be the focus and G be the point where the normal at P meets the axis of the ellipse then SG = eSP
Answer» <P> ANSWER :ES'p

Discussion

6800.	The value of e[lim_(x to 0) ("sinx"/x)^((sinx)/(x-sinx))+lim_(x to 1) x^(1/(1-x))]
Answer» ANSWER :2

Discussion

Explore topic-wise InterviewSolutions in .

Solve (dy)/(dx) = (3x- y - 1)^(2)

How many integer pairs (x,y) satisfy x^(2) + 4y^(2) -2xy -2x - 4y -8=0 ?

Which of the following is equivalent to1 le |x-2| le 4 ?

The locus of Z satisfying |z| + |z- 1| = 3 is

Equation of a line passing through point (2, -1, 3) and parallel to line (2x-1)/(2)=(1-y)/(1)=(z)/(3) is

From which of the following the distance of the point (1,2,3) is sqrt(10)?

If the total produce sales in July at Produce Stand P were $4,500, what were the approximate total fruit sales in December at Product Stand P?

a circular wheel with numbers 1 to 20 on its surface is rolled twice. What is the probability of getting two 13's ?

Evaluate the definite integrals . underset(-pi//2)overset(pi//2)int (cosx)/(1+e^(x))dx

If D=|{:(2,3,1),(5,-1,2),(7,4,-1):}| , performing R_(12(-1) on D then D will become ….

If y=xlog(x/(2-3x))" for "0ltxlt2/3," then "(d^(2)y)/(dx^(2))" at "x=1/2 is

The points in which the line (x-1)/(1)=(y-1)/(-1)=(z+3)/(1) cuts the surface x^(2)+y^(2)+z^(2)-20=0

A person standing at the junction (crossing) of two straight paths represented by the﻿ equations 2x-3y+4= 0 and 3x + 4y-5=0 wants to reach the path whose equation is 6x – 7y+8=0﻿ in the least time. Find equation of the path that he should follow.

"Let" f(x) =sqrtx "and" g(x) = 1 -x^2.Find natural domain of h(x) = 1-x.

If f is continuous function then which of the following is correct:

CH_(2)=CH-CH_(2)-CH_(2)-C-=CH underset((1 eq))overset(HBr)toProduct is

Write the direction ratios and direction cosines of the vectoroversetrarra=2overset^^i+3overset^^j-4overset^^k.

A number is selected from the set of all 4 digited numbers and found that the sum of the 4 digits of the selected number is 33. Find the probabiltiy that the selected number is divisible by 4.

Solve : x^3-15x^2+66x+80=0given that the roots as in AP.

If A+B+C=0^(@) then sin A +sin B+sin C=

Find the optimal solutionof the aboveLPP and the maximumvalue of Z

In a box there are 3 green and 7 white balls. Two balls are drawn from it without replacement. Find the probability of an event that selected second ball is green when selected first ball is also green.

A circle touches a rectangle ABCD of side lengths 2a and 2b at M and N on sides AB and AD respectively , it also passes through the point C. If perpendicular distance of the line MN from points C is 6 cm.Then value of ab is ____

Leta functionf(x)bedefinded by f(x) =(x-|x-1|)/(x) whichof thefollowingis nottrue ?

Delta ABC be a triangle inscribed in a circle |z|=1 when B(Z_1), C(Z_2) are the vertices perpendicular from Ais drawn to BC which meet circle at P(Z). Then reflection of P(Z) through BC is

Out of the following points, how many points are satisfied the inequality 2x-3y gt -5 ? (1, -1), (-1, 1), (1, -1), (-1, -1), (-2, 1), (2, -1), (-1, 2) and (-2, -1).

In triangle ABC, AB = AC and the length of median from B to the side AC is l. Find the cosine of angle A for which the area of triangle ABC is maximum.

For given vectors vec(a)=3hati+4hatj-5hatk and vec(b)=2hati+hatj find the unit vectors in the direction of the vector vec(a)+2vec(b).

{:("Column A","A regurlar polygong of 24 sides is inscribed in a circle","Column B"),("The perimenter of the polygon",,"The circumference of the circle"):}

A new tetrahedron is formed by joining the centroids of the faces of a given tetrahedron OABC. Then the ratio of the volume of the new tetrahedron to that of the given tetrahedron is

Find the area of the region bounded by the ellipse : (a) (x ^(2))/( 9) + (y ^(2))/(4) =1 (b) (i ) 16 x ^(2) + 9y ^(2) = 144 (ii) 4x ^(2) + 25 y ^(2) =1.

If veca, vecb, vecc are three non - coplanar vector such that vecaxx(vecbxxvecc)=(vecb+vecc)/(sqrt2), then the angle between veca and vecb is ……………. .

The number of triangles which are obtuse and which have the points (8,9),(8,16) and (20,25) as the feet of perpendiculars drawn from the vertices on the opposite sides is

Find the equation of circle passing through each of the following three points. (3,4),(3,2),(1,4)

Whichof thefollowingfunctionis thricedifferentiableat x=0?

Coefficient of x^25 in the expansion of the expression sum_(r = 0)^50 ""^50C_r (2x - 3)^r (2-x)^(n-r)is :

The two variable vectors 3xhati+yhatj-3hatk and xhati-4yhatj+4hatk are orthogonal to each other, then the locus of (x, y) is

Find the mean deviation from the median of the observations 1, 2, 3, 4 ?

Compute the following: [[a,b],[-b,a]]+[[a,b],[b,a]]

Integrate the following functions (2cosx- 3sinx)/(6cosx +4sinx)

Given that the events A and B are such that P(A)=1/2,P(AUB)=3/5 and P(B) =P.Find p if they are mutually exclusive

If [(2,-3),(6,5)][(1,0),(2,3)]=[(-4,-9),(16,15)] Write the equation after applying elementary column transformation C_(2)rarrC_(2)+2C_(1)

The quadrilateral by pairs of lines xy+x+y+1=0 ,xy+3x+4y+9=0 is

A = The maximum value of 4x^(2) + 4x + 5 B = The maximum value of 8x-x^(2) C = The maximum value of -x^(2) + 4x-4 D = The maximum value of -7x^(2) + 100 then

If the vectors 2hat(i)-hat(j)+hat(k),hat(i)+2hat(j)-3hat(k),3hat(i)+ahat(j)+5hat(k) are coplanar, then a =

Let 'S' be the focus and G be the point where the normal at P meets the axis of the ellipse then SG = eSP

The value of e[lim_(x to 0) ("sinx"/x)^((sinx)/(x-sinx))+lim_(x to 1) x^(1/(1-x))]

A person standing at the junction (crossing) of two straight paths represented by the equations 2x-3y+4= 0 and 3x + 4y-5=0 wants to reach the path whose equation is 6x – 7y+8=0 in the least time. Find equation of the path that he should follow.