14949 + Interview Questions in Maths in Class 11 Page 72 InterviewSolution

3551.	Passing through the point (-4, 3)with slope 1/2.
Answer» ANSWER :`X - 2Y + 10 = 0 `

Discussion

3552.	a die is thrown twice . What is the probability that at least one of the two numbers is 4?
Answer» ANSWER :`=(11)/(36)`.

Discussion

3553.	Find the bisector of the obtuse angle between the lines 12x+5y-4=0 and 3x+4y+7=0
Answer» ANSWER :`7x-9y-37=0`

Discussion

3554.	Show that the system of equations given below is not consistant 2x+6y=-11 6x+20y-6z=-3 6y-18z=-1
Answer» ANSWER :HENCE the GIVEN SYSTEM is INCONSISTENT.

Discussion

3555.	If(-4,3) arethecoordinates of a point P in the new systemwhen the origin is shifted to (1,5),then find original coordinatres of P.
Answer» ANSWER :8

Discussion

3556.	Show that (cosA)/(a)+(cosB)/(b)+(cosC)/(c)=(a^(2)+b^(2)+c^(2))/(2abc)
Answer» a bc `a+b+c` ABC Answer :D

Discussion

3557.	Prove that f (x) = x \|x\| is differentiable at x =0 andfind f'(0) also find f '(x) on R.
Answer» ANSWER :`0, F'(X) = 2\|x\| , x in R `

Discussion

3558.	Find the point to which the origin should be translated in order to make the first degree terms missing in the equation 3xy - 2x + y - 8 = 0
Answer» ANSWER :`((-1)/(3),(2)/(3))`

Discussion

3559.	Find (a) the eccentricities, (b) the co-ordinates of the foci (c )the equations of the directricies of the following hyperbolas (i) ((x -1) ^(2))/(9) - (y ^(2))/(4) =1 (ii) ((x +1) ^(2))/( 64) - ((y -2) ^(2))/(36) =1.
Answer» ANSWER :`X = + (32)/(5)`

Discussion

3560.	A and B are fixed points of \|PA-PB\|=K (constant) and KltAB then the locus of P is
Answer» Hyperbola an ellipse straight LINE a CIRCLE ANSWER :1

Discussion

3561.	If x^2 + xy + 3y^2 = 1 then (x + 6y)^3 (d^2y)/(dx^2) is
Answer» `0` `-12` `22` `-22` ANSWER :D

Discussion

3562.	Find the equation of locus of a point such that the difference of whose distances from (-5,0) and (5,0) is 8
Answer» ANSWER :`(X^(2))/(16)-(y^(2))/(9)=1`

Discussion

3563.	If bar(a), bar(b), bar(c ) are the sides and s is the semi perimeter of the tirangle ABC then the area of the triangle Delta = sqrt(s(s-a) (s-b) (s-c))
Answer» ANSWER :`Detla = SQRT(s(s-a) (s-b) (s-c))`

Discussion

3564.	If 1+sin^(2)theta=3sinthetacostheta then the solution set in [0,(pi)/(2)] is
Answer» `{(PI)/(4),cos^(-1)(1//3)}` `{(pi)/(4),tan^(-1)(1//2)}` `{(pi)/(3),tan^(-1)(1//3)}` `{(pi)/(6),SIN^(-1)(1//3)}` Answer :B

Discussion

3565.	Insert 6 arithmatic mean between 3 and 24.
Answer» ANSWER :`6,9,12,15,18,21`

Discussion

3566.	Four cards are drawn from a full pack of cards . Find the probability thatthere is one card of each suit,
Answer» ANSWER :`=(2197)/(20825)`.

Discussion

3567.	Determine the probability p, for each of the following events. (a) An odd number appears in a single toss of a fair die. (b) At least one head appears in two tosses of a fair coin. (c ) A king, 9 of hearts, or 3 of spades appears in drawing a single card from a well shuffled ordinary deck of 52 cards. The sum of 6 appears in a single toss of a pair of fair dice.
Answer» <P> Answer :(i) `(1)/(2)`(II) `p=(3)/(4)` (iii) `(3)/(26)` (iv) `(5)/(36)`

Discussion

3568.	25th percentile is 20 and 75th percentile is 50, then semi interquartile range is
Answer» 10 40 15 25 Answer :C

Discussion

3569.	The value of 'c' prescribed by Lagrange's mean value theorem , when f(x) = sqrt( x^(2) - 4) , a = 2 ,b = 3 is
Answer» `5//2` `SQRT(5)` `sqrt(3)` `sqrt(3+1)` ANSWER :B

Discussion

3570.	One card is drawn from a well shuffled deck of 52 cards. If each outcomes is equally likely, calculate the probability that the card will be (i) a diamond (ii) not a ace (iii) a black card (i.e., a club or, a spade) (iv) not a diamond (v) not a black card.
Answer» ANSWER :`7/9`

Discussion

3571.	How many litres of water will have to be added to 1125 litres of the 45% solution of acid so that the resulting mixture will contain more than 25% but less than 30% acid content ?
Answer» ANSWER :More than 562.5 LITRES but LESS than 900 litres.

Discussion

3572.	Determine the number of 5 cards combinations out of a deck of 52 cards, if at least one of the 5 cards has to be an ace ?
Answer» ANSWER :8,82,144

Discussion

3573.	Angle between the lines sqrt(3)x+y+1=0, x+1=0 is
Answer» `30^(@)` `60^(@)` `45^(@)` `120^(@)` ANSWER :A

Discussion

3574.	Find the value of P(7,3)
Answer» ANSWER :` 210 `

Discussion

3575.	Find Lt_(xtooo)((x+a)/(x+b))^(x), a, b are constants.
Answer» ANSWER :`E^(a-b)`

Discussion

3576.	Find the derivative of the function sin ^(2) x (sin ^(-1) x ) ^(2)
Answer» Answer :`SIN2X (sin^(-1)X)^(2)+ (2 sin^(2)x sin ^(-1) x)/(SQRT (1- x ^(2)) )`

Discussion

3577.	Express each of the complex number given in the exercise. i^(-39)
Answer» ANSWER :`0+i`

Discussion

3578.	The vector area of the triangle formed by the points vec(i) -vec(j) + vec(k), 2vec(i) + vec(j) -2vec(k) and 3vec(i) + vec(j) + 2vec(k) is
Answer» `4 VEC(i) -(7)/(2) vec(j)- vec(k)` `4vec(i) + (7)/(2) vec(j) + vec(k)` `4vec(i)-7vec(j) + 2vec(k)` `vec(i) -vec(j) + vec(k)` Answer :A

Discussion

3579.	Find the derivative of the following functions from first principle cos(x-(pi)/(8))
Answer» Answer :`-SIN(X-(PI)/(8))(because lim_(xto0)(sinx)/(x)=1)`

Discussion

3580.	If n gt 1 then
Answer» `N ! = ((n+1)/(2) )^(n)` `n!LT ((n+1) /(2) )^(n)` `n! GT ((n+1)/(2) )^(n) ` none Answer :B

Discussion

3581.	If the angle of tangents from vertices to Incircle are H.P then r_(1),r_(2), r_(3) then in
Answer» A.P G.P H.P A.G.P Answer :A

Discussion

3582.	If bar(a), bar(b) are two non collinear vectors, then bar(r)=sbar(a)+tbar(b) represents
Answer» line plane plane PASSING through origin sphere Answer :C

Discussion

3583.	The smallest positive value of x (in degress) for whiich tan (x + 100^(@)) = tan (x + 50^(@)) .tan xtan (x-50^(@)) is
Answer» `30^(@)` `45^(@)` `55^(@)` `15^(@)` ANSWER :A

Discussion

3584.	Find the variance and standard deviation for the following data:
Answer» ANSWER :6.77

Discussion

3585.	Equation of a line is 3x-4y+ 10 =0. Find its (ii) x -intercepts and y -intercepts.
Answer» ANSWER :(II) x-intercepts `a= -(10)/(3), and y-` intercepts `B= (5)/(2)`

Discussion

3586.	Use tables to find the acute angle between the lines 2y+x=0 and x/(1)+y/(2)=2.
Answer» ANSWER :`"tan"^(-1)(3/(4))="tan"^(-1)(0.75)=36^(@)52'`

Discussion

3587.	If every pair from among the equations x^(2)+px+qr=0,andx^(2)+rx+pq=0 have a common root, then (("sum of all distinct roots")/("Product of all distinct roots")) is
Answer» ANSWER :SUM of the ROOTS `= (-p + q + R)/(2)` Product of the roots = pqr

Discussion

3588.	If f(x) = sin^(-1)(x^2//sqrt(x^4+16)) then 17f'(1) is equal to
Answer»

Discussion

3589.	if ((a^2 + a),(3)) = ((a^2 + a),(9)), then a = ....
Answer» 3 9 12 6 Answer :A

Discussion

3590.	Find the coefficient of : y^(5) " in " (3y^(2)+1/(3y))^(10)
Answer» ANSWER :252

Discussion

3591.	(d)/(dx) {Sin ^(-1)"" ((5x + 12 sqrt(1- x ^(2)))/(12))}=
Answer» `1/(SQRT(1 - x^2))` `(-1)/(sqrt(1 + x^2))` `(2)/(sqrt(1 - x^2))` `0` ANSWER :A

Discussion

3592.	If bar(a)=bar(i)-2bar(j)+bar(k), bar(b)=4bar(i)+2bar(j)-bar(k), bar(c)=bar(i)+2bar(j)-bar(k) and bar(a)+lambdabar(b) is parallel to bar(c) then lambda=
Answer» `(-2)/3` `2/3` `3/2` `(-3)/2` ANSWER :A

Discussion

3593.	If sectheta-1=(sqrt(2)-1)tantheta, then general value of theta is:
Answer» `(NPI)/(2)` `npi` `2NPI` `3npi` SOLUTION :N//A

Discussion

3594.	Find the circumcentre of the triangle whose vertices are A(1,0),B(-1,2) and C(3,2)
Answer» ANSWER :`(1,2)`

Discussion

3595.	Evaluate the following limits : Lim_(x to 0) (e^(4x)-1)/x
Answer» ANSWER :4

Discussion

3596.	Find the domain and range of the function f = {(x, (x^2 -1)/(x - 1)): x in R, x ne 1}
Answer» Solution :DOMAIN = R - {1}, RANGE = R - (2)]

Discussion

3597.	4 cos (5 - 2 x) + 9e^(3x-6) + (24)/(6 - 4 x)
Answer» ANSWER :C

Discussion

3598.	What is the coefficient of 5th, 6th and 7th terms in the expansion of (1+x)^n?
Answer» SOLUTION :`^nC_4. ^nC_5. ^nC_6`

Discussion

3599.	Let f: [-3, 3] rarr R where f(x)=x^(2) + sin x + [(x^(2)+2)/(a)] be an odd function then the value of a is ( where [.] represents greatest integer function)
Answer» LESS than 11 11 greater than 11 12 Answer :C

Discussion

3600.	Find the polar form of the complex number (1-3i)/(1+2i)
Answer» Answer :`SQRT2[cos((-3PI)/4) + isin((-3pi)/4)]`

Discussion

Explore topic-wise InterviewSolutions in .

Passing through the point (-4, 3)with slope 1/2.

a die is thrown twice . What is the probability that at least one of the two numbers is 4?

Find the bisector of the obtuse angle between the lines 12x+5y-4=0 and 3x+4y+7=0

Show that the system of equations given below is not consistant 2x+6y=-11 6x+20y-6z=-3 6y-18z=-1

If(-4,3) arethecoordinates of a point P in the new systemwhen the origin is shifted to (1,5),then find original coordinatres of P.

Show that (cosA)/(a)+(cosB)/(b)+(cosC)/(c)=(a^(2)+b^(2)+c^(2))/(2abc)

Prove that f (x) = x |x| is differentiable at x =0 andfind f'(0) also find f '(x) on R.

Find the point to which the origin should be translated in order to make the first degree terms missing in the equation 3xy - 2x + y - 8 = 0

Find (a) the eccentricities, (b) the co-ordinates of the foci (c )the equations of the directricies of the following hyperbolas (i) ((x -1) ^(2))/(9) - (y ^(2))/(4) =1 (ii) ((x +1) ^(2))/( 64) - ((y -2) ^(2))/(36) =1.

A and B are fixed points of |PA-PB|=K (constant) and KltAB then the locus of P is

If x^2 + xy + 3y^2 = 1 then (x + 6y)^3 (d^2y)/(dx^2) is

Find the equation of locus of a point such that the difference of whose distances from (-5,0) and (5,0) is 8

If bar(a), bar(b), bar(c ) are the sides and s is the semi perimeter of the tirangle ABC then the area of the triangle Delta = sqrt(s(s-a) (s-b) (s-c))

If 1+sin^(2)theta=3sinthetacostheta then the solution set in [0,(pi)/(2)] is

Insert 6 arithmatic mean between 3 and 24.

Four cards are drawn from a full pack of cards . Find the probability thatthere is one card of each suit,

25th percentile is 20 and 75th percentile is 50, then semi interquartile range is

The value of 'c' prescribed by Lagrange's mean value theorem , when f(x) = sqrt( x^(2) - 4) , a = 2 ,b = 3 is

One card is drawn from a well shuffled deck of 52 cards. If each outcomes is equally likely, calculate the probability that the card will be (i) a diamond (ii) not a ace (iii) a black card (i.e., a club or, a spade) (iv) not a diamond (v) not a black card.

How many litres of water will have to be added to 1125 litres of the 45% solution of acid so that the resulting mixture will contain more than 25% but less than 30% acid content ?

Determine the number of 5 cards combinations out of a deck of 52 cards, if at least one of the 5 cards has to be an ace ?

Angle between the lines sqrt(3)x+y+1=0, x+1=0 is

Find the value of P(7,3)

Find Lt_(xtooo)((x+a)/(x+b))^(x), a, b are constants.

Find the derivative of the function sin ^(2) x (sin ^(-1) x ) ^(2)

Express each of the complex number given in the exercise. i^(-39)

The vector area of the triangle formed by the points vec(i) -vec(j) + vec(k), 2vec(i) + vec(j) -2vec(k) and 3vec(i) + vec(j) + 2vec(k) is

Find the derivative of the following functions from first principle cos(x-(pi)/(8))

If n gt 1 then

If the angle of tangents from vertices to Incircle are H.P then r_(1),r_(2), r_(3) then in

If bar(a), bar(b) are two non collinear vectors, then bar(r)=sbar(a)+tbar(b) represents

The smallest positive value of x (in degress) for whiich tan (x + 100^(@)) = tan (x + 50^(@)) .tan xtan (x-50^(@)) is

Find the variance and standard deviation for the following data:

Equation of a line is 3x-4y+ 10 =0. Find its (ii) x -intercepts and y -intercepts.

Use tables to find the acute angle between the lines 2y+x=0 and x/(1)+y/(2)=2.

If every pair from among the equations x^(2)+px+qr=0,andx^(2)+rx+pq=0 have a common root, then (("sum of all distinct roots")/("Product of all distinct roots")) is

If f(x) = sin^(-1)(x^2//sqrt(x^4+16)) then 17f'(1) is equal to

if ((a^2 + a),(3)) = ((a^2 + a),(9)), then a = ....

Find the coefficient of : y^(5) " in " (3y^(2)+1/(3y))^(10)

(d)/(dx) {Sin ^(-1)"" ((5x + 12 sqrt(1- x ^(2)))/(12))}=

If bar(a)=bar(i)-2bar(j)+bar(k), bar(b)=4bar(i)+2bar(j)-bar(k), bar(c)=bar(i)+2bar(j)-bar(k) and bar(a)+lambdabar(b) is parallel to bar(c) then lambda=

If sectheta-1=(sqrt(2)-1)tantheta, then general value of theta is:

Find the circumcentre of the triangle whose vertices are A(1,0),B(-1,2) and C(3,2)

Evaluate the following limits : Lim_(x to 0) (e^(4x)-1)/x

Find the domain and range of the function f = {(x, (x^2 -1)/(x - 1)): x in R, x ne 1}

4 cos (5 - 2 x) + 9e^(3x-6) + (24)/(6 - 4 x)

What is the coefficient of 5th, 6th and 7th terms in the expansion of (1+x)^n?

Let f: [-3, 3] rarr R where f(x)=x^(2) + sin x + [(x^(2)+2)/(a)] be an odd function then the value of a is ( where [.] represents greatest integer function)

Find the polar form of the complex number (1-3i)/(1+2i)