14949 + Interview Questions in Maths in Class 11 Page 66 InterviewSolution

3251.	If 9 boys and 5 girls are to be seated in a row, find the probability that 4 particular persons never sit together (not even two of them.)
Answer» ANSWER :`=90/91`

Discussion

3252.	If the slope of one line of the pair of ax^(2)+2hxy+by^(2)=0 is double that of the other, then
Answer» `8H^(2)=9ab` `9h^(2)=8ab` `3h^(2)=4AB` `H^(2)=ab` Answer :A

Discussion

3253.	If roots of the equation 2 x^(2) - 4 x + 2 sin theta - 1 = 0are of opposite sign, then 'theta' belongs to
Answer» `((PI)/( 6), (5 pi)/(6))` ` (0, (pi)/( 6)) cup ((5 pi)/(6), pi)` ` ((13 pi)/( 6), (17 pi)/( 6))` `(0, pi)` ANSWER :B

Discussion

3254.	Iftan(pi//4+ theta ) + tan(pi//4- theta )= k sec 2 theta, thenthe value of k is .
Answer» 1 2 3 4 Answer :B

Discussion

3255.	If bar(a), bar(b), bar(c) are the position vectors of the vertices A, B, C of the triangle ABC, then the equation of the median from A to BC is
Answer» `BAR(R)=bar(a)+t(bar(B)+bar(C))` `bar(r)=bar(a)+t[1/2(bar(b)+bar(c))-bar(a)]` `bar(r)=bar(a)+t(bar(b))+bar(c)` `bar(r)=-bar(a)+t(bar(b))+bar(c)` ANSWER :B

Discussion

3256.	P(m,n)(m,nin N) is any point in the inerior of the the quadrilateral formed by the pair of lines xy=0 and two lines 2x+y-2=0 and 4x+5y=20 then the possible number of positions of the points P is
Answer» 4 5 6 11 Answer :C

Discussion

3257.	underset(x to 0)"Lt" ((1-cos 2x)(3+cos x))/(x tan 4x )) is equal to
Answer» 4 3 2 `(1)/(2)` ANSWER :C

Discussion

3258.	Find the value of x for which A=[(e^(2x+1),e^(x-2)),(e^(2-x),e^(x-7))]is singular:
Answer» -3 3 2 -2 Answer :C

Discussion

3259.	If 3costheta+4sintheta=lambda has a solution find the range of lambda.
Answer» ANSWER :`[-5,5]`

Discussion

3260.	sin alpha + sin beta= 1/4 and cos alpha + cos beta = 1/3 The vlaue of tan (alpha + beta) is
Answer» `25/7` `25/12` `25/13` `24/7` ANSWER :D

Discussion

3261.	Find the term independent of x in the expansion of (root(3)(x)+1/(2 root(3)(x)))^18,x > 0.
Answer» ANSWER :The REQUIRED TERM is `^18`Cunderset9 `1/2^9`.

Discussion

3262.	Write the negation of the following statements and check whether the resulting statements are true, The sum of 3 and 4 is 9.
Answer» ANSWER :1

Discussion

3263.	Fourcards are drawn at random from a pack of 52 playing cards , Find the probability of getting all the four cards of the same suit
Answer» ANSWER :`(4""^(13)C_(4))/(""^(52)C_(4))=(198)/(20825)`

Discussion

3264.	Fourcards are drawn at random from a pack of 52 playing cards , Find the probability of getting all the four cards of the same number ,
Answer» ANSWER :`(13)/(""^(52)C_(4))=(13)/(270725)`

Discussion

3265.	Following are thescores of 12 students in a class test ofof 30marks : 18,20,9,15,21,26,14,13,27,22,16,28 Find D_(7)andP_(33).
Answer» <P> ANSWER :`D_(7)=24;P_(33)=15.5`

Discussion

3266.	Write the negation of the following statements and check whether the resulting statements are true, There does not exist a quadrilateral which has all its sides equal.
Answer» ANSWER :1

Discussion

3267.	A= {1, 2, 3, 4, 5}, B= {1, 3, 5, 6}, C= {1, 2, 3}, then find the following sets. A- (B cap C)
Answer» ANSWER :`={2, 4, 5}`

Discussion

3268.	Solutions of the equation sin (sqrt(1 + sin 2 theta)) = sin theta + cos theta " is " (n in Z)
Answer» `N pi - (pi)/( 4)` ` n pi + (pi)/( 12)` ` n pi + (pi)/( 6)` ` n pi - (pi)/(6)` Answer :A

Discussion

3269.	A table has 7 seats, 4 being on one side facing the window and 3 being on the opposite side. In how many ways can 7 people be seated at the table. If 3 people , X,Y and Z must sit on the side facing the window ?
Answer» ANSWER :` 2160` ` 2880`

Discussion

3270.	Define (i) f(x)=(1+5x)^(1//x)is continuous at x = 0.
Answer» ANSWER :`E^(5)`

Discussion

3271.	Find a sample space associated with the experiment of rolling a pair of dice (one is blue and other is red) once is Also, find the number od element of this sample space.
Answer» ANSWER :S = {(X, Y)}: x

Discussion

3272.	In the hexagon PQRSTU, RS\|\|PU\|\|QT. Which sides or diagonals have infinite slope?
Answer» ANSWER :PQ, UT

Discussion

3273.	Let A (5,2), B (3,-3) and C (-4,3) be the vertices of a Delta ABC. Find the equation of BC
Answer» SOLUTION :6X + 7Y + 3 = 0

Discussion

3274.	The point P on the line passing through A(3bar(i)+2bar(j)-3bar(k)) and parallel to the vectors 2bar(i)-2bar(j)+bar(k) such that AP = 6 is
Answer» `7bar(i)-2BAR(J)-BAR(K)` `5bar(i)-2bar(k)` `bar(i)+4bar(j)-4bar(k)` `bar(i)-4bar(j)+4bar(k)` ANSWER :A

Discussion

3275.	If z_(1) =2 -i, z_(2)=1+i, find \|(z_(1) + z_(2) + 1)/(z_(1)-z_(2) + 1)\|
Answer» ANSWER :`SQRT(2)`

Discussion

3276.	In the given figure, AB is the diameter of the circle centered at O. If angle COA = 60^(@) , AB = 2r , AC = d . and CD = l, then l is equal to
Answer» `d SQRT3` `d// sqrt3` `3D` `sqrt3 d//2` ANSWER :A

Discussion

3277.	Consider the line 4x-3y+12=0 Which among the following lines is perpendicular to the line 4x-3y+12=0
Answer» `2x+3y-8=0` `4x-3y+5=0` `x+y=7` `3x+4y+9=0` ANSWER :D

Discussion

3278.	The value of ( sin theta )/( sin^(2) (pi//8 + theta //2)-sin^(2)(pi//8- theta //2))=
Answer» 2 `(1)/(2)` `SQRT(2)` `(1)/(sqrt(2)` ANSWER :C

Discussion

3279.	Write the following in roster form.(iii) {x inN:4x + 9 < 52}
Answer» Answer :1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Discussion

3280.	If the equation 12x^2-10xy+2y^2+14x-5y+c=0 represents a pair of straight lines, find the value of c . Find the separate equations of the straight lines and also the angle between them .
Answer» ANSWER :`TAN^(-1)(1/7)`

Discussion

3281.	If the paris x^(2)-2pxy-y^(2)=0 and x^(2)-2qxy-y^(2)=0 are such that one pair bisects the angle between the other and p=3 then q=
Answer» 3 `-1` `-1//3` `-1//2` ANSWER :C

Discussion

3282.	Find the 20^(th) and n^(th) term of the G.P.(5)/(2),(5)/(4),(5)/8) ……..?
Answer» ANSWER :`5/(2^(20)) ,5/(2^n)`

Discussion

3283.	Find the equation of a straight line on which length of perpendicular from the origin is four units and the line makes an angle of 120° with the positive direction of X -axis. Thinking Process : Equation of line which makes an angle alpha with positive side of X axis and whose length of perpendicular from origin p is given by x cos alpha+ y sin alpha = p.
Answer» ANSWER :`sqrt( 3) + y =8`, which is required equation of line.

Discussion

3284.	A tower substends angles alpha,2alpha,3alpha at A,B,C all lying on horizontal line through the foot of the tower the AB/BC=
Answer» `(Sin3alpha)/(Sin2alpha)` `1+2Cos2alpha` `2+2Cos2alpha` `(Sin2alpha)/(SINALPHA)` ANSWER :B

Discussion

3285.	If a straight line makes an angle cos^(-1)(1/sqrt(3)) with each of the positive x, y and z-axis, a vector parallel to that line is
Answer» `BAR(i)` `bar(i)+bar(J)` `bar(j)+bar(K)` `bar(i)+bar(j)+bar(k)` ANSWER :D

Discussion

3286.	Let f(x)=log(log_(1//3)(log_(7)(sinx+a))) be defined for every real value of x, then the possible value of a is
Answer» 3 4 5 6 Answer :A::B::C

Discussion

3287.	2Tan^(-1)((sqrt(a-b))/(a+b)"tan"x/2)=
Answer» `COS^(-1)((a cos THETA+b)/(a+b cos theta))` `Cos^(-1)((a cos theta-b)/(a-b cos theta))` `Cos^(-1)((a+b cos theta)/(acos theta +b))` `Cos^(-1)((a-b cos theta)/(acos theta -b))` Answer :A

Discussion

3288.	The unit vector perpendicular to vectors vec(i)-vec(j) and vec(i) + vec(j) forming a right handed system is
Answer» `VEC(K)` `-vec(k)` `(1)/(SQRT2) (vec(i)-vec(J))` `(1)/(sqrt2) (vec(i)+vec(j))` Answer :A

Discussion

3289.	A ladder 20 feet long whose top is resting against a vertical wall on a level plane begins to slide outward. At the moment when the foot of the ladder is 12 feet from the wall, it is sliding at the rate of 2 feet per second. How fast is the top sliding downwards at this instant? When the foot and top of the ladder are sliding at the same rate, find the distance of the foot from the wall.
Answer» ANSWER :`4. 3//2 FT//sec, 10sqrt2 ft`

Discussion

3290.	((sin2A)/(secA-1))((sec2A)/(sec2A+1))=
Answer» `"TAN"A/2` `-"Tan"A/2` `"COT"A/2` `-"Tan"A/2` ANSWER :C

Discussion

3291.	A line makes the same angle theta, with each of the x and z axis. If the angle beta, which it makes with y-axis, is such that sin^(2)beta=3sin^(2)theta, " then " cos^(2)theta=
Answer» ANSWER :`COS^(2) THETA = 3//5`

Discussion

3292.	If the middle term in the expansion of (1 + x)^(2n) is (1.3.5…(2n - 1))/(n!) k^(n).x^(n), the value of k is
Answer» 4 1 0 2 Answer :D

Discussion

3293.	The probability that student will get an reward for sports is 0.38 and another award for studies is 0.42 and the probability of getting both award is 0.2. Find the probability that (i)he will get atleast one award,(ii)he will get only one of the reward.
Answer» ANSWER :`0.6,0.4`

Discussion

3294.	Solve the inequalities 5x + 1 gt -24 , 5x -1 lt 24
Answer» ANSWER :`(-5,5)` `(##NCERT_TAM_MAT_XI_C06_E04_007_A01##)`

Discussion

3295.	If2 tan A + cot A = tan B , thencot A +2 tan (A-B)=
Answer» -1 0 1 `1//2` ANSWER :B

Discussion

3296.	Find the sum to n terms of the series whose n^(th) term is n^3-3^n
Answer» SOLUTION :`[(N(n+1))/2]^2-3/2(3^n-1)`

Discussion

3297.	If 0 lt A lt B lt (pi)/(4) and sin (A+B)=(24)/(25) and cos (A-B)= (4)/(5), then find the value of tan 2A.
Answer» ANSWER :`(3)/(4)`

Discussion

3298.	If A.M. and G.M. of roots of a quadratic equation are 8 and 5, respectively, thenobtain the quadratic equation.
Answer» ANSWER :`x^2 –16x + 25 = 0`

Discussion

3299.	Find the odd man out:
Answer» `F(X)=x^(3)` `f(x)=x^(3)+3X` f(x)=sinx f(x)=cosx Answer :D

Discussion

3300.	Sin40^(@) - Sin80^(@) + Sin160^(@) =
Answer» 0 -1 1 2 Answer :A

Discussion

Explore topic-wise InterviewSolutions in .

If 9 boys and 5 girls are to be seated in a row, find the probability that 4 particular persons never sit together (not even two of them.)

If the slope of one line of the pair of ax^(2)+2hxy+by^(2)=0 is double that of the other, then

If roots of the equation 2 x^(2) - 4 x + 2 sin theta - 1 = 0are of opposite sign, then 'theta' belongs to

Iftan(pi//4+ theta ) + tan(pi//4- theta )= k sec 2 theta, thenthe value of k is .

If bar(a), bar(b), bar(c) are the position vectors of the vertices A, B, C of the triangle ABC, then the equation of the median from A to BC is

P(m,n)(m,nin N) is any point in the inerior of the the quadrilateral formed by the pair of lines xy=0 and two lines 2x+y-2=0 and 4x+5y=20 then the possible number of positions of the points P is

underset(x to 0)"Lt" ((1-cos 2x)(3+cos x))/(x tan 4x )) is equal to

Find the value of x for which A=[(e^(2x+1),e^(x-2)),(e^(2-x),e^(x-7))]is singular:

If 3costheta+4sintheta=lambda has a solution find the range of lambda.

sin alpha + sin beta= 1/4 and cos alpha + cos beta = 1/3 The vlaue of tan (alpha + beta) is

Find the term independent of x in the expansion of (root(3)(x)+1/(2 root(3)(x)))^18,x > 0.

Write the negation of the following statements and check whether the resulting statements are true, The sum of 3 and 4 is 9.

Fourcards are drawn at random from a pack of 52 playing cards , Find the probability of getting all the four cards of the same suit

Fourcards are drawn at random from a pack of 52 playing cards , Find the probability of getting all the four cards of the same number ,

Following are thescores of 12 students in a class test ofof 30marks : 18,20,9,15,21,26,14,13,27,22,16,28 Find D_(7)andP_(33).

Write the negation of the following statements and check whether the resulting statements are true, There does not exist a quadrilateral which has all its sides equal.

A= {1, 2, 3, 4, 5}, B= {1, 3, 5, 6}, C= {1, 2, 3}, then find the following sets. A- (B cap C)

Solutions of the equation sin (sqrt(1 + sin 2 theta)) = sin theta + cos theta " is " (n in Z)

A table has 7 seats, 4 being on one side facing the window and 3 being on the opposite side. In how many ways can 7 people be seated at the table. If 3 people , X,Y and Z must sit on the side facing the window ?

Define (i) f(x)=(1+5x)^(1//x)is continuous at x = 0.

Find a sample space associated with the experiment of rolling a pair of dice (one is blue and other is red) once is Also, find the number od element of this sample space.

In the hexagon PQRSTU, RS||PU||QT. Which sides or diagonals have infinite slope?

Let A (5,2), B (3,-3) and C (-4,3) be the vertices of a Delta ABC. Find the equation of BC

The point P on the line passing through A(3bar(i)+2bar(j)-3bar(k)) and parallel to the vectors 2bar(i)-2bar(j)+bar(k) such that AP = 6 is

If z_(1) =2 -i, z_(2)=1+i, find |(z_(1) + z_(2) + 1)/(z_(1)-z_(2) + 1)|

In the given figure, AB is the diameter of the circle centered at O. If angle COA = 60^(@) , AB = 2r , AC = d . and CD = l, then l is equal to

Consider the line 4x-3y+12=0 Which among the following lines is perpendicular to the line 4x-3y+12=0

The value of ( sin theta )/( sin^(2) (pi//8 + theta //2)-sin^(2)(pi//8- theta //2))=

Write the following in roster form.(iii) {x inN:4x + 9 < 52}

If the equation 12x^2-10xy+2y^2+14x-5y+c=0 represents a pair of straight lines, find the value of c . Find the separate equations of the straight lines and also the angle between them .

If the paris x^(2)-2pxy-y^(2)=0 and x^(2)-2qxy-y^(2)=0 are such that one pair bisects the angle between the other and p=3 then q=

Find the 20^(th) and n^(th) term of the G.P.(5)/(2),(5)/(4),(5)/8) ……..?

A tower substends angles alpha,2alpha,3alpha at A,B,C all lying on horizontal line through the foot of the tower the AB/BC=

If a straight line makes an angle cos^(-1)(1/sqrt(3)) with each of the positive x, y and z-axis, a vector parallel to that line is

Let f(x)=log(log_(1//3)(log_(7)(sinx+a))) be defined for every real value of x, then the possible value of a is

2Tan^(-1)((sqrt(a-b))/(a+b)"tan"x/2)=

The unit vector perpendicular to vectors vec(i)-vec(j) and vec(i) + vec(j) forming a right handed system is

((sin2A)/(secA-1))((sec2A)/(sec2A+1))=

A line makes the same angle theta, with each of the x and z axis. If the angle beta, which it makes with y-axis, is such that sin^(2)beta=3sin^(2)theta, " then " cos^(2)theta=

If the middle term in the expansion of (1 + x)^(2n) is (1.3.5…(2n - 1))/(n!) k^(n).x^(n), the value of k is

The probability that student will get an reward for sports is 0.38 and another award for studies is 0.42 and the probability of getting both award is 0.2. Find the probability that (i)he will get atleast one award,(ii)he will get only one of the reward.

Solve the inequalities 5x + 1 gt -24 , 5x -1 lt 24

If2 tan A + cot A = tan B , thencot A +2 tan (A-B)=

Find the sum to n terms of the series whose n^(th) term is n^3-3^n

If 0 lt A lt B lt (pi)/(4) and sin (A+B)=(24)/(25) and cos (A-B)= (4)/(5), then find the value of tan 2A.

If A.M. and G.M. of roots of a quadratic equation are 8 and 5, respectively, thenobtain the quadratic equation.

Find the odd man out:

Sin40^(@) - Sin80^(@) + Sin160^(@) =