14949 + Interview Questions in Maths in Class 11 Page 269 InterviewSolution

13401.	If P = (1,2,-3), Q(1,0,-1) and translate the axes by Q is origin, then new coordinates of P is:
Answer» (0, 2, 2) (-2, 0, 1) (1, 2, 0) (0, 2, -2) ANSWER :d

Discussion

13402.	A tower stands at the top a hill whose height is three times the height of the tower. The tower is found to subtend an angle of Tan^(-1)(1/7) at a point 2 km away on the horizontal throught the foot of the hill. Then the height of the tower is
Answer» `(1)/(2)km` or `(1)/(3)km` `(1)/(3)km` or `(2)/(3)km` `(2)/(3)km` or `(1)/(2)km` `(3)/(4)km` or `(1)/(2)km` Answer :C

Discussion

13403.	Find the maximum and minimum values, if any, of the functions given by g(x) = x^(3) + 1
Answer» ANSWER :does not EXIST

Discussion

13404.	Write the equation of the line through the points (1,-1) and (3,5).
Answer» ANSWER :`-3x+y+4=0`.

Discussion

13405.	Arrangethe periods of the followingfunctions in ascendingorder (A) tan (2x-7) (B) sin x cos x (C) sin 3x+ cos 3x(D) sin^(3)x-cos^(3)x
Answer» TAN (2 X-7) SIN x cos x sin 3X + cos 3x `sin^(3)- cos^(3) x` Answer :1

Discussion

13406.	If ""_nP_r=840 and ""^nC_r=35, then r is equal to....
Answer» ANSWER :(THEREFORE 4 ! = 24)

Discussion

13407.	If sqrt(x+y)+sqrt(y-x)=c ,then (d^2y)/(dx^2)=
Answer» `2/C` `(-2)/c^2` `2/c^2` `(-2)/c` ANSWER :C

Discussion

13408.	A line is such that its segment between the lines 5x - y + 4 = 0 " and " 3x + 4y - 4 = 0is bisected at the point (1, 5) . Obtain its equation.
Answer» ANSWER :`107x - 3Y - 92 = 0 `

Discussion

13409.	A= {1, 2, 3} and B= { x : x in N, x is a prime number less than 5}, Find A xx B and B xx A
Answer» ANSWER :`A XX B= {(1,2)(1,3)(2,2)(2,3)(3,2)(3,3)}` `B xx A= {(2,1)(3,1) (2,2) (3,2)(2,3)(3,3)}`

Discussion

13410.	If the function f(x) satisfies lim_(xrarr1)(f(x)-2)/(x^(2)-1)=pi, evaluate lim_(xrarr1)f(x).
Answer» ANSWER :2

Discussion

13411.	Consider the expansion of ((4x)/5-5/(4x))^8 The middle term in the expansion is …{4th,5th,6th]
Answer» SOLUTION :5TH TERM

Discussion

13412.	Find the maximum value of 3x + 4yfor x gt 0, y gt 0 such that x^(2)y^(2) = 6.
Answer» ANSWER :10

Discussion

13413.	If ""^((n+2)) C_8 :"" ^((n-2)) P_4= 57 : 16 then find n.
Answer» ANSWER :19

Discussion

13414.	Write the negation of the following simple statements. Every real number is an irrational number.
Answer» ANSWER :IRRATIONAL NUMBER

Discussion

13415.	Obtain the equation at the line in Ex. (1) to (10) satisfying given condition : Passes from point (1, -2) and makes equal intercepts an axes.
Answer» ANSWER :`X + y + 1 = 0`

Discussion

13416.	Let y(2^("log"_(2^(1//4))x) - 3log_(27)(x^2 + 1)^3 - 2x)/(7^(4"log"_(49)^(x)) - x - 1)and(dy)/(dx) = ax + b , then the value ofa + b is ..........
Answer» ANSWER :C

Discussion

13417.	Let A and B be two sets such that n(A) =3 and n(B) =2. If (x, 1), (y, 2), (z,1) are in A xx B, find A and B, where x, y and z are distinct elements.
Answer» ANSWER :A= {x,y,Z} and B= {1, 2}

Discussion

13418.	The centroid of the triangle formed by the points (2,-1,1),(1,-3,-5),(3,-4,-4) is
Answer» (2,-1,1) (1,-3,-5) (3,-4,-4) `(2,-8//3,-8//3)` ANSWER :C

Discussion

13419.	If a =sin^(2)x + cos^(4)xthenAAX E R
Answer» `(13)/(11)LTA lt 1` `1 LE A le2` `(3)/(4) leA le (13)/(16)` `(3)/(4) leA le 1` ANSWER :4

Discussion

13420.	……..of the following is the equation of circle passes from (-1,-2) and concentric to the circle x^(2) + y^(2) - 3x + 4y - c = 0.
Answer» `X^(2) + y^(2) -3x + 4y - 1 = 0` `x^(2) + y^(2) - 3x + 4y = 0` `x^(2) + y^(2) - 3x + 4y + 2 = 0` NONE of these Answer :B

Discussion

13421.	The values of x, between 0 and 2 pi. satisfying the equation cos 3 x + cos 2 x = sin ""(3 x)/( 2) + sin (x)/(2) are
Answer» `(PI)/(7)` `(5 pi)/(7)` `(9pi)/(7)` `(13 pi)/(7)` Answer :A::B::C::D

Discussion

13422.	If p is realnumberand the middle term in the expansionof (p/2+2)^(8) is 1120 , then find the value of p .
Answer» <P> ANSWER :` :. p = 2 `

Discussion

13423.	If A+B, A are acute angles such that sin (A+B)=(24)/(25) and tan A=(3)/(4), then find the value of cos B.
Answer» ANSWER :`(4)/(5)`

Discussion

13424.	For a data containing100 observations,the mean is 8. For 50 observations selected from these 100observations, the mean is 10. Find the mean of the other 50 observations.
Answer» ANSWER :6

Discussion

13425.	Find the angle between the lines joining the origin to the points of intersection of the curve x^2+2xy+y^2+2x+2y-5=0 and the line 3x-y+1=0.
Answer» ANSWER :`COS^(-1)((13)/(sqrt(193)))`

Discussion

13426.	If the line joining the points (-1,2,3) (2,-1,4) is perpendicular to the line joining (x,-2,4) and (1,2,3) then x =
Answer» 3 10 `(-3)/(10)` `(-10)/(3)` ANSWER :D

Discussion

13427.	If 3sinx+4cosx=5 then the value of tan(x//2) is
Answer» `(1pmsqrt(2))/(4)` `(-1pmsqrt(2))/(4)` `(-1pmsqrt(2))/(3)` `1//3` ANSWER :D

Discussion

13428.	A die I thrown, find the probability of following events: (i) A prime number will appear, (ii) A number les than or equal to 3 will appear, (iii) A number les than or equal to one will appear, (iv) A number more than 6 will appear, (v) A number less than 6 will appear.
Answer» ANSWER :(i) `1/2` (II) `2/3` (ii) `1/6` (IV) 0 (V) `5/6`

Discussion

13429.	Which of the following relations are functions? Give reason {(2,0), (4,8), (2,1), (3,6)}
Answer» ANSWER :It is not a FUNCTION

Discussion

13430.	Find the modulus and arguments of the complex numbers. (i) (1+i)/(1-i), (ii) 1/(1+i)
Answer» ANSWER :(i) MODULUS of `(1+i)/(1-i)` is 1 and the argument is `pi/2`. (II) modulus of `1/(1+i)` is `1/sqrt(2)`,argument is `-pi/4`.

Discussion

13431.	Median of the data 9,15,20,22,8,17,10,18,14,25 is …..
Answer» ANSWER :16

Discussion

13432.	f(x) = (1 - cos (1 - cos x ))/(x^(4))is continuous at x = 0 then f(0) =
Answer» `1/2` `1/4` `1/6` `1/8` ANSWER :D

Discussion

13433.	Find the mean deviation about the median for the data : 36,72,46,42,60,45,53,46,51,49
Answer» ANSWER :7

Discussion

13434.	Find co-ordinates of the point which divides line segement joining points (2, -1, 4) and (4, 3, 2) in ratio 2 : 3. Externally
Answer» ANSWER :`(-2,-9,8)`

Discussion

13435.	Find co-ordinates of the point which divides line segment joining points (2, -1, 4) and (4, 3, 2) in ratio 2 : 3 Internally.
Answer» ANSWER :`(14/3,3/5,16/5)`

Discussion

13436.	Let A(4, 7, 8), B(2, 3, 4)and C(2,5,7) be the vertices of DeltaABC. The length of the median AD is
Answer» `SQRT2` `sqrt2/2` `(sqrt77)/2` `(sqrt89)/2` ANSWER :C

Discussion

13437.	The value of tan75^(@)-cot75^(@) is
Answer» `2sqrt(3)` `2+sqrt(3)` `2-sqrt(3)` 1 Answer :A

Discussion

13438.	If sin theta = a/(b+c) then show that cos theta = (2sqrt(bc))/(b+c) cos ((A)/(2))
Answer» ` COS theta ` ` SIN theta ` ` cot theta ` ` TAN theta ` ANSWER :A

Discussion

13439.	For which interval, the function (x^(2)-3x)/(x-1) satisfies all the conditions of Rolle's theorem
Answer» `[0,3]` `[-3,0]` `[1,5,3]` For no interval Answer :D

Discussion

13440.	Find the number of 4 letter words with or without meaning, which can be formed out of the letters of the word 'FATE' where the repetition of letters is not allowed.
Answer» ANSWER :24

Discussion

13441.	If the orthocentre and the circucentre of are (-3,5,2) ,(6,2,5) then its centroid is
Answer» (3,3,4) `(3/2,7/2,9/2)` `((-9)/2,7/2,(-3)/2)` `(9/2,(-3)/2,3/2)` ANSWER :A

Discussion

13442.	A coin is tossed. If the out come is a head, a die is thrown. If the die shows up an even number, the die is thrown again. What is the sample space for the experiment?
Answer» ANSWER :{T,H1, H3, H5, H21, H22, H23, H24, H5, H26, H41, H42, H43, H44, H45, H46, H61, H62, H63, H64, H65, H66}

Discussion

13443.	Find the derivative of log((x^(2)+x+2)/(x^(2)-x+2)) w.r.to x.
Answer» ANSWER :`(4-2 X ^(2))/( x ^(4) + 3X ^(2) + 4)`

Discussion

13444.	Find the value of 'a' so thatf(x) = {{:(ax + 3" if " x lt 3 ),( 3 - x + 2x^(2) " if " x ge 3 ):} is continuous on R .
Answer» ANSWER :a=5

Discussion

13445.	If =sin px and y_(n) is the nth derivative of y then \|(y,y_(1),y_(2)),(y_(3),y_(4),y_(5)),(y_(6),y_(7),y_(8))\|=
Answer» `1` `0` `-1` `2` ANSWER :B

Discussion

13446.	Solve cos x = 1/2.
Answer» Answer :` X = 2 N PI pm pi /3 ,` where ` n in Z`

Discussion

13447.	The value of 'x' in Lagrange's mean value theorem for f(x) = log (sinx ) in [(pi)/( 6), ( 5pi )/(6)] is
Answer» `( pi )/( 4)` `( pi )/( 2)` `( 2pi )/( 3)` `( 3PI )/( 4)` Answer :B

Discussion

13448.	Find locus of a point so that its distance from the axis of x is always one half its distance from the origin.
Answer» ANSWER :`\|y\|=c^(2)`

Discussion

13449.	In Delta ABC the roots of the equation x^3-(r+4R)x^2+s^2x-s^2r=0 are
Answer» `R,r_(1),r_(2)` `r,r_(2),r_(3)` `r,r_(1),r_(3)` `r_(1),r_(2),r_(3)` ANSWER :D

Discussion

13450.	(10!)/(8!) = 9 .
Answer» ANSWER :FALSE STATEMENT

Discussion

Explore topic-wise InterviewSolutions in .

If P = (1,2,-3), Q(1,0,-1) and translate the axes by Q is origin, then new coordinates of P is:

A tower stands at the top a hill whose height is three times the height of the tower. The tower is found to subtend an angle of Tan^(-1)(1/7) at a point 2 km away on the horizontal throught the foot of the hill. Then the height of the tower is

Find the maximum and minimum values, if any, of the functions given by g(x) = x^(3) + 1

Write the equation of the line through the points (1,-1) and (3,5).

Arrangethe periods of the followingfunctions in ascendingorder (A) tan (2x-7) (B) sin x cos x (C) sin 3x+ cos 3x(D) sin^(3)x-cos^(3)x

If ""_nP_r=840 and ""^nC_r=35, then r is equal to....

If sqrt(x+y)+sqrt(y-x)=c ,then (d^2y)/(dx^2)=

A line is such that its segment between the lines 5x - y + 4 = 0 " and " 3x + 4y - 4 = 0is bisected at the point (1, 5) . Obtain its equation.

A= {1, 2, 3} and B= { x : x in N, x is a prime number less than 5}, Find A xx B and B xx A

If the function f(x) satisfies lim_(xrarr1)(f(x)-2)/(x^(2)-1)=pi, evaluate lim_(xrarr1)f(x).

Consider the expansion of ((4x)/5-5/(4x))^8 The middle term in the expansion is …{4th,5th,6th]

Find the maximum value of 3x + 4yfor x gt 0, y gt 0 such that x^(2)y^(2) = 6.

If ""^((n+2)) C_8 :"" ^((n-2)) P_4= 57 : 16 then find n.

Write the negation of the following simple statements. Every real number is an irrational number.

Obtain the equation at the line in Ex. (1) to (10) satisfying given condition : Passes from point (1, -2) and makes equal intercepts an axes.

Let y(2^("log"_(2^(1//4))x) - 3log_(27)(x^2 + 1)^3 - 2x)/(7^(4"log"_(49)^(x)) - x - 1)and(dy)/(dx) = ax + b , then the value ofa + b is ..........

Let A and B be two sets such that n(A) =3 and n(B) =2. If (x, 1), (y, 2), (z,1) are in A xx B, find A and B, where x, y and z are distinct elements.

The centroid of the triangle formed by the points (2,-1,1),(1,-3,-5),(3,-4,-4) is

If a =sin^(2)x + cos^(4)xthenAAX E R

……..of the following is the equation of circle passes from (-1,-2) and concentric to the circle x^(2) + y^(2) - 3x + 4y - c = 0.

The values of x, between 0 and 2 pi. satisfying the equation cos 3 x + cos 2 x = sin ""(3 x)/( 2) + sin (x)/(2) are

If p is realnumberand the middle term in the expansionof (p/2+2)^(8) is 1120 , then find the value of p .

If A+B, A are acute angles such that sin (A+B)=(24)/(25) and tan A=(3)/(4), then find the value of cos B.

For a data containing100 observations,the mean is 8. For 50 observations selected from these 100observations, the mean is 10. Find the mean of the other 50 observations.

Find the angle between the lines joining the origin to the points of intersection of the curve x^2+2xy+y^2+2x+2y-5=0 and the line 3x-y+1=0.

If the line joining the points (-1,2,3) (2,-1,4) is perpendicular to the line joining (x,-2,4) and (1,2,3) then x =

If 3sinx+4cosx=5 then the value of tan(x//2) is

A die I thrown, find the probability of following events: (i) A prime number will appear, (ii) A number les than or equal to 3 will appear, (iii) A number les than or equal to one will appear, (iv) A number more than 6 will appear, (v) A number less than 6 will appear.

Which of the following relations are functions? Give reason {(2,0), (4,8), (2,1), (3,6)}

Find the modulus and arguments of the complex numbers. (i) (1+i)/(1-i), (ii) 1/(1+i)

Median of the data 9,15,20,22,8,17,10,18,14,25 is …..

f(x) = (1 - cos (1 - cos x ))/(x^(4))is continuous at x = 0 then f(0) =

Find the mean deviation about the median for the data : 36,72,46,42,60,45,53,46,51,49

Find co-ordinates of the point which divides line segement joining points (2, -1, 4) and (4, 3, 2) in ratio 2 : 3. Externally

Find co-ordinates of the point which divides line segment joining points (2, -1, 4) and (4, 3, 2) in ratio 2 : 3 Internally.

Let A(4, 7, 8), B(2, 3, 4)and C(2,5,7) be the vertices of DeltaABC. The length of the median AD is

The value of tan75^(@)-cot75^(@) is

If sin theta = a/(b+c) then show that cos theta = (2sqrt(bc))/(b+c) cos ((A)/(2))

For which interval, the function (x^(2)-3x)/(x-1) satisfies all the conditions of Rolle's theorem

Find the number of 4 letter words with or without meaning, which can be formed out of the letters of the word 'FATE' where the repetition of letters is not allowed.

If the orthocentre and the circucentre of are (-3,5,2) ,(6,2,5) then its centroid is

A coin is tossed. If the out come is a head, a die is thrown. If the die shows up an even number, the die is thrown again. What is the sample space for the experiment?

Find the derivative of log((x^(2)+x+2)/(x^(2)-x+2)) w.r.to x.

Find the value of 'a' so thatf(x) = {{:(ax + 3" if " x lt 3 ),( 3 - x + 2x^(2) " if " x ge 3 ):} is continuous on R .

If =sin px and y_(n) is the nth derivative of y then |(y,y_(1),y_(2)),(y_(3),y_(4),y_(5)),(y_(6),y_(7),y_(8))|=

Solve cos x = 1/2.

The value of 'x' in Lagrange's mean value theorem for f(x) = log (sinx ) in [(pi)/( 6), ( 5pi )/(6)] is

Find locus of a point so that its distance from the axis of x is always one half its distance from the origin.

In Delta ABC the roots of the equation x^3-(r+4R)x^2+s^2x-s^2r=0 are

(10!)/(8!) = 9 .