14949 + Interview Questions in Maths in Class 11 Page 94 InterviewSolution

4651.	If bar(i)-2bar(j), 3bar(j)+bar(k), lambdabar(i)+3bar(j) are coplanar then lambda=
Answer» -1 `1/2` `-3/2` 2 Answer :C

Discussion

4652.	Convert the following complex number in the polar form : (1-i)/(1+i)
Answer» ANSWER :`sqrt(2)("COS"(pi)/(4)+i"SIN"(pi)/(4))`

Discussion

4653.	If A=[(2,-2),(2,3)] and A^(2)-5A+kI_(2)=0 then k =
Answer» ANSWER :10

Discussion

4654.	1/(cos290^@)+1/(sqrt3sin250^@)=lamda then 3lamda^2 =
Answer» 16 4 `4//sqrt3` `16//3` ANSWER :A

Discussion

4655.	Find the circumcentre of the triangle formed by the points (2,1),(1,-2) and (-2,3).
Answer» ANSWER :`(-6/7, 2/7)`

Discussion

4656.	Which of the following are examples of the null set Set of even prime numbers.
Answer» ANSWER :it is not an EMPTY SET

Discussion

4657.	If f:[-6, 6]rarr RR defined by f(x)=x^(2)-3" for " x in Rthen (fofof)(-1)+(fofof)(0)+(fofof)(1)=
Answer» `F(4sqrt(2))` `f(3 SQRT(2))` `f(2sqrt(2))` `f(sqrt(2))` ANSWER :A

Discussion

4658.	If a line makes angles cos^(-1)(1//5),cos^(-1)(3//5) with X and Y- axes respectively, then the angle made by the line with Z-axis is
Answer» `COS^(-1)(1//5)` `cos^(-1)(2//5)` `cos^(-1)SQRT(3//5)` `cos^(-1)(4//5)` ANSWER :C

Discussion

4659.	Solve the equations x-3y+2z=8,3x+4y+z=5,-4x+2y-9z=2 using Crammer's method
Answer» ANSWER :`z=-4`

Discussion

4660.	The total cost C(x) in Rupees associated with the production of x units of an item is given by C(x) = 0.007x^(3) - 0.003x^(2)+15x+4000. Find the marginal cost when 17 units are produced.
Answer» ANSWER :2.967

Discussion

4661.	If alpha,beta be the roots of x^(2)-a(x-1)+b=0, then the value of (1)/(alpha^(2)-a alpha)+(1)/(beta^(2)-a beta)+(2)/(a+b) is
Answer» `(4)/(a+b)` `(1)/(a+b)` 0 `-1` ANSWER :C

Discussion

4662.	((a^(2))/( sin A)+( b^(2))/(sin B) + ( c^(2))/( sin C) ) (sin ""(A)/(2)sin ""( B)/(2) sin"" ( C)/(2) )=
Answer» ` DELTA ` ` s ` ` R` ` R ` ANSWER :A

Discussion

4663.	Find a,b,and n in the expansion of (a+b)^n if the first three terms of the expansion are 729. 7290 and 30375, respectively.
Answer» ANSWER :a =3: b=5: n=6

Discussion

4664.	Let f be a non - negative function on the interval [0,1] . If int_(0)^(x)sqrt(1-(f'(t)))^(2)dt=int_(0)^(x)f(t)dt,0lexle1andf(0)=0 then
Answer» `f((1)/(2))lt(1)/(2)andf((1)/(3))GT(1)/(3)` `f((1)/(2))gt(1)/(2)andf((1)/(3))gt(1)/(3)` `f((1)/(2))lt(1)/(2)andf((1)/(3))lt(1)/(3)` `f((1)/(2))gt(1)/(2)andf((1)/(3))lt(1)/(3)` ANSWER :C

Discussion

4665.	All possible value of x for which the function f(x)=x In x-x+1 is positive is
Answer» `(1,OO)` `(1//E,oo)` `[e,oo)` `(0,1)UU(1,oo)` ANSWER :D

Discussion

4666.	If, in a rightangled triangle ABC, the hypo tenus AB =p, then bar(AB).bar(AC)+bar(BC).bar(BA)+bar(CA).bar(CB)=
Answer» P `P^(2)` `P^(3)` `P^(4)` ANSWER :B

Discussion

4667.	Evaluate Lt_(xto0)(cosx)^(1/x^(2))
Answer» ANSWER :`1/sqrte`

Discussion

4668.	Let R be the relation over the set of all straight lines in a plane such that l_(1) Rl_(2) hArr l_(1)bot l_(2). Then R is
Answer» SYMMETRIC REFLEXIVE TRANSITIVE an EQUIVALENCE relation Answer :C

Discussion

4669.	If f,g,h are such that f^(1)(x) = g(x), g^(1)(x) = h(x), h^(1)(x) = f(x), f(0) = 1, g(0) = 0 and h(0)=0 then the value of f^3(x)+g^3(x)+h^3(x)h(x)-3f(x)g(x)h(x)at x=5 is
Answer» 0 1 2 3 Answer :B

Discussion

4670.	Find the equation of the ellipse with focus at (0, 0), eccentricity is 5/6, and directrix is 3x+4y-1=0.
Answer» ANSWER :`27X^(2)+20Y^(2)-24xy+6x+8y-1=0`

Discussion

4671.	Find the direction ratios of the line joining the points (3,4,0) and (4,4,4).
Answer» ANSWER :(1,0,4)

Discussion

4672.	For the ellipse, 9x^(2)+16y^(2)=576, find the semi-major axis, the semi-minor axis, the eccentricity, the coordinates of the foci, the equations of the directrices, and the length of the latus rectum.
Answer» ANSWER :a = 8, b = 6, E `=sqrt(7)/4`, Foci `(pm2sqrt(7), 0)`, DIRECTRICES `x=pm32/7""sqrt(7)`

Discussion

4673.	If the transformed equation of curve is X^(2)+3XY-2Y^(2)+17X-7Y-11=0 when the axes are translated to the point (2,3) then find the original equation of the curve.
Answer» ANSWER :`X^(2)+3xy-2y^(2)+4x-y-20=0`

Discussion

4674.	Let A = {2, 3, 5, 7}. Examine whether the statements given below are true or false.(i) exists x in A" such that "x+3 gt9.(ii) exists x in A such that x is even. (iii) exists x in A" such that "x+2=6.(iv) AA x in A, x is prime.(v) AA x in A, x+2 lt10(vi) AA x in A, x+4 ge11
Answer» Solution :(i) TRUE (II) True (III) False (iv) True (v) True (VI) False

Discussion

4675.	If the letters of the wordGARDEN are permutedin all possible waysand thestringsthus formed are arranged in thedictionaryorder,then find the ranks of the words (i) GARDEN (ii) DANGER.
Answer» ANSWER :(i) 379 (II) 135

Discussion

4676.	Resolve into partial fractions(x)/((x-1)(x+1)^(2)
Answer» ANSWER :`(1)/(2(x+1)^(2)`

Discussion

4677.	Evaluate : (1.01)^(10)+(1-0.01)^(10)
Answer» ANSWER :`2.0090042`

Discussion

4678.	If 6a^2+12b^2+2c^2+17ab-10bc-7ac=0 then all the lines represented by ax+by+c=0 are concureent at the point
Answer» (1-,-3) (2,3) `(-3/2,-2)` `(-3/2,2)` ANSWER :C

Discussion

4679.	Find the component statements of the following and check whether they are true or not: Chadigarh is the capital of Haryana and UP.
Answer» ANSWER :FASLE

Discussion

4680.	If 5, x, y, z, 405 are the first five terms of a geometric progression, find the values of x, y, and z.
Answer» ANSWER :15, 45,135, or -15 ,45 , -135

Discussion

4681.	Find the derivatives of the function cos ^(-1) (5x)
Answer» Answer :`(5)/( SQRT (1- 25 X ^(2)))`

Discussion

4682.	If \|tan x\| = tan x + (1)/(cos x) and x in [0, 2pi], then find values of x
Answer» ANSWER :`(11pi)/(6)`

Discussion

4683.	Calculate the mean deviation about the mean of the set of first n natural numbers when n is an odd number .
Answer» ANSWER :`(n^1 - 1)/(4N)`

Discussion

4684.	The point of the ellipse 16x^(2) + 9y^(2) = 400. At which the ordinate decreases at the same rate at which the abscissa increases is
Answer» `(3,(16)/(3))` `(-3,(16)/(3))` `(3,(-16)/(3))` `(-4,(-16)/(3))` ANSWER :A

Discussion

4685.	Answer the equation: int tan^(-1)((x+a)/(1-ax))dx
Answer» Answer :`xtan^(-1)x-(1)/(2)LOG(1+x^(2))+xtan^(-1)a+c`

Discussion

4686.	Find the co-ordinates of the point which divides the line joining the points (-3,4) and (-1,-2) in the ratio l : m
Answer» SOLUTION :`((- L - 3M)/(l + m), (-2L + 4M)/(l+ m))`

Discussion

4687.	Aparticle just clears a wall of height b at distance a and strikes the groundat a distance c from the point of projection. The angle of projection is(1) tan^(-1)b/(a c)(2) "45"^o(3) tan^(-1)(b c)/(a(c-a)(4) tan^(-1)(b c)/a
Answer» 4 4.91 4.19 100 Answer :B

Discussion

4688.	If bara, barb, barc, bard are any four vectors then (baraxx barb) xx (barc xx bard) is a vector
Answer» `bot` to `BARA,barb,barc,BARD` equally inclined to `baraxxbarb` and `barcxxbard` ALONG the LINE of intersection of two planes, one containing `bara, barb` and the other containing `barc, bard` 2 and 3 Answer :D

Discussion

4689.	If f(n+1)=1/2{f(n)+9/(f(n))},ninNandf(n)gt0 for all ninN then find Lt_(ntooo)f(n).
Answer» ANSWER :3

Discussion

4690.	Fourcards are drawn at random from a pack of 52 playing cards , Find the probability of getting two red cards and two black cards ,
Answer» Answer :`(""^(26)C_(2)xx""^(26)C_(2))/(""^(52)C_(4))`

Discussion

4691.	Fill in the blanks to make each of the following a true statement : Each set has at least "………." subsets.
Answer» ANSWER :`=2`

Discussion

4692.	Find the angle between the lines joining the origin to the points of intersection of y^2 = x and x + y = 1.
Answer» ANSWER :`90^@`

Discussion

4693.	R= {(x, y): x in N, y in N and x + y = 10}. Write domain and range of R.
Answer» ANSWER :DOMAIN of R = {1,2,3,4,5,6,7,8,9}

Discussion

4694.	Let W,X,Y and Z be positive real number such that log(W.Z)+log(W.Y)=, log(Y.Z)+log(Y.X)+log(X.Z)=4 log(W.Z) + log(W.Y)=2, log(Y.Z)+log(Y.X)=3, log(X.Z)=4. The value of the product (WXYZ) equals (base of the log is 10)
Answer» `10^(2)` `10^(3)` `10^(4)` `10^(9)` SOLUTION :N//A

Discussion

4695.	If U= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A= {1, 2, 3, 5},B= {2, 4, 6, 7} and C= {2, 3, 4, 8}. Then, (C - A)'="……….."
Answer» Answer :`= {1, 2, 3, 5, 6, 7, 9, 10}`

Discussion

4696.	Find the second derivative of e ^(x) sin x cos 2x .
Answer» ANSWER :`e ^(x) (3 COS 3x - 4 sin 3x- cos x)`

Discussion

4697.	5 (2x -7) -3 (2x+4) le 0, 2x+19 le 6x+47.
Answer» ANSWER :`[-7,11]` `(##NCERT_TAM_MAT_XI_C06_E04_010_A01##)`

Discussion

4698.	Find the approximations of the following root(3)(7.8)
Answer» ANSWER :1.9834

Discussion

4699.	Calculate the standard deviation of the following distribuition :
Answer» ANSWER :`7.94`

Discussion

4700.	Four digit numbers are formed using the digits 0, 2, 3,5 without repetition. The probability of such a number divisible by 5 is
Answer» `1/5` `4/5` `1/30` `5/9` ANSWER :D

Discussion

Explore topic-wise InterviewSolutions in .

If bar(i)-2bar(j), 3bar(j)+bar(k), lambdabar(i)+3bar(j) are coplanar then lambda=

Convert the following complex number in the polar form : (1-i)/(1+i)

If A=[(2,-2),(2,3)] and A^(2)-5A+kI_(2)=0 then k =

1/(cos290^@)+1/(sqrt3sin250^@)=lamda then 3lamda^2 =

Find the circumcentre of the triangle formed by the points (2,1),(1,-2) and (-2,3).

Which of the following are examples of the null set Set of even prime numbers.

If f:[-6, 6]rarr RR defined by f(x)=x^(2)-3" for " x in Rthen (fofof)(-1)+(fofof)(0)+(fofof)(1)=

If a line makes angles cos^(-1)(1//5),cos^(-1)(3//5) with X and Y- axes respectively, then the angle made by the line with Z-axis is

Solve the equations x-3y+2z=8,3x+4y+z=5,-4x+2y-9z=2 using Crammer's method

The total cost C(x) in Rupees associated with the production of x units of an item is given by C(x) = 0.007x^(3) - 0.003x^(2)+15x+4000. Find the marginal cost when 17 units are produced.

If alpha,beta be the roots of x^(2)-a(x-1)+b=0, then the value of (1)/(alpha^(2)-a alpha)+(1)/(beta^(2)-a beta)+(2)/(a+b) is

((a^(2))/( sin A)+( b^(2))/(sin B) + ( c^(2))/( sin C) ) (sin ""(A)/(2)sin ""( B)/(2) sin"" ( C)/(2) )=

Find a,b,and n in the expansion of (a+b)^n if the first three terms of the expansion are 729. 7290 and 30375, respectively.

Let f be a non - negative function on the interval [0,1] . If int_(0)^(x)sqrt(1-(f'(t)))^(2)dt=int_(0)^(x)f(t)dt,0lexle1andf(0)=0 then

All possible value of x for which the function f(x)=x In x-x+1 is positive is

If, in a rightangled triangle ABC, the hypo tenus AB =p, then bar(AB).bar(AC)+bar(BC).bar(BA)+bar(CA).bar(CB)=

Evaluate Lt_(xto0)(cosx)^(1/x^(2))

Let R be the relation over the set of all straight lines in a plane such that l_(1) Rl_(2) hArr l_(1)bot l_(2). Then R is

If f,g,h are such that f^(1)(x) = g(x), g^(1)(x) = h(x), h^(1)(x) = f(x), f(0) = 1, g(0) = 0 and h(0)=0 then the value of f^3(x)+g^3(x)+h^3(x)h(x)-3f(x)g(x)h(x)at x=5 is

Find the equation of the ellipse with focus at (0, 0), eccentricity is 5/6, and directrix is 3x+4y-1=0.

Find the direction ratios of the line joining the points (3,4,0) and (4,4,4).

For the ellipse, 9x^(2)+16y^(2)=576, find the semi-major axis, the semi-minor axis, the eccentricity, the coordinates of the foci, the equations of the directrices, and the length of the latus rectum.

If the transformed equation of curve is X^(2)+3XY-2Y^(2)+17X-7Y-11=0 when the axes are translated to the point (2,3) then find the original equation of the curve.

Let A = {2, 3, 5, 7}. Examine whether the statements given below are true or false.(i) exists x in A" such that "x+3 gt9.(ii) exists x in A such that x is even. (iii) exists x in A" such that "x+2=6.(iv) AA x in A, x is prime.(v) AA x in A, x+2 lt10(vi) AA x in A, x+4 ge11

If the letters of the wordGARDEN are permutedin all possible waysand thestringsthus formed are arranged in thedictionaryorder,then find the ranks of the words (i) GARDEN (ii) DANGER.

Resolve into partial fractions(x)/((x-1)(x+1)^(2)

Evaluate : (1.01)^(10)+(1-0.01)^(10)

If 6a^2+12b^2+2c^2+17ab-10bc-7ac=0 then all the lines represented by ax+by+c=0 are concureent at the point

Find the component statements of the following and check whether they are true or not: Chadigarh is the capital of Haryana and UP.

If 5, x, y, z, 405 are the first five terms of a geometric progression, find the values of x, y, and z.

Find the derivatives of the function cos ^(-1) (5x)

If |tan x| = tan x + (1)/(cos x) and x in [0, 2pi], then find values of x

Calculate the mean deviation about the mean of the set of first n natural numbers when n is an odd number .

The point of the ellipse 16x^(2) + 9y^(2) = 400. At which the ordinate decreases at the same rate at which the abscissa increases is

Answer the equation: int tan^(-1)((x+a)/(1-ax))dx

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

Aparticle just clears a wall of height b at distance a and strikes the groundat a distance c from the point of projection. The angle of projection is(1) tan^(-1)b/(a c)(2) "45"^o(3) tan^(-1)(b c)/(a(c-a)(4) tan^(-1)(b c)/a

If bara, barb, barc, bard are any four vectors then (baraxx barb) xx (barc xx bard) is a vector

If f(n+1)=1/2{f(n)+9/(f(n))},ninNandf(n)gt0 for all ninN then find Lt_(ntooo)f(n).

Fourcards are drawn at random from a pack of 52 playing cards , Find the probability of getting two red cards and two black cards ,

Fill in the blanks to make each of the following a true statement : Each set has at least "………." subsets.

Find the angle between the lines joining the origin to the points of intersection of y^2 = x and x + y = 1.

R= {(x, y): x in N, y in N and x + y = 10}. Write domain and range of R.

Let W,X,Y and Z be positive real number such that log(W.Z)+log(W.Y)=, log(Y.Z)+log(Y.X)+log(X.Z)=4 log(W.Z) + log(W.Y)=2, log(Y.Z)+log(Y.X)=3, log(X.Z)=4. The value of the product (WXYZ) equals (base of the log is 10)

If U= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A= {1, 2, 3, 5},B= {2, 4, 6, 7} and C= {2, 3, 4, 8}. Then, (C - A)'="……….."

Find the second derivative of e ^(x) sin x cos 2x .

5 (2x -7) -3 (2x+4) le 0, 2x+19 le 6x+47.

Find the approximations of the following root(3)(7.8)

Calculate the standard deviation of the following distribuition :

Four digit numbers are formed using the digits 0, 2, 3,5 without repetition. The probability of such a number divisible by 5 is