14949 + Interview Questions in Maths in Class 11 Page 39 InterviewSolution

1901.	Angle between two lines is 45° and slope of one line is 2 then find slope of second line.
Answer» ANSWER :`(1)/(3)` OR `-3`

Discussion

1902.	If y = Sin ^(-1) (3x - 4x ^(3)) find(dy)/(dx).
Answer» ANSWER :`LT 1/2`

Discussion

1903.	If f(x)=x/(sqrt(1-x^2)),g(x) = x/(sqrt(1+x^2)) , then d/(dx)(fog(x)) =
Answer» 1 0 `-1` 2 Answer :A

Discussion

1904.	.......is the inequality represented by following graph .
Answer» ANSWER :`2X + y LE 4` .

Discussion

1905.	If A and B are two sets, then A cap (A cup B) equals to,
Answer» `A` `B` `PHI` `A CAP B` ANSWER :A

Discussion

1906.	If bara and barb are any two non-zero vectors, then find the angle between the vectors absbarb bara+absbara barb =absbarb bara-absbara barb
Answer» ANSWER :`90^(@)`

Discussion

1907.	Find thevalue of f_(1),f_(2) and f_(3) from the following data: given that mode =37
Answer» ANSWER :a=8; b=12

Discussion

1908.	If bare_(1),bare_(2) and bare_(3)are non-coplanar unit vectors andalpha=(bare_(1),bare_(2)), beta = (bare_(2),bare_(3)) and gamma = (bare_(3),bare_(1)) then what is the minimum value of cosalpha+cosbeta +cos gamma?
Answer» ANSWER :`-(3)/2`

Discussion

1909.	If A , B are two sets such that n(A)=100, n(B)=150, then the number of bijections from A onto B is
Answer» <P>100! 150! `""^(150)P_(100)` ZERO ANSWER :D

Discussion

1910.	Differential coefficient of (x^((l + m)/(m - n)))^(1/(n-1)).(x^((m +n)/(n -1)))^(1/(l - m)).(x^((n + 1)/(l - m)))^(1/(m -n)) w.r.tx is
Answer» `1` `0` `-1` `x^(lmn)` Answer :B

Discussion

1911.	Differentiate the following functions w.r.t. x: ( cos x)/( 5x)
Answer» ANSWER :`(- X SIN x - COS x)/( 5x^2)`

Discussion

1912.	A cone is made from a circular sheet of radius sqrt(3) by cutting out a sector and giving the cut edges of the remaining piece together .The maximum volume attainable for the cone is
Answer» `PI//3` `pi//6` `2pi//3` `3sqrt(3)pi` ANSWER :C

Discussion

1913.	The point on the curve y=x^(2) is nearest to (3,0) is
Answer» (1,-1) (-1,1) (-1,-1) (1,1) ANSWER :D

Discussion

1914.	If one root of k(x-1)^(2) =5x-7 is double the other root, show that k=2 or -25.
Answer» ANSWER :K = 2 or -25.

Discussion

1915.	The circumcentre of the triangle formed by the linesx+y=0, x-y=0 and lx+my=1 is
Answer» (2,1) (5/2,5/2) (5/4,5/4) (15/8,15/8) ANSWER :D

Discussion

1916.	Prove that: -4le5costheta+3cos(theta+pi/3)+3 ge10, for all values of theta.
Answer» SOLUTION :We have, `5costheta+3costheta(theta+pi/3)=5costheta+3costhetacospi/3-3sinthetasinpi/3=13/2costheta-(3sqrt(3))/(2)sintheta` Since `-SQRT((13/2)^(2)+(-3sqrt(3)/2)^(2)) le13/2 costheta-(3sqrt(3))/(2)sintheta le sqrt((13/2)^(2)+(-3sqrt(3))/(2)^(2))` `rArr -7 le 13/2 costheta-(3sqrt(3))/(2)sintheta le7` `rArr -7 le5costheta+3cos(theta+pi/3)le7` for all `theta`. `rArr -7+3 le5costheta+3cos(theta+pi/3)+3 ge7 +3` for all `theta` `rArr -4 LE5 costheta+3cos(theta+pi/3)+3 le10` for all `theta`

Discussion

1917.	Findthe periodof log _(e )(sin^-1(x- [x]))
Answer» ANSWER :`pi//2`

Discussion

1918.	lim_(xto(pi)/(4))(sqrt(2)sinx-1)/(cos(2x))=………..
Answer» `(1)/(2)` `2arqt(2)` `-(1)/(2)` `SQRT(2)` ANSWER :C

Discussion

1919.	Differentiate the following w.r.t. x : y= (x^2 - 3)/( x+4)
Answer» ANSWER :`(DY)/( DX) = (x^2 + 8X +3)/( (x+4)^2)`

Discussion

1920.	Find the distance of the line 4x - y=0 from the point P (4,1) measured along the line making an angle 135 degree with the positive x-axis.
Answer» ANSWER :`3sqrt(2)` UNITS

Discussion

1921.	Evaluate the following limits. Lt_(xto pi/4)(tanx)/x
Answer» ANSWER :`4/pi`

Discussion

1922.	If tantheta+tan4theta+tan7theta=tanthetatan4thetatan7theta then theta =
Answer» `(npi)/(4)` `(npi)/(7)` `(npi)/(12)` `npi` ANSWER :C

Discussion

1923.	The perimeter of a sector is given. The area is maximum when the angle of the sector is
Answer» `PI^(E)//6` `pi^(e)//4` `4^(e)` `2^(e)` ANSWER :D

Discussion

1924.	Let 40% of employees earn more than Rs. 18000 per month. Then to find the percentage of employees earn less than or equal to Rs. 18000 you have to calculate which percentile?
Answer» <P> ANSWER :We have to CALCULATE `P_(60)`

Discussion

1925.	If p^(th) term of an AP is q and q^(th) term is p, find (p+q)^(th) term.
Answer» ANSWER :ZERO

Discussion

1926.	Show that the following system of equations is consistent and solve it completely. x+y+4z=6," "3x+2y-2z=9," "5x+y+2z=13
Answer» ANSWER :`1//2`

Discussion

1927.	The value of theta which satisfy r sin theta = 3 and r = 4 ( 1+ sin theta ), 0 le theta le2 pi
Answer» `(pi)/(6)` `(pi)/(6),(5pi)/(6)` `(5 pi)/(6)` `(pi)/(3),(2 pi)/(3)` Answer :B

Discussion

1928.	Two systems of rectangular axes have the same origin. If a plane cuts them at distances a, b, c and a^(1),b^(1),c^(1) from the origin, then
Answer» `(1)/(a^(2))+(1)/(B^(2))-(1)/(C^(2))+(1)/(a^(,2))-(1)/(b^(,2))-(1)/(c^(,2))=0` `(1)/(a^(2))-(1)/(b^(2))-(1)/(c^(2))+(1)/(a^(,2))-(1)/(b^(,2))-(1)/(c^(,2))=0` `(1)/(a^(2))+(1)/(b^(2))+(1)/(c^(2))-(1)/(a^(,2))-(1)/(b^(,2))-(1)/(c^(,2))=0` `(1)/(a^(2))+(1)/(b^(2))+(1)/(c^(2))+(1)/(a^(,2))+(1)/(b^(,2))+(1)/(c^(,2))=0` ANSWER :C

Discussion

1929.	Which of the following statements are true I : In /_\ABC is in inscribed in a given circle then deltaa.secA+deltab.secB+deltac.secC=1 II : Approximate value of (1.0002)^(3000) is 1.6
Answer» Only I Only II both I and II NEITHER I nor II Answer :B

Discussion

1930.	Solve the quadratic equation x^(2)+x+1/sqrt2=0 ?
Answer» ANSWER :`((-1)+-sqrt2sqrt2-i)/(2)`

Discussion

1931.	The value of (127)^(1//3) to 4 decimal places is
Answer» 5.0267 5.4267 5.5267 5.0001 Answer :A

Discussion

1932.	Let F(x)= f(x)+g(x), G(x) = f(x) - g( x) and H(x)=(f( x))/( g(x))where f(x)= 1- 2 sin ^(2)x and g(x)=cos (2x) AA f: R to [-1,1] and g, R to [-1,1] Now answer the following Which of the following is correct
Answer» periods of `f(x), G(x)` and `F(x)` makes A.P with the common difference `pi/3` perod of f(x), g(x) and F(x) are same and is equal to `2PI` sum of the periods of f(x) , g(x) and F(x) is `3PI` sum of the periods of `f(x), g(x)` and `F(x)` is `6 pi` Answer :C

Discussion

1933.	Let F(x)= f(x)+g(x), G(x) = f(x) - g( x) and H(x)=(f( x))/( g(x))where f(x)= 1- 2 sin ^(2)x and g(x)=cos (2x) AA f: R to [-1,1] and g, R to [-1,1] Now answer the following If the solution of F(x)-G (x)=0 are x_1,x_2, x_3 --------- x_nWherex in [0,5 pi] then
Answer» 1)`x_(1), x_(2), x_(3) - - - - - x_(n)` are in A.P with COMMON DIFFERENCE `pi/4` 2)the no. of solutions of `F(X)-G(x)=0` is `10 AA x in [0, 5pi]` 3)the sum of all solutions of `F(x)-G(x) = 0` is `AA x in [0, 5pi]` is `25 pi` 4)b, c are true Answer :D

Discussion

1934.	Let F(x)= f(x)+g(x), G(x) = f(x) - g( x) and H(x)=(f( x))/( g(x))where f(x)= 1- 2 sin ^(2)x and g(x)=cos (2x) AA f: R to [-1,1] and g, R to [-1,1] Now answer the following IfF :R to [-2,2] then F(x) is
Answer» the domain of G(X) and H(x) are same the RANGE of G(x) and H(x) are same the UNION of the dmain of G(x) and H(x) are all real numbers None Answer :C

Discussion

1935.	Let F(x)= f(x)+g(x), G(x) = f(x) - g( x) and H(x)=(f( x))/( g(x))where f(x)= 1- 2 sin ^(2)x and g(x)=cos (2x) AA f: R to [-1,1] and g, R to [-1,1] Now answer the following Domain and range of H(x)are
Answer» R and {1} R and {0, 1} `R-{2n +1) pi/4}` R and {0} ANSWER :C

Discussion

1936.	Evaluate : lim_(xrarr1)(x^(15)-1)/(x^(10)-1)
Answer» `(3)/(2)` ANSWER :`(3)/(2)`

Discussion

1937.	Using binomial theorem, write the value of (a+b)^(6) + (a-b)^(6) and hence find the value of ( sqrt(3) + sqrt(2) )^(6) + ( sqrt(3) - sqrt(2) )^(6).
Answer» Answer :`(a+B)^(n) - (a-b)^(n) = 2 [""^(n) C_1 a^(n-1) b+""^(n) C_(3) a^(n-3) b^(3) + …]; 396 SQRT6`

Discussion

1938.	Find the angle between the line whose slope are2 and -1 .
Answer» ANSWER : `71^(@)34', (B) 26^(@)34'`

Discussion

1939.	Consider the two statements : P : Raj Kapoor is alive . Q : Raj Kapoor lives in Delhi .Write the followingstatements in Symbolic form. Either Raj Kapoor is alive or he lives inDelhi .
Answer» <P> ANSWER :`p VV Q`

Discussion

1940.	Consider the two statements : P : Raj Kapoor is alive . Q : Raj Kapoor lives in Delhi .Write the followingstatements in Symbolic form. Raj Kapoor is alive and he lives in Delhi.
Answer» <P> ANSWER :`p ^^ Q`

Discussion

1941.	Find the derivative of tan2x from the first principle.
Answer» ANSWER :`2 SEC ^(2) 2X`

Discussion

1942.	Consider the two statements : P : Raj Kapoor is alive . Q : Raj Kapoor lives in Delhi .Write the followingstatements in Symbolic form. It is not true thatRaj Kapoor is alive and helives in Delhi .
Answer» <P> ANSWER :`~ (p ^^ Q)`

Discussion

1943.	Consider the two statements : P : Raj Kapoor is alive . Q : Raj Kapoor lives in Delhi .Write the followingstatements in Symbolic form. Raj Kapoor is neither alive, nor does he live in Delhi.
Answer» <P> ANSWER :`~p ^^ ~Q`

Discussion

1944.	Forensic scientists use h=61.4+2.3F To predict the right h in centimeters for a female whose thigh bone (femur) measures F cm . If the height of the female lies between 160 to 170 cm find the range of values for the length of the thigh bone ?
Answer» ANSWER :`42.87 LT X lt 47.23`

Discussion

1945.	Show that (cosh(2x)-1)/(sinh(2x)) = (sinh(2x))/(1+cosh(2x))=tanhx
Answer» TANH(X) tanh(2X) COTH(x) coth(2x) ANSWER :A

Discussion

1946.	g(x+y)= g (x) + g(x) +3xy (x+y)AA, y in R and g'(0) = -4 Number of real roots of the equation g(x) = 0 is
Answer» 2 0 1 3 Answer :D

Discussion

1947.	Simplify : (1- omega) (1- omega^(2)) (1- omega^(4)) (1- omega^(8))
Answer» ANSWER :9

Discussion

1948.	If f(x)={{:((sqrt(1+kx)-sqrt1-kx)/(x),"for" -1 le x0),(2x^(2)+3x-2,"for" 0 le x le 1):} is continuous at x = 0 then find k.
Answer» ANSWER :k=-2

Discussion

1949.	Let n(A) = 4 and n(B) = k. The number of all possible injections from A to B is 120 then k =
Answer» 9 24 5 6 Answer :C

Discussion

1950.	If f(x)=(x^(n)-a^(n))/(x-a) for some constant 'a', then f'(a) is :
Answer» Answer :`(NX^(n)-ANX^(n-1)-x^(n)+a^(n))/((x-a)^(2))`

Discussion

Explore topic-wise InterviewSolutions in .

Angle between two lines is 45° and slope of one line is 2 then find slope of second line.

If y = Sin ^(-1) (3x - 4x ^(3)) find(dy)/(dx).

If f(x)=x/(sqrt(1-x^2)),g(x) = x/(sqrt(1+x^2)) , then d/(dx)(fog(x)) =

.......is the inequality represented by following graph .

If A and B are two sets, then A cap (A cup B) equals to,

If bara and barb are any two non-zero vectors, then find the angle between the vectors absbarb bara+absbara barb =absbarb bara-absbara barb

Find thevalue of f_(1),f_(2) and f_(3) from the following data: given that mode =37

If bare_(1),bare_(2) and bare_(3)are non-coplanar unit vectors andalpha=(bare_(1),bare_(2)), beta = (bare_(2),bare_(3)) and gamma = (bare_(3),bare_(1)) then what is the minimum value of cosalpha+cosbeta +cos gamma?

If A , B are two sets such that n(A)=100, n(B)=150, then the number of bijections from A onto B is

Differential coefficient of (x^((l + m)/(m - n)))^(1/(n-1)).(x^((m +n)/(n -1)))^(1/(l - m)).(x^((n + 1)/(l - m)))^(1/(m -n)) w.r.tx is

Differentiate the following functions w.r.t. x: ( cos x)/( 5x)

A cone is made from a circular sheet of radius sqrt(3) by cutting out a sector and giving the cut edges of the remaining piece together .The maximum volume attainable for the cone is

The point on the curve y=x^(2) is nearest to (3,0) is

If one root of k(x-1)^(2) =5x-7 is double the other root, show that k=2 or -25.

The circumcentre of the triangle formed by the linesx+y=0, x-y=0 and lx+my=1 is

Prove that: -4le5costheta+3cos(theta+pi/3)+3 ge10, for all values of theta.

Findthe periodof log _(e )(sin^-1(x- [x]))

lim_(xto(pi)/(4))(sqrt(2)sinx-1)/(cos(2x))=………..

Differentiate the following w.r.t. x : y= (x^2 - 3)/( x+4)

Find the distance of the line 4x - y=0 from the point P (4,1) measured along the line making an angle 135 degree with the positive x-axis.

Evaluate the following limits. Lt_(xto pi/4)(tanx)/x

If tantheta+tan4theta+tan7theta=tanthetatan4thetatan7theta then theta =

The perimeter of a sector is given. The area is maximum when the angle of the sector is

Let 40% of employees earn more than Rs. 18000 per month. Then to find the percentage of employees earn less than or equal to Rs. 18000 you have to calculate which percentile?

If p^(th) term of an AP is q and q^(th) term is p, find (p+q)^(th) term.

Show that the following system of equations is consistent and solve it completely. x+y+4z=6," "3x+2y-2z=9," "5x+y+2z=13

The value of theta which satisfy r sin theta = 3 and r = 4 ( 1+ sin theta ), 0 le theta le2 pi

Two systems of rectangular axes have the same origin. If a plane cuts them at distances a, b, c and a^(1),b^(1),c^(1) from the origin, then

Which of the following statements are true I : In /_\ABC is in inscribed in a given circle then deltaa.secA+deltab.secB+deltac.secC=1 II : Approximate value of (1.0002)^(3000) is 1.6

Solve the quadratic equation x^(2)+x+1/sqrt2=0 ?

The value of (127)^(1//3) to 4 decimal places is

Let F(x)= f(x)+g(x), G(x) = f(x) - g( x) and H(x)=(f( x))/( g(x))where f(x)= 1- 2 sin ^(2)x and g(x)=cos (2x) AA f: R to [-1,1] and g, R to [-1,1] Now answer the following Which of the following is correct

Let F(x)= f(x)+g(x), G(x) = f(x) - g( x) and H(x)=(f( x))/( g(x))where f(x)= 1- 2 sin ^(2)x and g(x)=cos (2x) AA f: R to [-1,1] and g, R to [-1,1] Now answer the following If the solution of F(x)-G (x)=0 are x_1,x_2, x_3 --------- x_nWherex in [0,5 pi] then

Let F(x)= f(x)+g(x), G(x) = f(x) - g( x) and H(x)=(f( x))/( g(x))where f(x)= 1- 2 sin ^(2)x and g(x)=cos (2x) AA f: R to [-1,1] and g, R to [-1,1] Now answer the following IfF :R to [-2,2] then F(x) is

Let F(x)= f(x)+g(x), G(x) = f(x) - g( x) and H(x)=(f( x))/( g(x))where f(x)= 1- 2 sin ^(2)x and g(x)=cos (2x) AA f: R to [-1,1] and g, R to [-1,1] Now answer the following Domain and range of H(x)are

Evaluate : lim_(xrarr1)(x^(15)-1)/(x^(10)-1)

Using binomial theorem, write the value of (a+b)^(6) + (a-b)^(6) and hence find the value of ( sqrt(3) + sqrt(2) )^(6) + ( sqrt(3) - sqrt(2) )^(6).

Find the angle between the line whose slope are2 and -1 .

Consider the two statements : P : Raj Kapoor is alive . Q : Raj Kapoor lives in Delhi .Write the followingstatements in Symbolic form. Either Raj Kapoor is alive or he lives inDelhi .

Consider the two statements : P : Raj Kapoor is alive . Q : Raj Kapoor lives in Delhi .Write the followingstatements in Symbolic form. Raj Kapoor is alive and he lives in Delhi.

Find the derivative of tan2x from the first principle.

Consider the two statements : P : Raj Kapoor is alive . Q : Raj Kapoor lives in Delhi .Write the followingstatements in Symbolic form. It is not true thatRaj Kapoor is alive and helives in Delhi .

Consider the two statements : P : Raj Kapoor is alive . Q : Raj Kapoor lives in Delhi .Write the followingstatements in Symbolic form. Raj Kapoor is neither alive, nor does he live in Delhi.

Forensic scientists use h=61.4+2.3F To predict the right h in centimeters for a female whose thigh bone (femur) measures F cm . If the height of the female lies between 160 to 170 cm find the range of values for the length of the thigh bone ?

Show that (cosh(2x)-1)/(sinh(2x)) = (sinh(2x))/(1+cosh(2x))=tanhx

g(x+y)= g (x) + g(x) +3xy (x+y)AA, y in R and g'(0) = -4 Number of real roots of the equation g(x) = 0 is

Simplify : (1- omega) (1- omega^(2)) (1- omega^(4)) (1- omega^(8))

If f(x)={{:((sqrt(1+kx)-sqrt1-kx)/(x),"for" -1 le x0),(2x^(2)+3x-2,"for" 0 le x le 1):} is continuous at x = 0 then find k.

Let n(A) = 4 and n(B) = k. The number of all possible injections from A to B is 120 then k =

If f(x)=(x^(n)-a^(n))/(x-a) for some constant 'a', then f'(a) is :