14949 + Interview Questions in Maths in Class 11 Page 76 InterviewSolution

3751.	Determine whether the following function is differentiable at the indicated values. (i) f(x) = x \|x\| at x=0 (ii) f(x) = }x^2 -1\| at x=1 (iii) f(x) = \|x\| + \|x-1\| at x=0,1 (iv) f(x) = sin \|x\| at x=0
Answer» Answer :(i) 0 (ii) `f(x)` is not differentiable at `x=1`. (III) `THEREFORE f(x)` is not differentiable at `x=0` (IV) `therefore f(x)` is not differentiable at `x=0`

Discussion

3752.	(sin A - sin B)/(cos A+ cos B) is equal to
Answer» `SIN ((A+B)/(2))` `2 TAN (A+B)` `COT ((A-B)/(2))` `tan ((A-B)/(2))` ANSWER :D

Discussion

3753.	If \|{:(a,b,c),(b,c,a),(c,a,b):}\|^(x)=\|{:(2bc-a^(2),c^(2),b^(2)),(c^(2),2ac-b^(2),a^(2)),(b^(2),a^(2),2ab-c^(2)):}\| then x =
Answer» 1 2 3 `1//2` ANSWER :B

Discussion

3754.	The range of f(x)=3x^(2)+7x+10 is
Answer» `[70/3, OO)` `[71/12, oo)` `[0, oo)` `(-oo, 70/3)` ANSWER :B

Discussion

3755.	If x =a (t - sint ) , y =a ( 1 + cos t )find (d ^(2) y )/(dx ^(2)).
Answer» ANSWER :`(1)/(4A) cosec ^(4) ((t)/(2)) `

Discussion

3756.	If z=4 + 3i, then verify thatz^(-1)= (bar(z))/(\|z\|^(2))
Answer» ANSWER :`(4-3i)/(25)`

Discussion

3757.	If DeltaABC the sides, b,c are given. If there is an error deltaA in measuring angle 'A' then deltaa=
Answer» `(DELTA)/(2A)deltaA` `(2Delta)/(a)deltaA` `bcsinAdeltaA` `2Delta` ANSWER :B

Discussion

3758.	f(x) is continuous on [a.b] then Statemant- I :underset(x to a^(+)) (Lt) f(x) = f(a) Statement-II : f is continuous for every x in (a,b) Statement-III underset (x to b^(-))(Lt) f(x) = f(b) Which of the following is true
Answer» I and III only only II I, II,III Only I , II ANSWER :C

Discussion

3759.	Prove that sum_(r=0)^(n) 3^( r" "n)C_(r ) =4^(n).
Answer» ANSWER :`=4^(N)`.

Discussion

3760.	The nonzero vectors bara,barb and barc " are related by " bara=8barb and barc=-7barb. Then the angle between bara and barc si
Answer» `PI/4` `pi/2` `pi` 0 Answer :C

Discussion

3761.	Choose the correctoption for the following lim_(xrarrinfty)[tan^(-1)x .(1+x)^((1/x).x^(-1)]:
Answer» 1 e `1/e` NONE of these Answer :B

Discussion

3762.	Let f be a function with domain [-3, 5] and let g(x)=[3x+4]. Then , the domain of (fog)(x) is
Answer» `(-3 , 1/3)` `[-3, 1/3)` `[ -3, 1/3)` `[-3, - 1/3]` ANSWER :C

Discussion

3763.	If alpha and beta are two different values of theta lying between 0 and 2pi which satisfy the equations 6costheta+8sin theta=9, find the value of sin2(alpha+beta).
Answer» ANSWER :`-(336)/(625)`

Discussion

3764.	Differentiate the following functions: x^(3) + 4x^(2) + 7x +2
Answer» ANSWER :`3X^(2)+8x+7`

Discussion

3765.	IF the perimeter of a triangle is 12 times the arithmetic mean of the sides of its angles then its circumference=
Answer» `1` `2` ` 3` ` 6` ANSWER :B

Discussion

3766.	The number of values ofx in [0, 2 pi]satisfying the equation \|cos x - sin x \| ge sqrt(2) , is
Answer» 0 1 2 3 Answer :C

Discussion

3767.	For numbers 6 and 24, A - G = .......
Answer» ANSWER :3

Discussion

3768.	If (2)/(3)=(x-(1)/(y))+(x^(2)-(1)/(y^(2)))+ ... "To" oo and xy =2 then calculate the values of x and y with the condition that x lt 1.
Answer» ANSWER :`X= (1)/(2) , y=4`

Discussion

3769.	Let (bcos x)/(2 cos 2x-1)=(b+sinx)/((cos^(2)x-3sin^(2)x)tanx), b in R Equation has solution if
Answer» `B in (-oo,1/2)-{-1,0,1/3}` `b in (-oo,1)-{-1,0,1/3}` `b in R-{-1,0,1/3}` `b in (-oo,1/2)` ANSWER :A

Discussion

3770.	Each of the following questions contain two statements-Statement I and Statement II. Each of the questions has following four choices A,B,C, and D only of which is correct. 2a is the length of transverse axis of the hyperbola. Vertex of hyperbola is the mid point on the line joining its centre and focus. Statement-I Length of latus rectum of hyperbola is 6a units. Statement-II: Eccentricity of the hyperbola is sqrt(2).
Answer» Statement-I is TRUE, Statement-II is true and Statement-II is a CORRECT EXPLANATION for Statement-I. Statement-I is true, Statement-II is true but Statement-II is not a correct explanation of Statement-I. Statement-I is true, Statement-II is FALSE. Statement-I is false,, Statement-II is true. Answer :C

Discussion

3771.	Each of the following questions contain two statements-Statement I and Statement II. Each of the questions has following four choices A,B,C, and D only of which is correct. 2a is the length of transverse axis of the hyperbola. Vertex of hyperbola is the mid point on the line joining its centre and focus. Statement-I Rectangular hyperbola xy = 4^(2) never intersects the parabola y^(2) = 4x at a real point. Statement-II: If the hyperbola (x^(2))/(b^(2))-(y^(2))/(a^(2))= 1be passing through the foci of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))= 1 , then the eccentricity of the hyperbola is sqrt(3).
Answer» Statement-I is TRUE, Statement-II is true and Statement-II is a CORRECT EXPLANATION for Statement-I. Statement-I is true, Statement-II is true but Statement-II is not a correct explanation of Statement-I. Statement-I is true, Statement-II is FALSE. Statement-I is false,, Statement-II is true. Answer :D

Discussion

3772.	Without using tables, give the valueof the following : sin4530^(@)
Answer» ANSWER :`-1/2`

Discussion

3773.	Find the set of values of x for which (tan3x-tan2x)/(1+tan3x.tan2x)=1.
Answer» Solution :We have, `(tan3x-tan2x)/(1+tan3x.tan2x)=1 rArr tan(3x-2x)=1 rArr tanx=1` `rArr tanx=tanx/4 rArr X=npi+pi/4,n in I` (using `tantheta=tanalpha ltimplies theta= npi+alpha)` But for this VALUE of x, `tan 2x` is not DEFINED. Hence the solution set for `x` is `PHI`.

Discussion

3774.	Determine whether the following measurements produce one triangle, two triangles or no triangle angleB = 88^(@), a = 23 , b = 2. Solve if solution exists.
Answer» ANSWER :SOLUTION of the GIVEN TRIANGLE does not EXIST.

Discussion

3775.	Express the following in the form a+bi (-2-(1)/(3)i)^(3)
Answer» ANSWER :`= -(22)/(3)- (107)/(27)i`

Discussion

3776.	A bag contains 8 red and 5 white balls. Two successive drawings of 3 balls are made such that (i) balls are replaced before the second draw, (ii) the balls are not replaced before the second draw. Find the probability that the first drawing will give 3 white and second 3 red balls.
Answer» Answer :(i)`P(ACAPB) = 5/143 XX 28/143 = 140/20449` (II)` therefore P(Ccap D ) = 5/143 xx 7/15 = 35 /2145 = 7 /429`

Discussion

3777.	Verify Rolle's theorem for the following functions: f(x)= sqrt(9-x^(2)), x in [-3, 3]
Answer» ANSWER :[0, 3]

Discussion

3778.	Equation of Y-axis is considered as _____
Answer» X = 0 and y = 0 y = 0 and Z = 0 x = 0 and z = 0 None of these Answer :C

Discussion

3779.	A function is matched below against an interval where it is supposed to be increasing Which of the following parts is incorrectly matched ? {:("Interval","Function"),((a)[2,oo),2x^(3)-3x^(2)-12x+6),((b)(-oo,oo),x^(3)-3x^(2)+3x+3),((c)(-oo,-4],x^(3)+6x^(2)+6),((d)(-oo,(1)/(3)],3x^(2)-2x+1):}
Answer» ANSWER :d

Discussion

3780.	Find a if the 17^th and 18^th terms of the expansin (2 + a)^50are equal.
Answer» ANSWER :1

Discussion

3781.	If f(x) = sin^(2)x + sin^(2)(x+pi//3) + cosx.cos(x+pi/3) and g(5//4) =1, then (gof)(x)=
Answer» 1 0 sin X `-COS x` ANSWER :A

Discussion

3782.	If equation (x^(2))/(2-r) + (y^(2))/(r-5) + 1 = 0 represents ellipse then …….
Answer» `r GT 2` `2 LT r lt 5` `r gt 5` NONE of these Answer :B

Discussion

3783.	2"tan"^(-1)1/3+"tan"^(-1)1/7=
Answer» 1)`pi` 2)`(pi)/2` 3)`(pi)/4` 4)`(3pi)/4` Answer :C

Discussion

3784.	If y = x ^(x) (x gt 0) ,find (dy)/(dx)
Answer» ANSWER :`(d)/(DX) (X ^(x)) = x^(x) (1 + LOG x)`

Discussion

3785.	Any term of an AP (except first) is equal to half the sum of terms which are equidistant from it.
Answer» ANSWER :1

Discussion

3786.	If the angles A,B,C of a triangle are in A.P and sides a,b,c are in G.P then a^2,b^2,c^2 are in
Answer» A.P G.P H.P all the above Answer :D

Discussion

3787.	Sum the series to infinity : sqrt(3) + (1)/(sqrt(3))+ (1)/(3sqrt(3))+...
Answer» ANSWER :`(3 SQRT(3))/(2)`

Discussion

3788.	One card is drawn from well -shufleddeck of 52 cards . If each out come is equally likely ,calculate the probability that the card will be (i) diamond (ii) not an ace (iii) a balck card ?
Answer» ANSWER :(i) `(1/4)` (II) `(3/4)` (III) `(1/2)`

Discussion

3789.	Evaluate the following limits : Lim_( x to 1) ((2x-3)(x-1))/(2x^(2)+x-3)
Answer» ANSWER :`-1/5`

Discussion

3790.	Let f(x)=sinx-cosx be defined on [0,2pi]. Determine the intervals in which f(x) is strictly decreasing and strictly increasing.
Answer» ANSWER :`(4ac-b^2)/(4A)`

Discussion

3791.	Ifx= a cos^(2) thetasin theta and y= a sin^(2) theta cos theta , " then " ((x^(2)+y^(2))^(3))/(x^(2)y^(2))=
Answer» `a^(2)` `2A^(2)` `3A^(2)` a Answer :A

Discussion

3792.	If an error of 0.01 cm is made while measuring the radius 5 cm of a circle, then error the relative error and the percentage error in the circumference and the area of the circle.
Answer» ANSWER :`0.02pi CM, 0.002, 0.2, 0.1,PI, 0.004`

Discussion

3793.	Determine real values of x and y for which each statement is true -(x+3y) i+ (2-y+1)= (8)/(i)
Answer» ANSWER :`X= (5)/(7), y= (17)/(7)`

Discussion

3794.	f(x)= underset(n to oo) (Lt) (sinx)^(2n) then set of points of discontinuity of f(x) is
Answer» `{(2n+1)PI//4, n in Z}` `{(2n+1)(pi)/(2)//n in Z} UU { npi, n in Z}` `{(2n+1)(pi)/(2)//n in Z}` `{(2n+1)(pi)/(6)//n in Z}` Answer :A

Discussion

3795.	Obtain equation of circle in Centre of origin and radius r = 6.
Answer» ANSWER :`X^(2) + y^(2) = 36`

Discussion

3796.	All the values of x satisfying sin 2x + sin 4x = 2 sin 3x are
Answer» `N PI // 3` ` 2 n pi` `n pi` `n pi + pi//3` ANSWER :A

Discussion

3797.	If cos theta + cos 3 theta - 2 cos 2 theta = 0 " then " theta=
Answer» `(2 n + 1) (pi)/(4), 2 m pi, m, n in Z` `(n pi)/(4), m pi, n, m in Z` `(2 n +1) (pi)/(3), 2 m pi, n, m in Z` `(2 n + 1) (pi)/(6) , MPI, n, m in Z` ANSWER :A

Discussion

3798.	cos((65pi)/4)=.........
Answer» ANSWER :`1/sqrt2`

Discussion

3799.	Coordinates of the centre of the circle given by the equation lambda x^(2) + (2lambda - 3)y^(2) - 4x + 6y - 1 =0 is ………
Answer» `((4)/(3),1)` `((2)/(3), - 1)` `(-(2)/(3), 1)` `((2)/(3) , 1)` ANSWER :B

Discussion

3800.	Let ABC be a triangle with incentre at I. Also, let P and Q be the feet of perpendiculars from A to BI and CI, respectively. Then which of the following result are correct?
Answer» `(AP)/(BI)=("SIN"(B)/(2)"COS"(C)/(2))/("sin"(A)/(2))` `(AQ)/(CI)=("sin"(C)/(2)"cos"(B)/(2))/("sin"(A)/(2))` `(AP)/(BI)=("sin"(C)/(2)"cos"(B)/(2))/("sin"(A)/(2))` `(AP)/(BI)+(AQ)/(CI)= SQRT(3) " if "angleA=60^(@)` ANSWER :A::B::D

Discussion

Explore topic-wise InterviewSolutions in .

Determine whether the following function is differentiable at the indicated values. (i) f(x) = x |x| at x=0 (ii) f(x) = }x^2 -1| at x=1 (iii) f(x) = |x| + |x-1| at x=0,1 (iv) f(x) = sin |x| at x=0

(sin A - sin B)/(cos A+ cos B) is equal to

If |{:(a,b,c),(b,c,a),(c,a,b):}|^(x)=|{:(2bc-a^(2),c^(2),b^(2)),(c^(2),2ac-b^(2),a^(2)),(b^(2),a^(2),2ab-c^(2)):}| then x =

The range of f(x)=3x^(2)+7x+10 is

If x =a (t - sint ) , y =a ( 1 + cos t )find (d ^(2) y )/(dx ^(2)).

If z=4 + 3i, then verify thatz^(-1)= (bar(z))/(|z|^(2))

If DeltaABC the sides, b,c are given. If there is an error deltaA in measuring angle 'A' then deltaa=

f(x) is continuous on [a.b] then Statemant- I :underset(x to a^(+)) (Lt) f(x) = f(a) Statement-II : f is continuous for every x in (a,b) Statement-III underset (x to b^(-))(Lt) f(x) = f(b) Which of the following is true

Prove that sum_(r=0)^(n) 3^( r" "n)C_(r ) =4^(n).

The nonzero vectors bara,barb and barc " are related by " bara=8barb and barc=-7barb. Then the angle between bara and barc si

Choose the correctoption for the following lim_(xrarrinfty)[tan^(-1)x .(1+x)^((1/x).x^(-1)]:

Let f be a function with domain [-3, 5] and let g(x)=[3x+4]. Then , the domain of (fog)(x) is

If alpha and beta are two different values of theta lying between 0 and 2pi which satisfy the equations 6costheta+8sin theta=9, find the value of sin2(alpha+beta).

Differentiate the following functions: x^(3) + 4x^(2) + 7x +2

IF the perimeter of a triangle is 12 times the arithmetic mean of the sides of its angles then its circumference=

The number of values ofx in [0, 2 pi]satisfying the equation |cos x - sin x | ge sqrt(2) , is

For numbers 6 and 24, A - G = .......

If (2)/(3)=(x-(1)/(y))+(x^(2)-(1)/(y^(2)))+ ... "To" oo and xy =2 then calculate the values of x and y with the condition that x lt 1.

Let (bcos x)/(2 cos 2x-1)=(b+sinx)/((cos^(2)x-3sin^(2)x)tanx), b in R Equation has solution if

Without using tables, give the valueof the following : sin4530^(@)

Find the set of values of x for which (tan3x-tan2x)/(1+tan3x.tan2x)=1.

Determine whether the following measurements produce one triangle, two triangles or no triangle angleB = 88^(@), a = 23 , b = 2. Solve if solution exists.

Express the following in the form a+bi (-2-(1)/(3)i)^(3)

A bag contains 8 red and 5 white balls. Two successive drawings of 3 balls are made such that (i) balls are replaced before the second draw, (ii) the balls are not replaced before the second draw. Find the probability that the first drawing will give 3 white and second 3 red balls.

Verify Rolle's theorem for the following functions: f(x)= sqrt(9-x^(2)), x in [-3, 3]

Equation of Y-axis is considered as _____

A function is matched below against an interval where it is supposed to be increasing Which of the following parts is incorrectly matched ? {:("Interval","Function"),((a)[2,oo),2x^(3)-3x^(2)-12x+6),((b)(-oo,oo),x^(3)-3x^(2)+3x+3),((c)(-oo,-4],x^(3)+6x^(2)+6),((d)(-oo,(1)/(3)],3x^(2)-2x+1):}

Find a if the 17^th and 18^th terms of the expansin (2 + a)^50are equal.

If f(x) = sin^(2)x + sin^(2)(x+pi//3) + cosx.cos(x+pi/3) and g(5//4) =1, then (gof)(x)=

If equation (x^(2))/(2-r) + (y^(2))/(r-5) + 1 = 0 represents ellipse then …….

2"tan"^(-1)1/3+"tan"^(-1)1/7=

If y = x ^(x) (x gt 0) ,find (dy)/(dx)

Any term of an AP (except first) is equal to half the sum of terms which are equidistant from it.

If the angles A,B,C of a triangle are in A.P and sides a,b,c are in G.P then a^2,b^2,c^2 are in

Sum the series to infinity : sqrt(3) + (1)/(sqrt(3))+ (1)/(3sqrt(3))+...

One card is drawn from well -shufleddeck of 52 cards . If each out come is equally likely ,calculate the probability that the card will be (i) diamond (ii) not an ace (iii) a balck card ?

Evaluate the following limits : Lim_( x to 1) ((2x-3)(x-1))/(2x^(2)+x-3)

Let f(x)=sinx-cosx be defined on [0,2pi]. Determine the intervals in which f(x) is strictly decreasing and strictly increasing.

Ifx= a cos^(2) thetasin theta and y= a sin^(2) theta cos theta , " then " ((x^(2)+y^(2))^(3))/(x^(2)y^(2))=

If an error of 0.01 cm is made while measuring the radius 5 cm of a circle, then error the relative error and the percentage error in the circumference and the area of the circle.

Determine real values of x and y for which each statement is true -(x+3y) i+ (2-y+1)= (8)/(i)

f(x)= underset(n to oo) (Lt) (sinx)^(2n) then set of points of discontinuity of f(x) is

Obtain equation of circle in Centre of origin and radius r = 6.

All the values of x satisfying sin 2x + sin 4x = 2 sin 3x are

If cos theta + cos 3 theta - 2 cos 2 theta = 0 " then " theta=

cos((65pi)/4)=.........

Coordinates of the centre of the circle given by the equation lambda x^(2) + (2lambda - 3)y^(2) - 4x + 6y - 1 =0 is ………

Let ABC be a triangle with incentre at I. Also, let P and Q be the feet of perpendiculars from A to BI and CI, respectively. Then which of the following result are correct?