14949 + Interview Questions in Maths in Class 11 Page 79 InterviewSolution

3901.	The maximum value of f(x)=x^3-2ax^2+a^2x(agt0) is
Answer» 0 `a^3` `4/(27)a^3` a Answer :C

Discussion

3902.	Find the perpendicular distance between the lines 3x+4y+5=0, 3x+4y+17=0
Answer» ANSWER : `12/(5)`

Discussion

3903.	Write the following sets in the set builder form : A= {1, (1)/(2), (1)/(3), (1)/(4), (1)/(5),"………."}
Answer» ANSWER :`A= {X : x= (1)/(N), n in N}`

Discussion

3904.	If d_(1),d_(2),d_(3) are the diameters of three ex-circles of a triangle then d_(2)d_(2)+d_(2)d_(3)+d_(3)d_(1)=
Answer» `DELTA^(2)` `4S^(2)` `4Delta^(2)` `ab+bc+ca` ANSWER :B

Discussion

3905.	Find the value of sin^(2)37(1^(@))/(2)-sin^(2)7(1)/(2)
Answer» ANSWER :`(1)/(2sqrt(2))`

Discussion

3906.	How many different numbers of six digits can be formed with the digits 3,1,7,0,9, 5 ?
Answer» ANSWER :` 600`

Discussion

3907.	The vector area of the parallelogram whose adjacent sides vec(i) + vec(j) + vec(k) and 2vec(i)-vec(j) + 2vec(k) is
Answer» `3(VEC(i) +vec(k))` `3(vec(i) -vec(k))` `2vec(i) + vec(j)-2vec(k)` `-2vec(i)-vec(j)-2vec(k)` ANSWER :B

Discussion

3908.	Find the derivativ of the function from first principles : cot (2x +3)
Answer» ANSWER :`(2X +3)`

Discussion

3909.	If the d.r'sof bar(OA),bar(OB) are (1,-2,3),(-3,4,5) then the d.c's of the normal to the plane bar(OAB) are
Answer» `((4)/(SQRT(29)),(3)/(sqrt(29)),-(2)/(sqrt(29)))` `((11)/(sqrt(171)),(7)/(sqrt(171)),(1)/(sqrt(171)))` `((3)/(sqrt(29)),-(2)/(sqrt(29)),-(4)/(sqrt(29)))` `((3)/(sqrt(29)),-(2)/(sqrt(29)),-(4)/(sqrt(29)))` ANSWER :B

Discussion

3910.	Derive the equation of the ellipse in the form (x^(2))/(a^(2))+(y^(2))/(b^(2))=1.
Answer» ANSWER :`(x^2)/(a^2)+(y^2)/(b^2)=1`.

Discussion

3911.	Find the derivatives of the function sin (tan ^(-1) (e ^(x)))
Answer» Answer :`(e ^(X) COS ( tan ^(-1) e ^(x)))/( e ^(2X) + 1)`

Discussion

3912.	Assertion (A) : The inverse of [(2,-1),(-4,2)] does not exist. Reason (R ) : The matrix is non -singular
Answer» Both A and R are TRUE and R is the correct explanation of A Both A and R are true and R is not a correct explanation of A A is true but R is FALSE A is false but R is true ANSWER :A::B

Discussion

3913.	If f(x) = cos x cos 2x cos 2^2 x cos^(2^3) x .....cos 2^(n-1) x and n gt 1 then f^(1)(pi/2) is
Answer» 1 0 `-1` `(-1)^(n-1)` ANSWER :A

Discussion

3914.	Domain of the function defined by f(x)= sqrt(x-1) + sqrt(3-x) is…..
Answer» `[1, OO)` `(-oo, 3)` (1,3) [1, 3] ANSWER :D

Discussion

3915.	Assertion (A) : In a DeltaABC the minimum value of tan^(2)A//2+tan^(2)B//2+tan^(2)C//2 is 1 Reason (R) : a^(2)+b^(2)+c^(2)-ab-bc-ca= ge0
Answer» A is FALSE, R is TRUE A is true, R is false A is true, R is true and R is not correct EXPLANATION of A A is true, R is true and R is correct explanation of A Answer :D

Discussion

3916.	Stationary point of y=(logx)/(x)(xgt0)is
Answer» (1,0) `(E,(1)/(e))` `((1)/(e),-e)` `((1)/(e),(1)/(e))` ANSWER :B

Discussion

3917.	For x,y,z, t in R, sin^(-1)x+cos^(-1)y+sec^(-1)zget^(2)-sqrt(2pi)t+3pi The value of cos^(-1)("min"{x,y,z}) is
Answer» 0 `(PI)/2` `pi` `(pi)/3` ANSWER :D

Discussion

3918.	If lim_(t rarrx)(e^(t)f(x)-e^(x)f(t))/((t-x)(f(x))^2)=2 and f(0) =1/2 , then find the value of f'(0)
Answer» 4 2 0 1 Answer :C

Discussion

3919.	Find two positive numbers whose difference is 12 and whose A.M. exceeds the G.M. by 2.
Answer» ANSWER :16 and 4

Discussion

3920.	If t_(n) denotes the nth term of the series 2 + 3+ 6+ 11,…….then t_(50) is
Answer» `(49)^(2)+2` `(49)^(2)` `(50)^(2)+ 1` `(40)^(2) + 2` ANSWER :D

Discussion

3921.	A = (2, 4, 5) and B=(3, 5, -4) are two points. If the xy-plane, yz-plane divide AB in the ratios a:b, p:q respectively then (a)/(b)+(p)/(q)=
Answer» `(23)/(12)` `(-7)/(12)` `(7)/(12)` `(-22)/(15)` ANSWER :c

Discussion

3922.	A box contains 6 redmarbles numbers form 1 through 6 and4 whitemarbles 12 through 15. Findthe probabilitythata marbledrawnat randomis whiteodd numbered.
Answer» 5 5 `(1)/(6)` `(1)/(5)` ANSWER :D

Discussion

3923.	The three planes determine a rectangular parallelopiped which has _____ of rectangular faces.
Answer» ANSWER :THREE POINTS

Discussion

3924.	A person is to walk from P to Q. However, he is restricted to walk only to the right of P or upward to, P but not necessarly in the order shown in the adjoining figure. Determine the number of paths, available to the person from P to Q.
Answer» ANSWER :126

Discussion

3925.	Find r if .^(5)P_(r )= .^(6)P_(r-1)
Answer» ANSWER :4

Discussion

3926.	Write the contrapositive and converse of the following statements. x is an even number implies that x is divisible by 4.
Answer» Answer :This statement can be WRITTEN as ''If X is an EVEN number, then x is divisible by 4''. The contrapositive is, If x is not divisible by 4, then x is not an even number. The converse is, If x is divisible by 4, then x is an even number.

Discussion

3927.	If f(x)is a polynomial of degree n such that f(0 ) =0 ,f(1)= (1)/(2), ............, f(n) = ( n)/( n+1). Then the value of f(n+1)is
Answer» 1 when n is ODD `(n)/(n+2)` when n is even `- (n)/(n+1)` when n is odd `-1`when n is even ANSWER :A::B

Discussion

3928.	Let f:[-10, 10] rarr R, where f(x)= sinx +[x^(2)//a], be an addfunction. Then the set of values of parameter a is/are
Answer» `(-10, 10)-{10}` (0, 10) `[100, OO)` `(100, oo)` ANSWER :D

Discussion

3929.	If f(x)=sin(sinx) an f f'(x) +tan xf'(x)+g(x)=0, then g(x) is :
Answer» `COS^(2)X cos(sinx)` `sin^(2)x cos(COSX)` `sin^(2)x sin (cosx)` `cos^(2) x sin (sinx)` Answer :D

Discussion

3930.	If a le sin^(-1)x+cos^(-1)x+tan^(-1)x le b, then
Answer» `a=(pi)/4,b=(3PI)/4` `a=0,b=(pi)/2` `a=(pi)/2,b=pi` `a=pi,b=0` Answer :A

Discussion

3931.	Find the centre of the circle x^2+y^2-5x+2y-48=0
Answer» SOLUTION :(5/2,-1)

Discussion

3932.	What is inelastic collision? In which way it is different from elastic collision. Mention few examples in day to day life for inelastic collision.
Answer» Solution :(i) In a collision, the total initial kinetic energy of the bodies (before collision) is not equal to the total final kinetic energy of the bodies (after collision) then, it is called as inelastic collision. (ii) Momentum is conserved. Kinetic energy is not conserved in inelastic collision. MECHANICAL energy is DISSIPATED into heat, light, sound, etc. When a light body collides against any massive body at rest it sticks to it. (iii) Total kinetic energy before collision `ne` Total kinetic energy after collision. Total kinetic energy before collision – Total kinetic energy after collision = loss in energy during collision = `DeltaQ.` (iv) Even though kinetic energy is not conserved but the total energy is conserved. (V) Loss in kinetic energy during collision is transformed to another form of energy like sound, thermal, etc. (vi) If the two colliding bodies stick together after collision such COLLISIONS are known as completely inelastic collision or perfectly inelastic collision. (vii) For example when a clay putty is thrown on a MOVING vehicle, the clay putty (or Bubblegum) sticks to the moving vehicle and they move together with the same velocity.

Discussion

3933.	Find the values of x and y, lying between 0 and 360 which satisfy the equations, sin2x^(@)=0.6428
Answer» ANSWER :`x=20^(@)` or `90^(@)` or `200^(@)` or `250^(@)`

Discussion

3934.	Given statements in (a) and (b) identify the statements given below as contrapositive or converse of each other. (a) if you live in delhi , then you have winter clothes . (i) if you do not have winter clothes, then clothes. (ii) if you have winter clothes, then you its in delhi. (b)if a quadrilateral is a parallelogram, then its diagonals bisect each other. (i) if the diagonals of a quadrilateral do not bisect each other, then the quadrilateral is not a parallelogram. (ii) if the diagonals of a quadrilateral bisect each other, then it is a paralleogram.
Answer» SOLUTION :(a) (i) CONTRAPOSITIVE (II) CONVERSE (B) (i) Contrapositive (ii) Converse

Discussion

3935.	A die is thrown once . Find P(an ace),
Answer» ANSWER :0

Discussion

3936.	An aeroplane is moving one kilometer high from west to east horizontally . From a point on the ground due south the angle of elevation of the aeroplane is 60^(@), and after 10 second, the angle of elevation of the aeroplane is observed as 30^(@) . Then the speed (in m/s)of the bird is
Answer» `240sqrt(3)km//hr` `485km//hr` `364km//hr` `523km//hr` ANSWER :A

Discussion

3937.	Evaluate underset(n=2)overset(10)Sigma 4^(n)
Answer» ANSWER :`(16)/(3) [4^(9)-1]`

Discussion

3938.	Find the domain and range of f(x)=[cosx].
Answer» ANSWER :`D_(F)=R,`R_(f)={-1,0,1}`

Discussion

3939.	P (vecp) and Q (vecq) are the position vectors of two fixed points and R(vecr) is the postion vector of a variable point. If R moves such that (vecr-vecp)xx (vecr-vecq)=vec0then the locus of R is
Answer» a plane containing the origian O and PARALLEL to TWO non-collinear vectors `vec(OP) and vec(OQ) ` the surface of a sphere described on PQ as its diameter a line passing through points P and Q a setof lines parallel to line PQ Solution :`r (vecr)` moves on PQ

Discussion

3940.	Evaluate Lt_(x to oo) (x^2-sinx)/(x^2 - 2)
Answer» ANSWER :1

Discussion

3941.	Let f(x)=int_(0)^(x)(sint)/(t)dt,xgt0, then
Answer» `F(X)`has a local MAXIMA at `x=npi(N=2k,kinI^(+))` f(x) has a local minima at `x=npi(n=2k,kinI^(+))` f(x) has neither maxima nor minima at `x=npi(n inI^(+))` f(x) has local maxima at `x=npi(n=2k-1,kinI^(+))` Answer :B::D

Discussion

3942.	If f(x) = (1 - x)^n then the value of f(0) + f'(0) + (f^('')(0))/(2!) + ….+ (f^('')(0))/(n!) is equal to
Answer» `2^n` `0` `2^(n - 1)` `1` ANSWER :B

Discussion

3943.	The plane determined by the points (-1,2,-2),(0,1,1)and(1,1,2) passes through
Answer» `(1,1,0)` `(-1,1,0)` `(1,2,0)` `(1,0,-1)` ANSWER :B

Discussion

3944.	If 3 tan (theta - 15^(@))=tan (theta + 15^(@)), 0 lt theta lt pi then theta =
Answer» `pi//2` `pi//4` `pi//6` `pi//3` ANSWER :B

Discussion

3945.	Construct index number from the following data for 1991 and 1992 taking 1990 as base by using the method of simple average of price relatives:
Answer» ANSWER :`128.13,114`

Discussion

3946.	The values of theta satisfying cosec theta + 2 = 0 in (0, 2pi) are
Answer» `210^(@), 300^(@)` `240^(@),300^(@)` `210^(@),240^(@)` `210^(@),330^(@)` ANSWER :D

Discussion

3947.	If y = (ax+b)^(cx+d) then (dy)/(dx) =
Answer» `y{(a(cx+d))/((ax+b))+CLOG(ax+b)}` `y{(a(cx+d))/((ax+b))-clog(ax+b)}` `y{((cx+d))/((ax+b))+LOG(ax+b)}` `y{((cx+d))/((ax+b))-log(ax+b)}` ANSWER :A

Discussion

3948.	If tan^(2)theta=sin^(2)(pi//2) then theta =
Answer» `npipm(pi)/(2)` `npipm(pi)/(4)` `npipm(pi)/(6)` `npipm(pi)/(3)` Answer :B

Discussion

3949.	If sin^(-1)(cos^(-1)x)lt1 and cos^(-1)(cos^(-1)x)lt1 then x in
Answer» `(SIN1, SIN (sin1))` `(cos(cos1),cos(sin1))` `(cos(sin1),cos(cos1))` `phi` (EMPTY set) Answer :C

Discussion

3950.	Let B(1,-3) and D(0,4) represents two vertices of a rhombus ABCD in xy plane, then coordinaters of vertix A if alngleBAD=60^(@) can be equal to :
Answer» `((1-7sqrt3)/2,(1-sqrt3)/2)` `((1+7sqrt3)/2,(1+sqrt3)/2)` `((1+7sqrt3)/2,(1+sqrt3)/2)` `((-1-sqrt3)/2,(-1-sqrt3)/2)` ANSWER :A::B

Discussion

Explore topic-wise InterviewSolutions in .

The maximum value of f(x)=x^3-2ax^2+a^2x(agt0) is

Find the perpendicular distance between the lines 3x+4y+5=0, 3x+4y+17=0

Write the following sets in the set builder form : A= {1, (1)/(2), (1)/(3), (1)/(4), (1)/(5),"………."}

If d_(1),d_(2),d_(3) are the diameters of three ex-circles of a triangle then d_(2)d_(2)+d_(2)d_(3)+d_(3)d_(1)=

Find the value of sin^(2)37(1^(@))/(2)-sin^(2)7(1)/(2)

How many different numbers of six digits can be formed with the digits 3,1,7,0,9, 5 ?

The vector area of the parallelogram whose adjacent sides vec(i) + vec(j) + vec(k) and 2vec(i)-vec(j) + 2vec(k) is

Find the derivativ of the function from first principles : cot (2x +3)

If the d.r'sof bar(OA),bar(OB) are (1,-2,3),(-3,4,5) then the d.c's of the normal to the plane bar(OAB) are

Derive the equation of the ellipse in the form (x^(2))/(a^(2))+(y^(2))/(b^(2))=1.

Find the derivatives of the function sin (tan ^(-1) (e ^(x)))

Assertion (A) : The inverse of [(2,-1),(-4,2)] does not exist. Reason (R ) : The matrix is non -singular

If f(x) = cos x cos 2x cos 2^2 x cos^(2^3) x .....cos 2^(n-1) x and n gt 1 then f^(1)(pi/2) is

Domain of the function defined by f(x)= sqrt(x-1) + sqrt(3-x) is…..

Assertion (A) : In a DeltaABC the minimum value of tan^(2)A//2+tan^(2)B//2+tan^(2)C//2 is 1 Reason (R) : a^(2)+b^(2)+c^(2)-ab-bc-ca= ge0

Stationary point of y=(logx)/(x)(xgt0)is

For x,y,z, t in R, sin^(-1)x+cos^(-1)y+sec^(-1)zget^(2)-sqrt(2pi)t+3pi The value of cos^(-1)("min"{x,y,z}) is

If lim_(t rarrx)(e^(t)f(x)-e^(x)f(t))/((t-x)(f(x))^2)=2 and f(0) =1/2 , then find the value of f'(0)

Find two positive numbers whose difference is 12 and whose A.M. exceeds the G.M. by 2.

If t_(n) denotes the nth term of the series 2 + 3+ 6+ 11,…….then t_(50) is

A = (2, 4, 5) and B=(3, 5, -4) are two points. If the xy-plane, yz-plane divide AB in the ratios a:b, p:q respectively then (a)/(b)+(p)/(q)=

A box contains 6 redmarbles numbers form 1 through 6 and4 whitemarbles 12 through 15. Findthe probabilitythata marbledrawnat randomis whiteodd numbered.

The three planes determine a rectangular parallelopiped which has _____ of rectangular faces.

A person is to walk from P to Q. However, he is restricted to walk only to the right of P or upward to, P but not necessarly in the order shown in the adjoining figure. Determine the number of paths, available to the person from P to Q.

Find r if .^(5)P_(r )= .^(6)P_(r-1)

Write the contrapositive and converse of the following statements. x is an even number implies that x is divisible by 4.

If f(x)is a polynomial of degree n such that f(0 ) =0 ,f(1)= (1)/(2), ............, f(n) = ( n)/( n+1). Then the value of f(n+1)is

Let f:[-10, 10] rarr R, where f(x)= sinx +[x^(2)//a], be an addfunction. Then the set of values of parameter a is/are

If f(x)=sin(sinx) an f f'(x) +tan xf'(x)+g(x)=0, then g(x) is :

If a le sin^(-1)x+cos^(-1)x+tan^(-1)x le b, then

Find the centre of the circle x^2+y^2-5x+2y-48=0

What is inelastic collision? In which way it is different from elastic collision. Mention few examples in day to day life for inelastic collision.

Find the values of x and y, lying between 0 and 360 which satisfy the equations, sin2x^(@)=0.6428

A die is thrown once . Find P(an ace),

An aeroplane is moving one kilometer high from west to east horizontally . From a point on the ground due south the angle of elevation of the aeroplane is 60^(@), and after 10 second, the angle of elevation of the aeroplane is observed as 30^(@) . Then the speed (in m/s)of the bird is

Evaluate underset(n=2)overset(10)Sigma 4^(n)

Find the domain and range of f(x)=[cosx].

P (vecp) and Q (vecq) are the position vectors of two fixed points and R(vecr) is the postion vector of a variable point. If R moves such that (vecr-vecp)xx (vecr-vecq)=vec0then the locus of R is

Evaluate Lt_(x to oo) (x^2-sinx)/(x^2 - 2)

Let f(x)=int_(0)^(x)(sint)/(t)dt,xgt0, then

If f(x) = (1 - x)^n then the value of f(0) + f'(0) + (f^('')(0))/(2!) + ….+ (f^('')(0))/(n!) is equal to

The plane determined by the points (-1,2,-2),(0,1,1)and(1,1,2) passes through

If 3 tan (theta - 15^(@))=tan (theta + 15^(@)), 0 lt theta lt pi then theta =

Construct index number from the following data for 1991 and 1992 taking 1990 as base by using the method of simple average of price relatives:

The values of theta satisfying cosec theta + 2 = 0 in (0, 2pi) are

If y = (ax+b)^(cx+d) then (dy)/(dx) =

If tan^(2)theta=sin^(2)(pi//2) then theta =

If sin^(-1)(cos^(-1)x)lt1 and cos^(-1)(cos^(-1)x)lt1 then x in

Let B(1,-3) and D(0,4) represents two vertices of a rhombus ABCD in xy plane, then coordinaters of vertix A if alngleBAD=60^(@) can be equal to :