28278 + Interview Questions in Maths in Class 12 Page 107 InterviewSolution

5301.	For n=6k,kinZ,((1-isqrt3)/2)^(n)+((-1-isqrt3)/2)^(n) has the value
Answer» `-1` 0 1 2 Answer :D

Discussion

5302.	Write an anti derivative for each of the following functions using the method of inspection: (i) cos2x (ii) 3x^(2)+4x^(3) (iii) 1/x,xne0
Answer» ANSWER :`(i) (1)/(2) SIN 2x, (ii) x^(2)+x^(4) (iii) log\|x\|`

Discussion

5303.	If intsqrt(1+3sqrt(x))/(3sqrt(x^(2)))dx=2f(x)+C, then f(27) is equal to
Answer» ANSWER :8

Discussion

5304.	If a ne0 and the line 2bx+3cy+4d =0 passes through the points of intersection of the parabolas y^(2)=4ax and x^(2)=4ay then
Answer» `d^(2) +(2B +3c )^(2) = 0 ` ` d^(2) +(3b -2C) ^(2)=0 ` ` d^(2) +(2b -3c) ^(2) =0 ` ` d^(2) +( 3b+ 2c) ^(2) =0 ` ANSWER :A

Discussion

5305.	If 0 lt theta lt pi/2, x = sum_(n=0)^(oo)cos^(2n) theta, y =sum_(n=0)^(oo)sin^(2n)theta, and z=sum_(n=0)^(oo) cos^(2n)theta sin^(2n) theta then show that (i) xyz=xy+z (ii) xyz=x+y+z
Answer» `xz+yz=xy+z` `xyz=yz+x` `xy+z=xy+zx` `x+y+z=xyz+z` ANSWER :A

Discussion

5306.	If x is an integer and x in [1,5] then the probability that x^(2)-3x+2 gt 0
Answer» `(4)/(5)` `(1)/(5)` `(2)/(5)` `(3)/(5)` Answer :D

Discussion

5307.	Find the area of the region enclosed by the loop of the folium of Descartes x^(3) + y^(3) = 3axy
Answer» ANSWER :`(3)/(2)a^(2)`

Discussion

5308.	Choose the correct answer. Area bounded by the curvey=x^3,The x-axis and the ordinates. x=-2 and x=1 is:
Answer» -9 `- 15/4` `15/4` `17/4` ANSWER :D

Discussion

5309.	Sum of two skew symmetric matrices is always …… matrix.
Answer» Answer :Hence SUM of two SKEW symmetric matrix is also skew symmetric .

Discussion

5310.	If \|{:(3,5,2),(1,4,7),(2,1,0):}\|=k\|{:(3,5,4),(1,4,14),(4,2,0):}\| then k=……
Answer» `1/4` 4 `1/2` 2 Answer :A

Discussion

5311.	The sum of the series 1.2 + 2.3+ 3.4+…….. up to 20 tems is
Answer» ANSWER :3080

Discussion

5312.	If \|x\| is so small that x^(2) and higher powers of x may be neglected then find the approx-imate values of the following ((4+3x)^(1//2))/((3-2x)^(2))
Answer» ANSWER :`(2)/(9)+(41)/(108)x`

Discussion

5313.	If \|x\| is so small that x^(2) and higher powers of x may be neglected then find the approx-imate values of the following ((1-(2x)/(3))^(3//2)(32+5x)^(1//5))/((3-x)^(3))
Answer» Answer :`~=(2)/(27)(1+(X)/(32))`

Discussion

5314.	I. underset(x to 0)"Lt "sqrts does not exist II. underset(x to 1)"Lt" (\|x\|)/(x) does not exist.
Answer» only I is true only II is true both I and II are true neither I nor II are true Answer :D

Discussion

5315.	Find the derivative of tan (2x+3).
Answer» ANSWER :`2 SEC^(2) (2x+3)`.

Discussion

5316.	Let f(x) be a differentiable function in the interval (0,2) , then the value of int_0^2 f(x) dx is :
Answer» F( c) for some `c in (0,2)` 2F (c ) for some `c in (0,2)` f.(c ) for some `c in (0,1) ` NONE of these Solution :Let us consider a function `g(t)= int_0^t f(x)dx` Now applying lagrange.s mean value theorem in (0,2) ` RARR (g(2) - g(0))/(2-0) = g.(c ) `, where `c in (0,2) rarr int_0^2 f(x)dx = 2f(c ) `, where `c in (0,2)`.

Discussion

5317.	Eight coins are tossed together. The probability of getting exactly 3 heads is ..........
Answer» `(1)/(256)` `(7)/(32)` `(5)/(32)` `(3)/(32)` ANSWER :B

Discussion

5318.	Light rays entering the eye is controlled by :
Answer» PUPIL Iris Cornea Lens Answer :A

Discussion

5319.	For events A and B if P(A) = 0.3, P(B) = 0.6 and P(B \| A) = 0.5 then find P( A \| B) and P(A cup B).
Answer» ANSWER :`(1)/(4), 0.75`

Discussion

5320.	Let f: N to R be defined by f(x) = 4x^(2) + 12x+ 15. Show that f: N to S where S is the range of function f, is invertible. Also find the inverse of f.
Answer» ANSWER :`rArr f^(1) (x) = ( SQRT( x-6) -3)/( 2) in ` CODOMAIN 'R'

Discussion

5321.	If alpha, beta, gamma are roots of x^(3) + 2x^(2) - 3x - 1 = 0, then the value of alpha^(4) + beta^(4) + gamma^(4) is
Answer» 123 36 149 795 Answer :3

Discussion

5322.	If A and B'are independent events, then P(A' cup B)= 1- P(A) * P(B').
Answer» ANSWER :1

Discussion

5323.	Locus of the mid-points of all chords of the parabola y^(2)=4ax which are drwan through the vertax is a parabola, then its latus rectum is
Answer» `(a)/(2)` a 2a `(3a)/(2)` Solution :The unit vectors in the direction of the given vectors are `(6HAT(i)+2hat(j)+3hat(k))/(sqrt(36+4+9))=(6hat(i)+2hat(j)+3hat(k))/(7),(3hat(i)-2hat(j)+6hat(k))/(7)" and "(2hat(i)-3hat(j)-6hat(k))/(7)` Since `F_(1),F_(2)" and "F_(3)` are the forces of magnitude 5,3 and 1 units, we have `F_(1)=(5)/(7)(6hat(i)+2j+3k)` `F_(2)=(3)/(7)(3i-2j+6k)" and "F_(3)=(1)/(7)(2i-3j-6k)` Therefore the resultant is `R=F_(1)+F_(2)+F_(3)=(1)/(7)(41i+j+27k)" and " AB=3i+4k`. Hence the work done is `vec(R).vec(AB)=(1)/(7)(41xx3+27xx4)=(231)/(7)=33" units"`.

Discussion

5324.	If tangent are drawn from any point on the circle x^(2)+y^(2)=25 to the ellipse x^(2)/(16)+(y^(2))/(9)=1, then the angle between the tangents is,
Answer» `(2PI)/(3)` `(PI)/(4)` `(pi)/(3)` `pi/2` ANSWER :D

Discussion

5325.	Let k be a real number such that the inequalitysqrt(x-3) +sqrt(6 -x) ge khas a solution then the maximum value of k issqrt3 (2) sqrt6 -sqrt3 (3)sqrt6(4) sqrt6 +sqrt3
Answer» ANSWER :3

Discussion

5326.	int_(0)^(1) sqrt((1-x)/(1+x)dx=
Answer» `(PI)/(2)-1` `(pi)/(2)+1` `pi-1` `(3PI)/(2)` ANSWER :A

Discussion

5327.	int_(0)^(1) ln Sin((pi x)/(2))dx=
Answer» LN 2 `-ln 2` ln 4 1 Answer :B

Discussion

5328.	If radii of director circle of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 and hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 are in the ratio 1:3 and 4e_(1)^(2)-e_(2)^(2)=lambda, where e_1 and e_2 are the eccetricities of ellipse and hyperbola respectively, then the value of lambda is
Answer» ANSWER :`(7)`

Discussion

5329.	Write the principal value branch of cos^(-1)x
Answer» Answer :principal value BRANCH of `COS^(-1)x` is `[0,PI]`

Discussion

5330.	If F(x)and g(x) are two integralable functions defined on [a,b], then \|int_(a)^(b) f(x) g(x) dx\|, is
Answer» less than `sqrt(overset(B)underset(a)INT F(X) DX overset(b)underset(a)int g(x)dx)` less than or equal to `sqrt(overset(b)underset(a)int f^(2)(x) dx overset(b)underset(a)int g^(2)(x)dx)` less than or equal to `sqrt({overset(b)underset(a)int f^(2)(x) dx}{ overset(b)underset(a)int g^(2)(x)dx})` none of these Answer :C

Discussion

5331.	{:(" " Lt),( x rarr 0):} int_(0)^(x^(2))(sin sqrt(t)dt)/(x^(3))=
Answer» `1/3` `2/3` `4/3` 0 Answer :B

Discussion

5332.	Find the following integrals int(2x-3cosx+e^(x))dx
Answer» Answer :`x^(2) - 3 sinx + E^(x) + C`

Discussion

5333.	Simple organisms like sponges and cnideria circulate_____from their surrounding through their body cavities.
Answer» Lymph Blood Colourless plasma Water Answer :A

Discussion

5334.	If F(x)=Ax^(2)+Bx+C,and f(x) is integer when x is integer then
Answer» (A+B+C) is an INTEGER (A+B+C) is an integer (8A+2C)is an integer A,BC are integers Answer :A::B::C::D

Discussion

5335.	Let a given line l_(1) intersect the X andy - axes at P and Q respectively.Let another line L_(2),perpendicular to L_(1), cut the X and Y -axes at R and S, respectively.Show that the locus of the point of intersection of the line PS and QR is a circle passing through the origin.
Answer» Answer :`x^(2) +y^(2) + 2( 0+-3sqrt( 6))x+( 55 +- 24 SQRT( 6))=0`

Discussion

5336.	If normals to parabola y^(2)=4x at points A, B, C intersect at (11, 0), then
Answer» <P>`{:("P","Q","R","S"),("2","1","4","3"):}` `{:("P","Q","R","S"),("4","1","2","4"):}` `{:("P","Q","R","S"),("4","1","2","3"):}` `{:("P","Q","R","S"),("2","4","1","3"):}` ANSWER :B

Discussion

5337.	The sum of all two digit natural numbers which leave a remainder 5 when they are divided by 7 is equal to
Answer» 715 702 615 602 Answer :B

Discussion

5338.	A continuous and differentiable function f satisfies the condition, int_(0)^(x)f(t)dt=f^(2)(x)-1 for all real x. Then
Answer» f is monotonic INCREASING `AA x in R` f is monotonic DECREASING `AA x in R` f is NON monotonic the graph of `y=f(x)` is a straight line Answer :A::D

Discussion

5339.	Evaluate the following integrals. int(1)/(5-4sintheta)d theta
Answer» ANSWER :`(2)/(3)TAN^(-1)((5tanx-4)/(3))+c`

Discussion

5340.	If alpha, beta, gamma are the roots of x^(3) - px + q = 0 then alpha^(6) + beta^(6) + gamma^(6) =
Answer» `-2p^(3) - 3p^(3)` `-2p^(3) + 3p^(3)` `2p^(3) - 3p^(3)` `2p^(3) + 3p^(2)` Answer :4

Discussion

5341.	Find the value of x if the vectors (x,x+1,x+2),(x+3,x+4,x+5) and (x+6,x+7,x+8) are coplanar.
Answer» ANSWER :`X in R`

Discussion

5342.	If f(x) =int_(-1)^(x) \|t\|dt then for any x ge 0, f(x)=
Answer» `1/2 (1-x^(2))` `(1-x^(2))` `1/2(1+x^(2))` `1+x^(2)` ANSWER :C

Discussion

5343.	A and B throw a pair of dice alternately. A wins the game if he gets a total of 6 and B winsif she gets a total of 7. If A starts the game, find the probability of winning the game by Ain third throw of the pair of dice.
Answer» ANSWER :`(775)/(7776)~~0.1`

Discussion

5344.	Let P(x) be a function defined on R such that P(x) = P'(1--x), AA x in [0, 1], P(0)=1, P(1) =41 then int_(0)^(1)P(x)dx=
Answer» `SQRT(41)` 21 41 42 Answer :B

Discussion

5345.	If (1-i)/(1+i) is a root of the equation ax^(2)+bx+1=0. Where a, b are real than (a,b) is :
Answer» `(1,1)` `(1,-1)` `(0,1)` `(1,0)` ANSWER :D

Discussion

5346.	Find the value of the expression ((3 ^(4) + 3 ^(2) +1) .(5 ^(4) + 5 ^(2) + 1). (7 ^(4) + 7 ^(2) + 1). (9 ^(4) + 9^(2) +1). (11^(4) + 11 ^(2) +1). (13 ^(4)+ 13 ^(2) +1))/((2 ^(4) + 2 ^(2) + 1). (4 ^(4) + 4 ^(2) + 1). (6 ^(4).6 ^(2) +1) .(8^(4) + 8 ^(2) +1). (10^(4) + 10 ^(2) +1). (12^(4) +12 ^(2) +1)) When written in lowest from.
Answer» ANSWER :61

Discussion

5347.	There are four boxes, A, B C and D containing marbles. A contains 1 red, 6 white and 3 black marbles, B contains 6 red, 2 white and 2 black marbles, C contains 8 red, 1 white an 1 black marles, and D contains 6 white and 4 black marbles. One of the boxes is selected at random and a single marble is drawnfrom it. If the marble is red, what is the probability that it was drawn from the box A?
Answer» <P> Solution :Let `E_1,E_2,E_3,E_4` be the events of selecting boxes A, B, C, D REPECTIVELY. Then, `P(E_1)=P(E_2)=P(E_3)=P(E_4)=1/4`. Let E = EVENT that the marble drawn is red. Then, `P(E//E_1)=1/10,P(E//E_2)=6/10=3/5,P(E//E_3)=8/10=4/5,P(E//E_4)=0.` `:. P(E_1//E)=(P(E//E_1).P(E_1))/(P(E//E_1).P(E_1)+P(E//E_2).P(E_2)+P(E//E_3).P(E_3)+P(E//E_4).P(E_4))`

Discussion

5348.	Using the digits 0,1,2,3,& 4, the number of ten digit sequences can be written so that the difference between any two consecutive digits is 1, is equal to k, then k/72 is equal to
Answer» Solution :`A_(n)` denotes no. of `n` DIGITS sequence that end in 0 or 4 `B_(n)` denotes no. of `n` digit sequence that end in 1 or 3 `C_(n)` denotes of `n` digit sequence that end in 2 `A_(n+1)=B_(n)` ( `:'` each sequence in `A_(n+1)` can be converted into a sequence in `B_(n)` by DELETING its lat digit). `B_(n+1)=A_(n)+2C_(n)` ( `:'` each sequence in `A_(n)` can be converted into sequence in `B_(n+1)` by ADDING `a 1` (if it ENDS with 0) or a 3 ( ifit ends with 4) to its end 8 each sequence in`C_(n)` can be converted into a sequence in `B_(n+1)` by adding a 1 or 3 to it `C_(n+1)=B_(n)` (by deleting 2 at its end) `B_(n+1)=3B_(n-1)` for `nge2, B_(1)=2, B_(2)=4` `:. A_(10)+B_(10)+C_(10)=2B_(9)+B_(10)=4.3^(4)+4.3^(4)=648`

Discussion

5349.	The magnitude and amplitude of ((1+isqrt(3))(2+2i))/((sqrt(3)-i)) are respectively
Answer» `2,(3PI)/(4)` `4,(3pi)/(4)` `2sqrt(2),(PI)/(4)` `2sqrt(2),(3pi)/(4)` ANSWER :D

Discussion

5350.	Let the function y =f(x)be continuous on the interval [a, b], its range being the same interval a le y le b. Prove that on this closed interval there exists at least one point x such that f(x) =x. Explain this geometrically.
Answer» ANSWER :`F(X)-x`

Discussion

Explore topic-wise InterviewSolutions in .

For n=6k,kinZ,((1-isqrt3)/2)^(n)+((-1-isqrt3)/2)^(n) has the value

Write an anti derivative for each of the following functions using the method of inspection: (i) cos2x (ii) 3x^(2)+4x^(3) (iii) 1/x,xne0

If intsqrt(1+3sqrt(x))/(3sqrt(x^(2)))dx=2f(x)+C, then f(27) is equal to

If a ne0 and the line 2bx+3cy+4d =0 passes through the points of intersection of the parabolas y^(2)=4ax and x^(2)=4ay then

If 0 lt theta lt pi/2, x = sum_(n=0)^(oo)cos^(2n) theta, y =sum_(n=0)^(oo)sin^(2n)theta, and z=sum_(n=0)^(oo) cos^(2n)theta sin^(2n) theta then show that (i) xyz=xy+z (ii) xyz=x+y+z

If x is an integer and x in [1,5] then the probability that x^(2)-3x+2 gt 0

Find the area of the region enclosed by the loop of the folium of Descartes x^(3) + y^(3) = 3axy

Choose the correct answer. Area bounded by the curvey=x^3,The x-axis and the ordinates. x=-2 and x=1 is:

Sum of two skew symmetric matrices is always …… matrix.

If |{:(3,5,2),(1,4,7),(2,1,0):}|=k|{:(3,5,4),(1,4,14),(4,2,0):}| then k=……

The sum of the series 1.2 + 2.3+ 3.4+…….. up to 20 tems is

If |x| is so small that x^(2) and higher powers of x may be neglected then find the approx-imate values of the following ((4+3x)^(1//2))/((3-2x)^(2))

If |x| is so small that x^(2) and higher powers of x may be neglected then find the approx-imate values of the following ((1-(2x)/(3))^(3//2)(32+5x)^(1//5))/((3-x)^(3))

I. underset(x to 0)"Lt "sqrts does not exist II. underset(x to 1)"Lt" (|x|)/(x) does not exist.

Find the derivative of tan (2x+3).

Let f(x) be a differentiable function in the interval (0,2) , then the value of int_0^2 f(x) dx is :

Eight coins are tossed together. The probability of getting exactly 3 heads is ..........

Light rays entering the eye is controlled by :

For events A and B if P(A) = 0.3, P(B) = 0.6 and P(B | A) = 0.5 then find P( A | B) and P(A cup B).

Let f: N to R be defined by f(x) = 4x^(2) + 12x+ 15. Show that f: N to S where S is the range of function f, is invertible. Also find the inverse of f.

If alpha, beta, gamma are roots of x^(3) + 2x^(2) - 3x - 1 = 0, then the value of alpha^(4) + beta^(4) + gamma^(4) is

If A and B'are independent events, then P(A' cup B)= 1- P(A) * P(B').

Locus of the mid-points of all chords of the parabola y^(2)=4ax which are drwan through the vertax is a parabola, then its latus rectum is

If tangent are drawn from any point on the circle x^(2)+y^(2)=25 to the ellipse x^(2)/(16)+(y^(2))/(9)=1, then the angle between the tangents is,

Let k be a real number such that the inequalitysqrt(x-3) +sqrt(6 -x) ge khas a solution then the maximum value of k issqrt3 (2) sqrt6 -sqrt3 (3)sqrt6(4) sqrt6 +sqrt3

int_(0)^(1) sqrt((1-x)/(1+x)dx=

int_(0)^(1) ln Sin((pi x)/(2))dx=

If radii of director circle of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 and hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 are in the ratio 1:3 and 4e_(1)^(2)-e_(2)^(2)=lambda, where e_1 and e_2 are the eccetricities of ellipse and hyperbola respectively, then the value of lambda is

Write the principal value branch of cos^(-1)x

If F(x)and g(x) are two integralable functions defined on [a,b], then |int_(a)^(b) f(x) g(x) dx|, is

{:(" " Lt),( x rarr 0):} int_(0)^(x^(2))(sin sqrt(t)dt)/(x^(3))=

Find the following integrals int(2x-3cosx+e^(x))dx

Simple organisms like sponges and cnideria circulate_____from their surrounding through their body cavities.

If F(x)=Ax^(2)+Bx+C,and f(x) is integer when x is integer then

Let a given line l_(1) intersect the X andy - axes at P and Q respectively.Let another line L_(2),perpendicular to L_(1), cut the X and Y -axes at R and S, respectively.Show that the locus of the point of intersection of the line PS and QR is a circle passing through the origin.

If normals to parabola y^(2)=4x at points A, B, C intersect at (11, 0), then

The sum of all two digit natural numbers which leave a remainder 5 when they are divided by 7 is equal to

A continuous and differentiable function f satisfies the condition, int_(0)^(x)f(t)dt=f^(2)(x)-1 for all real x. Then

Evaluate the following integrals. int(1)/(5-4sintheta)d theta

If alpha, beta, gamma are the roots of x^(3) - px + q = 0 then alpha^(6) + beta^(6) + gamma^(6) =

Find the value of x if the vectors (x,x+1,x+2),(x+3,x+4,x+5) and (x+6,x+7,x+8) are coplanar.

If f(x) =int_(-1)^(x) |t|dt then for any x ge 0, f(x)=

A and B throw a pair of dice alternately. A wins the game if he gets a total of 6 and B winsif she gets a total of 7. If A starts the game, find the probability of winning the game by Ain third throw of the pair of dice.

Let P(x) be a function defined on R such that P(x) = P'(1--x), AA x in [0, 1], P(0)=1, P(1) =41 then int_(0)^(1)P(x)dx=

If (1-i)/(1+i) is a root of the equation ax^(2)+bx+1=0. Where a, b are real than (a,b) is :

Using the digits 0,1,2,3,& 4, the number of ten digit sequences can be written so that the difference between any two consecutive digits is 1, is equal to k, then k/72 is equal to

The magnitude and amplitude of ((1+isqrt(3))(2+2i))/((sqrt(3)-i)) are respectively

Let the function y =f(x)be continuous on the interval [a, b], its range being the same interval a le y le b. Prove that on this closed interval there exists at least one point x such that f(x) =x. Explain this geometrically.