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

501.	Find deltay and dy for the following functions y=e^(x)+x,x=5 and deltax=0.002
Answer» Answer :`Delta y = E^(5) (e^(0.02)-1) + 0.02 dy = (e^(5) + 1) (0.02)`

Discussion

502.	Find thesum first 'n'terms of the series (3+7+13+21+31+..)?
Answer» ANSWER :`n/3(n^2+3n+5)`

Discussion

503.	Find Delta y and dy for the following functions for the values of x and Delta x which are shown against each of the functions. y = x^(2) + 3x + 6,x = 10 and Delta x = 0.01
Answer» ANSWER :`DELTA y = 0.2301, DY = 0.23`

Discussion

504.	Find Delta y and dy for the following functions for the values of x and Delta x which are shown against each of the functions. y = f(x) = x^(2) + x, x = 1, Delta x = 0.1
Answer» ANSWER :0.31, 0.3

Discussion

505.	Evaluate (n!)/((n-r)!) whenn= 6 and r=2 ?
Answer» ANSWER :30

Discussion

506.	f(x) = {{:((k cos x)/(pi-2x ), " if " , x ne (pi)/(2)),(3, "if" , x = (pi)/(2)):}"continuous at " x = (pi)/(2) " thenk" =
Answer» 1 4 6 8 Answer :C

Discussion

507.	Find the 6^(th) term in expansion of ((x^(3))/2-2/(x^(2)))^(9)
Answer» ANSWER :`- 252 X^(2)`

Discussion

508.	Solve 2 cos^(2) theta = 3 sin theta
Answer» ANSWER :`THETA = MX +(-1)^(N)pi/6 , n in I `

Discussion

509.	Evaluate the following limits : Lt_(xto0)(1+2x)^(1//x)
Answer» ANSWER :`E^(2)`

Discussion

510.	Let 'p' any point on x-y+3=0 and 'A' be fixed point (3,4). If the family of lines givne by (3sectheta+5cosectheta)x+(7sectheta-3cosec theta)y+11(sectheta-cosec theta)0 are concurrent at B for all permissible value of'theta' and maximum ofabs(PA-PB)=2sqrt2n(n in N) then n =
Answer» ANSWER :1

Discussion

511.	ThreeplyaersA,B and C playa game . Theprobabilitythat A,B, and C will finishthegameare respectively (1)/(2) ,(1)/(3)and (1)/(4).Theprobabilitythat the gameis not finishedis
Answer» `(1)/(8)` 1 `(1)/(4)` `(3)/(4)` ANSWER :D

Discussion

512.	If y = Tan^(-1)((cosx)/(1+sinx)) then (dy)/(dx)=
Answer» 1 `-1` `(-1)/2` `1/3` ANSWER :C

Discussion

513.	int(2^(8x+3))/(2^(4x+3))dx:
Answer» `(1)/(4)(2^(4x))/(log8)+c` `(1)/(8)(2^(8x))/(LOG4)+c` `(16^(x))/(log2)+c` `((24)^(x))/(log24)+c` Answer :C

Discussion

514.	A particle moves along a line by s = (1)/(3)t^(2) + 8t + 5, it changes its direction when
Answer» t = 1 , t = 2 t = 2, t = 4 t = 0, t = 4 t = 2, t = 3 Answer :B

Discussion

515.	If f and g are real functions defined by f(x)= x^(2) + 7 and g(x)= 3x + 5. Then, find each of the following f(3) + g(-5)
Answer» ANSWER :6

Discussion

516.	If a, b and c represent the lengths of sides of a triangle, then the possible integral value of a/(b + c) + b/(c + a) + c/(a + b)is ………………
Answer» 2 1 3 4 Answer :A

Discussion

517.	Find the conjugate of (3-i)^2/(2+i)
Answer» ANSWER :2 + 4I

Discussion

518.	Find sets A, B and C such that AcapB, BcapC and AcapC are non-empty sets and AcapBcapC=phi.
Answer» ANSWER :We MAY take `A = { 1, 2 }, B = { 1, 3 }, C = { 2 , 3 }`

Discussion

519.	Maximum/Minimum value of ax^(2) + bx + c occurs at x = - (b)/(2a), and its value is :
Answer» `DELTA` `(Delta)/(a)` `(Delta)/(4A)` `- (Delta)/(4a)` ANSWER :D

Discussion

520.	Find the domain of f(x)=sqrt((4-x^(2))/([x]+2))
Answer» `(-oo, -2) UU (2, oo)` `R-{-2}` `[-1, 2)` `(-oo, -2)uu [-1, 2]` Answer :D

Discussion

521.	If E_(1),E_(2),E_(3) and E_(4) are the four elementary outcomes in a sample space and P(E_(1))=0.1,P(E_(2))=0.5,P(E_(3))=0.1, then the probability of E_(4) is ……….
Answer» ANSWER :C

Discussion

522.	The number of values of y in [-2pi,2pi] satisfying the equation \|sin2x\|+\|cos2x\|=\|siny\| is
Answer» 3 4 5 6 Answer :B

Discussion

523.	Find the 20^(th) term of the series 2xx4+4xx6+6xx8+………n^(th) terms ?
Answer» ANSWER :1680

Discussion

524.	If sin^(-1)x:[-1, 1] to [pi/2, (3pi)/2] and cos^(-1)x:[-1, 1] to [0, pi] be two bijective functions, respectively inverses of bijective functions sinx:[pi/2, (3pi)/2] to [-1, 1] and cosx:[0, pi] to [-1, 1]" then "sin^(-1)x+cos^(-1)x is
Answer» `PI/2` `pi` `(3PI)/2` not a constant Answer :D

Discussion

525.	If tantheta = 3andtheta lies in third quadrant, then the value of sintheta is
Answer» `(1)/(SQRT(10))` `-(1)/(sqrt(10))` `-(3)/(sqrt(10))` `(3)/(sqrt(10))` ANSWER :C

Discussion

526.	For any sets A and B, prove taht : (i)A cap B' =phi rArr A sub B (ii)A 'cup B =U rArr a sub B.
Answer» SOLUTION :(i) `A cap B'=phi rArr A-B = phi rArr A subB` (II) ` A' CUP B =U rArr A cap (A ' cup B) = Acap U rArr (A cap A')cup (A cap B) =A` `rArr phi (A cap B)=A rArr A cap B = A rArr A cub B`.

Discussion

527.	How many different words can be formed of the letters of the word 'MALKENKOV' so thatthe vowels may occupy odd places ?
Answer» ANSWER :` 2880 `

Discussion

528.	Number of solution of the equation cos^(4)2x+2sin^(2)2x=17(cosx+sinx)^(8), 0 lt x lt 2pi is
Answer» 4 8 10 16 Answer :A

Discussion

529.	Find the cartesian equation of the curve whose parametric equations are : x=4"cos"theta, y=3"sin"theta
Answer» ANSWER :`X^(2)/16+y^(2)/9=1`

Discussion

530.	Point P(x, y) satisfying the equation Sin^(-1)x+Cos^(-1)y+Cos^(-1)(2xy)=pi/2 lies on
Answer» the BISECTOR of the first and third QUADRANT bisector of the second and fourth quadrant. the rectangle FORMED bythe lines `x=pm1 and y=pm1`. a unit circle with CENTRE at the origin. Answer :D

Discussion

531.	cos^(-1)(x//a)+cos^(-1)(y//b)=theta,then (x^(2))/(a^(2))-(2xy)/(ab)cos theta+(y^(2))/(b^(2))=
Answer» `SIN^(2)THETA` `COS^(2)theta` `TAN^(2)theta` `cot^(2)theta` Answer :A

Discussion

532.	Find the derivative of ax^(2)+bx+c from the first principle.
Answer» Answer :`THEREFORE F (X) = 2 AC + b.`

Discussion

533.	Express the equation 2x^2+2y^2-3x+4y-1 = 0 in standard form
Answer» SOLUTION :`x^2+y^2-3/2x+2y-1/2 = 0`

Discussion

534.	If e^((sin^(2)+sin^(4)x+sin^(6)x+...oo)log2)=8and0ltxlt(pi)/(2) then (cos x)/(cosx + sin x) =
Answer» `(sqrt(3)+1)/(2)` `(sqrt(3)-1)/(2)` `(2)/(sqrt(3)+1)` `(2)/(sqrt(3)-1)` ANSWER :B

Discussion

535.	Write down the converse of following statements: If the sum of squares of two sides foa triangle is equal to the square of third side of a triangle, then the triangle is right angled.
Answer» ANSWER :if thetriangle is right angled then sum of TWO sides of triangle is equal to SQUARE of its THIRD side.

Discussion

536.	Express (1-i)/(sqrt3+i) in polar form
Answer» Answer :`(1)/SQRT2[cos((-5pi)/12) + ISIN((-5pi)/12)]`

Discussion

537.	Let f: R rarr R and g: R rarr R be two given functions such that f is inective and g is surjective. Then which of the following is injective
Answer» gof fog gog fof Answer :D

Discussion

538.	Assertion (A) : A and B are mutually exclusive events then A and B cannot be independent. Reason (R) : P(A nn B) = 0 ne P(A) P(B).
Answer» Both A and R are TRUE and R is the correct explanation of A Both A and R are true but R is not the correct explanation of A A is true R is false A is false R is true Answer :A::B::C::D

Discussion

539.	""^(n-1)C_3+""^(n-1)C_4 gt ""^(n)C_3if
Answer» ` N gt 7 ` `n ge 7` ` n gt 6` ` n ge 6` ANSWER :A

Discussion

540.	Solve sin x =-1for principal solution as well as general solution: (i) x in{ angle with measures given in radians} (ii) x in {angle with measures given in degres}.
Answer» ANSWER :`K in I`

Discussion

541.	If the axes are rotated through an angle60^(0), fine the coordinates of the point (6sqrt3,4) in the new system.
Answer» ANSWER :`:. (X, Y) = (5 sqrt(3), -7)`

Discussion

542.	An integer is chosen at random from the first 100 positive integers. What is the probability that the integer chosen is a prime or multiple of 8?
Answer» ANSWER :`37/100`

Discussion

543.	Equation of pair of lines through (0,0) and forming an equitateral triagnle with the line 2x-3y+4=0 is
Answer» `23x^2+3y^2-8xy=0` `23x^2-3y^2+48xy=0` `23x^2+3y^2-16xy=0` `23x^2+3y^2+48xy=0` ANSWER :D

Discussion

544.	A letter is selected randomly from the English alphabet. The probability that the selected letter is vowel is ………
Answer» `(21)/(26)` `(5)/(26)` `(3)/(26)` `(1)/(13)` Answer :B

Discussion

545.	Find a point at which origin is shifted such that transformed equation of x^(2)+xy-3x-y+2=0 has no first degree term and constant term. Also find the transformed equation.
Answer» Solution :LET origin be shifted to the point `(h,k)`. `:. "Put" X=X+h` and `y=Y+k` `(X+h)^(2)+(X+h)(Y+k)-3(X+h)-(Y+k)+2=0` `implies X^(2)+2hX+h^(2)+XY+hY+kX+hk-3X-3h-Y-k+2=0` `impliesX^(2)+XY+X(2h+k-3)+Y(h-1)+(h^(2)+hk-3h-k+2)=0`……`(1)` This EQUATION will be independent with first degree term and constant term if `{:(,2h+k-3=0),(,h-1=0),("and",h^(2)+hk-3h-k+2=0):}}impliesh=1,k=1` `:.` Required point `=(1,1)` and transformed equation is `X^(2)+XY=0`.

Discussion

546.	A quadratic equation whose roots are sin^(2) 18^(@) , cos^(2) 36^(@)are
Answer» `16X^(2)-12x+1=0` `16x^(2)+12x+1=0` `16x^(2)-12x-1=0` `16x^(2)-10x-1=0` ANSWER :A

Discussion

547.	Find the sum of the series 0.6 +0.66 +0.666+ ... to the n terms
Answer» ANSWER :`(2N)/(3) -(2)/(27) (1-10^(-n))`

Discussion

548.	Suppose that the midpoints of the sides BC,CA and AB of a triangle ABC are (5,7,11),(0,8,5), and (2,3,-1). Find the co-ordinates of A,B and C.
Answer» SOLUTION :(-3,4,-7)(7,2,5)(3,12,17)

Discussion

549.	A teacher wants to arrange 5 students on the platform such that the boy 'YUSUF' occupies the first position and the girls 'GEETA' and 'SEETA' are always together. How many such arrangements are possible ?
Answer» ANSWER :12

Discussion

550.	Evaluate the following limits : Lim_(x to pi/2) (e^(sin x)-1)/(sin x)
Answer» ANSWER :`e-1`

Discussion

Explore topic-wise InterviewSolutions in .

Find deltay and dy for the following functions y=e^(x)+x,x=5 and deltax=0.002

Find thesum first 'n'terms of the series (3+7+13+21+31+..)?

Find Delta y and dy for the following functions for the values of x and Delta x which are shown against each of the functions. y = x^(2) + 3x + 6,x = 10 and Delta x = 0.01

Find Delta y and dy for the following functions for the values of x and Delta x which are shown against each of the functions. y = f(x) = x^(2) + x, x = 1, Delta x = 0.1

Evaluate (n!)/((n-r)!) whenn= 6 and r=2 ?

f(x) = {{:((k cos x)/(pi-2x ), " if " , x ne (pi)/(2)),(3, "if" , x = (pi)/(2)):}"continuous at " x = (pi)/(2) " thenk" =

Find the 6^(th) term in expansion of ((x^(3))/2-2/(x^(2)))^(9)

Solve 2 cos^(2) theta = 3 sin theta

Evaluate the following limits : Lt_(xto0)(1+2x)^(1//x)

Let 'p' any point on x-y+3=0 and 'A' be fixed point (3,4). If the family of lines givne by (3sectheta+5cosectheta)x+(7sectheta-3cosec theta)y+11(sectheta-cosec theta)0 are concurrent at B for all permissible value of'theta' and maximum ofabs(PA-PB)=2sqrt2n(n in N) then n =

ThreeplyaersA,B and C playa game . Theprobabilitythat A,B, and C will finishthegameare respectively (1)/(2) ,(1)/(3)and (1)/(4).Theprobabilitythat the gameis not finishedis

If y = Tan^(-1)((cosx)/(1+sinx)) then (dy)/(dx)=

int(2^(8x+3))/(2^(4x+3))dx:

A particle moves along a line by s = (1)/(3)t^(2) + 8t + 5, it changes its direction when

If f and g are real functions defined by f(x)= x^(2) + 7 and g(x)= 3x + 5. Then, find each of the following f(3) + g(-5)

If a, b and c represent the lengths of sides of a triangle, then the possible integral value of a/(b + c) + b/(c + a) + c/(a + b)is ………………

Find the conjugate of (3-i)^2/(2+i)

Find sets A, B and C such that AcapB, BcapC and AcapC are non-empty sets and AcapBcapC=phi.

Maximum/Minimum value of ax^(2) + bx + c occurs at x = - (b)/(2a), and its value is :

Find the domain of f(x)=sqrt((4-x^(2))/([x]+2))

If E_(1),E_(2),E_(3) and E_(4) are the four elementary outcomes in a sample space and P(E_(1))=0.1,P(E_(2))=0.5,P(E_(3))=0.1, then the probability of E_(4) is ……….

The number of values of y in [-2pi,2pi] satisfying the equation |sin2x|+|cos2x|=|siny| is

Find the 20^(th) term of the series 2xx4+4xx6+6xx8+………n^(th) terms ?

If sin^(-1)x:[-1, 1] to [pi/2, (3pi)/2] and cos^(-1)x:[-1, 1] to [0, pi] be two bijective functions, respectively inverses of bijective functions sinx:[pi/2, (3pi)/2] to [-1, 1] and cosx:[0, pi] to [-1, 1]" then "sin^(-1)x+cos^(-1)x is

If tantheta = 3andtheta lies in third quadrant, then the value of sintheta is

For any sets A and B, prove taht : (i)A cap B' =phi rArr A sub B (ii)A 'cup B =U rArr a sub B.

How many different words can be formed of the letters of the word 'MALKENKOV' so thatthe vowels may occupy odd places ?

Number of solution of the equation cos^(4)2x+2sin^(2)2x=17(cosx+sinx)^(8), 0 lt x lt 2pi is

Find the cartesian equation of the curve whose parametric equations are : x=4"cos"theta, y=3"sin"theta

Point P(x, y) satisfying the equation Sin^(-1)x+Cos^(-1)y+Cos^(-1)(2xy)=pi/2 lies on

cos^(-1)(x//a)+cos^(-1)(y//b)=theta,then (x^(2))/(a^(2))-(2xy)/(ab)cos theta+(y^(2))/(b^(2))=

Find the derivative of ax^(2)+bx+c from the first principle.

Express the equation 2x^2+2y^2-3x+4y-1 = 0 in standard form

If e^((sin^(2)+sin^(4)x+sin^(6)x+...oo)log2)=8and0ltxlt(pi)/(2) then (cos x)/(cosx + sin x) =

Write down the converse of following statements: If the sum of squares of two sides foa triangle is equal to the square of third side of a triangle, then the triangle is right angled.

Express (1-i)/(sqrt3+i) in polar form

Let f: R rarr R and g: R rarr R be two given functions such that f is inective and g is surjective. Then which of the following is injective

Assertion (A) : A and B are mutually exclusive events then A and B cannot be independent. Reason (R) : P(A nn B) = 0 ne P(A) P(B).

""^(n-1)C_3+""^(n-1)C_4 gt ""^(n)C_3if

Solve sin x =-1for principal solution as well as general solution: (i) x in{ angle with measures given in radians} (ii) x in {angle with measures given in degres}.

If the axes are rotated through an angle60^(0), fine the coordinates of the point (6sqrt3,4) in the new system.

An integer is chosen at random from the first 100 positive integers. What is the probability that the integer chosen is a prime or multiple of 8?

Equation of pair of lines through (0,0) and forming an equitateral triagnle with the line 2x-3y+4=0 is

A letter is selected randomly from the English alphabet. The probability that the selected letter is vowel is ………

Find a point at which origin is shifted such that transformed equation of x^(2)+xy-3x-y+2=0 has no first degree term and constant term. Also find the transformed equation.

A quadratic equation whose roots are sin^(2) 18^(@) , cos^(2) 36^(@)are

Find the sum of the series 0.6 +0.66 +0.666+ ... to the n terms

Suppose that the midpoints of the sides BC,CA and AB of a triangle ABC are (5,7,11),(0,8,5), and (2,3,-1). Find the co-ordinates of A,B and C.

A teacher wants to arrange 5 students on the platform such that the boy 'YUSUF' occupies the first position and the girls 'GEETA' and 'SEETA' are always together. How many such arrangements are possible ?

Evaluate the following limits : Lim_(x to pi/2) (e^(sin x)-1)/(sin x)