14949 + Interview Questions in Maths in Class 11 Page 7 InterviewSolution

301.	Given that f(x) is a differentiable function of x and that f(x) ,f(y)= f(x) + f(y) +f(xy) -2and that f(1)=2 ,f(2) = 5 Then f(3) is equal to
Answer» 10 24 15 19 Answer :A

Discussion

302.	Let L be the line belonging to the family of straight lines (a+2b)x+(a-3b)y+a-8b=0 a,b in R, which is the farthest from the point (2,2) The equation of line L is
Answer» x+4y+7=0 2x+3y+4=0 4x-y-6=0 none of these Answer :A::B::D

Discussion

303.	Let L be the line belonging to the family of straight lines (a+2b)x+(a-3b)y+a-8b=0 a,b in R, which is the farthest from the point (2,2) Area enclosed by the line L and the coordinate axes is
Answer» `4//3 SQ. UNITS` `9//2 sq. units` `49/8 sq. units` NONE of these Answer :A

Discussion

304.	Let L be the line belonging to the family of straight lines (a+2b)x+(a-3b)y+a-8b=0 a,b in R, which is the farthest from the point (2,2) If L is concurrent with lines x-2y+1=0 and 3x-4y+lambda =0, then the value of lambda is
Answer» 2 1 -4 5 Answer :C

Discussion

305.	Mid points of sides at DeltaABC are (-2, 3, 5), (4, -1, 7) and (6, 5, 3). Then find coordinates of the verticies A, B and C.
Answer» Answer :A(12, 1, 5), B(0, 9, 1), C(-4, -3, 9)

Discussion

306.	Find the vector area and area of the triangle with vertices bar(i) + bar(j)-bar(k), 2bar(i)- 3bar(j) + bar(k), 3 bar(i) + bar(j)- 2bar(k).
Answer» ANSWER :`(1)/(2) SQRT(105)` sq unit

Discussion

307.	If a_(1) lt ( 28)^((1)/( 3)) - 3 lt b_(1), then (a_(1) b_(1)) ( a_(1) , b_(1)) is
Answer» `((1)/(28),(1)/(27))` `((1)/(27), ( 1)/( 28))` (27,28) `((1)/(27),(1)/(26))` ANSWER :A

Discussion

308.	If a and b positive numbers (altb), then the range of values of k for which a real lambda be found such that equation ax^2+2lambdaxy+by^2+2k(x+y+1)=0 represent a pair of straight lines is
Answer» `altk^2ltb` `alek^2leb` `k^2lea or k^2geb` `kle2a or kge2b` ANSWER :D

Discussion

309.	Which of the following are sets? Justify your answer : The collection of hard chapter in Maths.
Answer» ANSWER :it is not a SET

Discussion

310.	A + B = 90^(@) rArr cos A - cos B in
Answer» [-1, 1] `[-SQRT(2), sqrt(2)]` `[-sqrt(3), sqrt(3)]` [-2, 2] Answer :B

Discussion

311.	If 2/11 Is the probability of occurring an event, what is the probability of the eventwill not occurs.
Answer» ANSWER :`9/11`

Discussion

312.	Incircle of DeltaABC touches the sides BC, AC, and AB at D, E, and F, respectively. Then answer the following questions: The length of side EF is
Answer» `r"sin"(A)/(2)` `2R"sin"(A)/(2)` `r"COS"(A)/(2)` `2r"cos"(A)/(2)` ANSWER :D

Discussion

313.	A straight line is parallel to the lines 3x-y-3=0 and 3x-y+5=0, and lies between them. Find its equation if its distances from these lines are in the ratio 3 : 5.
Answer» ANSWER : `3x-y=0`

Discussion

314.	Incircle of DeltaABC touches the sides BC, AC, and AB at D, E, and F, respectively. Then answer the following questions: angleDEF is equal to
Answer» `(pi-B)/(2)` `pi-2B` `A-C` NONE of these Answer :A

Discussion

315.	Incircle of AABC touches the sides BC, AC, and AB at D, E, and F, respectively. Then answer the following questions: Area of DeltaDEF is
Answer» `2R^(2) sin (2A)sin(2B) sin(2C)` `2r^(2)"cos"(A)/(2)"cos"(B)/(2)"cos"(C)/(2)` `2r^(2)sin(A-B)sin(B-C)sin(C-A)` None of these Answer :B

Discussion

316.	If 7,4 sqrt(3), sqrt(13), are the sides of DeltaABC then least angle is
Answer» `45^(@)` `60^(@)` `90^(@)` `30^(@)` ANSWER :D

Discussion

317.	a^(2) sin 2C + c ^(2) sin 2A =
Answer» ` DELTA` ` 2 Delta` ` 3 Delta ` ` 4 Delta ` ANSWER :D

Discussion

318.	Rolle's theorem cannot be applicable for
Answer» `f(X) = cos x -1 ` in `[0, 2PI]` `f(x) = x ( x - 2)^(2)` in [0,2] f(x) = `3+ (x-1)^(2//3)` in [ 0,3] f(x)` = SIN^(2) x ` in [ 0 ` pi `] Answer :C

Discussion

319.	Convert the complex number -16/(1+isqrt(3)) into polar form.
Answer» Answer :`8(COS (2PI)/3 + I sin(2pi)/3)`

Discussion

320.	Find the mean deviation from the median for the following data:
Answer» ANSWER :5.1

Discussion

321.	Show that cos^4""pi/8+cos^4""(3pi)/8+cos^4""(5pi)/8+cos^4""(7pi)/8=3/2
Answer» `1/2` `3/2` `3/4` `1/4` ANSWER :B

Discussion

322.	z=i+sqrt(3)=r(cos theta+sin theta)
Answer» ANSWER :`(PI)/(6)`

Discussion

323.	Translate the following statements into symbolic form: Either o or x+1 is an odd integer.
Answer» Answer :`:.PVVQ:` A NUMBER is EITHER divisible by 2 or 3.

Discussion

324.	Evaluate the following limits : Lim_(x to 0) (1+ax)^(b/x)
Answer» ANSWER :`E^(AB)`

Discussion

325.	If f(x) = sqrt(1+cos^2(x^2)) , then f'((sqrtpi)/2) is
Answer» `sqrtpi/6` `-sqrtpi/6` `1//sqrt6` `pi//sqrt6` ANSWER :B

Discussion

326.	If y=x^((logx)^log(logx)) , then (dy)/(dx) is
Answer» `y/x((Inx^(LOGX-1))+2ln(ln(logx))` `y/x(logx)^(log(logx))(2LOG(logx)+1)` `y/(xInx)[(Inx)^2+2ln(logx)]` `y/x(LOGY)/(logx)[2log(logx)+1]` ANSWER :D

Discussion

327.	Find the coefficient of the term invloving x^10 in the expansion of (x^2 -2)^11
Answer» ANSWER :29568

Discussion

328.	If [x]^(2)- 5[x] + 6= 0, where [.] denote the greatest integer function, then
Answer» `x in [3, 4]` `x in [2, 3]` `x in [2, 3]` `x in [2, 4]` ANSWER :C

Discussion

329.	Statement-I : The locus of the point, whose distance from the X-axis is twice its distance from the y-axis is y^(2)=4x Statement-II : The locus of the point (cottheta+costheta,cottheta-costheta) is (x^(2)-y^(2))^(2)=16xy Then the correct statement is
Answer» only I only II both I and II neither I nor II Answer :2

Discussion

330.	Solve: sqrtx+5 lt x-2 Solve sqrt-x^(2) + 4x +5 = x -22x^(2) - x + 15lt0
Answer» ANSWER :`((-inftysqrt29)/(2))((5+sqrt29)/(2),INFTY),]`

Discussion

331.	Find the points of local maximum or local minimum for the following (x-3)^4
Answer» ANSWER :MINIMUM VALUE = 0 at `x=-pi/6`

Discussion

332.	tan[1/2cos^(-1)((sqrt(5))/3)]=
Answer» `(3+sqrt(5))/2` `3+sqrt(5)` `1/2(3-sqrt(5))` `2-sqrt(3)` ANSWER :C

Discussion

333.	Convert the following into simplest form (iii) Cosec (5pi + theta)
Answer» ANSWER :`-COSEC THETA`

Discussion

334.	Find the ecentricity of the given hyperbola 9y^2 -25x^2=225
Answer»

Discussion

335.	Find (dy)/(dx) in the following : y= sin^(-1) (2x sqrt(1-x^(2))), (1)/(sqrt(2)) lt x lt (1)/(sqrt(2)).
Answer» ANSWER :`(2)/( 1 + X ^(2))`

Discussion

336.	If (1,3) (2,1) (9,4) are collinear then a is:
Answer» `(1)/(2)` 2 0 `-(1)/(2)` ANSWER :A

Discussion

337.	If A and B are symmetric matrices then ABA is
Answer» DIAGONAL MATRIX SYMMETRIC matrix skew symmetric matrix identity matrix Answer :B

Discussion

338.	Differentiate the following functions w.r.t. x: (sin 3x)/( x-6)
Answer» ANSWER :`(3 (x-6) COS 3X - SIN 3x )/(( x-6)^2)`

Discussion

339.	The maximum and minimum values of f(x)=4x^(3)+3x^(2)-6x+5are
Answer» `8,7//2` `10,13//4` `3,5//7` `2,8//7` ANSWER :B

Discussion

340.	Define a relation R on the set N of natural numbers by R= {(x, y): y= x+5, x is a natural number less than 4, x, y in N}. Depict this relationship using roster form. Write down the domain and the range.
Answer» ANSWER :R={(1,6),(2,7),(3,8)} DOMAIN of R ={1,2,3} RANGE of R={6,7,8}

Discussion

341.	Find the value of theta, " if " m^(2) sin . Pi/2 - n^(2) sin . (3pi)/2 + 2 mn sectheta = (m-n)^(2) , 0 le theta le pi.
Answer» ANSWER :`THETA = PI`

Discussion

342.	If theta _(1) ,theta _(2), theta _(3),.....theta _(n) are in A.P. then (sin theta_(1) + sin theta _(2 ) +...+ sin theta _(n))/( cos theta_(1) + cos theta _(2) + ...+ cos theta _(n))
Answer» 0 `tan (THETA _(1) + theta _(n))` `tan ((theta _(1) + theta _(n))/( 2))` `tan ((theta_(1) - theta_(n))/(2))` ANSWER :C

Discussion

343.	Find the coefficient of (i) a^(6) b^(3) in the expansion of (2a - (b)/(3) )^9
Answer» ANSWER :`(-1792)/(9)`

Discussion

344.	sin 2x+cosx=0
Answer» Answer :`X = NPI + (-1) ^(n) (7pi)/(6) or (2n +1) (PI)/(2), n in Z`

Discussion

345.	Solve inequality 5x+1 gt - 24, 5x-1 lt 24 and represent solution graphically on number line.
Answer» ANSWER :`(-5,5)` `(##NCERT_TEL_MAT_XI_C06_E04_007_A01##)`

Discussion

346.	Simplify the following (21)/(14i)
Answer» ANSWER :`(-3)/(2)i`

Discussion

347.	Solve the following equations: x^(2)-5ix-6=0
Answer» ANSWER :`3I, 2I`

Discussion

348.	If sin 3alpha = 4 sin alpha sin (x + alpha)sin(x-alpha), then x =
Answer» `N PI +-pi//4, AA n in Z` `n pi +-pi//3, AA n in Z` `n pi +-pi//9, AA n in Z` `n pi +-pi//12, AA n in Z` ANSWER :B

Discussion

349.	Let ABC be a triangle such that angle ACB = pi//6and c denote the lengths of the side opposite to A,B and C, respectively. The value (s) of x for which a= x^(2) + x + 1, b = x^(2) - 1 , " and " c = 2 x + 1is are
Answer» `-(2 + SQRT3)` `1 + sqrt3` `2 + sqrt3` `4sqrt3` ANSWER :B

Discussion

350.	How many different numbers of 4 digits each can be formed with the ten digits 0,1,2,…9 when digits are not repeated?
Answer» ANSWER :``4536`

Discussion

Explore topic-wise InterviewSolutions in .

Given that f(x) is a differentiable function of x and that f(x) ,f(y)= f(x) + f(y) +f(xy) -2and that f(1)=2 ,f(2) = 5 Then f(3) is equal to

Let L be the line belonging to the family of straight lines (a+2b)x+(a-3b)y+a-8b=0 a,b in R, which is the farthest from the point (2,2) The equation of line L is

Let L be the line belonging to the family of straight lines (a+2b)x+(a-3b)y+a-8b=0 a,b in R, which is the farthest from the point (2,2) Area enclosed by the line L and the coordinate axes is

Let L be the line belonging to the family of straight lines (a+2b)x+(a-3b)y+a-8b=0 a,b in R, which is the farthest from the point (2,2) If L is concurrent with lines x-2y+1=0 and 3x-4y+lambda =0, then the value of lambda is

Mid points of sides at DeltaABC are (-2, 3, 5), (4, -1, 7) and (6, 5, 3). Then find coordinates of the verticies A, B and C.

Find the vector area and area of the triangle with vertices bar(i) + bar(j)-bar(k), 2bar(i)- 3bar(j) + bar(k), 3 bar(i) + bar(j)- 2bar(k).

If a_(1) lt ( 28)^((1)/( 3)) - 3 lt b_(1), then (a_(1) b_(1)) ( a_(1) , b_(1)) is

If a and b positive numbers (altb), then the range of values of k for which a real lambda be found such that equation ax^2+2lambdaxy+by^2+2k(x+y+1)=0 represent a pair of straight lines is

Which of the following are sets? Justify your answer : The collection of hard chapter in Maths.

A + B = 90^(@) rArr cos A - cos B in

If 2/11 Is the probability of occurring an event, what is the probability of the eventwill not occurs.

Incircle of DeltaABC touches the sides BC, AC, and AB at D, E, and F, respectively. Then answer the following questions: The length of side EF is

A straight line is parallel to the lines 3x-y-3=0 and 3x-y+5=0, and lies between them. Find its equation if its distances from these lines are in the ratio 3 : 5.

Incircle of DeltaABC touches the sides BC, AC, and AB at D, E, and F, respectively. Then answer the following questions: angleDEF is equal to

Incircle of AABC touches the sides BC, AC, and AB at D, E, and F, respectively. Then answer the following questions: Area of DeltaDEF is

If 7,4 sqrt(3), sqrt(13), are the sides of DeltaABC then least angle is

a^(2) sin 2C + c ^(2) sin 2A =

Rolle's theorem cannot be applicable for

Convert the complex number -16/(1+isqrt(3)) into polar form.

Find the mean deviation from the median for the following data:

Show that cos^4""pi/8+cos^4""(3pi)/8+cos^4""(5pi)/8+cos^4""(7pi)/8=3/2

z=i+sqrt(3)=r(cos theta+sin theta)

Translate the following statements into symbolic form: Either o or x+1 is an odd integer.

Evaluate the following limits : Lim_(x to 0) (1+ax)^(b/x)

If f(x) = sqrt(1+cos^2(x^2)) , then f'((sqrtpi)/2) is

If y=x^((logx)^log(logx)) , then (dy)/(dx) is

Find the coefficient of the term invloving x^10 in the expansion of (x^2 -2)^11

If [x]^(2)- 5[x] + 6= 0, where [.] denote the greatest integer function, then

Statement-I : The locus of the point, whose distance from the X-axis is twice its distance from the y-axis is y^(2)=4x Statement-II : The locus of the point (cottheta+costheta,cottheta-costheta) is (x^(2)-y^(2))^(2)=16xy Then the correct statement is

Solve: sqrtx+5 lt x-2 Solve sqrt-x^(2) + 4x +5 = x -22x^(2) - x + 15lt0

Find the points of local maximum or local minimum for the following (x-3)^4

tan[1/2cos^(-1)((sqrt(5))/3)]=

Convert the following into simplest form (iii) Cosec (5pi + theta)

Find the ecentricity of the given hyperbola 9y^2 -25x^2=225

Find (dy)/(dx) in the following : y= sin^(-1) (2x sqrt(1-x^(2))), (1)/(sqrt(2)) lt x lt (1)/(sqrt(2)).

If (1,3) (2,1) (9,4) are collinear then a is:

If A and B are symmetric matrices then ABA is

Differentiate the following functions w.r.t. x: (sin 3x)/( x-6)

The maximum and minimum values of f(x)=4x^(3)+3x^(2)-6x+5are

Define a relation R on the set N of natural numbers by R= {(x, y): y= x+5, x is a natural number less than 4, x, y in N}. Depict this relationship using roster form. Write down the domain and the range.

Find the value of theta, " if " m^(2) sin . Pi/2 - n^(2) sin . (3pi)/2 + 2 mn sectheta = (m-n)^(2) , 0 le theta le pi.

If theta _(1) ,theta _(2), theta _(3),.....theta _(n) are in A.P. then (sin theta_(1) + sin theta _(2 ) +...+ sin theta _(n))/( cos theta_(1) + cos theta _(2) + ...+ cos theta _(n))

Find the coefficient of (i) a^(6) b^(3) in the expansion of (2a - (b)/(3) )^9

sin 2x+cosx=0

Solve inequality 5x+1 gt - 24, 5x-1 lt 24 and represent solution graphically on number line.

Simplify the following (21)/(14i)

Solve the following equations: x^(2)-5ix-6=0

If sin 3alpha = 4 sin alpha sin (x + alpha)sin(x-alpha), then x =

Let ABC be a triangle such that angle ACB = pi//6and c denote the lengths of the side opposite to A,B and C, respectively. The value (s) of x for which a= x^(2) + x + 1, b = x^(2) - 1 , " and " c = 2 x + 1is are

How many different numbers of 4 digits each can be formed with the ten digits 0,1,2,…9 when digits are not repeated?