14949 + Interview Questions in Maths in Class 11 Page 139 InterviewSolution

6901.	The system of equations (sin 3 theta) x - y+z=0,(cos 2 theta)x+4y+3z=0, 2x+7y+7z=0 has non trivial solutions if
Answer» `n PI +(-1)^(n)pi//6, AA n in Z` `n pi+(-1)^(n) pi//3, AA n in Z` `n pi+(-1)^(n)pi//9, AA n in Z` `n pi +(-1)^(n)(pi)/12, AA n in Z` ANSWER :A

Discussion

6902.	The real number x when added to its inverse gives the minimum value of the sum at x=
Answer» 1 `-1` `-2` 2 Answer :A

Discussion

6903.	The mean and standard deviation of 20 observations are found to be 10 and 2, respectively. On rechecking , it was found that an observation 8 was incorrect . Calculate the correct mean and standard deviation in each of the following cases: (i) If wrong item is omitted. (ii) If it is replaced by 12.
Answer» ANSWER :(i) 10,1, 1.99 (II) 10.2, 1.98

Discussion

6904.	Find the coordinates of the vertex 'C' of DeltaABC if its centroid is the origin and the vertices A,B are (1,1,1) are (-2,4,1) respectively.
Answer» ANSWER :`1,-5,-2`

Discussion

6905.	A chimney leans towards north. At equal distance due north and south of it in a horizontal plalne, The elevation of the tops are alpha and beta respecctively. The inclination of the top of the chimney to the vertical is
Answer» `TAN^(-1)[(SIN(alpha-beta))/(sin alphasinbeta)]` `Tan^(-1)[(2sin(alpha-beta))/(sin alphasinbeta)]` `Tan^(-1)[(sin(alpha-beta))/(2sin alphasinbeta)]` `Tan^(-1)[(sin(alpha-beta))/(2cosalphacosbeta)]` ANSWER :C

Discussion

6906.	The P. V. of the points A, B, C, D are 3bari-2barj-bark,2bari+3barj-4bark,-bari+barj+2bark,4bari+5barj+lamdabark respectively. If the points A, B, C, D lie on the same plane, then lamda=
Answer» `-8` `(-145)/17` `(-146)/17` `-7` Answer :C

Discussion

6907.	Which of the following sentences are statements? Give reasons for your answer Today is a windy day.
Answer» ANSWER :It is not CLEAR from the CONTEXT which DAY is referred and therefore, it is not a statement.

Discussion

6908.	The value of Sin^(-1)(sin12)+Cos^(-1)(cos12)=
Answer» `0` `24-2pi` `4pi-24` `8pi` ANSWER :A

Discussion

6909.	Prove that (sec A-"cosec A")(1+tan A+cot A)=tan A sec A-cot A " cosec "A
Answer» ANSWER :`(SIN^(3) A-COS^(3)A)/(sin^(2) A cos ^(2) A)`

Discussion

6910.	Iff :R to Ris defindbyf(x) ={:{ ( a^(2) cos x + b^(2) sin^(2) x ,xle 0) , ( e^(ax + b), x gt 0) :} is a continuousfucntion , then
Answer» B = 2log \|a\| 2b = LOG \|a\| b = log \|2a\| `b^(2) = log \|a\| ` ANSWER :A

Discussion

6911.	Prove that, cos2xcos""(x)/(2)-cos3xcos""(9x)/(2)=sin5xsin""(5x)/(2).
Answer» ANSWER :`SIN " (5X)/(2)=R.H.S.`

Discussion

6912.	Find a G.P. for which sum of the first two terms is – 4 and the fifth term is 4 times the third term.
Answer» ANSWER :`4, -8, 16, -32`…….

Discussion

6913.	If y = 2^(2 ^(x)),then (dy)/(dx) =
Answer» `y.(LOG2)^2)2^x` `y(log2).2^x` `Y2(log2)^(2))2^x` `-y(log2).2^x` ANSWER :A

Discussion

6914.	Evaluate lim_(x rarr 0) (3^x - 2^x)/(tan x)
Answer» SOLUTION :LOG (3/2)

Discussion

6915.	Find the number of four letter arrangements of the letters of the word ' SHOOT' . How many of them begin with O?
Answer» ANSWER :` 60 : 24`

Discussion

6916.	Evaluate Lt_(xto0)((e^(x^(2))-cosx)/x^(2)).
Answer» ANSWER :`3/2`

Discussion

6917.	If f is an even function defined on the interval (-5, 5) then find the total number of real values of x satisfying the equations f(x)=f((x+1)/(x+2)) are
Answer» 1 2 4 8 Answer :C

Discussion

6918.	The value of the sum in the50^( th) bracket of (1) + (2+3) + ( 4+ 5+ 6) + ( 7+8+ 9 + 10) + … is
Answer» `62525` `65225` `56225` `55625` ANSWER :A

Discussion

6919.	[baribarjbark]+[barjbarkbari]+[barkbaribarj]+[baribarkbarj]+[barjbaribark]+[barkbarjbari]=
Answer» 1 2 6 0 Answer :D

Discussion

6920.	Find the derivative of x^(2) - 2" at "x = 10.
Answer» ANSWER :20

Discussion

6921.	Find the derivative of the function f(x)=2x^(2)+3x-5 at x=-1 .Also prove that f'(0)+3f'(-1)=0
Answer» ANSWER :-1

Discussion

6922.	A card is drawn from a well shuffled pack of 52 cards . Findthe probability of a black card
Answer» ANSWER :`(26)/(52),i.e,(1)/(2)`

Discussion

6923.	Let f(x) be twice differentiable function for all real x and f(1) = 1, f(2) = 4 , f(3) = 9. Then which one of the following statements is definitelly true ?
Answer» `F'' (X)= 2 ` for all `x in ( 1,3)` `f'(x) = f'(x) = 5` for some `x in (2,3)` `f'' (x) = 3` for all `x in ( 2,3)` `f'' (x) = f(x_(0))` Answer :A

Discussion

6924.	If m cos^(2) A + n sin^(2) A = p, then cot^(2) A=
Answer» `(p+n)/(m+p)` `(p-n)/(p-m)` `(p-n)/(m-p)` `(n+1)/(m+p)` ANSWER :C

Discussion

6925.	The maximum value of the function f(x)=sinx is……
Answer» 1 `sqrt3/2` `1/2` 2 Answer :A

Discussion

6926.	Find the transformed equation ofx^(2) + y^(2) + 2x - 4y + 1 = 0 when the origin is shifted to the point (-1, 2)
Answer» ANSWER :`X^(2) + Y^(2) - 4 = 0`

Discussion

6927.	Find the coefficient of : x^(40) " in " (1^(2)+2x)^(20)
Answer» ANSWER :1

Discussion

6928.	In the triangle ABC with vertices A(2,3), B(4,1) and C(1,2), find the equation and length of altitude from the vertex A.
Answer» ANSWER :`x-y+1=0`, which is REQUIRED ALTITUDE.

Discussion

6929.	An integeris chosenform {2k//-9k lek le 10}. Theprobabilitythatit is divisbleby both 4and 6si
Answer» `(1)/(10)` `(1)/(20)` `(1)/(4)` `(3)/(20)` ANSWER :D

Discussion

6930.	Evaluate the following limits : lim _( xto pi) ( sin x)/(pi - x)
Answer» ANSWER :1

Discussion

6931.	IF a circlepasses through the point (0,0) (a,0),(0,b) then find the coordinates of its centre. Thinking process :
Answer» ANSWER :`=((a)/(2), (b)/(2))` is REQUIRED CENTRE of circle.

Discussion

6932.	If f(x)=(1)/(2)x^(2)+3x,x=2,deltax=0.5,deltaf=
Answer» 2.5 0.25 2.625 2.7 Answer :C

Discussion

6933.	How many solutionsare there for the equation sin^(2)x=(1)/(4) in [-2pi,2pi].
Answer» ANSWER :8

Discussion

6934.	The smallest +ve integer n for which n! lt ( (n+1)/( 2) )^(n) holds is
Answer» 1 2 3 4 Answer :B

Discussion

6935.	Find n if : P(2n, 3) = 100 P(n,2)
Answer» ANSWER :` 13`

Discussion

6936.	If all the rectangles of a given perimeter 2P , theone having the smallest diagonal is square whose side is
Answer» <P>`(P)/(2)` P 2P `(P)/(3)` ANSWER :A

Discussion

6937.	If r = [ 2 phi +cos^2(2phi+pi//4)]^(1//2) , then what is the value of the derivative of dr// dphi at phi = pi//4 ?
Answer» `2((1)/(pi+1))^(1//2)` `2((2)/(pi+1))^(2)` `((1)/(pi+1))^(1//2)` `2((2)/(pi+1))^(1//2)` ANSWER :D

Discussion

6938.	If f(x)= overset(x^(2)+1) underset(x^(2)) int e^(-t^(2)) dt then the following f(x) decreases in
Answer» (-2,2) `(0,OO)` no VALUE of X `(-oo,0)` ANSWER :B

Discussion

6939.	(cos 6 theta + 6 cos 3 theta + 15 cos 2 theta + 10)/( cos 5 theta + 5 cos 3 theta + 10)=
Answer» `SIN THETA ` `COS theta ` `2 sin theta ` `2 cos theta ` ANSWER :D

Discussion

6940.	If 0^(@)ltthetalt180^(@) then sqrt(2+sqrt(2+sqrt(2+......sqrt(2(1+costheta))))) there being 'n' number of 2's equal to
Answer» `2"cos"(theta/(2^(N)))` `2"cos"(theta/(2^(n+1)))` `2"cos"(theta/(2^(n-1)))` `2"SIN"(theta/(2^(n)))` ANSWER :A

Discussion

6941.	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

6942.	Statement-I: If mcos(theta + alpha) =ncos(theta-alpha) then tan alpha tan theta =(m+n)/(m-n) Statement:II If (sin(alpha + beta))/(sin(alpha-beta)) =(a+b)/(a-b), then tan alpha cot beta =a/b Which of the above statements is correct?
Answer» Only I Only II Both I and II Neither I nor II Answer :B

Discussion

6943.	Find the middle terms in the expansions of(3 - x^3/6^7)
Answer» ANSWER :`105/8` `x^9,.35/48 x^12`

Discussion

6944.	A triangle has base 10 and base angles are 50, 70If the perimeter of triangle is x + y cosZ where Z^(0) in (0, 90^(@)) " then " x + y + z=
Answer» 60 55 50 40 Answer :D

Discussion

6945.	If (cos^(2)theta)/(a)=(sin^(2)theta)/(b) then (cos^(4)theta)/(a)+(sin^(4)theta)/(b)=0
Answer» `(1)/(a+B)` `(1)/((a+b)^(2))` `(1)/(a^(2))+(1)/(b^(2))` a+b Answer :A

Discussion

6946.	.......is the angle of elevation of sun if height of building and its shadow are equal .
Answer» ANSWER :`45^@`

Discussion

6947.	If sin (120^(@) - alpha) = sin (120^(@) - beta) and 0 lt alpha,beta lt pi then all the values of alpha,beta are
Answer» `alpha = beta` `alpha + beta = (PI)/(3)` `alpha = beta or alpha +beta = (pi)/(3)` `alpha = beta = 0` ANSWER :C

Discussion

6948.	If (cosA)/(1-sinA)=tan(k+A/2), then k=
Answer» `(PI)/2` `-(pi)/4` `(pi)/4` `-(pi)/2` ANSWER :C

Discussion

6949.	The periodof cos (cos x) + cos(Sinx )is
Answer» `(pi)/(2)` `2pi` `(pi)/(4)` `(2pi)/(3)` ANSWER :1

Discussion

6950.	If f(x)=(cos^(2)x +sin^(4)x)/(sin^(2)x +cos^(4)x) for x in Rthen f(2018)=
Answer» 1 2 3 4 Answer :A

Discussion

Explore topic-wise InterviewSolutions in .

The system of equations (sin 3 theta) x - y+z=0,(cos 2 theta)x+4y+3z=0, 2x+7y+7z=0 has non trivial solutions if

The real number x when added to its inverse gives the minimum value of the sum at x=

The mean and standard deviation of 20 observations are found to be 10 and 2, respectively. On rechecking , it was found that an observation 8 was incorrect . Calculate the correct mean and standard deviation in each of the following cases: (i) If wrong item is omitted. (ii) If it is replaced by 12.

Find the coordinates of the vertex 'C' of DeltaABC if its centroid is the origin and the vertices A,B are (1,1,1) are (-2,4,1) respectively.

A chimney leans towards north. At equal distance due north and south of it in a horizontal plalne, The elevation of the tops are alpha and beta respecctively. The inclination of the top of the chimney to the vertical is

The P. V. of the points A, B, C, D are 3bari-2barj-bark,2bari+3barj-4bark,-bari+barj+2bark,4bari+5barj+lamdabark respectively. If the points A, B, C, D lie on the same plane, then lamda=

Which of the following sentences are statements? Give reasons for your answer Today is a windy day.

The value of Sin^(-1)(sin12)+Cos^(-1)(cos12)=

Prove that (sec A-"cosec A")(1+tan A+cot A)=tan A sec A-cot A " cosec "A

Iff :R to Ris defindbyf(x) ={:{ ( a^(2) cos x + b^(2) sin^(2) x ,xle 0) , ( e^(ax + b), x gt 0) :} is a continuousfucntion , then

Prove that, cos2xcos""(x)/(2)-cos3xcos""(9x)/(2)=sin5xsin""(5x)/(2).

Find a G.P. for which sum of the first two terms is – 4 and the fifth term is 4 times the third term.

If y = 2^(2 ^(x)),then (dy)/(dx) =

Evaluate lim_(x rarr 0) (3^x - 2^x)/(tan x)

Find the number of four letter arrangements of the letters of the word ' SHOOT' . How many of them begin with O?

Evaluate Lt_(xto0)((e^(x^(2))-cosx)/x^(2)).

If f is an even function defined on the interval (-5, 5) then find the total number of real values of x satisfying the equations f(x)=f((x+1)/(x+2)) are

The value of the sum in the50^( th) bracket of (1) + (2+3) + ( 4+ 5+ 6) + ( 7+8+ 9 + 10) + … is

[baribarjbark]+[barjbarkbari]+[barkbaribarj]+[baribarkbarj]+[barjbaribark]+[barkbarjbari]=

Find the derivative of x^(2) - 2" at "x = 10.

Find the derivative of the function f(x)=2x^(2)+3x-5 at x=-1 .Also prove that f'(0)+3f'(-1)=0

A card is drawn from a well shuffled pack of 52 cards . Findthe probability of a black card

Let f(x) be twice differentiable function for all real x and f(1) = 1, f(2) = 4 , f(3) = 9. Then which one of the following statements is definitelly true ?

If m cos^(2) A + n sin^(2) A = p, then cot^(2) A=

The maximum value of the function f(x)=sinx is……

Find the transformed equation ofx^(2) + y^(2) + 2x - 4y + 1 = 0 when the origin is shifted to the point (-1, 2)

Find the coefficient of : x^(40) " in " (1^(2)+2x)^(20)

In the triangle ABC with vertices A(2,3), B(4,1) and C(1,2), find the equation and length of altitude from the vertex A.

An integeris chosenform {2k//-9k lek le 10}. Theprobabilitythatit is divisbleby both 4and 6si

Evaluate the following limits : lim _( xto pi) ( sin x)/(pi - x)

IF a circlepasses through the point (0,0) (a,0),(0,b) then find the coordinates of its centre. Thinking process :

If f(x)=(1)/(2)x^(2)+3x,x=2,deltax=0.5,deltaf=

How many solutionsare there for the equation sin^(2)x=(1)/(4) in [-2pi,2pi].

The smallest +ve integer n for which n! lt ( (n+1)/( 2) )^(n) holds is

Find n if : P(2n, 3) = 100 P(n,2)

If all the rectangles of a given perimeter 2P , theone having the smallest diagonal is square whose side is

If r = [ 2 phi +cos^2(2phi+pi//4)]^(1//2) , then what is the value of the derivative of dr// dphi at phi = pi//4 ?

If f(x)= overset(x^(2)+1) underset(x^(2)) int e^(-t^(2)) dt then the following f(x) decreases in

(cos 6 theta + 6 cos 3 theta + 15 cos 2 theta + 10)/( cos 5 theta + 5 cos 3 theta + 10)=

If 0^(@)ltthetalt180^(@) then sqrt(2+sqrt(2+sqrt(2+......sqrt(2(1+costheta))))) there being 'n' number of 2's equal to

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))

Statement-I: If mcos(theta + alpha) =ncos(theta-alpha) then tan alpha tan theta =(m+n)/(m-n) Statement:II If (sin(alpha + beta))/(sin(alpha-beta)) =(a+b)/(a-b), then tan alpha cot beta =a/b Which of the above statements is correct?

Find the middle terms in the expansions of(3 - x^3/6^7)

A triangle has base 10 and base angles are 50, 70If the perimeter of triangle is x + y cosZ where Z^(0) in (0, 90^(@)) " then " x + y + z=

If (cos^(2)theta)/(a)=(sin^(2)theta)/(b) then (cos^(4)theta)/(a)+(sin^(4)theta)/(b)=0

.......is the angle of elevation of sun if height of building and its shadow are equal .

If sin (120^(@) - alpha) = sin (120^(@) - beta) and 0 lt alpha,beta lt pi then all the values of alpha,beta are

If (cosA)/(1-sinA)=tan(k+A/2), then k=

The periodof cos (cos x) + cos(Sinx )is

If f(x)=(cos^(2)x +sin^(4)x)/(sin^(2)x +cos^(4)x) for x in Rthen f(2018)=