14949 + Interview Questions in Maths in Class 11 Page 229 InterviewSolution

11401.	Find the points at which the function f(x)=x^3-6x^2+9x+15 attain local maxima and local minima
Answer» ANSWER :15

Discussion

11402.	Find the derivative of the function (sqrtx + 1) (x ^(2) - 4x + 2), x gt 0
Answer» ANSWER :`(SQRTX +1) (2x -4) + (1)/(2sqrtx) (X ^(2)- 4x +2)`

Discussion

11403.	Assertion: sin(cot^(-1)(1/2))=tan(cos^(-1)x) then the value of x=(sqrt(5))/3 Reason R: cos(tan^(-1)(sin(cot^(-1)x)))=sqrt(((1+x^(2))/(2+x^(2))))
Answer» Both A and R are true and R is correct EXPLANATION of A Both A and R are true and R is not correct explanation of A A is true, R is false A is false but R is true Answer :A

Discussion

11404.	The pressure P and the volume v of a gas are connected by the relation pv^(1//4)=a constant. The percentage increase in the pressure corresponding to a diminution of 1/2% in the volume is
Answer» ANSWER :`1//8`

Discussion

11405.	If ther is an error 0.01 cm in the measurement of the radius 10 cm of a cylinder of fixed height 20 cm then percentage error in the volume is
Answer» 0.2 0.02 0.002 0.0002 Answer :A

Discussion

11406.	Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination.
Answer» ANSWER :778320

Discussion

11407.	If A.M and G.M of two positive numbers aand b 10 and 8 respectively , find the numbers ?
Answer» ANSWER :the NUMBER a and B are 4, 16or 16, 4 respectively.

Discussion

11408.	Statement 1 : If 27a+9b+3c+d=0, then the equation f(x) =4ax^(3) + 3b^(2) +2cx + d=0 . Has at least one real root lying between (0,3). Statement 2 : If f(x) is continuous in [a,b], derivablein (a,b) such that f(a) =f(b) , then at least one point c in (a,b) such that f(c ) = 0.
Answer» If both the statement are TRUE and STATEMENT 2 is the correct explanation of STATMEMENT -1 If both the statement are TRUE and STATEMENT2 is NOT the correctexplanation of STATEMENT-1 If STATEMENT -1 is TRUE and STATEMENT 2 is FALSE If STATEMENT-1 is FALSE and STATEMENT 2 is TRUE Answer :A

Discussion

11409.	Prove the following cos4x=1-8"sin"^(2)xcos^(2)x
Answer» ANSWER :`=1-8 "SIN"^(2)XCOS^(2)x=RHS`

Discussion

11410.	Draw the graphs of the following : y = 2^(x) if-2,2,
Answer» ANSWER :`(##AKS_ELT_AI_MAT_XI_VIB_P02_C01_E01_024_A01##)`

Discussion

11411.	OBCA is a rhombus with side length one unit and angleAOB = theta. " If " sintheta = (24)/(25), then find the lengths of the diagonals.
Answer» ANSWER :`8/5`

Discussion

11412.	Solve cos2theta=2sin^(2)theta and find general solution.
Answer» ANSWER :`npipm(PI)/(6)`

Discussion

11413.	Line through the points (-2, 6) " and " (4, 8) is perpendicular to the line through the points (8, 12) and (x, 24) . Find the value of x.
Answer» ANSWER :`X = 4`

Discussion

11414.	An experiment consists of recording boy-girl composition of families with 2 children. (i) What is the sample space if we are interested in knowing whether it is a boy or girl in the order of their births ? (ii) What is the sample space if we are interested in the number of girls in the family ?
Answer» Answer :(i){BB, BG, GB, GG} (II) {0, 1, 2}

Discussion

11415.	If f(x)=Sin^(-1){3-(x-6)^(4)}^(1//3) then f^(-1)(x)=
Answer» `6+root(4)(3+sin^(3)X)` `6+root(4)(3-sin^(3)x)` `6+root(4)(3+sinx)` `6+root(4)(3-sinx)` ANSWER :B

Discussion

11416.	The solution of system of simultanesous x equations for x and y:4^(sinx)+3^(1//cosy)=11,5xx16^(sinx)-2xx3^(1//cosy)=2
Answer» `x=npi+(-1)^(n)(PI)/6, n in Z` `y=2 m pi +-(pi)/3 , m INZ` `x=n pi +(-1)^(n)(pi)/3, n in Z` `2mpi+-(pi)/6, m in Z` ANSWER :A::B

Discussion

11417.	Write down the negation of following compound statements. 35 is a prime number or a composite number.
Answer» ANSWER :not COMPOSITE NUMBER.

Discussion

11418.	If the position vectors of the vertices of DeltaABC" ""are"" "3hat(i)+4hat(j)-hat(k),hat(i)+3hat(j)+hat(k)and5(hat(i)+hat(j)+hat(k)), respectively. Then, the magnitude of the altitude from A onto the side BC is
Answer» `(4)/(3) sqrt5` `(5)/(3)sqrt5` `(7)/(3)sqrt5` `(8)/(3) sqrt5` ANSWER :A

Discussion

11419.	If there is an error 0.01 cm in the measurement of the radius 10 cm of a cylinder of fixed height 20 cm then error in valume, (cubic cm)
Answer» `4PI` `2.5pi` 0.06 0.6 Answer :A

Discussion

11420.	If the intercept of a line between the corrdinatinate axes is divided by the point (-5,4) in the ration 1 : 2 , then find the equation of the line .
Answer» ANSWER :`8x-5y+60=0`

Discussion

11421.	Find the modulus and argument of the complex number (1+2i)/(1-3i)
Answer» ANSWER :`1/sqrt(2), (3PI)/4`

Discussion

11422.	4Tan^(-1)""1/5-Tan^(-1)""1/239=
Answer» `PI` `pi/2` `pi/4` `(3PI)/4` ANSWER :C

Discussion

11423.	Find lim_(xrarr1)f(x), where f(x)={{:(x^(2)-1",",xle1),(-x^(2)-1",",xgt1):}
Answer» ANSWER :LIMIT does not EXIST at `X = 1`

Discussion

11424.	The minimumvalue of Sinx ((1-cos x)/(sin x) + (sin x)/( 1-cos x)) is
Answer» `1` `2` `3` `4` Answer :B

Discussion

11425.	Find sum_(1)^(infty) 1/((k+1)(k+2))
Answer» ANSWER :`1/2`

Discussion

11426.	If 7cos^(2)x+sinx cos x-3=0 then x=
Answer» `x=N pi+(pi)/4, n inZ` `x=kpi+tan^(-1)(4/3), k in Z` `x=kpi+tan^(-1)(3/4), k in Z` `x=npi+(pi)/3, n in Z` ANSWER :B::C

Discussion

11427.	Solve the equations: 2^(x^(2)):2^(x)=8:1
Answer» ANSWER :`(1pmsqrt(13))/(2)`

Discussion

11428.	69.13 xx 0.34 xx 0.014
Answer» ANSWER :0.3291

Discussion

11429.	Let A and B denote the statements A: cos alpha + cos beta + cos gamma=0, B:sin alpha + sin beta + sin gamma=0, If cos(beta - gamma) + cos(gamma - alpha) + cos(alpha - beta)=-3/2, then
Answer» A is TRUE and B is false A is FLASE and B is true Both A and B are true Both A and B are false. Answer :C

Discussion

11430.	If 4x+3y+k=0 touch the circle 2x^(2)+2y^(2)=5x then k=
Answer» `5/4` or `(-45)/4` `(-5)/4` or `(-45)/4` `-5/4` or `45/4` `5/4` or `45/4` ANSWER :A

Discussion

11431.	Assertion (A) : In rolling die, getting numberReason (R) : In a die contains only numbers 1,2,3,4,5,6
Answer» Both (A) and (R) are TRUE and (R) is the CORRECT EXPLANTION of (A) Both (A) and (R) are the true but (R) is not the correct explantionof (A) (A) is true (R)is FALSE (A) is false (R)is true Answer :(a) is false (R)is true

Discussion

11432.	Find the point on y-axis which is equidistant from the points (3,1,2) and (5,5,3),
Answer» ANSWER :`0,5,0`

Discussion

11433.	Find the equation of circle with centre at (-3,2) and radius 4 units.
Answer» ANSWER :`(x+3)^(2)+(y-2)^(2)=16`

Discussion

11434.	A line has intercepls a and b on the coordinate axes. When the axes are rotated an angle alpha Keeping the origin fixed. The line makes equal intercepts on the coordinate axes, then tan alpha=
Answer» `(a+B)/(a-b)` `(a-b)/(a+b)` `a^2-b^2` `a^2+b^2` ANSWER :B

Discussion

11435.	If""^(n)C_4= ""^(n)C_6,find n.
Answer» ANSWER :`10 `

Discussion

11436.	Which term of the G.P., 2,8,32, ... up to n terms is 131072 ?
Answer» ANSWER :`9^(TH)` TERMS

Discussion

11437.	Find the equation of a circle whose centre is (3, -1) and which cuts off a chord of length 6 units on the line 2x - 5y + 18 = 0.
Answer» Answer :`X^(2) + y^(2) - 6x + 2Y = 28`, is REQUIRED CIRCLES.

Discussion

11438.	Find the covariance between X and Y when n = 10 , SigmaX = 60 , Sigma Y = 60 and Sigma XY = 305 .
Answer» ANSWER :`-5.5`

Discussion

11439.	If bara,barb,barc are threevectors of equal magnitude and angle between each pair of vectors is pi//3 " such that " abs(bara+barb+barc) = sqrt6, " then " absbara=
Answer» 2 -1 1 `sqrt6/3` ANSWER :C

Discussion

11440.	The perpendicular distance from origin to the plane barr.(2bari+3barj+6bark)=21 is
Answer» 1 2 3 4 Answer :C

Discussion

11441.	If 'theta' is the angle between the unit vectors bara, barb," then " abs(bara+barb) =
Answer» `SIN(theta//2)` `2SIN(theta//2)` `COS(theta//2)` `2COS(theta//2)` ANSWER :D

Discussion

11442.	Number of solutions of equation 2"sin"x/2cos^(2)x-2"sin"x/2sin^(2)x=cos^(2)x-sin^(2)x for x in [0,4pi]
Answer» 6 8 10 12 Answer :C

Discussion

11443.	If (n +1 ) ! = 12 (n-1) ! then n = ........... n in N
Answer» ANSWER :3

Discussion

11444.	If sum_(r=1)^(10)tan^(-1)(3/(9r^(2)+3r-1))=cot^(-1)(m/n) (where m and n are coprime) then the value of ((2m+n))/8 is
Answer» ANSWER :4

Discussion

11445.	Find deltay and dy for the following functions y=5x^(2)+6x+6,x=2 and deltax=0.001
Answer» ANSWER :0.026005, 0.026

Discussion

11446.	State the converse and contrapositive of each of the following statements: q:I go to a beach whenever it is a sunny day.
Answer» ANSWER :it is not SUNNY DAY.

Discussion

11447.	Evaluate the following limits : Lim_(x to 0 ) (" cosec " x - cot x)/x
Answer» ANSWER :`1/2 `

Discussion

11448.	The sides of the rectangle of greatest area that can be inscribed in the ellipse x^(2)+4y^(2)=64 are
Answer» `3sqrt(5),5sqrt(5)` `5sqrt(3),3sqrt(3)` `5sqrt(2),3sqrt(2)` 5,3 Answer :C

Discussion

11449.	Find the n^(th) term of series 1.2.5+2.3.6+3.4.7.+…
Answer» SOLUTION :`N(n+1)(n+4)`

Discussion

11450.	State how continuity is destroyed at x=x_0 for each of the following graphs.
Answer» ANSWER :F(X)is not CONTINUOUS

Discussion

Explore topic-wise InterviewSolutions in .

Find the points at which the function f(x)=x^3-6x^2+9x+15 attain local maxima and local minima

Find the derivative of the function (sqrtx + 1) (x ^(2) - 4x + 2), x gt 0

Assertion: sin(cot^(-1)(1/2))=tan(cos^(-1)x) then the value of x=(sqrt(5))/3 Reason R: cos(tan^(-1)(sin(cot^(-1)x)))=sqrt(((1+x^(2))/(2+x^(2))))

The pressure P and the volume v of a gas are connected by the relation pv^(1//4)=a constant. The percentage increase in the pressure corresponding to a diminution of 1/2% in the volume is

If ther is an error 0.01 cm in the measurement of the radius 10 cm of a cylinder of fixed height 20 cm then percentage error in the volume is

Determine the number of 5 card combinations out of a deck of 52 cards if there﻿ is exactly one ace in each combination.﻿

If A.M and G.M of two positive numbers aand b 10 and 8 respectively , find the numbers ?

Statement 1 : If 27a+9b+3c+d=0, then the equation f(x) =4ax^(3) + 3b^(2) +2cx + d=0 . Has at least one real root lying between (0,3). Statement 2 : If f(x) is continuous in [a,b], derivablein (a,b) such that f(a) =f(b) , then at least one point c in (a,b) such that f(c ) = 0.

Prove the following cos4x=1-8"sin"^(2)xcos^(2)x

Draw the graphs of the following : y = 2^(x) if-2,2,

OBCA is a rhombus with side length one unit and angleAOB = theta. " If " sintheta = (24)/(25), then find the lengths of the diagonals.

Solve cos2theta=2sin^(2)theta and find general solution.

Line through the points (-2, 6) " and " (4, 8) is perpendicular to the line through the points (8, 12) and (x, 24) . Find the value of x.

An experiment consists of recording boy-girl composition of families with 2 children. (i) What is the sample space if we are interested in knowing whether it is a boy or girl in the order of their births ? (ii) What is the sample space if we are interested in the number of girls in the family ?

If f(x)=Sin^(-1){3-(x-6)^(4)}^(1//3) then f^(-1)(x)=

The solution of system of simultanesous x equations for x and y:4^(sinx)+3^(1//cosy)=11,5xx16^(sinx)-2xx3^(1//cosy)=2

Write down the negation of following compound statements. 35 is a prime number or a composite number.

If the position vectors of the vertices of DeltaABC" ""are"" "3hat(i)+4hat(j)-hat(k),hat(i)+3hat(j)+hat(k)and5(hat(i)+hat(j)+hat(k)), respectively. Then, the magnitude of the altitude from A onto the side BC is

If there is an error 0.01 cm in the measurement of the radius 10 cm of a cylinder of fixed height 20 cm then error in valume, (cubic cm)

If the intercept of a line between the corrdinatinate axes is divided by the point (-5,4) in the ration 1 : 2 , then find the equation of the line .

Find the modulus and argument of the complex number (1+2i)/(1-3i)

4Tan^(-1)""1/5-Tan^(-1)""1/239=

Find lim_(xrarr1)f(x), where f(x)={{:(x^(2)-1",",xle1),(-x^(2)-1",",xgt1):}

The minimumvalue of Sinx ((1-cos x)/(sin x) + (sin x)/( 1-cos x)) is

Find sum_(1)^(infty) 1/((k+1)(k+2))

If 7cos^(2)x+sinx cos x-3=0 then x=

Solve the equations: 2^(x^(2)):2^(x)=8:1

69.13 xx 0.34 xx 0.014

Let A and B denote the statements A: cos alpha + cos beta + cos gamma=0, B:sin alpha + sin beta + sin gamma=0, If cos(beta - gamma) + cos(gamma - alpha) + cos(alpha - beta)=-3/2, then

If 4x+3y+k=0 touch the circle 2x^(2)+2y^(2)=5x then k=

Assertion (A) : In rolling die, getting numberReason (R) : In a die contains only numbers 1,2,3,4,5,6

Find the point on y-axis which is equidistant from the points (3,1,2) and (5,5,3),

Find the equation of circle with centre at (-3,2) and radius 4 units.

A line has intercepls a and b on the coordinate axes. When the axes are rotated an angle alpha Keeping the origin fixed. The line makes equal intercepts on the coordinate axes, then tan alpha=

If""^(n)C_4= ""^(n)C_6,find n.

Which term of the G.P., 2,8,32, ... up to n terms is 131072 ?

Find the equation of a circle whose centre is (3, -1) and which cuts off a chord of length 6 units on the line 2x - 5y + 18 = 0.

Find the covariance between X and Y when n = 10 , SigmaX = 60 , Sigma Y = 60 and Sigma XY = 305 .

If bara,barb,barc are threevectors of equal magnitude and angle between each pair of vectors is pi//3 " such that " abs(bara+barb+barc) = sqrt6, " then " absbara=

The perpendicular distance from origin to the plane barr.(2bari+3barj+6bark)=21 is

If 'theta' is the angle between the unit vectors bara, barb," then " abs(bara+barb) =

Number of solutions of equation 2"sin"x/2cos^(2)x-2"sin"x/2sin^(2)x=cos^(2)x-sin^(2)x for x in [0,4pi]

If (n +1 ) ! = 12 (n-1) ! then n = ........... n in N

If sum_(r=1)^(10)tan^(-1)(3/(9r^(2)+3r-1))=cot^(-1)(m/n) (where m and n are coprime) then the value of ((2m+n))/8 is

Find deltay and dy for the following functions y=5x^(2)+6x+6,x=2 and deltax=0.001

State the converse and contrapositive of each of the following statements: q:I go to a beach whenever it is a sunny day.

Evaluate the following limits : Lim_(x to 0 ) (" cosec " x - cot x)/x

The sides of the rectangle of greatest area that can be inscribed in the ellipse x^(2)+4y^(2)=64 are

Find the n^(th) term of series 1.2.5+2.3.6+3.4.7.+…

State how continuity is destroyed at x=x_0 for each of the following graphs.

Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination.