14949 + Interview Questions in Maths in Class 11 Page 167 InterviewSolution

8301.	Differentiate the following functions w.r.t. x: sec ax
Answer» ANSWER :`a SEC AX TAN ax`

Discussion

8302.	If tan5x=cot3x then x=(ninz)
Answer» `(2n+1)(pi)/(4)` `(2n+1)(pi)/(8)` `(2n+1)(pi)/(16)` `(2n+1)(pi)/(32)` Answer :C

Discussion

8303.	Consider a plane x + y - z= 1 and point A (1,2,-3). A line L has the equation x =1 + 3r ,y =2- r and z =3 + 4r The equation of the plane containing line L and point A has the equation
Answer» `4sqrt26` `20` `10sqrt13` 40 Answer :D

Discussion

8304.	If Tan40^(@) + 2 Tan 10^(@) = Cotx then x =
Answer» `75^(@)` `85^(@)` `30^(@)` `40^(@)` ANSWER :D

Discussion

8305.	The maximum valuue of the function f(x)=Sin(x+pi/6)+Cos(x+pi/6) in the interval (0,pi/2) occurs at x=
Answer» `PI/(12)` `pi/6` `pi/4` `pi/3` ANSWER :A

Discussion

8306.	Set A has three elements and B = {a, b, c,d} then numbers of elements in 'AxB' are …........
Answer» ANSWER :FALSE STATEMENT

Discussion

8307.	If Delta_1 = \|(x,a,b),(b,x,a),(a,b,x)\| and Delta_2 = \|(x,a),(a,x)\| are the given determinants , then
Answer» `Delta_1 = 3(Delta_2)^2` `d/(DX) (Delta_1) = 3 Delta_2` `d/(dx) (Delta_1) = 3(Delta_2)^2` `Delta_1 = 3(Delta_2)^(3//2)` ANSWER :B

Discussion

8308.	Convert each of the complex numbers given inthe polar form. sqrt(3)-i
Answer» Answer :`-2("COS"(pi)/(6)+i"SIN"(pi)/(6))`

Discussion

8309.	Write each of the statement in the form if p, then q: p: It is necessary to have a password to log on the server.
Answer» ANSWER :if you LOG to the SERVER then you MUST have PASSWORDS.

Discussion

8310.	sin 3 theta * cos^(3) theta + cos 3 theta * sin^(3) theta =
Answer» `3SIN 4theta` `3/2"SIN " 4theta` `3/4" sin " 4theta` `2SIN 4theta` ANSWER :C

Discussion

8311.	Solve the following system of equations. (a) By using Cramer's rule and Matrix inversion method, when the coefficient matrix is non - singular. (b) By using Gauss-Jordan method, also determine whether the system has unique solution, or infinite number of solutions or solution and find the solution if exist. x+y+2z=1 2x+y+z=2 x+2y+2z=1
Answer» ANSWER :`x=1,y=0,z=0`

Discussion

8312.	Describe the sample space of this experiment : Two dice are rolled .
Answer» ANSWER :`(##SCH_OPM_ISC_MAT_XI_C22_E01_006_A01##)`

Discussion

8313.	Solve the following system of equations by using Cramer's rule. x-y+3z=5,4x+2y-z=0,x+3y+z=5.
Answer» ANSWER :`x=0,y=1,z=2`

Discussion

8314.	Solve the following system of equations. (a) By using Cramer's rule and Matrix inversion method, when the coefficient matrix is non - singular. (b) By using Gauss-Jordan method, also determine whether the system has unique solution, or infinite number of solutions or solution and find the solution if exist. x+y+z=1 2x+2y+3z=6 x+4y+8z=3
Answer» ANSWER :`x=7,y=-10,z=4`

Discussion

8315.	Solve the following system of equations. (a) By using Cramer's rule and Matrix inversion method, when the coefficient matrix is non - singular. (b) By using Gauss-Jordan method, also determine whether the system has unique solution, or infinite number of solutions or solution and find the solution if exist. 5x-6y+4z=15 7x+4y-3z=19 2x+y+6z=46
Answer» ANSWER :`x=3,y=4,z=6`

Discussion

8316.	Solve the following system of equations. (a) By using Cramer's rule and Matrix inversion method, when the coefficient matrix is non - singular. (b) By using Gauss-Jordan method, also determine whether the system has unique solution, or infinite number of solutions or solution and find the solution if exist. 2x-y+3z=9 x+y+z=6 x-y+z-2
Answer» ANSWER :`x=1,y=2,z=3`

Discussion

8317.	Solve the following system of equations. (a) By using Cramer's rule and Matrix inversion method, when the coefficient matrix is non - singular. (b) By using Gauss-Jordan method, also determine whether the system has unique solution, or infinite number of solutions or solution and find the solution if exist. x+y+z=9 2x+5y+7z=52 2x+y-z=0
Answer» ANSWER :`x=1,y=3,z=5`

Discussion

8318.	Solve the following system of equations. (a) By using Cramer's rule and Matrix inversion method, when the coefficient matrix is non - singular. (b) By using Gauss-Jordan method, also determine whether the system has unique solution, or infinite number of solutions or solution and find the solution if exist. 2x+6y+11=0 6x+20y-6z+3=0 6y-18z+1=0
Answer» ANSWER :No SOLUTION

Discussion

8319.	If s and p are respectively the sum and the product of the slopes of the lines 3x^(2)-2xy-15y=0, then s:p=
Answer» `4:3` `2:3` `3:5` `3:4` ANSWER :B

Discussion

8320.	Find equation of line whose y- intercept is (4)/(3) and perpendicular to the line 3x-4y+11=0.
Answer» ANSWER :`4x+3y-4=0`

Discussion

8321.	2+ 4+ 7 + 11 + 16 + ….. upto n terms is equal to
Answer» `(1)/( 6) ( N^(2) + 3N+ 8)` `(n)/( 6) ( n^(2) + 3n + 8)` `(1)/( 6) ( n^(2) - 3n + 8) ` `(n)/( 6) ( n^(2) - 3n+ 8)` Answer :B

Discussion

8322.	The sum of two numbers is 16. If their product is maximum then the numbers are
Answer» 12,4 10,6 8,8 2,14 Answer :C

Discussion

8323.	For 0 lt x le pi, sin h^(-1)(cot x) =
Answer» `log_(e)(COT""(x)/(2))` `log_(e)(TAN""(x)/(2))` `log_(e)(1+cot x)` `log_(e) (1+tan x)` ANSWER :A

Discussion

8324.	Write each sentence in the " If ................Then " form. Vertical angles are equal.
Answer» ANSWER :If TWO ANGLES are VERTICAL angles, then they are EQUAL.

Discussion

8325.	If one of the lines given by 6x^(2)-xy+4cy^(2)=0 is 3x+4y=0 then 'c' equals
Answer» 1 -1 3 -3 Answer :D

Discussion

8326.	Find the angle whose "sin" e is 0.6479.
Answer» ANSWER :`40^(@)` 23'

Discussion

8327.	Ifsin A cos B = (1)/(4) and 3 tan A = tan Bthen triangle is
Answer» RIGHT ANGLED EQUILATERAL ISOSCELES Scalane ANSWER :A

Discussion

8328.	Consider 3 non-collinear points A(9,3), B(7,-1), and C(1,-1). Let P(a,b) be the center and R is the radius of circle 'S' passing through points A,B,C. Also H(barx,bary) are the coordinates of the othocentre of triangle ABC whose area be denoted by Delta. If D,E and F are the middle points BC,CA and AB respectively then the area of the triangle DEFis
Answer» 12 6 4 3 Answer :A::B::C::D

Discussion

8329.	Consider 3 non-collinear points A(9,3), B(7,-1), and C(1,-1). Let P(a,b) be the center and R is the radius of circle 'S' passing through points A,B,C. Also H(barx,bary) are the coordinates of the othocentre of triangle ABC whose area be denoted by Delta. The value of a+b+R equals
Answer» 3 12 13 none of these Answer :D

Discussion

8330.	Consider 3 non-collinear points A(9,3), B(7,-1), and C(1,-1). Let P(a,b) be the center and R is the radius of circle 'S' passing through points A,B,C. Also H(barx,bary) are the coordinates of the othocentre of triangle ABC whose area be denoted by Delta. The ordered pair (barx,bary) is :
Answer» (9,6) (9,-6) (9,-5) (9,5) ANSWER :B

Discussion

8331.	Find the area of the triangle formed by the vertex and the ends of the latus rectum of the parabola x^(2)=-36y.
Answer» ANSWER :162 SQUARE UNIT.

Discussion

8332.	A function f is defined as follows :f(x) = {{:(0," for ",x lt 0),(x ," for ",0 le x lt 1),(-x^(2)+4x-2," for ",1lexlt3),(4-x ," for ",xge3):}Is the function continuous ?
Answer» ANSWER :It is CONTINUOUS at X =3

Discussion

8333.	If the lines represented by x^(2)-2pxy-y^(2)=0 are rotated about the origin through an
Answer» ANSWER :A

Discussion

8334.	There are two boxes. One box contains 3white balls and 2 black balls. The other boxcontains 7 yellow balls and 3 black balls. If abox is selected at random and from it, a ball isdrawn, the probability that the ball is black is
Answer» `(7)/(20)` `(1)/(5)` `(3)/(20)` `(1)/(3)` Answer :A

Discussion

8335.	There are 8 points in a plane, no three of them are collinear .The number of triangles that canbe formed is:
Answer» 125 900 13 56 Answer :D

Discussion

8336.	Solve the system of equations x-y+z=0,x+2y-z=0,2x+y+3z=0
Answer» ANSWER :`z=0`.

Discussion

8337.	A and B are mutually exclusive events. If P(B)=0.4 and P(A) =0.5 then P(A'capB')=……
Answer» 0.9 0.1 0.2 0.23 Answer :B

Discussion

8338.	Write the negation of the following simple statements. cow has four legs.
Answer» ANSWER :COW does not have FOUR LEGS.

Discussion

8339.	If line (a+4)x +(a^(2)-9)y+(a-4)=0 passes from origin then a = ..............
Answer» ANSWER :4

Discussion

8340.	Solve the equation 5sin^(2)x-7sinx cosx+16cos^(2)x=4
Answer» Solution :To solve this equation we use the fundamental formula of trignometric identities, `sin^(2)x + cos^(2)x=1` writing the equation in the form, `5SIN^(2)x-7sinx.cosx+16cos^(2)x=4(sin^(2)x+cos^(3)x)` `RARR sin^(2)x-7sinxcosx+12cos^(2)x=0` Dividing by `cos^(2)x` on both side we GET `tan^(2)x-7tanx+12=0` Now it can be factorized as: `(tanx-3)(tanx-4)=0` `rArr tanx=3,4` i.e., `tanx=tan(tan^(-1)3)` or `tanx=tan(tan^(-1)4)` `rArr x=npi+tan^(-1)3` or `x=npi+tan^(-1)4, n in I`.ANS.

Discussion

8341.	If the centriod of triangle formed by the lines 2y^(2)+5xy-3x^(2)=0 and x+y=k is ((1)/(18),(11)/(18)) then k =
Answer» `-1` 0 1 2 Answer :C

Discussion

8342.	If alpha,beta are the roots of the equation lamda(x^(2)-x)+x+5=0 and if lamda_(1) and lamda_(2) are two values of lamda obtained from (alpha)/(beta)+(beta)/(alpha)=4, then (lamda_(1))/(lamda_(2)^(2))+(lamda_(2))/(lamda_(1)^(2)) equals.
Answer» 4192 4144 4096 4048 Answer :D

Discussion

8343.	Let A, B C be three angles such that A = pi/4 and tan B tan C = p. Set of all possible values of p such that A, B , C are angles of a triangle.
Answer» `(- infty, infty)` `(- infty, 0)` `(3 + 2 SQRT2, infty)` `(- infty, 0) CUP [3 + 2 sqrt2, infty)` Answer :D

Discussion

8344.	There are three events A, B, and C, one of which one and only one can happen. The oddsare 7 to 4 against A and 3 to 5 favour of B. Find the odds against C.
Answer» ANSWER :`=(65)/(23)`

Discussion

8345.	ABCDEF is a regualar hexagon whose centre is O. Then bar(AB)+bar(AC)+bar(AD)+bar(AE)+bar(AF) is
Answer» `2BAR(AO)` `3BAR(AO)` `5bar(AO)` `6bar(AO)` ANSWER :D

Discussion

8346.	Solve the equation 3cos2theta+2=7sintheta
Answer» Answer :`{NPI+(-1)^(N)(pi)/(6)//ninZ}`

Discussion

8347.	If cosh 2x = 199 , then cothx =
Answer» `(5)/(3 SQRT(11))` `(5)/(6 sqrt(11))` `(7)/(3 sqrt(11))` `(10)/(3 sqrt(11))` Answer :D

Discussion

8348.	If Sin theta = ((a-4)/(2)) then
Answer» `1 le a le 8` `0 le a le 2` `2 le a le 6` `-2 le a le 2` ANSWER :C

Discussion

8349.	The vertices of a DeltaABC are A(1, 1), B(7, 3) and C(3, 6). State the slope ofthe altitude to AC
Answer» ANSWER : `(-2)/(5)`

Discussion

8350.	lim_(xto0)(tanx-5x)/(7x-sinx)=….
Answer» `(2)/(3)` `-(2)/(3)` `(5)/(7)` `-(5)/(7)` ANSWER :B

Discussion

Explore topic-wise InterviewSolutions in .

Differentiate the following functions w.r.t. x: sec ax

If tan5x=cot3x then x=(ninz)

Consider a plane x + y - z= 1 and point A (1,2,-3). A line L has the equation x =1 + 3r ,y =2- r and z =3 + 4r The equation of the plane containing line L and point A has the equation

If Tan40^(@) + 2 Tan 10^(@) = Cotx then x =

The maximum valuue of the function f(x)=Sin(x+pi/6)+Cos(x+pi/6) in the interval (0,pi/2) occurs at x=

Set A has three elements and B = {a, b, c,d} then numbers of elements in 'AxB' are …........

If Delta_1 = |(x,a,b),(b,x,a),(a,b,x)| and Delta_2 = |(x,a),(a,x)| are the given determinants , then

Convert each of the complex numbers given inthe polar form. sqrt(3)-i

Write each of the statement in the form if p, then q: p: It is necessary to have a password to log on the server.

sin 3 theta * cos^(3) theta + cos 3 theta * sin^(3) theta =

Describe the sample space of this experiment : Two dice are rolled .

Solve the following system of equations by using Cramer's rule. x-y+3z=5,4x+2y-z=0,x+3y+z=5.

If s and p are respectively the sum and the product of the slopes of the lines 3x^(2)-2xy-15y=0, then s:p=

Find equation of line whose y- intercept is (4)/(3) and perpendicular to the line 3x-4y+11=0.

2+ 4+ 7 + 11 + 16 + ….. upto n terms is equal to

The sum of two numbers is 16. If their product is maximum then the numbers are

For 0 lt x le pi, sin h^(-1)(cot x) =

Write each sentence in the " If ................Then " form. Vertical angles are equal.

If one of the lines given by 6x^(2)-xy+4cy^(2)=0 is 3x+4y=0 then 'c' equals

Find the angle whose "sin" e is 0.6479.

Ifsin A cos B = (1)/(4) and 3 tan A = tan Bthen triangle is

Consider 3 non-collinear points A(9,3), B(7,-1), and C(1,-1). Let P(a,b) be the center and R is the radius of circle 'S' passing through points A,B,C. Also H(barx,bary) are the coordinates of the othocentre of triangle ABC whose area be denoted by Delta. The value of a+b+R equals

Consider 3 non-collinear points A(9,3), B(7,-1), and C(1,-1). Let P(a,b) be the center and R is the radius of circle 'S' passing through points A,B,C. Also H(barx,bary) are the coordinates of the othocentre of triangle ABC whose area be denoted by Delta. The ordered pair (barx,bary) is :

Find the area of the triangle formed by the vertex and the ends of the latus rectum of the parabola x^(2)=-36y.

A function f is defined as follows :f(x) = {{:(0," for ",x lt 0),(x ," for ",0 le x lt 1),(-x^(2)+4x-2," for ",1lexlt3),(4-x ," for ",xge3):}Is the function continuous ?

If the lines represented by x^(2)-2pxy-y^(2)=0 are rotated about the origin through an

There are two boxes. One box contains 3white balls and 2 black balls. The other boxcontains 7 yellow balls and 3 black balls. If abox is selected at random and from it, a ball isdrawn, the probability that the ball is black is

There are 8 points in a plane, no three of them are collinear .The number of triangles that canbe formed is:

Solve the system of equations x-y+z=0,x+2y-z=0,2x+y+3z=0

A and B are mutually exclusive events. If P(B)=0.4 and P(A) =0.5 then P(A'capB')=……

Write the negation of the following simple statements. cow has four legs.

If line (a+4)x +(a^(2)-9)y+(a-4)=0 passes from origin then a = ..............

Solve the equation 5sin^(2)x-7sinx cosx+16cos^(2)x=4

If the centriod of triangle formed by the lines 2y^(2)+5xy-3x^(2)=0 and x+y=k is ((1)/(18),(11)/(18)) then k =

If alpha,beta are the roots of the equation lamda(x^(2)-x)+x+5=0 and if lamda_(1) and lamda_(2) are two values of lamda obtained from (alpha)/(beta)+(beta)/(alpha)=4, then (lamda_(1))/(lamda_(2)^(2))+(lamda_(2))/(lamda_(1)^(2)) equals.

Let A, B C be three angles such that A = pi/4 and tan B tan C = p. Set of all possible values of p such that A, B , C are angles of a triangle.

There are three events A, B, and C, one of which one and only one can happen. The oddsare 7 to 4 against A and 3 to 5 favour of B. Find the odds against C.

ABCDEF is a regualar hexagon whose centre is O. Then bar(AB)+bar(AC)+bar(AD)+bar(AE)+bar(AF) is

Solve the equation 3cos2theta+2=7sintheta

If cosh 2x = 199 , then cothx =

If Sin theta = ((a-4)/(2)) then

The vertices of a DeltaABC are A(1, 1), B(7, 3) and C(3, 6). State the slope ofthe altitude to AC

lim_(xto0)(tanx-5x)/(7x-sinx)=….