14949 + Interview Questions in Maths in Class 11 Page 170 InterviewSolution

8451.	How many terms of the A.P. 54, 51, 48,……are needed to give the sum 513?
Answer» ANSWER :18 or 19

Discussion

8452.	If the angles of a triangle are in AP and the least angle is 30^(@) .Then , the geatest angle (in radian ) is
Answer» `(7 PI)/12` `(2 pi)/3` `(5 pi)/6` `pi/2` Answer :D

Discussion

8453.	Find the coordinates of the foci, the vertices, the lengths of major and minor axes and the eccentricity of the ellipse 9x^(2)+4y^(2)=36
Answer» ANSWER :Foci are `(0, SQRT(5)) and (0, - sqrt(5))`,Vertices are (0,3) and (0, -3), Length of the major axis is 6 units, the length of the minor axis is 4 units and the eccentricity of the ELLIPSE is `(sqrt(5))/(3)`

Discussion

8454.	lim_(x to0) (sin (pi cos^(2)x))/(x^(2)) is equal to ,
Answer» `(PI)/(2)` 1 `-pi` `pi` ANSWER :D

Discussion

8455.	............are the total numbers words formed by the letters of the word 'KUMAR' .
Answer» ANSWER :120

Discussion

8456.	How many four digit numbers divisible by 4 can be made with the digit 1, 2, 3, 4, 5, 6. If the repetition of the digit is not allowed ?
Answer» ANSWER :96

Discussion

8457.	If 2x^2-5xy+2y^2=0 represents two equal sides of an isosceless triangle andthird side passing through (3/2,3/2) then equation of third side is
Answer» x+y-1=0 x-y+3=0 x+y-3=0 x+y-6=0 Answer :C

Discussion

8458.	Are the points A(3, 6, 9), Q(10, 20, 30) and C(25, -41, 5), the vertices of a right angled triangle ?
Answer» ANSWER :`AB^(2)+BC^(2)NEAC^(2)`

Discussion

8459.	Differentiate the following functions w.r.t. x: tan 2x
Answer» ANSWER :`2 SEC^(2) 2X

Discussion

8460.	The vertices of a triangle are (1,4), (2,-5) and (3,7). Prove that its medians meet at one point.
Answer»

Discussion

8461.	Calculate the mean deviation and coefft. of mean deviation for the following frequency distribution from both mean and median.
Answer» Answer :(i) Mean DEVIATION = 8.09 COEFFT. of mean deviation = 0.355 (II) Median deviation = 7.9 Coefft. of mean deviation = 0.395

Discussion

8462.	Simplify: (sqrt(-2))/(sqrt(-8))
Answer» ANSWER :`(1)/(2)`

Discussion

8463.	Determine the mode for the following observations : 10,11,10,12,11,10,11,11,11,12,13,11,12.
Answer» ANSWER :11

Discussion

8464.	Evaluate the following limits : Lim_(x to oo) (3x^(2)+x-1)/(x^(2)-x+7)
Answer» ANSWER :`OO`

Discussion

8465.	Find the value of f(0) so thatf (x) = (1 + 2x)^(1//3x)is continuous at x = 0
Answer» ANSWER :`E^(2//3)`

Discussion

8466.	Find out which of the following sentences are statements and which are not. Justify your answer .br The earth is a planet
Answer» SOLUTION :STATEMENT

Discussion

8467.	Find equation of line passess from point (2, 3) and cuts line segment of length ( 2 sqrt2)/( 3). between the lines 2x + y = 3 and 2x + y = 5.
Answer» Answer :`x - y + 1 = 0, X - 7Y + 19 = 0`

Discussion

8468.	1 to 7, describe the sample space for the indicated experiment. A die is thrown two times.
Answer» ANSWER :`S={(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)` `{(2,1) (2,2) (2,3) (2,4), (2,5) (2,6)` `{(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)` `{(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)` `{(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)` `{(6,1) (6,2), (6,3) (6,4) (6,5) (6,6)`

Discussion

8469.	Which of the following sentences are statements? Justify Every set is an infinite set.
Answer» ANSWER :It is STATEMENT.

Discussion

8470.	If alphabe a repeated root of a quadratic equation f(x) = 0 and A(x),B(x) , C(x) be polynomials of degree 3,4,5 respectively , then F(x)=\|(A(x),B(x),C(x)),(A(alpha),B(alpha),C(alpha)),(A^1(alpha),B^1(alpha),C^1(alpha))\|
Answer» not DIVISIBLE by `(x-alpha)` divisible by `(x -alpha)` , not by `(x -alpha)^2` divisible by `(x-alpha)^2` , not by F(x) divisible by f(x) Answer :D

Discussion

8471.	One die of red colour, one of die white colour and one of blue colour are placed in a bag. One die is selected at random and rolled, its colour and the number on its uppermost face is noted. Describe the sample space.
Answer» Answer :{R1, R2, R3, R4, R5, R6, W1, W2, W3, W4, W5, W6, B1, B2, B3, B4, B5, B6}

Discussion

8472.	How many committeeof five person with a chairperson can be selected from 12 persons ?
Answer» ANSWER :` = 12 X 330 = 3960`

Discussion

8473.	If 1/2tan^(-1)((2x)/(x^(2)-1))+"cos"^(-1)(x^(2)-1)/(x^(2)+1)=(2pi)/3 then x=
Answer» `2-SQRT(3)` `sqrt(3)-sqrt(2)` `2+sqrt(3)` `+sqrt(3)` ANSWER :A

Discussion

8474.	If f''(x) = 12x - 6 and f(1) = 30 , f' (1) = 5 find f(x)
Answer» Answer :`F(x) = 2x^(3) - 3X^(2) + 5x + 26`

Discussion

8475.	Image of (2,3) w.r.t to (-1,3) is
Answer» (3,-2) (1,1) (-4,3) (3,7) ANSWER :C

Discussion

8476.	three identical dice are rolled . Find the probability that the same number will appear on each of them .
Answer» ANSWER :`=(1)/(36)`.

Discussion

8477.	Find the domain of the following functions. f(x)= (1)/(sqrt(x + \|x\|))
Answer» ANSWER :`(0, OO)`

Discussion

8478.	Find the coefficient of : x^(11) " in " (x^(3)-2/(x^(2)))^(12)
Answer» ANSWER :`-25344`

Discussion

8479.	Find the domain of the following functions. f(x)= (1)/(sqrt(x-\|x\|))
Answer» ANSWER :`PHI`

Discussion

8480.	Find the sum to 10 terms of 1 + sqrt(3) +3 + ....
Answer» ANSWER :121`( SQRT(3)+1))`

Discussion

8481.	f:R rarr R , f(x)=(x^(2)+4x+30)/(x^(2)-8x+18) is
Answer» one-one & onto many-one & onto one-one & into many-one & into Answer :D

Discussion

8482.	A plane containing the point (3,2,0) and the line (x-1)/(1) = (y-2)/(5) = (z-3)/(4)and also contains the point
Answer» `(0, -3 ,1)` `(0, 7, 10)` `(0, 7, -10)` `(0,3,1)` ANSWER :A

Discussion

8483.	Assertion (A): The points A(2,3,5) B(4,6,10), C(8,12,20) are collinear. Reason (R ) : Two lines will be parallel if their D.R's are proportional.
Answer» Both A and R are ture and R is the CORRECT explanation of A Both A and R are TRUE but R is notthe correct explanation of A A is true but R is false A is false But R is true Answer :A

Discussion

8484.	If -(pi)/2 lt alpha lt (pi)/2 then prove that tan^(-1)((3sin 2 alpha)/(5+3 cos alpha))+tan^(-1)((tan alpha)/4)=
Answer» `ALPHA` `2ALPHA` `3 alpha` `4alpha` ANSWER :A

Discussion

8485.	The sets S_(1) , S_(2) , S_(3) , …. are given by S_(1) = {(2)/(1) } , S_(2) = { (3)/(2) , (5)/(2) } , S_(3) = { (4)/(3) , (7)/( 3) , (10)/( 3) } , S_(4) = { ( 5)/( 4) , (9)/( 4) , (13)/( 4) , (17)/( 4) }, ….. then the sum of the numbers in the set S_25) is
Answer» `322` `324` `325` `326` ANSWER :D

Discussion

8486.	Assertion (A) :f(x) = (1)/( 1 + e^(1//e))(x ne 0) " and " f(0) = 0is right continuous at x = 0 Reason (R) : underset(x to 0+)(Lt ) (1)/(1 + e^(1//x)) = 0The correct answer is
Answer» Both (A) and (R) are true and (R)is the CORRECT explanation of (A) Both (A) and (R)are true and (R)is not the correct explanation of (A) (A) is true but (R) is FALSE (A) is false but (R) is TURE ANSWER :A

Discussion

8487.	A(2, 5), B(4, -11) are two fixed points and C is a point which moves on the line 3x+4y+5=0. Find the locus of the centroid of the triangle ABC.
Answer» ANSWER : `9x+12y+11=0`

Discussion

8488.	If the Point (a^3//(a-1),(a^2-3)//(a-1)),(b^2//(b-1),(b^2-3)//(b-1)), and (c^3//c-1,(c^2-3)/(c-1)), where a,b,c are different from 1, lie on the line lx+my+n=0 then
Answer» `a+b+c=-m/L` `ab+bc+ca=n/l` `abc=((m+n))/l` `abc-(bc+ca+ab)+3(a+b+c)=0` Answer :A::C

Discussion

8489.	Let A be a non-empty set of real numbers and f:A rarr A be such that f(f(x))=x for all x in A. Then f is
Answer» a biection one-one but not onto onto but not one-one neither one-one nor onto Answer :A

Discussion

8490.	If (a,a^(2)) falls inside the angle made of the lines y=x/2,xgt0 and y=3x,xgt0 then a belongs to
Answer» `(0,1/2)` `(3,OO)` `(1/2,3)` `(-3,-1/2)` ANSWER :C

Discussion

8491.	If alpha,beta are the roots of ax^(2)+bx+c=0, find the value of (i) ((alpha)/(beta)-(beta)/(alpha))^(2) (ii) (alpha^(3))/(beta)+(beta^(3))/(alpha).
Answer» Answer :(i) `(b^(2)(b^(2)-4ac))/(a^(2)C^(2))` (ii) `(b^(4)+2A^(2)c^(2)-4ab^(2)c)/(a^(3)c)`.

Discussion

8492.	A can hit a target 4 times out of 5 trial. B can hit 3 times of 4 trials and C can hit 2 times out of 3 trials. If all three hit the target sumultaneously, find the probability of hitting the target.
Answer» SOLUTION :N/a

Discussion

8493.	In triangle ABC , a = 4, b = 3 and angle A = 60^(@). Thenc is root of the equation
Answer» `C^(2) - 3C + 7 = 0 ` `c^(2) + 3c - 7 = 0 ` `c^(2) + 3c + 7 = 0 ` `c^(2) - 3c - 7 = 0 ` ANSWER :D

Discussion

8494.	XOY'Z represents third octant.
Answer» ANSWER :TRUE STATEMENT

Discussion

8495.	If acos2theta+bsin2theta=c has alphaandbeta as its roots, then prove that tanalpha+tanbeta=(2b)/(a+c).
Answer» ANSWER :`(2B)/(a+c)`

Discussion

8496.	If [sin^(-1)cos^(-1)sin^(-1)tan^(-1)x]=1, where [.] denotes the greatest integer function, then x is given by the interval
Answer» `[TAN SIN COS 1, tan sin cos sin 1]` `(tan sin cos 1, tan sin cos sin 1)` `[-1,1]` `[sin cos tan 1, sin cos sin tan 1]` ANSWER :A

Discussion

8497.	If tan(picostheta)=cot(pisintheta) then the value of cos(theta-(pi)/(4)) is ……….
Answer» `(1)/(sqrt(2))` `PM(1)/(2sqrt(2))` `pm(1)/(2)` `pm1` ANSWER :B

Discussion

8498.	If tantheta_(1), tantheta_(2),tan theta_(3), and tantheta_(4) are the roots of the equation x^4-x^3sin2beta+x^2cos2beta-xcos beta -sin beta = 0 then tan(theta_(1)+theta_(2)+theta_(3)+theta_4) is equal to
Answer» `SIN BETA` `cos beta` `TAN beta ` `cot beta` ANSWER :D

Discussion

8499.	A die is thrown once . Find P(an even number ),
Answer» ANSWER :`(3).(6),i.e,(1)/(2)`

Discussion

8500.	Obtain the equation of the line which satisfying given condition : (1) Passes from points A(-1, 8) and B(4, -2).
Answer» ANSWER :`2X + y - 6 = 0`

Discussion

Explore topic-wise InterviewSolutions in .

How many terms of the A.P. 54, 51, 48,……are needed to give the sum 513?

If the angles of a triangle are in AP and the least angle is 30^(@) .Then , the geatest angle (in radian ) is

Find the coordinates of the foci, the vertices, the lengths of major and minor axes and the eccentricity of the ellipse 9x^(2)+4y^(2)=36

lim_(x to0) (sin (pi cos^(2)x))/(x^(2)) is equal to ,

............are the total numbers words formed by the letters of the word 'KUMAR' .

How many four digit numbers divisible by 4 can be made with the digit 1, 2, 3, 4, 5, 6. If the repetition of the digit is not allowed ?

If 2x^2-5xy+2y^2=0 represents two equal sides of an isosceless triangle andthird side passing through (3/2,3/2) then equation of third side is

Are the points A(3, 6, 9), Q(10, 20, 30) and C(25, -41, 5), the vertices of a right angled triangle ?

Differentiate the following functions w.r.t. x: tan 2x

The vertices of a triangle are (1,4), (2,-5) and (3,7). Prove that its medians meet at one point.

Calculate the mean deviation and coefft. of mean deviation for the following frequency distribution from both mean and median.

Simplify: (sqrt(-2))/(sqrt(-8))

Determine the mode for the following observations : 10,11,10,12,11,10,11,11,11,12,13,11,12.

Evaluate the following limits : Lim_(x to oo) (3x^(2)+x-1)/(x^(2)-x+7)

Find the value of f(0) so thatf (x) = (1 + 2x)^(1//3x)is continuous at x = 0

Find out which of the following sentences are statements and which are not. Justify your answer .br The earth is a planet

Find equation of line passess from point (2, 3) and cuts line segment of length ( 2 sqrt2)/( 3). between the lines 2x + y = 3 and 2x + y = 5.

1 to 7, describe the sample space for the indicated experiment. A die is thrown two times.

Which of the following sentences are statements? Justify Every set is an infinite set.

If alphabe a repeated root of a quadratic equation f(x) = 0 and A(x),B(x) , C(x) be polynomials of degree 3,4,5 respectively , then F(x)=|(A(x),B(x),C(x)),(A(alpha),B(alpha),C(alpha)),(A^1(alpha),B^1(alpha),C^1(alpha))|

One die of red colour, one of die white colour and one of blue colour are placed in a bag. One die is selected at random and rolled, its colour and the number on its uppermost face is noted. Describe the sample space.

How many committeeof five person with a chairperson can be selected from 12 persons ?

If 1/2tan^(-1)((2x)/(x^(2)-1))+"cos"^(-1)(x^(2)-1)/(x^(2)+1)=(2pi)/3 then x=

If f''(x) = 12x - 6 and f(1) = 30 , f' (1) = 5 find f(x)

Image of (2,3) w.r.t to (-1,3) is

three identical dice are rolled . Find the probability that the same number will appear on each of them .

Find the domain of the following functions. f(x)= (1)/(sqrt(x + |x|))

Find the coefficient of : x^(11) " in " (x^(3)-2/(x^(2)))^(12)

Find the domain of the following functions. f(x)= (1)/(sqrt(x-|x|))

Find the sum to 10 terms of 1 + sqrt(3) +3 + ....

f:R rarr R , f(x)=(x^(2)+4x+30)/(x^(2)-8x+18) is

A plane containing the point (3,2,0) and the line (x-1)/(1) = (y-2)/(5) = (z-3)/(4)and also contains the point

Assertion (A): The points A(2,3,5) B(4,6,10), C(8,12,20) are collinear. Reason (R ) : Two lines will be parallel if their D.R's are proportional.

If -(pi)/2 lt alpha lt (pi)/2 then prove that tan^(-1)((3sin 2 alpha)/(5+3 cos alpha))+tan^(-1)((tan alpha)/4)=

The sets S_(1) , S_(2) , S_(3) , …. are given by S_(1) = {(2)/(1) } , S_(2) = { (3)/(2) , (5)/(2) } , S_(3) = { (4)/(3) , (7)/( 3) , (10)/( 3) } , S_(4) = { ( 5)/( 4) , (9)/( 4) , (13)/( 4) , (17)/( 4) }, ….. then the sum of the numbers in the set S_25) is

Assertion (A) :f(x) = (1)/( 1 + e^(1//e))(x ne 0) " and " f(0) = 0is right continuous at x = 0 Reason (R) : underset(x to 0+)(Lt ) (1)/(1 + e^(1//x)) = 0The correct answer is

A(2, 5), B(4, -11) are two fixed points and C is a point which moves on the line 3x+4y+5=0. Find the locus of the centroid of the triangle ABC.

If the Point (a^3//(a-1),(a^2-3)//(a-1)),(b^2//(b-1),(b^2-3)//(b-1)), and (c^3//c-1,(c^2-3)/(c-1)), where a,b,c are different from 1, lie on the line lx+my+n=0 then

Let A be a non-empty set of real numbers and f:A rarr A be such that f(f(x))=x for all x in A. Then f is

If (a,a^(2)) falls inside the angle made of the lines y=x/2,xgt0 and y=3x,xgt0 then a belongs to

If alpha,beta are the roots of ax^(2)+bx+c=0, find the value of (i) ((alpha)/(beta)-(beta)/(alpha))^(2) (ii) (alpha^(3))/(beta)+(beta^(3))/(alpha).

A can hit a target 4 times out of 5 trial. B can hit 3 times of 4 trials and C can hit 2 times out of 3 trials. If all three hit the target sumultaneously, find the probability of hitting the target.

In triangle ABC , a = 4, b = 3 and angle A = 60^(@). Thenc is root of the equation

XOY'Z represents third octant.

If acos2theta+bsin2theta=c has alphaandbeta as its roots, then prove that tanalpha+tanbeta=(2b)/(a+c).

If [sin^(-1)cos^(-1)sin^(-1)tan^(-1)x]=1, where [.] denotes the greatest integer function, then x is given by the interval

If tan(picostheta)=cot(pisintheta) then the value of cos(theta-(pi)/(4)) is ……….

If tantheta_(1), tantheta_(2),tan theta_(3), and tantheta_(4) are the roots of the equation x^4-x^3sin2beta+x^2cos2beta-xcos beta -sin beta = 0 then tan(theta_(1)+theta_(2)+theta_(3)+theta_4) is equal to

A die is thrown once . Find P(an even number ),

Obtain the equation of the line which satisfying given condition : (1) Passes from points A(-1, 8) and B(4, -2).