14949 + Interview Questions in Maths in Class 11 Page 85 InterviewSolution

4201.	Find the equation of the circle through the points (0,0), (2,0) and (0,4). Also find the coordinates of its centre and its radius.
Answer» ANSWER :`SQRT(5)`

Discussion

4202.	For any two sets A and B, prove that : P(A)=P(B)rArrA=B
Answer»

Discussion

4203.	If 4bar(i) + (2p)/3 bar(j)+ pbar(k)is parallel to the vector bar(i) + 2bar(j) + 3bar(k), find p.
Answer» ANSWER :p=12

Discussion

4204.	The solution of the inequality log_(1//2)sin^(-1)x gt log_(1//2)cos^(-1)x is
Answer» `X in [0, 1/sqrt(2)]` `x in (1/sqrt(2), 1]` `x in (0, 1/sqrt(2))` none of these Answer :C

Discussion

4205.	Evaluate Lt_(xto0)(1-cos(x))/x^(2)
Answer» ANSWER :`1/2(pi/180)^(2)`

Discussion

4206.	When a circular oil drop expands on water, its area increases at the uniform rate of 40 sq. cm per minute. Find the rate of increase in the radius and circumference of the circle when the radius is 5 cm.
Answer» ANSWER :`4//pi cm//m, 8cm//m`

Discussion

4207.	A_(1),A_(2),A_(3)...........A_(n) are arithmetic mean between two number a and b then a A_1 , A_(2) , ...............An , b becomes arithmetic sequence.
Answer» ANSWER :TRUE STATEMENT

Discussion

4208.	Write down the contrapositive of the following statements.: If x=y and y=3 then x=3
Answer» ANSWER :If `X!=3` then `x!=y` or `y!=3`

Discussion

4209.	Let A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and B = { 2, 3, 5, 7 }. Find A∩ B and hence show that A ∩ B = B.
Answer» ANSWER :`A CAP B= B`

Discussion

4210.	If the plane x + y + z =1 is routated through an angle 90^(@) about its line of intersection with the plane x - 2y + 3z =0, then the new position of the plane is
Answer» `X - 5y + 4z =1` ` x- 5y + 4z =-1` ` x - 8Y + 7Z =2` ` x -8y + 7z =-2` ANSWER :D

Discussion

4211.	A variable plane is at a constant distance 3p from the origin and meets the axes A, B and C. The locus of the centroid of the triangle ABC is
Answer» <P>`x^(-2)+y^(-2)+z^(-2)=p^(-2)` `x^(-2)+y^(-2)+z^(-2)=4P^(-2)` `x^(-2)+y^(-2) +z^(-2)=10P^(-2)` `x^(2)+y^(2)+z^(2)=p^(2)` ANSWER :A

Discussion

4212.	A committee of 3 persons is to be constituted from a group of 2 men and 3 women. a. In how many ways can this be done? b. How many of these committees would consist of 1 man and 2 women?
Answer» ANSWER :6

Discussion

4213.	Angle made by the the arc of length 55 cm at center is ......if length of radius is 25 cm
Answer» ANSWER :`126 ` DEGREE

Discussion

4214.	For agt bgt cgt0, the distance between (1,1) and the point of intersection of the the lines ax+by+c=0 and bx+ay+c=0 less than 2sqrt2. Then and
Answer» `a+B-cgt0` `a-b+clt0` `a-b+clt0` `a+b-cgt0` ANSWER :B

Discussion

4215.	(2,7) is the centroid of the triangle with verticies (4, 8) and (-2, 6) then its third vertex is …........
Answer» `(0,0)` `(4,7)` `(7,4)` `(7,7)` ANSWER :B

Discussion

4216.	Show that the tangent of an angle between the lines (x)/(a) + (y)/( b) = 1 and (x)/( a) - (y)/( b) = 1 is (2 ab)/( a^(2) - b^(2) ).
Answer» ANSWER :`theta= TAN^(-1)""((2ab)/( a^(2) - B^(2) ))`

Discussion

4217.	sin^(-1)(x^(2)+2x+2)+tan^(-1)(x^(2)-3x-k^(2))gt(pi)/2 for k in
Answer» (-1,0) (0,1) (1,2) (0,2) ANSWER :A::B::C::D

Discussion

4218.	Evaluate the following limits. Lt_(xto0)(sinax)/(xcosx)
Answer» ANSWER :a

Discussion

4219.	A staight line through the point A(3,4) is such that its intercept between the axes is bisected at A. Its equation is
Answer» `x+y =7` `3x-4y+7=0` `4x+3y=24` `3x+4y=25` ANSWER :C

Discussion

4220.	7^(13) + 6^(13) is divisible by
Answer» `13` `26` `42` `85` ANSWER :A

Discussion

4221.	Write down the contrapositive of the following statements.: If x and y are negative integers, then x.y is positive.
Answer» ANSWER :NEGATIVE INTEGER.

Discussion

4222.	For all sets A and B, A cup (B - A) = A cup B.
Answer» ANSWER :R.H.S.

Discussion

4223.	Using binomial theorem, evaluate : (999)^(3).
Answer» ANSWER :997002999

Discussion

4224.	Find lim_(nrarrinfty) 1/2.3 +1/3.4 +……
Answer» ANSWER :`1/2`

Discussion

4225.	Find the equation of circle passing through the points (1,-2) and (3,-4) and touches the X-axis.
Answer» ANSWER :`X^(2)+y^(2)+10x+20y+25=0orx^(2)+y^(2)-6x+4y+9=0`

Discussion

4226.	Evaluate the following limits : Lim_(x to 0) (3^(x)-1)/x
Answer» ANSWER :LOG 3

Discussion

4227.	If sin^3 x cos 3x + cos^3 x sin 3x= 3//8 , then the value of 8 sin 4x is ............
Answer» ANSWER :4

Discussion

4228.	Find the acute angle between pair of lines represented by following equations. x^(2)-7xy+12y^(2)=0
Answer» ANSWER :`TAN^(-1)((1)/(13))`

Discussion

4229.	Obtain equation of ellipse satisfying given conditions Foci (0, pm 4) and eccentricity (4)/(5)
Answer» ANSWER :`(x^(2))/(9) + (y^(2))/(25) = 1`

Discussion

4230.	If P,Q are two points on the line 3x+4y+15=0 such that OP=OQ=9, then the area of DeltaOPQ is
Answer» `6sqrt(2)` `9sqrt(2)` `12SQRT(2)` `18sqrt(2)` ANSWER :D

Discussion

4231.	Differentiate by first principle f(x)=sqrt(3x+4)
Answer» ANSWER :`(3)/(2sqrt(3)x+4))`

Discussion

4232.	Let bara = bari+barj+bark and barb =2bari+3barj+bark. Find The vector components of barb "in the direction " bara " and perpendicular to that of " bara.
Answer» ANSWER :`2bari+2barj+2bark and BARI -BARK`

Discussion

4233.	Find Lt_(xtooo)([ax+b])/x(agt0). Where [.] denotes GIF.
Answer» ANSWER :a

Discussion

4234.	Which one of the following is equal to {x:x inR,2ltxle4} a){2,3,4} b){3,4} c){2,4} d){2,3}
Answer» {2,3,4} {3,4} {2,4} {2,4} ANSWER :D

Discussion

4235.	Prove that tan 7 (1^(@))/(2) = sqrt2 - sqrt3-sqrt4 + sqrt6 = (sqrt3 - sqrt2) (sqrt2 -1).
Answer» ANSWER :`(SQRT2 -1)`

Discussion

4236.	Show that the points A(0,1,2),B(2,-1,3)a n dC(1,-3,1)are vertices of an isosceles right-angled triangle.
Answer» ANSWER :AB=BC

Discussion

4237.	Evaluate Lt_(x to 0)(log(1 + x^3))/(sin^3 x)
Answer» ANSWER :1

Discussion

4238.	With the help of tables, find the values, correct to places of decimals, of each of the following : sin267^(@)
Answer» ANSWER :`-0.9986`

Discussion

4239.	If the system of equations x+2y+3z=lamdax,3x+y+2z=lamday,2x+3y+z=lamdaz has non trivial solution then lamda=
Answer» 6 12 18 16 Answer :A

Discussion

4240.	Find the value of x and y given that (x + yi) (2-3i)=4+i
Answer» ANSWER :`X= (5)/(13), y= (14)/(13)`

Discussion

4241.	Esamine whether the following statements are true or false : (i) {a,b} cancel(sub) {b,c} (ii) {a} in {a,b,c} (iii){phi} sub {a, b, c } (iv) {a,e} sub {x:x " is a vowel in the English alphabet "} (v) {x:xin W, x+5 =5}=phi (vi)a in {{a} , b} (vii) {a} sub {{a},b} (viii) {b,c} sub {a, c}} (ix) {a,a,b,b}={a,b} (x) {a,b,a, b,a,b...} " is an infinte set". (xi) If A= set of all circles of unit radius in a plane and B= set of all circles in the same plane thenA sub B.
Answer» Solution :(ii) `a in {a,b,c}` is true, So, ` {a}, in { a,b,c}` is a false. (iii) `phi sub {a,b,c} " is true and " {phi} sub { a,b,c}` is false. (iv) `{a, E} sub {a, e, i,o,u}` is true. (V) ` {X:xin W, x + 5=5}={0}`. (vi) `{{a} , b }` has two elements , namely `{a}` and b. (vii) `{a}in {{ a} , b}`. So `{a}, sub {{a} , b}` is false. (viii) ` {b,c} in {a, {b, c}}`. So , ` {b, c } sub {a,{b,c}}` is false (ix) REPETITION of elements in a set has no meaning. (x) Given set ` = {a,b}`, which is finite.

Discussion

4242.	The periodof Sin (sinx ) + Sin (Cosx)is
Answer» `PI` `2PI` `(pi)/(2)` `(pi)/(4)` ANSWER :2

Discussion

4243.	Approximate value of sqrt(4.08) is
Answer» 2 2.02 2.0291 2.04 Answer :B

Discussion

4244.	Statement-1 : The digit in the unit place of 183!+3^( 183) is 7. Statement-2: 183! have unit place 0 and 3^( 4k+3) ends with 7.
Answer» Statement-1 is TRUE, Statement-2 is true, Statement-2 is not a CORRECT EXPLANATION for Statement-1. Statement-1 is true, Statement-2 is FALSE. Statement-1 is false, Statement-2 is true. Statement-1 is true, Statement-2 is true, Statement-2 is correct explanation for Statement-1. Answer :D

Discussion

4245.	If sin alpha = A sin (alpha+beta), A ne 0 then The value of tan beta is
Answer» `(SIN alpha(1+A COS beta))/(A cos alpha cos beta)` `(sin alpha(1-A cos beta))/(A cos alpha cos beta)` `(cos alpha(1-A sin beta))/(A cos alpha cos beta)` `(cos alpha(1+A sin beta))/(A cos alpha cos beta)` Answer :B

Discussion

4246.	If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8 } and D = { 7, 8, 9, 10 }, find A ∪ C
Answer» ANSWER :`{1, 2, 3, 4, 5, 6, 7,8 }`

Discussion

4247.	cot x = 3/4,x lies in third quadrant.
Answer» ANSWER :`SIN X =- 4/5, cosec x =- 5/4, COS x =- 3/5, sec x =- 5/3, TAN x =- 4/3`

Discussion

4248.	sin^(3)20^(@)+sin^(3)40^(@)-sin^(3)80^(@)=
Answer» `(3SQRT3)/8` `-(3sqrt3)/8` `(3sqrt3)/2` 0 Answer :B

Discussion

4249.	If f: R to Ris defined by f(x)=7+ cos(5x+3) " for " x in R , then the period of f is
Answer» `2PI` `PI` `(pi)/(5)` `(2pi)/(5)` ANSWER :D

Discussion

4250.	If f(x)={{:(mx^(2)+n","xlt0),(nx+m","0lexle1),(nx^(3)+m","xgt1):} For what integers m and n does both lim_(xto0)f(x) and lim_(xto1)f(x) exist?
Answer» Answer :For `lim_(xrarr0)f(X)` to EXISTS, we need `m=N;lim_(xrarr1)f(x)` exists for any integral VALUE of m and n.

Discussion

Explore topic-wise InterviewSolutions in .

Find the equation of the circle through the points (0,0), (2,0) and (0,4). Also find the coordinates of its centre and its radius.

For any two sets A and B, prove that : P(A)=P(B)rArrA=B

If 4bar(i) + (2p)/3 bar(j)+ pbar(k)is parallel to the vector bar(i) + 2bar(j) + 3bar(k), find p.

The solution of the inequality log_(1//2)sin^(-1)x gt log_(1//2)cos^(-1)x is

Evaluate Lt_(xto0)(1-cos(x))/x^(2)

When a circular oil drop expands on water, its area increases at the uniform rate of 40 sq. cm per minute. Find the rate of increase in the radius and circumference of the circle when the radius is 5 cm.

A_(1),A_(2),A_(3)...........A_(n) are arithmetic mean between two number a and b then a A_1 , A_(2) , ...............An , b becomes arithmetic sequence.

Write down the contrapositive of the following statements.: If x=y and y=3 then x=3

Let A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and B = { 2, 3, 5, 7 }. Find A∩ B and hence show that A ∩ B = B.

If the plane x + y + z =1 is routated through an angle 90^(@) about its line of intersection with the plane x - 2y + 3z =0, then the new position of the plane is

A variable plane is at a constant distance 3p from the origin and meets the axes A, B and C. The locus of the centroid of the triangle ABC is

A committee of 3 persons is to be constituted from a group of 2 men and 3 women. a. In how many ways can this be done? b. How many of these committees would consist of 1 man and 2 women?

Angle made by the the arc of length 55 cm at center is ......if length of radius is 25 cm

For agt bgt cgt0, the distance between (1,1) and the point of intersection of the the lines ax+by+c=0 and bx+ay+c=0 less than 2sqrt2. Then and

(2,7) is the centroid of the triangle with verticies (4, 8) and (-2, 6) then its third vertex is …........

Show that the tangent of an angle between the lines (x)/(a) + (y)/( b) = 1 and (x)/( a) - (y)/( b) = 1 is (2 ab)/( a^(2) - b^(2) ).

sin^(-1)(x^(2)+2x+2)+tan^(-1)(x^(2)-3x-k^(2))gt(pi)/2 for k in

Evaluate the following limits. Lt_(xto0)(sinax)/(xcosx)

A staight line through the point A(3,4) is such that its intercept between the axes is bisected at A. Its equation is

7^(13) + 6^(13) is divisible by

Write down the contrapositive of the following statements.: If x and y are negative integers, then x.y is positive.

For all sets A and B, A cup (B - A) = A cup B.

Using binomial theorem, evaluate : (999)^(3).

Find lim_(nrarrinfty) 1/2.3 +1/3.4 +……

Find the equation of circle passing through the points (1,-2) and (3,-4) and touches the X-axis.

Evaluate the following limits : Lim_(x to 0) (3^(x)-1)/x

If sin^3 x cos 3x + cos^3 x sin 3x= 3//8 , then the value of 8 sin 4x is ............

Find the acute angle between pair of lines represented by following equations. x^(2)-7xy+12y^(2)=0

Obtain equation of ellipse satisfying given conditions Foci (0, pm 4) and eccentricity (4)/(5)

If P,Q are two points on the line 3x+4y+15=0 such that OP=OQ=9, then the area of DeltaOPQ is

Differentiate by first principle f(x)=sqrt(3x+4)

Let bara = bari+barj+bark and barb =2bari+3barj+bark. Find The vector components of barb "in the direction " bara " and perpendicular to that of " bara.

Find Lt_(xtooo)([ax+b])/x(agt0). Where [.] denotes GIF.

Which one of the following is equal to {x:x inR,2ltxle4} a){2,3,4} b){3,4} c){2,4} d){2,3}

Prove that tan 7 (1^(@))/(2) = sqrt2 - sqrt3-sqrt4 + sqrt6 = (sqrt3 - sqrt2) (sqrt2 -1).

Show that the points A(0,1,2),B(2,-1,3)a n dC(1,-3,1)are vertices of an isosceles right-angled triangle.

Evaluate Lt_(x to 0)(log(1 + x^3))/(sin^3 x)

With the help of tables, find the values, correct to places of decimals, of each of the following : sin267^(@)

If the system of equations x+2y+3z=lamdax,3x+y+2z=lamday,2x+3y+z=lamdaz has non trivial solution then lamda=

Find the value of x and y given that (x + yi) (2-3i)=4+i

The periodof Sin (sinx ) + Sin (Cosx)is

Approximate value of sqrt(4.08) is

Statement-1 : The digit in the unit place of 183!+3^( 183) is 7. Statement-2: 183! have unit place 0 and 3^( 4k+3) ends with 7.

If sin alpha = A sin (alpha+beta), A ne 0 then The value of tan beta is

If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8 } and D = { 7, 8, 9, 10 }, find A ∪ C

cot x = 3/4,x lies in third quadrant.

sin^(3)20^(@)+sin^(3)40^(@)-sin^(3)80^(@)=

If f: R to Ris defined by f(x)=7+ cos(5x+3) " for " x in R , then the period of f is

If f(x)={{:(mx^(2)+n","xlt0),(nx+m","0lexle1),(nx^(3)+m","xgt1):} For what integers m and n does both lim_(xto0)f(x) and lim_(xto1)f(x) exist?