14949 + Interview Questions in Maths in Class 11 Page 86 InterviewSolution

4251.	Find image of point (-8, 12) with respect to line 4x+7y+ 13=0.
Answer» ANSWER :`(-16, -2)`

Discussion

4252.	The 9th term of an AP is equal to 6 times the second term. If its 5th term is 22 find the AP.
Answer» 0 22 198 220 Answer :A

Discussion

4253.	A vertical pole subtends an angle Tan^-1(1/2) at a point P on the ground. IF the angles subtended by the upper half and the lower half of the pole at P are respectively alpha and beta, then (tan alpha , tan beta)=
Answer» `(1/4,1/5)` `(1/5,2/9)` `(2/9,1/4)` `(1/4,2/9)` ANSWER :B

Discussion

4254.	If 0 lt theta lt pi, then minimum value of 3 sin theta + cosec^(3) theta is
Answer» 4 3 5 6 Answer :D

Discussion

4255.	The slop of the tangent to the curce at a point (x,y) on it is proportional to (x-2). If the slop of the tangent ot the curve at (10,-9) on it is -3, then the equation of the curcve is
Answer» `y=k(x-y)^(2)` `y=(-3)/(16)(x-2)+1` `y=(-3)/(16)(x-2)^(2)+3` `y=(-3)/(8)(x-2)^(2)+3` Answer :C

Discussion

4256.	Show that the angle of rotation of the axes to eliminate xy term in the equation ax^(2) + 2hxy + by^(2) = 0 " is " (1)/(2) Tan^(-1) ((2h)/(a - b)) " when " a ne b and pi //4 when a = b
Answer» ANSWER :`RARR 2 THETA = PI //2 rArr theta = pi//4`

Discussion

4257.	If ABC is a triangle and tan"" (A)/(2) , tan"" (B)/(2) , tan "" (C )/( 2) are in H.P. then the minimum value of cot"" (B)/(2) is equal to
Answer» `- SQRT3` `sqrt3` `2` `-2` ANSWER :B

Discussion

4258.	Find n If : ""^(n)P_4 : "" ^(n-1)P_3 = 9: 1
Answer» ANSWER :` 9`

Discussion

4259.	If I_(n)is the area of n-sided regular polygon inscribed in a circle of unit radius and O_(n)be the area of the polygon circumscribing the given circle, then (O_(n)(1 + sqrt(1 - ((2I_(n))/n)^(2))))/I_(n) =
Answer» 1 2 3 4 Answer :B

Discussion

4260.	Evaluate the following limits : Lim_(x to 0 ) (tan (x+a) -tana)/(3x)
Answer» ANSWER :`1/3 SEC^(2)a `

Discussion

4261.	If the sum of the first 4 terms of an arithmetic progression is p, the sum of the first 8 terms is q and the sum of the first 12 terms is r, express 3p+r in terms of q.
Answer» ANSWER :3p-r =3Q

Discussion

4262.	If 4 cot 2 theta = cot^(2) theta - tan ^(2) theta " then " theta =
Answer» `n pi PM (pi)/(6) , n in Z` `n pi pm (pi)/(3) , n in Z` `n pi pm (pi)/(4), n in Z` `(2 n + 1) pm (pi)/(2), n in Z` Answer :C

Discussion

4263.	Find the point at which is shifted such that the transformed equations of the following equations has no first degree term : (i) 2x^(2)+3y^(2)+4x-12y+10=0 (ii) x^(2)+y^(2)-xy-5x+4y+5=0
Answer» ANSWER :`(i) (-1,2)` `(II) (2,-1)`

Discussion

4264.	If f(x)=(9^(x))/(9^(x)+3) then f((1)/(1996))+f((2)/(1996))+.......+f((1995)/(1996))=
Answer» 997 997.5 998 998.5 Answer :B

Discussion

4265.	Domain of f(x)= sqrt(a^(2)-x^(2)) (a gt 0) is
Answer» `(-a, a)` `[-a, a]` `[0, a]` `(-a, 0]` ANSWER :B

Discussion

4266.	Write the values of i^2, i^4 and i^6
Answer» ANSWER :`-1, 1, -1`

Discussion

4267.	If 2x + 3y = 7 makes equal angles with pair of lines 9x^(2)+12xy+ky^(2)=0 then k=
Answer» 7 14 `-14` `-7` ANSWER :B

Discussion

4268.	Show that y=ax^(2)+bx+c represents a parabola. Also find equation its axis.
Answer» ANSWER :`X=(-B)/(2A)`

Discussion

4269.	Find what values of a so that the expression x^(2)-(a+2)x+4 is always positive.
Answer» ANSWER :`-6 LT a lt 2`.

Discussion

4270.	Find the coordinates of the point which divides the line segment joining the points (-2, 3, 5) and (1, -4, 6) in the ratio (i) 2 : 3 internally, (ii) 2 : 3 externally.
Answer» ANSWER :(-8, 17, 3)

Discussion

4271.	If the lines y = 3x + 1 and 2y = x + 3 are equally inclined to the line y = mx + 4, ((1)/(2) lt m lt 3), then the values of m are
Answer» Answer :`(1 PM 5 SQRT 2)/7`

Discussion

4272.	Show that product of the perpendicular distances from origin to pair of lines represented by ax^(2)+2hxy+by^(2)+2gx+2fy+c=0 is (\|c\|)/(sqrt((a-b)^(2)+4h^(2)))
Answer» ANSWER :`(\|C\|)/(SQRT((a-b)^(2)4H^(2)))`

Discussion

4273.	Consider the expansion of (x/9+9y)^2n The number of terms in the expansion is….
Answer» 2n n+1 2n+1 2n-1 Answer :C

Discussion

4274.	Let L be the line joing the origin to the point of interesection of the lines represecnted by 2x^(2)-3xy-2y^(2)+10x+5y=0. If L is perpendicular to the line kx+y+3=0, then k=
Answer» `(1)/(2)` `(-1)/(2)` `-1` `(1)/(3)` ANSWER :B

Discussion

4275.	The periodof 3sin^(5) x + cos^(3) xis
Answer» `PI` `2PI` `(pi)/(2)` `(3PI)/(2)` ANSWER :2

Discussion

4276.	A students has freedom to study any subject of his choice. In a group of students with number 1 to 300, the students whose number is divisible by 3 select arts faculty. The students whose number divisible by 5 select commerce faculty and the students whose number is divisible by 10 select science faculty. Find the number of students who select only one faculty.
Answer» ANSWER :`= 100`

Discussion

4277.	Let P(k) = (1+"cos"(pi)/(4k))(1+"cos"((2k-1)pi)/(4k))(1 + "cos" ((2k+1)pi)/(4k))(1+"cos"((4k-1)pi)/(4k)). Then
Answer» `P(3) = (1)/(16)` `P(4) = (2- sqrt(2))/(16)` `P(5) = (3 - sqrt(5))/(32)` `P(6) = (2 - sqrt(3))/(16)` Answer :A::B::C::D

Discussion

4278.	If the areaofDelta ABCwith sidesa,b,c isDelta,then the areaof the triangleswhosesides areak, bk, ck is
Answer» ` ( abc) /(Delta ^(3)) ` `0` ` 4Rr^(2) ` ` (1)/ ( r ) ` ANSWER :A

Discussion

4279.	Find the direction cosines of the two lines which are connected by the relations l-5m+3n=0,7l^(2)+5m^(2)-3n^(2)=0
Answer» ANSWER :`((-1)/(sqrt(6)),(1)/(sqrt(6)),(2)/(sqrt(6))),((1)/(sqrt(14)),(2)/(sqrt(14)),(3)/(sqrt(14)))`

Discussion

4280.	Which of the following sentences are statements? Give reasons for your answer: The square of a number is an even number.
Answer» ANSWER :It is not a STATEMENT.

Discussion

4281.	A man starts from the point P(-3,4) and reaches the point Q (0,10 Touching x axis R (alpha,0) " such that PR+RQis minimum " alpha =
Answer» `3/5` `(-3)/5` 3 `4/5` ANSWER :A

Discussion

4282.	Find'the centre and radius of the circle (i) x^(2) +y^(2) + 4x - 1= 0 (ii) 2 x^(2) + 2y^(2) = 3x - 5y + 7
Answer» ANSWER :`(-2,2);3`

Discussion

4283.	If bar(a)= 2bar(i) - 3bar(j) + 5bar(k), bar(b)= - bar(i) + 4bar(j)+ 2bar(k) then find (bar(a) + bar(b)) xx (bar(a) - bar(b)) and unit vector perpendicular to both bar(a) + bar(b) " & " bar(a)- bar(b).
Answer» ANSWER :`+- (1)/(sqrt(782)) (26 BAR(i) + 9bar(j)- 5 bar(k))`

Discussion

4284.	If x_(1) and x_(2) are two distinct roots of the equation a cos x + b sin x = c, "then" tan ((x_(1) + x_(2))/(2)) is equal to
Answer» `(a)/(B)` `(b)/(a)` `(C)/(a)` `(a)/(c)` ANSWER :B

Discussion

4285.	Find solution ofsin x = 1/2 ,x in quadrant II
Answer»

Discussion

4286.	If y = Tan^(-1)((3a^2x-x^3)/(a^3-3ax^2))then (dy)/(dx)=
Answer» `(3A)/(a^2+x^2)` `(1)/(a^2+x^2)` `(-3a^2)/(a^2+x^2)` `(-3a)/(a^2+x^2)` ANSWER :A

Discussion

4287.	cos^(2)""((pi)/(4) +x ) - sin^(2) ""((pi)/4- x ) =
Answer» -1 0 1 2 Answer :B

Discussion

4288.	sqrt3 cot20^(@)-4cos20^(@)=
Answer» 0 1 `-1` 4 Answer :B

Discussion

4289.	variance of 6 observation is 250 then sum(x_i-barx)^2=1200.
Answer» ANSWER :FALSE STATEMENT

Discussion

4290.	Let f be a function whose domain is the set of all real number. If f(x)=\|x\|-x, what is the range of f?
Answer» ANSWER :`R_(F)=[0,OO)`

Discussion

4291.	Evaluate : lim_(x to oo) sqrt(x^(2)+x +1) - sqrt(x^(2)+1)
Answer» ANSWER :`1/2 `

Discussion

4292.	Find the realtion between a and b if lim_(xrarr2)f(x)exists where f(x)={[ax +bif xgt3 5ax-3bx +2if xlt 2
Answer» ANSWER :`8a-7b+2=0`

Discussion

4293.	The range of f(x)=\|x-2\|+\|x-12\| is
Answer» `[2, OO)` `(12, oo)` `[10, oo)` `[14, oo)` Answer :C

Discussion

4294.	Find the value of :""^(50)C_(47)
Answer» ANSWER :` 19600`

Discussion

4295.	Find the derivative of x^(n)+ax^(n-1)+a^(2)x^(n-1)+ . . .+a^(n-1)x+a^(n) for some fixed real number a.
Answer» ANSWER :`NX^(n-1)+a(n-1)X^(n-2)+a^(2)(n-2)x^(n-3)+…+a^(n-1)`

Discussion

4296.	Evaluate the following limits : Lim_(xto3) (x^(3)-8x^(2)+45)/(2x^(2)-3x-9)
Answer» ANSWER :`-7/3`

Discussion

4297.	Prove that (tanA+secA-1)/(tanA-secA+1)=(1+sinA)/(cosA) Thinking Process : Here, use the formula i.e., sec^(2)A-tan^(2)A=1anda^(2)-b^(2)=(a+b)(a-b) to solve the above problems.
Answer» ANSWER :`(1+sinA)/(COSA)`

Discussion

4298.	Evaluate the following limits : Lim_(xto0) ((tan x- sin x)/(x^(3)))
Answer» ANSWER :`1/2`

Discussion

4299.	If a five-digit number divisible by 3 is to be formed using the number 0, 1, 2, 3, 4 and 5 without repetitioins, then the total number of ways this can done is
Answer» 216 600 240 3125 Answer :A::B

Discussion

4300.	If l, m, n are d.c's of vector bar(OP) then maximum value of lmn is
Answer» `1/sqrt(3)` `1/(2sqrt(3))` `1/(3sqrt(3))` `2/sqrt(3)` ANSWER :C

Discussion

Explore topic-wise InterviewSolutions in .

Find image of point (-8, 12) with respect to line 4x+7y+ 13=0.

The 9th term of an AP is equal to 6 times the second term. If its 5th term is 22 find the AP.

A vertical pole subtends an angle Tan^-1(1/2) at a point P on the ground. IF the angles subtended by the upper half and the lower half of the pole at P are respectively alpha and beta, then (tan alpha , tan beta)=

If 0 lt theta lt pi, then minimum value of 3 sin theta + cosec^(3) theta is

The slop of the tangent to the curce at a point (x,y) on it is proportional to (x-2). If the slop of the tangent ot the curve at (10,-9) on it is -3, then the equation of the curcve is

Show that the angle of rotation of the axes to eliminate xy term in the equation ax^(2) + 2hxy + by^(2) = 0 " is " (1)/(2) Tan^(-1) ((2h)/(a - b)) " when " a ne b and pi //4 when a = b

If ABC is a triangle and tan"" (A)/(2) , tan"" (B)/(2) , tan "" (C )/( 2) are in H.P. then the minimum value of cot"" (B)/(2) is equal to

Find n If : ""^(n)P_4 : "" ^(n-1)P_3 = 9: 1

If I_(n)is the area of n-sided regular polygon inscribed in a circle of unit radius and O_(n)be the area of the polygon circumscribing the given circle, then (O_(n)(1 + sqrt(1 - ((2I_(n))/n)^(2))))/I_(n) =

Evaluate the following limits : Lim_(x to 0 ) (tan (x+a) -tana)/(3x)

If the sum of the first 4 terms of an arithmetic progression is p, the sum of the first 8 terms is q and the sum of the first 12 terms is r, express 3p+r in terms of q.

If 4 cot 2 theta = cot^(2) theta - tan ^(2) theta " then " theta =

Find the point at which is shifted such that the transformed equations of the following equations has no first degree term : (i) 2x^(2)+3y^(2)+4x-12y+10=0 (ii) x^(2)+y^(2)-xy-5x+4y+5=0

If f(x)=(9^(x))/(9^(x)+3) then f((1)/(1996))+f((2)/(1996))+.......+f((1995)/(1996))=

Domain of f(x)= sqrt(a^(2)-x^(2)) (a gt 0) is

Write the values of i^2, i^4 and i^6

If 2x + 3y = 7 makes equal angles with pair of lines 9x^(2)+12xy+ky^(2)=0 then k=

Show that y=ax^(2)+bx+c represents a parabola. Also find equation its axis.

Find what values of a so that the expression x^(2)-(a+2)x+4 is always positive.

Find the coordinates of the point which divides the line segment joining the points (-2, 3, 5) and (1, -4, 6) in the ratio (i) 2 : 3 internally, (ii) 2 : 3 externally.

If the lines y = 3x + 1 and 2y = x + 3 are﻿ equally inclined to the line y = mx + 4,﻿ ((1)/(2) lt m lt 3﻿), then the values of m are

Show that product of the perpendicular distances from origin to pair of lines represented by ax^(2)+2hxy+by^(2)+2gx+2fy+c=0 is (|c|)/(sqrt((a-b)^(2)+4h^(2)))

Consider the expansion of (x/9+9y)^2n The number of terms in the expansion is….

Let L be the line joing the origin to the point of interesection of the lines represecnted by 2x^(2)-3xy-2y^(2)+10x+5y=0. If L is perpendicular to the line kx+y+3=0, then k=

The periodof 3sin^(5) x + cos^(3) xis

Let P(k) = (1+"cos"(pi)/(4k))(1+"cos"((2k-1)pi)/(4k))(1 + "cos" ((2k+1)pi)/(4k))(1+"cos"((4k-1)pi)/(4k)). Then

If the areaofDelta ABCwith sidesa,b,c isDelta,then the areaof the triangleswhosesides areak, bk, ck is

Find the direction cosines of the two lines which are connected by the relations l-5m+3n=0,7l^(2)+5m^(2)-3n^(2)=0

Which of the following sentences are statements? Give reasons for your answer: The square of a number is an even number.

A man starts from the point P(-3,4) and reaches the point Q (0,10 Touching x axis R (alpha,0) " such that PR+RQis minimum " alpha =

Find'the centre and radius of the circle (i) x^(2) +y^(2) + 4x - 1= 0 (ii) 2 x^(2) + 2y^(2) = 3x - 5y + 7

If bar(a)= 2bar(i) - 3bar(j) + 5bar(k), bar(b)= - bar(i) + 4bar(j)+ 2bar(k) then find (bar(a) + bar(b)) xx (bar(a) - bar(b)) and unit vector perpendicular to both bar(a) + bar(b) " & " bar(a)- bar(b).

If x_(1) and x_(2) are two distinct roots of the equation a cos x + b sin x = c, "then" tan ((x_(1) + x_(2))/(2)) is equal to

Find solution ofsin x = 1/2 ,x in quadrant II

If y = Tan^(-1)((3a^2x-x^3)/(a^3-3ax^2))then (dy)/(dx)=

cos^(2)""((pi)/(4) +x ) - sin^(2) ""((pi)/4- x ) =

sqrt3 cot20^(@)-4cos20^(@)=

variance of 6 observation is 250 then sum(x_i-barx)^2=1200.

Let f be a function whose domain is the set of all real number. If f(x)=|x|-x, what is the range of f?

Evaluate : lim_(x to oo) sqrt(x^(2)+x +1) - sqrt(x^(2)+1)

Find the realtion between a and b if lim_(xrarr2)f(x)exists where f(x)={[ax +bif xgt3 5ax-3bx +2if xlt 2

The range of f(x)=|x-2|+|x-12| is

Find the value of :""^(50)C_(47)

Find the derivative of x^(n)+ax^(n-1)+a^(2)x^(n-1)+ . . .+a^(n-1)x+a^(n) for some fixed real number a.

Evaluate the following limits : Lim_(xto3) (x^(3)-8x^(2)+45)/(2x^(2)-3x-9)

Prove that (tanA+secA-1)/(tanA-secA+1)=(1+sinA)/(cosA) Thinking Process : Here, use the formula i.e., sec^(2)A-tan^(2)A=1anda^(2)-b^(2)=(a+b)(a-b) to solve the above problems.

Evaluate the following limits : Lim_(xto0) ((tan x- sin x)/(x^(3)))

If a five-digit number divisible by 3 is to be formed using the number 0, 1, 2, 3, 4 and 5 without repetitioins, then the total number of ways this can done is

If l, m, n are d.c's of vector bar(OP) then maximum value of lmn is

If the lines y = 3x + 1 and 2y = x + 3 are equally inclined to the line y = mx + 4, ((1)/(2) lt m lt 3), then the values of m are