14949 + Interview Questions in Maths in Class 11 Page 70 InterviewSolution

3451.	If alpha, beta, gamma are the roots of the equation x^(3)+mx^(2)+3x+m=0, then the general value of Tan^(-1)alpha+Tan^(-1)beta+Tan^(-1)gamma is
Answer» `(2n+1)pi/2` `npi` `(npi)/2` dependent upon the VALUE of m Answer :B

Discussion

3452.	(sintheta+sin2theta)/(1+costheta+cos2theta)
Answer» `TAN""(THETA)/2` `cot""(theta)/2` `TANTHETA` `cot theta` Answer :C

Discussion

3453.	Find the sum to infinity in each of the following G.P (-3)/(4), (3)/(16), (-3)/(64)……..
Answer» ANSWER :`(-3)/(5)`

Discussion

3454.	In Delta ABC, if 8R^(2) = a^(2) + b^(2) + c^(2), then the triangle is a
Answer» RIGHT ANGLED ISOSCELES EQUILATERAL Scalane ANSWER :A

Discussion

3455.	The maximum value of f(x)=tan^(-1)(((sqrt(12)-2).x^(2))/(x^(4)+2x^(2)+3)) is
Answer» `18^(0)` `36^(0)` `22.5^(0)` `15^(0)` ANSWER :D

Discussion

3456.	Find the solution of six x - (sqrt3)/(2).
Answer» Answer :`x = n PI + (-1)^(n) (4pi)/(3),` where `n in Z`

Discussion

3457.	OPQR is square ('O' being origin and M,N are middle points of sides PQ, QR respectively and the ratio of areas of square and triangle OMN is p/q(where P,q are relatively prime ) then P-q is
Answer» ANSWER :5

Discussion

3458.	Separate the equation of the line x^(2)+xy+y^(2)=0
Answer» ANSWER :`X^(2)+xy+y^(2)=0`

Discussion

3459.	Find the angle made by the straight line y=-sqrt(3)x+3 with positive direction of x-axis.
Answer» ANSWER :`(2PI)/3`

Discussion

3460.	If f(x) = sin^(-1) x, then f'(x) is
Answer» 1 for all X `-1` for all x `-1` and 2ND and 3RD quadrant 1 in 4th quadrant Answer :C::D

Discussion

3461.	Find the eccentricity and the equations of the directrices of the ellipse 7x^(2)+16y^(2)=112.
Answer» ANSWER :`e=3/4, 3X PM 16=0`

Discussion

3462.	If log4=1.3868, then the approximate value of log(4.01)
Answer» 1.3968 1.3898 1.3893 1.9338 Answer :C

Discussion

3463.	Find the slopes of the lines (i) Parallel (ii) Perpendicular to the line passing through (6,3),(-4,5).
Answer» ANSWER :(i) `-1/5` (II) 5

Discussion

3464.	Out of 100 students, two sections of 40 and 60 are formed. If you and your friend are among the 100 students, what is th probability that (a) you both enter the same section? (b) you both enter the different sections ?
Answer» ANSWER :(i) `(17)/(33)` (II) `(16)/(33)`

Discussion

3465.	{:("Column -I","Column -II"),((A)f(x)=(x)/(1+xtanx)"has maximum value in the domain when x= of definition of function","P Any real"),((B)f(x)=((x)/(1+tanx))^(-1)"has minimum value when x=","Q"(pi)/(4)),((C)f(x)=((x)/(1+xcotx)) " is monotonically increasing when" x=,"R cosx"),((D)f(x)=((x)/(1+xcotx))^(-1) "has minimum value in "(0,(pi)/(4)) "thenx= of point of intercection of y=x and y = cos x","S sinx"),(,"T The x - coordinate"):}
Answer» ANSWER :A-t;,B-t;C-p;D-q

Discussion

3466.	If from point P(4,4) perpendiculars to the straight lines 3x+4y+5 and y=mx+7 meet at Q and R and area of triangle PQR is maximum, then m is equal to
Answer» `4/3` `-4/3` -1 1 Answer :C

Discussion

3467.	lim_(xrarr0)(e)^(e^x)/(e^x+1)=2e
Answer» ANSWER :FALSE STATEMENT

Discussion

3468.	Assertion A : The equation sin^(-1)x=3sin^(-1)(a) has a solution for -1/2leale1/2 Reason : AA x in [-1,1], sin^(-1)x in [0,2pi]
Answer» 1)Both A and R are true and R is CORRECT explanation of A 2)Both A and R are true and R is not correct explanation of A 3)A is true, R is FALSE 4)A is false but R is true Answer :C

Discussion

3469.	Number of solutions of \|cosx\|=2[x] is (Where [x] is integral part of x)
Answer» 0 1 2 infinite Answer :A

Discussion

3470.	Compute a price index for the following data by simple aggregate method. {:("Prices in 2008 (in ₹)", 20, 30, 25, 40, 50),("Price in 2010 (in ₹ )" , 25, 30, 35, 45, 55):}
Answer» ANSWER :`117.14`

Discussion

3471.	In Delta ABC, if B=60^@,C=45^@ and D divides BC internally in the ratio 1:3 then (sinangleBAD)/(sinangleCAD)=
Answer» `(1)/(sqrt(6))` `(1)/(3)` `(1)/(sqrt(3))` `(sqrt(2))/(sqrt(3))` ANSWER :A

Discussion

3472.	The point of intersection of the lines x-y+1=0 and x+y+5=0 is P. A circle with centre at (1, 0) passes through P. The tangent to the circle at P meets the x-axis at (k, 0).The value of k is :
Answer» 2 `-3` `-2` `-4` Solution :`L_(1):X-y+1=0` `L_(2):x+y+5=0` `rArr""x= -3, y=-2` `rArr""P-=(-3, -2)` EQUATION of circle `(x-1)^(2)+y^(2)=20` `rArr""x^(2)+y^(2)-2x-19=0` Equation of tangent at P is `rArr""2x+y+8=0` `"PUT "y=0` `rArr""x=-4` `"Point is "(-4,0)` `rArr""k=-4`

Discussion

3473.	Find the derivative of Sec^-1(1/(2x^2-1))
Answer» ANSWER :`(-2)/( SQRT (1- X ^(2)))`

Discussion

3474.	The voltage E of a thermocouple as a function of temperature is given by E=6.2T+0.0002T^(3). When T changes from 100^(@) to 101^(@) the approximate change in E.
Answer» 12 12.1 12.12 12.2 Answer :D

Discussion

3475.	-3 le 4 - (7x)/(2) le 18
Answer» ANSWER :`[-4,2]`

Discussion

3476.	Lines axpm bypm c =0 represents …....... of the following.
Answer» Rectangle Square Rhombus None of these Answer :C

Discussion

3477.	If A=35^(@), B= 15^(@) and C=40^(@) , thentan A* tan B+ tan B* tan C+ tan C* tan A=
Answer» 0 1 2 3 Answer :B

Discussion

3478.	Find Re ((z_(1)z_(2))/(z_(1))), give z_(1)=2-i and z_(2)=-2+i
Answer» ANSWER :`1/3`

Discussion

3479.	Find equation of the line through the point(0, 2) making an angle (2pi)/(3) with the positive x-axis. Also, find the equation of line parallel to it and crossing the y-axis at a distance of 2 units below the origin.
Answer» ANSWER :`SQRT3 X + y - 2 = 0 " and " sqrt3 x + y + 2 = 0 `

Discussion

3480.	Let f is a real valued function defined on the interval (-1,1) such that e^(-x)f(x) = 2 + int_0^x sqrt(t^4 + 1 dt) AA x in (-1,1) and f^(-1) is the inverse of f. If (f^(-1)(2)) = 1/k then k is
Answer»

Discussion

3481.	Find the derivative of the following functions from first principle: (-x)^(-1)
Answer» ANSWER :`(1)/(X^(2))`

Discussion

3482.	In DeltaABC,(b-c)/(b+c)cot""A/2+(b+c)/(b-c) tan""A/2=
Answer» ` 2 COSEC (B-C) ` ` cosec (B-C) ` ` cosec ((B-C)/( 2))` ` cosec ((B+C)/(2))` ANSWER :A

Discussion

3483.	In a school there are 20 teachers who teach mathematics or physics. Of these, 12 teach mathematics and 4 teach both physics and mathematics. How many teach physics ?
Answer» ANSWER :`= 12`

Discussion

3484.	Without using tables, give the value of each of the following : sin120^(@)
Answer» ANSWER :`(SQRT(3))/(2)`

Discussion

3485.	The pair of lines a^(2)x^(2)+2h(a+b)xy+b^(2)y^(2)=0 and ax^(2)+2hxy+by^(2)=0 are
Answer» PERPENDICULAR equally inclined to each other such that each BISECTS the angle between the other parallel Answer :B

Discussion

3486.	A function f is defined as follows: f(x)={:{(0,for,x lt0),(x , for,0lexlt1),(-x^2+4x-2,for,1lexlt3),(4-x,for,x ge 3):}
Answer» ANSWER :1,3

Discussion

3487.	Find the value of m so that the roots of the equation (4-m)x^(2)+(2m+4)x+(8m+1)=0 may be equal.
Answer» ANSWER :m=0,3.

Discussion

3488.	Find the value of(ix) cot 765^(@)
Answer» ANSWER :1

Discussion

3489.	A box , constructed from a rectangular metal sheet , is 21 cm by 16 cm by cuttingequal squares of sides x from the corners of the sheet and the turning up the projected portions . Thevalue of x so that volume of the box ismaximum is
Answer» 1 2 3 4 Answer :C

Discussion

3490.	If in two circles, arcs of the same length subtend angles 60^(@)and75^(@) at the centre, find the ratio of their radii.
Answer» ANSWER :`5:4`

Discussion

3491.	If sin x + cos x =a then \|sin x- cos x\|=
Answer» `SQRT(1-a^(2))` `sqrt(a^(2)-1)` `sqrt(2-a^(2))` `sqrt(a^(2)-2))` ANSWER :C

Discussion

3492.	If the coordinate axes are rotated through an angle (pi)/(6) about the origin, then transformed equation of sqrt(3)x^2-4xy+sqrt(3)y^2=0 is
Answer» `SQRT(3) y^(2) + xy = 0` `x^(2) - y^(2) = 0` `sqrt(3) y^(2) - xy = 0` `sqrt(3) y^(2) - 2XY = 0` ANSWER :C

Discussion

3493.	Arrange the following values in the ascending order of P,Q,R. If A + B + C = n then (i) P = (cosA)/(sin B sinC) + (cos B)/(sinA sinC) + (cos C)/(sinAsin B) (ii) Q = sumcotA.cotB iii) R = tan 3 A + tan 3B + tan 3C - tan 3 A tan 3B tan3C =
Answer» <P>R,Q,P Q,P,R P,Q,R P,R,Q Answer :A

Discussion

3494.	Two lines L _(1) :x =5 , (y)/(3 - alpha) = (z)/(-2) and L _(2) : x = alpa , (y)/(-1) = (z)/(2- alpha ) are coplanar. Then alphacan take value (s)
Answer» 1 2 3 4 Answer :A::D

Discussion

3495.	If f(x)=tan^(-1)x-(1//2)logx. Then
Answer» the least value of f(x) on `[1//SQRT(3),sqrt(3)]` is `pi//6+(1//4)LOG3` the least value of f(x) on `[1//sqrt(3),sqrt(3)]` is `pi//3-(1//4)log3` f(x) decreases on `(-oo,0)` f(x) increases on `(-oo,0)` ANSWER :B

Discussion

3496.	Unit vector coplanar with bari+barj+2bark,bari+2barj+bark and perpendicular to bari+barj+bark is
Answer» `(bari+bark)/(SQRT2)` `(bari-bark)/(sqrt2)` `(bari+bark)/(sqrt2)` `(barj-bark)/(sqrt2)` ANSWER :D

Discussion

3497.	If x+y=k and xgt09,ygt0 then x^2+y^2 is minimum if
Answer» `XGTY` `XLTY` x=y x=2y Answer :C

Discussion

3498.	The unit vector in ZOX-plane making angles 45^(@) and 60^(@) " respectively with " bara = 2bari+2barj-bark and barb= barj-bark is
Answer» `1/SQRT2(-bari+2bark)` `1/sqrt2(bari-bark)` `1/(3sqrt2)(bari+2bark)` `1/(sqrt2)(bari+bark+barj)` ANSWER :B

Discussion

3499.	Express2cos theta + 3 sin thetain the formr cos ( theta - alpha ), where r is positive, stating the values of r andalpha. What is the maximum value of 2 cos theta + 3 sin theta ?
Answer» ANSWER :`SQRT13`

Discussion

3500.	The radius of the base of a cone is increasing at the rate of 3 cm/min and altitude is decreasing at the rate of 4 cm/min. The rate of change of lateral surface when the radius is 7 cm and altitude is 24 is
Answer» `180pi CM^(2)` / MIN `7pi cm^(2)` `27pi cm^(2)` /min `54pi cm^(2)` /min Answer :A

Discussion

Explore topic-wise InterviewSolutions in .

If alpha, beta, gamma are the roots of the equation x^(3)+mx^(2)+3x+m=0, then the general value of Tan^(-1)alpha+Tan^(-1)beta+Tan^(-1)gamma is

(sintheta+sin2theta)/(1+costheta+cos2theta)

Find the sum to infinity in each of the following G.P (-3)/(4), (3)/(16), (-3)/(64)……..

In Delta ABC, if 8R^(2) = a^(2) + b^(2) + c^(2), then the triangle is a

The maximum value of f(x)=tan^(-1)(((sqrt(12)-2).x^(2))/(x^(4)+2x^(2)+3)) is

Find the solution of six x - (sqrt3)/(2).

OPQR is square ('O' being origin and M,N are middle points of sides PQ, QR respectively and the ratio of areas of square and triangle OMN is p/q(where P,q are relatively prime ) then P-q is

Separate the equation of the line x^(2)+xy+y^(2)=0

Find the angle made by the straight line y=-sqrt(3)x+3 with positive direction of x-axis.

If f(x) = sin^(-1) x, then f'(x) is

Find the eccentricity and the equations of the directrices of the ellipse 7x^(2)+16y^(2)=112.

If log4=1.3868, then the approximate value of log(4.01)

Find the slopes of the lines (i) Parallel (ii) Perpendicular to the line passing through (6,3),(-4,5).

Out of 100 students, two sections of 40 and 60 are formed. If you and your friend are among the 100 students, what is th probability that (a) you both enter the same section? (b) you both enter the different sections ?

If from point P(4,4) perpendiculars to the straight lines 3x+4y+5 and y=mx+7 meet at Q and R and area of triangle PQR is maximum, then m is equal to

lim_(xrarr0)(e)^(e^x)/(e^x+1)=2e

Assertion A : The equation sin^(-1)x=3sin^(-1)(a) has a solution for -1/2leale1/2 Reason : AA x in [-1,1], sin^(-1)x in [0,2pi]

Number of solutions of |cosx|=2[x] is (Where [x] is integral part of x)

Compute a price index for the following data by simple aggregate method. {:("Prices in 2008 (in ₹)", 20, 30, 25, 40, 50),("Price in 2010 (in ₹ )" , 25, 30, 35, 45, 55):}

In Delta ABC, if B=60^@,C=45^@ and D divides BC internally in the ratio 1:3 then (sinangleBAD)/(sinangleCAD)=

The point of intersection of the lines x-y+1=0 and x+y+5=0 is P. A circle with centre at (1, 0) passes through P. The tangent to the circle at P meets the x-axis at (k, 0).The value of k is :

Find the derivative of Sec^-1(1/(2x^2-1))

The voltage E of a thermocouple as a function of temperature is given by E=6.2T+0.0002T^(3). When T changes from 100^(@) to 101^(@) the approximate change in E.

-3 le 4 - (7x)/(2) le 18

Lines axpm bypm c =0 represents …....... of the following.

If A=35^(@), B= 15^(@) and C=40^(@) , thentan A* tan B+ tan B* tan C+ tan C* tan A=

Find Re ((z_(1)z_(2))/(z_(1))), give z_(1)=2-i and z_(2)=-2+i

Find equation of the line through the point(0, 2) making an angle (2pi)/(3) with the positive x-axis.﻿ Also, find the equation of line parallel to it and crossing the y-axis at a distance of 2 units﻿ below the origin.

Let f is a real valued function defined on the interval (-1,1) such that e^(-x)f(x) = 2 + int_0^x sqrt(t^4 + 1 dt) AA x in (-1,1) and f^(-1) is the inverse of f. If (f^(-1)(2)) = 1/k then k is

Find the derivative of the following functions from first principle: (-x)^(-1)

In DeltaABC,(b-c)/(b+c)cot""A/2+(b+c)/(b-c) tan""A/2=

In a school there are 20 teachers who teach mathematics or physics. Of these, 12 teach mathematics and 4 teach both physics and mathematics. How many teach physics ?

Without using tables, give the value of each of the following : sin120^(@)

The pair of lines a^(2)x^(2)+2h(a+b)xy+b^(2)y^(2)=0 and ax^(2)+2hxy+by^(2)=0 are

A function f is defined as follows: f(x)={:{(0,for,x lt0),(x , for,0lexlt1),(-x^2+4x-2,for,1lexlt3),(4-x,for,x ge 3):}

Find the value of m so that the roots of the equation (4-m)x^(2)+(2m+4)x+(8m+1)=0 may be equal.

Find the value of(ix) cot 765^(@)

A box , constructed from a rectangular metal sheet , is 21 cm by 16 cm by cuttingequal squares of sides x from the corners of the sheet and the turning up the projected portions . Thevalue of x so that volume of the box ismaximum is

If in two circles, arcs of the same length subtend angles 60^(@)and75^(@) at the centre, find the ratio of their radii.

If sin x + cos x =a then |sin x- cos x|=

If the coordinate axes are rotated through an angle (pi)/(6) about the origin, then transformed equation of sqrt(3)x^2-4xy+sqrt(3)y^2=0 is

Arrange the following values in the ascending order of P,Q,R. If A + B + C = n then (i) P = (cosA)/(sin B sinC) + (cos B)/(sinA sinC) + (cos C)/(sinAsin B) (ii) Q = sumcotA.cotB iii) R = tan 3 A + tan 3B + tan 3C - tan 3 A tan 3B tan3C =

Two lines L _(1) :x =5 , (y)/(3 - alpha) = (z)/(-2) and L _(2) : x = alpa , (y)/(-1) = (z)/(2- alpha ) are coplanar. Then alphacan take value (s)

If f(x)=tan^(-1)x-(1//2)logx. Then

Unit vector coplanar with bari+barj+2bark,bari+2barj+bark and perpendicular to bari+barj+bark is

If x+y=k and xgt09,ygt0 then x^2+y^2 is minimum if

The unit vector in ZOX-plane making angles 45^(@) and 60^(@) " respectively with " bara = 2bari+2barj-bark and barb= barj-bark is

Express2cos theta + 3 sin thetain the formr cos ( theta - alpha ), where r is positive, stating the values of r andalpha. What is the maximum value of 2 cos theta + 3 sin theta ?

The radius of the base of a cone is increasing at the rate of 3 cm/min and altitude is decreasing at the rate of 4 cm/min. The rate of change of lateral surface when the radius is 7 cm and altitude is 24 is

Find equation of the line through the point(0, 2) making an angle (2pi)/(3) with the positive x-axis. Also, find the equation of line parallel to it and crossing the y-axis at a distance of 2 units below the origin.