14949 + Interview Questions in Maths in Class 11 Page 87 InterviewSolution

4301.	If sin^(3) theta + sin theta cos theta + cos^(3) theta = 1, " then " theta = (n in z)
Answer» `2 N PI` `2 n pi + (pi)/(2)` `2 n pi - (pi)/(2)` `n pi` ANSWER :A::B

Discussion

4302.	Find the absolute maximum and absolute minimu values of f(x) = x^(40) - x^(20) on [0, 1].
Answer» ANSWER :`-(1)/(4)`

Discussion

4303.	Pearson's coefficient of correlation r always follow:(a)rle1(b)rlt-1(c)\|r\|le1(d)\|r\|ge1
Answer» `rle1` `rlt-1` `\|r\|le1` `\|r\|ge1` ANSWER :C

Discussion

4304.	Write down all the subsets of the following sets : {0, 1}
Answer» ANSWER :`PHI, {0}, {1}, {0, 1}`

Discussion

4305.	Find the component statements of the following compound statements: Plants use sunlight, water and carbon dioxide for photosynthesis.
Answer» ANSWER :PHOTOSYNTHESIS.

Discussion

4306.	Sum to n terms the series 7+77+777+....
Answer» Answer :`(70)/(81)(10^(n)-1) -(7N)/(9)`

Discussion

4307.	Find lambda in order that the equation x^(2)+lambda xy+y^(2)-5x=7y+6=0 may represents two straight line. Write down the equation to the lines parallel to these and passing through (1,2).
Answer» Answer :`lambda= (5)/(2)` or `(10)/(3)` : (2x+y-4)(X + 2y -5) = 0 or (3X + y-5) (x+3y-7) = 0

Discussion

4308.	If \|{:(1+x,2,3),(1,2+x,3),(1,2,3+x):}\|=0 then x =
Answer» 1 `-1` `-6` 6 Answer :C

Discussion

4309.	P is a point inside a Delta ABCof area K (K gt 0). The lengths of perpendiculars drawn to the sides BC, CA, ABof lengths a,b,c are respectivelyp_(1), p_(2) , p_(3) , a/p_(1) + b/p_(2) + c/p_(3) is minimum when
Answer» P is incentre of `DELTA ABC` P is equidistant to all the 3 SIDES `P_(1) = P_(2) = P_(3) = (2K)/(a + b+ c) ` P is ORTHOCENTRE of `Delta ABC` Answer :A::B::C

Discussion

4310.	(r_1)/( R ) =sin A + sin B + sin Cthen the triangles is
Answer» RIGHT ANGLED ISOSCELES EQUILATERAL Scalane ANSWER :A

Discussion

4311.	Let U = { 1, 2, 3, 4, 5, 6, 7, 8, 9 }, A= { 1, 2, 3, 4}, B = { 2,4, 6, 8 } and C = { 3, 4, 5, 6 }. Find B'
Answer» Answer :`{1, 3, 5, 7, 9 }`

Discussion

4312.	(a) A ball is thrown vertically upward from the groundwith an initial velocityof 39.2 m/sec. if the onlyforceconsdieredis thatattributedto theacceleration due to gravity , find (i) How longwill it takefor the ballto strike the ground ? (ii) the speed with whichwill it strike the ground ? and(iii)how highthe ball will rise ? (OR) (b) A wound is healingin such a way that t days sinceSundaythe areaof the woundhas beendecreasingat a rate of-3 /( ( t+2)^(2))cm^(2) per day. If onMonday the areaof the woundwas2 cm^(2) (i) What was thearea of the wound on Sunday ? (ii) What is theanticipatedarea of the woundon Thursday if itcontinues to heal at the same rate ?
Answer» Answer :(a)`39.2t - 4.9 t^(2)` (i) `t = 8 SEC` (II)v = 39.2 m/sec (b)(i)2.5 sq.CM (ii)1.5 sq. cm. (b)` 1/x^(2)`

Discussion

4313.	Solve : x^2 - 2x + 4 = 0
Answer» ANSWER :`x-=1pmisqrt3`

Discussion

4314.	If sin x + cos x = 1then x =
Answer» `2 n PI , ( 4 n + 1) (pi)/( 2), n in Z` `n pi, ( 4 n + 1) (pi)/( 2) , NIN Z` `n pi , ( 2 n + 1) (pi)/(2) n in Z` ` 2 n pi,( 2 n + 1) (pi)/( 2) , n in Z` ANSWER :A

Discussion

4315.	The vector equation of the plane passing through the origin and the line of intersection of the planes vecr. Veca = lamda = vecr.vecb = mu is
Answer» `vec. (LAMDA veca - MU vecb) =0` `VECR.(lamda vecb-mu veca) =0` `vecr.(lamda veca + mu vecb) =0` `vecr.(lamda vecb + mu veca) =0` Answer :B

Discussion

4316.	Consider two consecutive odd natural numbers both of which are larger than 10, such that their sum is less than 40. Derive two inequalities in x.
Answer» Solution :`X gt 10, x + (x+2) LT 40`

Discussion

4317.	Consider two consecutive odd natural numbers both of which are larger than 10, such that their sum is less than 40. Find all pairs of odd natural numbers having the given properties .
Answer» SOLUTION :[(11,13),(13,15),(15,17),(17,19)]

Discussion

4318.	If f:RrarrRis defined by f(x)=\|x-2\|+\|x+2\| for x epsilon R ,then lim_(xrarr2^-)f(x) is :
Answer» `-2` `-1` 0 1 Answer :C

Discussion

4319.	If f(x)={{:(mx^(2)+n",",xlt0),(nx+m",",0lexle1),(nx^(3)+m",",xgt1):}. For what integers m and n does both lim_(xrarr0)f(x) and lim_(xrarr1)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

4320.	For some constants a and b ,find the derivate of:x^2/2-(a+b)x
Answer» ANSWER :2x-a-b

Discussion

4321.	Find k if lines 5x - ky- 7=0 and 2x + 3y + 5 =0 are mutually perpendicular.
Answer» ANSWER :`10/3`

Discussion

4322.	When the origin is shifted to (4, -5) by the translation of axes, find the coordinates of the point (i) (-2, 4) with reference to new axes. (ii) (4, -5) with reference to new axes.
Answer» ANSWER :(i)(-6, 9) (II) (0,0)

Discussion

4323.	If f(x) = (x^(2)-9)/(x-3) , find it Lim_(x to 3) f(x) exists .
Answer» Answer : =6 , THEREFORE , `Lim_(x to 3 ) f(x)` EXISTS and is EQUAL to 6 .

Discussion

4324.	Find the domain of each of the following functions given by f(x)= x\|x\|
Answer» ANSWER :F= R

Discussion

4325.	A stone is dropped into a quiet pond and waves move in circles outward from the place where it strikes, at a speed of 30 cm per second. At the instant when the radius of the wave ring is 50 mt, find the rate of increase in the area and in the circumference of the wave ring.
Answer» ANSWER :`30 PI m//sec, 0.6pi SQ. m//sec`

Discussion

4326.	If A+B+C=180^@ " then " sin 3A+ sin 3B+ sin 3C=
Answer» `4"COS"(3A)/(2)"cos"(3B)/(2) "cos"(3C)/(2)` `-4"cos"(3A)/(2)"cos"(3B)/(2) "cos"(3C)/(2)` `1-4"cos"(3A)/(2)"cos"(3B)/(2) "cos"(3C)/(2)` `1-4"sin"(3A)/(2)"sin"(3B)/(2) "sin"(3C)/(2)` ANSWER :B

Discussion

4327.	Find the maximum or minimum values of the following functions. x + (1)/(x), x gt 0
Answer» ANSWER :At X = 1, MINIMUM value = 2

Discussion

4328.	cos ^(2) ((pi)/(4)beta)- sin ^(2) (alpha - (pi)/(4))=
Answer» `SIN (ALPHA + BETA) sin (alpha - beta)` `COS (alpha + beta) cos (alpha - beta)` `sin (alpha + beta) cos (alpha + beta)` `sin (alpha + beta) cos (alpha - beta)` ANSWER :D

Discussion

4329.	A= {x : x in Z, x" is a solution of " x^(4)- 16= 0} then A= "……….".
Answer» `{-2, 2}` `{2}` `{-4}` `{-4, 4, -2, 2}` ANSWER :A

Discussion

4330.	Equation at sides of rectangle are x=a, x=a', y=b and y=b'. Obtain equation of its diagonals.
Answer» ANSWER :`y(a' - a) - X(B' - b) = a'b - AB'` `y(a' - a) + x(b' - b) = a'b' - ab`

Discussion

4331.	Number of solutions of \|(1)/(\|x\|-1)\|=x+sinx, is
Answer» 1 2 3 none of these Answer :A

Discussion

4332.	Let A= {1, 2, 3}, B= {3, 4} and C= {4, 5, 6}. Find (A xx B) uu (A xx C)
Answer» ANSWER :{(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,3),(3,4),(3,5),(3,6)}

Discussion

4333.	If one of the roots of 25cos^(2)theta+5costheta-12=0 is alpha then the value of sin2theta is ……….. ((pi)/(2)ltthetaltpi).
Answer» `(-24)/(23)` `(-13)/(18)` `(13)/(18)` `-(24)/(25)` ANSWER :A

Discussion

4334.	If tan 3 theta + tan theta = 2 tan 2 theta , " then " thetais equal to ( n in z)
Answer» `n PI` `(n pi)/(4)` `(n pi)/(2)` `(n pi)/(3)` ANSWER :A

Discussion

4335.	Find the centroid of the triangle formed by the points (2,7) (3,-1)(-5,6).
Answer» ANSWER :(0,4)

Discussion

4336.	In a triangle ABC, if D and E are mid points of sides AB and AC respectively. Show thatvecBE+ vecDC=(3)/(2)vecBC.
Answer» ANSWER :` 3/2 VEC(BC)`

Discussion

4337.	Obtain equation of the circle with centre (2,-5) and passes from point (3,2)
Answer» Answer :`X^(2) + y^(2) - 4X + 10y - 50 = 0`

Discussion

4338.	If cos (alpha - beta) + cos (beta - gamma) + cos (gamma - alpha) = (-3)/(2) then prove that cos alpha + cos beta+ cos gamma = sin alpha + sin beta + sin gamma = 0.
Answer» Answer :Hence ` SQRT(3)` is an IRRATIONAL NUMBER. Hence proved.

Discussion

4339.	A card is drawn from a well - shuffled pack of playing cards . What is the probability that it is elther aspade or an ace or both .
Answer» ANSWER :`=(4)/(13)`.

Discussion

4340.	Evaluate : cos24^(@)+cos55^(@)+cos125^(@)+cos204^(@)+cos300^(@).
Answer» ANSWER :`(1)/(2)`

Discussion

4341.	Solve the following equations Cos theta- Cos 7 theta = Sin 4 theta
Answer» Answer :`(npi)/(4)or(npi)/(3)+(-1)^(n)(PI)/(18)`

Discussion

4342.	Write the sample space at an event that coin is tossed till to head is obtained observe that it is an example of finite or infinite sample space.
Answer» ANSWER :`S={H,TH,T TH,T T TH,T T T TH,......}`

Discussion

4343.	If y=((a-x)sqrt(a-x)-(b-x)sqrt(x-b))/(sqrt(a-x)+sqrt(x-b)) then dy/dx wherever it is defined is
Answer» `(X+(a+B))/SQRT((a-x)(x-b))` `(2X-a-b)/(2sqrt((a-x)(x-b))` `((a+b))/(2sqrt((a-x)(x-b)))` `(2x+(a+b))/(2sqrt((a-x)(x-b)))` ANSWER :B

Discussion

4344.	A spring was hung from a hook in the ceiling.A number of different weights were attached to the spring to make it strech, and the total length of spring was measured each time shown in the following table:Q (v) How long will the spring be when 6 kilograms of weight omn it?
Answer» ANSWER :5 CM

Discussion

4345.	A spring was hung from a hook in the ceiling.A number of different weights were attached to the spring to make it strech, and the total length of spring was measured each time shown in the following table:Q (iv) If the spring has to stretch to 9 cm long, how much weight should be added?
Answer» ANSWER :14 KG

Discussion

4346.	If the focus of a parabola is (0,-3) and its directrix is y = 3, then its equation is ……..
Answer» `X^(2) = - 12Y` `x^(2) = 12y` `y^(2) = - 12X` `y^(2) = 12x` ANSWER :A

Discussion

4347.	If NN denotes the set of all positive integersand if f:NN rarrN is defined by f(n)= the sum of positive divisors of n then f(2^(k).3), where k is a positive integer is
Answer» `2^(k+1)-1` `2(2^(k+1)-1)` `3(2^(k+1)-1)` `4(2^(k+1)-1)` ANSWER :D

Discussion

4348.	Solve the following equations and write general solutions 4 sin theta sin 2 theta sin 4 theta = sin 3 theta
Answer» ANSWER :`{npi}uu{(npi)/(3)PM(PI)/(9)}`

Discussion

4349.	Find the direction cosines and direction rations for the followingvectors (i)3 hati - 4hatj + 8 hatk (ii)3hati + hatj + hatk (iii)hatj (iv)5 hati - 3hatj - 48 hatk (v)3hati - 3hatk+ 4 hatj (vi)hati -hatk OR ( b) Showthat the pointswhoseposition vectors 4hati + 5hatj + hatk , - hatj - hatk , 3 hati + 9 hatj+ 4hatk and- 4 hati + 4 hatj + 4 hatk are conplanar.
Answer» Answer :(i) `8/sqrt(79)` (ii) ` sqrt 11` (III)0,1,0 (IV) `sqrt( 2338)` (v)`sqrt(34)` (vi) ` (-1)/SQRT2` (b) 3

Discussion

4350.	If the distance between the points (x, -8, 4) and (3, -5, 4) is 5 unit find x.
Answer» ANSWER :X = 7 OR -1

Discussion

Explore topic-wise InterviewSolutions in .

If sin^(3) theta + sin theta cos theta + cos^(3) theta = 1, " then " theta = (n in z)

Find the absolute maximum and absolute minimu values of f(x) = x^(40) - x^(20) on [0, 1].

Pearson's coefficient of correlation r always follow:(a)rle1(b)rlt-1(c)|r|le1(d)|r|ge1

Write down all the subsets of the following sets : {0, 1}

Find the component statements of the following compound statements: Plants use sunlight, water and carbon dioxide for photosynthesis.

Sum to n terms the series 7+77+777+....

Find lambda in order that the equation x^(2)+lambda xy+y^(2)-5x=7y+6=0 may represents two straight line. Write down the equation to the lines parallel to these and passing through (1,2).

If |{:(1+x,2,3),(1,2+x,3),(1,2,3+x):}|=0 then x =

P is a point inside a Delta ABCof area K (K gt 0). The lengths of perpendiculars drawn to the sides BC, CA, ABof lengths a,b,c are respectivelyp_(1), p_(2) , p_(3) , a/p_(1) + b/p_(2) + c/p_(3) is minimum when

(r_1)/( R ) =sin A + sin B + sin Cthen the triangles is

Let U = { 1, 2, 3, 4, 5, 6, 7, 8, 9 }, A= { 1, 2, 3, 4}, B = { 2,4, 6, 8 } and C = { 3, 4, 5, 6 }. Find B'

Solve : x^2 - 2x + 4 = 0

If sin x + cos x = 1then x =

The vector equation of the plane passing through the origin and the line of intersection of the planes vecr. Veca = lamda = vecr.vecb = mu is

Consider two consecutive odd natural numbers both of which are larger than 10, such that their sum is less than 40. Derive two inequalities in x.

Consider two consecutive odd natural numbers both of which are larger than 10, such that their sum is less than 40. Find all pairs of odd natural numbers having the given properties .

If f:RrarrRis defined by f(x)=|x-2|+|x+2| for x epsilon R ,then lim_(xrarr2^-)f(x) is :

If f(x)={{:(mx^(2)+n",",xlt0),(nx+m",",0lexle1),(nx^(3)+m",",xgt1):}. For what integers m and n does both lim_(xrarr0)f(x) and lim_(xrarr1)f(x) exist?

For some constants a and b ,find the derivate of:x^2/2-(a+b)x

Find k if lines 5x - ky- 7=0 and 2x + 3y + 5 =0 are mutually perpendicular.

When the origin is shifted to (4, -5) by the translation of axes, find the coordinates of the point (i) (-2, 4) with reference to new axes. (ii) (4, -5) with reference to new axes.

If f(x) = (x^(2)-9)/(x-3) , find it Lim_(x to 3) f(x) exists .

Find the domain of each of the following functions given by f(x)= x|x|

A stone is dropped into a quiet pond and waves move in circles outward from the place where it strikes, at a speed of 30 cm per second. At the instant when the radius of the wave ring is 50 mt, find the rate of increase in the area and in the circumference of the wave ring.

If A+B+C=180^@ " then " sin 3A+ sin 3B+ sin 3C=

Find the maximum or minimum values of the following functions. x + (1)/(x), x gt 0

cos ^(2) ((pi)/(4)beta)- sin ^(2) (alpha - (pi)/(4))=

A= {x : x in Z, x" is a solution of " x^(4)- 16= 0} then A= "……….".

Equation at sides of rectangle are x=a, x=a', y=b and y=b'. Obtain equation of its diagonals.

Number of solutions of |(1)/(|x|-1)|=x+sinx, is

Let A= {1, 2, 3}, B= {3, 4} and C= {4, 5, 6}. Find (A xx B) uu (A xx C)

If one of the roots of 25cos^(2)theta+5costheta-12=0 is alpha then the value of sin2theta is ……….. ((pi)/(2)ltthetaltpi).

If tan 3 theta + tan theta = 2 tan 2 theta , " then " thetais equal to ( n in z)

Find the centroid of the triangle formed by the points (2,7) (3,-1)(-5,6).

In a triangle ABC, if D and E are mid points of sides AB and AC respectively. Show thatvecBE+ vecDC=(3)/(2)vecBC.

Obtain equation of the circle with centre (2,-5) and passes from point (3,2)

If cos (alpha - beta) + cos (beta - gamma) + cos (gamma - alpha) = (-3)/(2) then prove that cos alpha + cos beta+ cos gamma = sin alpha + sin beta + sin gamma = 0.

A card is drawn from a well - shuffled pack of playing cards . What is the probability that it is elther aspade or an ace or both .

Evaluate : cos24^(@)+cos55^(@)+cos125^(@)+cos204^(@)+cos300^(@).

Solve the following equations Cos theta- Cos 7 theta = Sin 4 theta

Write the sample space at an event that coin is tossed till to head is obtained observe that it is an example of finite or infinite sample space.

If y=((a-x)sqrt(a-x)-(b-x)sqrt(x-b))/(sqrt(a-x)+sqrt(x-b)) then dy/dx wherever it is defined is

A spring was hung from a hook in the ceiling.A number of different weights were attached to the spring to make it strech, and the total length of spring was measured each time shown in the following table:Q (v) How long will the spring be when 6 kilograms of weight omn it?

A spring was hung from a hook in the ceiling.A number of different weights were attached to the spring to make it strech, and the total length of spring was measured each time shown in the following table:Q (iv) If the spring has to stretch to 9 cm long, how much weight should be added?

If the focus of a parabola is (0,-3) and its directrix is y = 3, then its equation is ……..

If NN denotes the set of all positive integersand if f:NN rarrN is defined by f(n)= the sum of positive divisors of n then f(2^(k).3), where k is a positive integer is

Solve the following equations and write general solutions 4 sin theta sin 2 theta sin 4 theta = sin 3 theta

If the distance between the points (x, -8, 4) and (3, -5, 4) is 5 unit find x.