14949 + Interview Questions in Maths in Class 11 Page 109 InterviewSolution

5401.	Evaluate the following limits. Lt_(xto-4)(x+4)/(x^(2)-x-20)
Answer» ANSWER :`-1//9`

Discussion

5402.	If f(x) = 2 sin^(-1)sqrt(1-x) +sin^(-1)(2-sqrt(x(1-x)) where x in (0,(1)/2), then f'(x) is
Answer» `2/sqrt(X(1-x))` ZERO `-2/sqrt(x(1-x))` `PI` ANSWER :B

Discussion

5403.	If x and y are acute angles such that cos x+ cosy=(3)/(2) and sinx + sin y=(3)/4 " then " sin(x+y)=
Answer» `3/4` `3/5` `4/5` `2/5` ANSWER :C

Discussion

5404.	For an ideal gas a process PV diagram is a circle. An adiabatic from A passes through C. An isothrem from A passes through B. We take a part of the circular cyclic process. Comment on the sign of the quantity of column -I {:("Column"-I,"Column"-II),((A)"Heat given to the gas in going from A to C along circle",(P)"Positve"),((B)"Heat given to the gas in going from B to C along circle",(Q)"Negative"),((C)"Heat given to the gas in going from C to D along circle",(R)"Zero"),(,(S)"can't be said"):}
Answer» SOLUTION :(A)A to C along circe net work DONE is + ve and triangleV is - ve But `(triangle omega - triangleV) gt` 0 So, `TRIANGLEQ = triangle omega - triangle U` `triangleQ gt 0` (B)Bto CALONG circle there is compression so work done is (-ve) and `triangleU is (-ve) so triangleQ is -ve` (c) Same as B to C along circle

Discussion

5405.	Equation of a plane passing through (1,1,1) and containing x-axis is ax+by+cz+d=0(bgt0) then
Answer» `clta=dltb` `dlta=bltc` `bltc=dlta` `dlta=cltb` ANSWER :A

Discussion

5406.	If A is any square matrix of order 'n' Observe the following list {:("List-I","List-II"),("(A) \| adjA \|",(1)\|A\|^(n-2)A),("(B) adj (adjA)",(2)\|A\|^(n(n-1))),("(C) (adjA)"^(-1),(3)\|A\|^((n-1)^(2))),("(D) \| adj(adj A)\|",(4)\|A\|^(n-1)):} , Match from List - I to List - II
Answer» `{:(A,B,C,D),(4,5,1,3):}` `{:(A,B,C,D),(4,5,1,2):}` `{:(A,B,C,D),(4,1,5,2):}` `{:(A,B,C,D),(4,1,5,3):}` ANSWER :D

Discussion

5407.	Solve the triangle ABC if a=5, b=4 and C=68^(@)
Answer» ANSWER :`B=46^@, 40'; A=65^(@) 20'; c=5.1`

Discussion

5408.	Find the angle in radian through which a pendulum swings if its length is 75 cm and the tip describes an arc of length (i) 10 cm (ii) 15 cm (iii) 21 cm
Answer» ANSWER :`(i) (2)/(15)` (II) `1/5` (III) `7/25`

Discussion

5409.	Find lambda so that x^(2) + 5xy + 4y^(2) + 3x + 2y + lambda = 0 may represent a pair of straight lines. Find also the angle between them for this value of a lambda
Answer» ANSWER :`LAMBDA= (-10)/(9), tan^(-1)((3)/(5))`

Discussion

5410.	The stationary points of y=sinx are
Answer» `X=pi/4` `x=npi,NINZ` `x=(2n+1)pi/2,ninz` `x=2npi,ninz` ANSWER :C

Discussion

5411.	Find the mean deviation using median for the following datas:
Answer» SOLUTION :NA

Discussion

5412.	Given that f (n theta ) = (2 sin 2 theta )/( cos 2 theta - cos 4 n theta ) and f (theta) + f (2 theta) + f ( 3 theta) +…+ f (n theta) = (sin lamda theta)/( sin theta sin mutheta)then the vlaue
Answer» ANSWER :1

Discussion

5413.	a^(2)x^(2)+2xy+9y^(2)=0 represent a pair of distinct lines then 'a' lies in
Answer» `[-(1)/(3),(1)/(3)]` `(-(1)/(3),(1)/(3))` `[-(1)/(2),(1)/(2)]` `(-(1)/(2),(1)/(2))` ANSWER :B

Discussion

5414.	What is the number of ways of choosing 3 cards from a pack of 52 playing cards ? In how many of these three cards are face cards. In how many of these cards are of same colour ? In how may of these cards of the same suit ?
Answer» ANSWER :22100, 220, 5200, 1144

Discussion

5415.	Reduce the equation sqrt3x + y - 8 = 0into normal form. Find the values of p and omega.
Answer» <P> ANSWER :`p= 4 " and " OMEGA= 30^(@)`

Discussion

5416.	Let f.g.hbe real valued functions defined on the interval [0,1] by f( x) = e^(x^(2)) +e^(-x^(2)) , g (x)= x.e^(x^(2))+e^(-x^(2))and h (x) = x^(2) ,e^(x^(2)) +e^(-x^(2))If a,b,c denote respectively the absolute max. values of f.g.h on [0,1] then
Answer» `a=B` and `C != b` `a=c` and `a != b` `a != b` and `c != b` `a=b=c` ANSWER :D

Discussion

5417.	From the following data, using mean, calculate mean deviation and the coefficient of mean deviation. 15, 17, 19, 25, 30, 35, 48
Answer» ANSWER :M.D = 9.14, COEFFT. of M.D = 0.338

Discussion

5418.	The P.V.'s of the vertices of a DeltaABC are bar(i)+bar(j)+bar(k), 4bar(i)+bar(j)+bar(k), 4bar(i)+5bar(j)+bar(k). The P.V. of the circumcentre of DeltaABC is
Answer» `5/2bar(i)+3BAR(J)+BAR(K)` `5bar(i)+3/2bar(j)+bar(k)` `5bar(i)+3bar(j)+1/2bar(k)` `bar(i)+bar(j)+bar(k)` ANSWER :A

Discussion

5419.	Product of the intercepts of a straight line is 1 and the lines passes through (-12,1) then its equation is
Answer» `2x+25y=1` `x+13y=1` `x+16y=4` `16x+y=4` ANSWER :C

Discussion

5420.	A box contains 10 red marbles, 20 blue marbles and 30 green marbles. 5 marbles are drawn fromthe box.What is the probability that ( I ) all will be blue ? ( ii) atleast one will be green?
Answer» Answer :(i) `(""^(20)C_(5))/(""^(60)C_(5))` (II) `1 - (""^(30)C_(5))/(""^(60)C_(4))`

Discussion

5421.	sinx + sin^(2) x = 1 rArr cos^(2) x + cos^(4) x=
Answer» 0 1 2 -1 Answer :B

Discussion

5422.	If 8x^(2)-14xy+5y^(2)=0represents two sides of a triangle and centriod of the triangle is (2, 2) then midpoint of third side is
Answer» (2,-2) (-2,2) `((4)/(3),(4)/(3))` (3,3) ANSWER :D

Discussion

5423.	The weights of coffee in 70 jars is shown in the following table Determin variance and standard deviation of the above distribution
Answer» SOLUTION : `thereforesigma^(2)=(Sigmaf_(i)d_(i)^(2))/(Sigmaf_(i))-((Sigmaf_(i)d_(i))/(Sigmaf_(i)))^(2)=(102)/(70)-((-38)/(70))^(2)` Now =1.4571-02916=1.1655 `sigma=sqrt(1.1655)=1.08g`

Discussion

5424.	( x) /( y ) + (y)/(z) , ( z)/(x) + (z)/(x) + (x)/(y)then the area of the triangle is
Answer» `XYZ` ` 1` ` sqrt((X)/(y) + (y)/(Z) + (z) /(x) ) ` ` (x)/(y) + (y)/(z) + (z) /(x)` Answer :C

Discussion

5425.	The locus of the point P such that PA^2+PB^2=2PC^2 where A=(1,3,2),B=(2,4,-3),C=(-2,1,3) is
Answer» `X^(2)+y^(2)+Z^(2)-6y-8z+12 =0` `x^(2)+y^(2)+z^(2)-6y-8z+29 =0` `2(x^(2)+y^(2)+z^(2))-x+y-4z+12 =0` `14x+10y-14-15 = 0` ANSWER :D

Discussion

5426.	Kavita draws a card from a pack of cards . What is the probability that she drawsa heart or a spade ?
Answer» ANSWER :`(1)/(2)`

Discussion

5427.	Find the principal solutions of the equation sinx=sqrt(3)/(2).
Answer» ANSWER :`X = PI /3 and (2PI)/(3).`

Discussion

5428.	Find the component statement of the compound statement given below :Rekha is studying in class eleven and she has to offer 5 subjects.
Answer» ANSWER :COMPOUND statement The COMPONENT statements are. Rekha is studying in class eleven. She has to offer 5 SUBJECTS.

Discussion

5429.	For each of the following compound statements first identify the connecting words and then break it into component statements: Gandhiji was born in Porbandar and Porbandar is in Gujarat.
Answer» ANSWER :GUJARAT

Discussion

5430.	The point of intersection of the curves y=cosh(x) and y=sech(x) is
Answer» (0, 0) (1, 1) (0, 1) (1, 0) ANSWER :C

Discussion

5431.	For each of the following compound statements first identify the connecting words and then break it into component statements: (1)^(2)=1 or (1)^(3)=1
Answer» ANSWER :1

Discussion

5432.	For each of the following compound statements first identify the connecting words and then break it into component statements: Triangle has three sides and three angles.
Answer» ANSWER :3 ANGLES, 3 SIDES

Discussion

5433.	If sin A+sin 2A+sin ^(3) A=cos A+cos 2A+cos 3A, then tan 2A is equal to
Answer» 1 `-1` `1/2` `-1/2` ANSWER :A

Discussion

5434.	For each of the following compound statements first identify the connecting words and then break it into component statements: 3+4=7 and 2+2=4
Answer» ANSWER :4

Discussion

5435.	For each of the following compound statements first identify the connecting words and then break it into component statements: There are 5 days in a week or there are 24 hours ina day.
Answer» ANSWER :24 HOURS in a DAY

Discussion

5436.	If -1 lt x lt 0," then "cos^(-1)x is equal to
Answer» `"sec"^(-1)1/x` `PI-sin^(-1)sqrt(1-x^(2))` `pi+"tan"^(-1)(sqrt(1-x^(2)))/x` `"cot"^(-1)x/(sqrt(1-x^(2)))` ANSWER :A::B::C::D

Discussion

5437.	Domain of the function sqrt(log {(5x-x ^(2))//6}) is
Answer» `(2,3)` `[2,3]` `[1,2]` `[1,3]` ANSWER :B

Discussion

5438.	Insert three numbers between 1 and 256 so that the resulting sequence is a G.P.
Answer» ANSWER :`4, 16, 64`

Discussion

5439.	Let h(x) be differentiable for all x and let f(x) = (kx+e^(x)),h(x) where k is some constant . If h(0) = 5 , h'(0) =- 2 and f'(0)= 18 , then the value of k is
Answer» 5 4 3 `2.2` ANSWER :C

Discussion

5440.	The sum of the first three terms of a G.P. is (13)/(12) and their product is -1. Find the G.P.
Answer» ANSWER :`(4)/(3) , -1 , (3)/(4),...... , or (3)/(4)-1, (4)/(3)`

Discussion

5441.	Two vertical poles 20m and 80m heigh stand apart on a horizontal plane. The height of the point of intersection of the lines joining the top of each pole to the foot of the other is
Answer» 13m 14m 15m 16m Answer :A

Discussion

5442.	If the letters of the word REGULATIONS bearranged at random, find the probability that there will be exactly fourletters between the Rand the E.
Answer» ANSWER :`=(6)/(55)`.

Discussion

5443.	lim_(xto1)(x^(365)-365x+364)/((x-1)^(2)) =………..
Answer» 66.463 64.34 66.63 64.436 Answer :A

Discussion

5444.	One of the solution of \|y-cosa\|lex, where x and a are values that satisfy the given equation is
Answer» `y in [-5,7]` `y in [-7,5]` `y INN [5,7]` `y in [-7,-5]` ANSWER :B

Discussion

5445.	Let {{:(x^(3)+x^(2)+3x+sinx\|(3+"sin"(1)/(x)),x ne0),(0,x=0):} Then the number of points where f(x) attrains its minimum value is ___________
Answer» ANSWER :1

Discussion

5446.	Find the difference of slopes of the lines represented by y^2- 2xy sec^2 alpha+(3+tan^2 alpha)(-1+tan^2 alpha)x^2=0
Answer» ANSWER :4

Discussion

5447.	The middle point of line segment joining (3,-1) and (1,1) is shifted by 2units (increasing y) perpendicular to line segment. Coordinates of point in new position is
Answer» `(2+SQRT(2),sqrt(2))` `(2-sqrt(2),sqrt(2))` `(1-sqrt(2),sqrt(2))` `(1+sqrt(2),sqrt(2))` ANSWER :A

Discussion

5448.	Statement 1: If the quadrilateral Q_(1)formed by joining midpoints of sides of another quadrilateral Q_(2) is cyclic, then Q_(1) is necessarily a rectangle. Statement 2 : The quadrilateral Q_(1) formed by joining midpoints of sides of another quadrilateral Q_(2) is always a parallelogram.
Answer» Statement-1 is TRUE, Statement-2 is True, Statement-2 is a CORRECT EXPLANATION for Statement-1 Statement-1 is True, Statement-2 is True, Statement-2 NOT a correct explanation for Statement-1 Statement-1 is True, Statement-2 is FALSE Statement -1 is False, Statement-2 is True Answer :A

Discussion

5449.	If \|vec(a)\| = \|vec(b)\|=2, then (vec(a) xx vec(b))^(2) + (vec(a).vec(b))^(2)=
Answer» 2 4 8 16 Answer :D

Discussion

5450.	Determine the x- intercept 'a' and the y-intercept 'b' of the following lines. Sketch each. x-y-7=0
Answer» ANSWER : `a=7, b=-7`

Discussion

Explore topic-wise InterviewSolutions in .

Evaluate the following limits. Lt_(xto-4)(x+4)/(x^(2)-x-20)

If f(x) = 2 sin^(-1)sqrt(1-x) +sin^(-1)(2-sqrt(x(1-x)) where x in (0,(1)/2), then f'(x) is

If x and y are acute angles such that cos x+ cosy=(3)/(2) and sinx + sin y=(3)/4 " then " sin(x+y)=

Equation of a plane passing through (1,1,1) and containing x-axis is ax+by+cz+d=0(bgt0) then

If A is any square matrix of order 'n' Observe the following list {:("List-I","List-II"),("(A) | adjA |",(1)|A|^(n-2)A),("(B) adj (adjA)",(2)|A|^(n(n-1))),("(C) (adjA)"^(-1),(3)|A|^((n-1)^(2))),("(D) | adj(adj A)|",(4)|A|^(n-1)):} , Match from List - I to List - II

Solve the triangle ABC if a=5, b=4 and C=68^(@)

Find the angle in radian through which a pendulum swings if its length is 75 cm and the tip describes an arc of length (i) 10 cm (ii) 15 cm (iii) 21 cm

Find lambda so that x^(2) + 5xy + 4y^(2) + 3x + 2y + lambda = 0 may represent a pair of straight lines. Find also the angle between them for this value of a lambda

The stationary points of y=sinx are

Find the mean deviation using median for the following datas:

Given that f (n theta ) = (2 sin 2 theta )/( cos 2 theta - cos 4 n theta ) and f (theta) + f (2 theta) + f ( 3 theta) +…+ f (n theta) = (sin lamda theta)/( sin theta sin mutheta)then the vlaue

a^(2)x^(2)+2xy+9y^(2)=0 represent a pair of distinct lines then 'a' lies in

What is the number of ways of choosing 3 cards from a pack of 52 playing cards ? In how many of these three cards are face cards. In how many of these cards are of same colour ? In how may of these cards of the same suit ?

Reduce the equation sqrt3x + y - 8 = 0into normal form. Find the values of p and omega.

Let f.g.hbe real valued functions defined on the interval [0,1] by f( x) = e^(x^(2)) +e^(-x^(2)) , g (x)= x.e^(x^(2))+e^(-x^(2))and h (x) = x^(2) ,e^(x^(2)) +e^(-x^(2))If a,b,c denote respectively the absolute max. values of f.g.h on [0,1] then

From the following data, using mean, calculate mean deviation and the coefficient of mean deviation. 15, 17, 19, 25, 30, 35, 48

The P.V.'s of the vertices of a DeltaABC are bar(i)+bar(j)+bar(k), 4bar(i)+bar(j)+bar(k), 4bar(i)+5bar(j)+bar(k). The P.V. of the circumcentre of DeltaABC is

Product of the intercepts of a straight line is 1 and the lines passes through (-12,1) then its equation is

A box contains 10 red marbles, 20 blue marbles and 30 green marbles. 5 marbles are drawn fromthe box.What is the probability that ( I ) all will be blue ? ( ii) atleast one will be green?

sinx + sin^(2) x = 1 rArr cos^(2) x + cos^(4) x=

If 8x^(2)-14xy+5y^(2)=0represents two sides of a triangle and centriod of the triangle is (2, 2) then midpoint of third side is

The weights of coffee in 70 jars is shown in the following table Determin variance and standard deviation of the above distribution

( x) /( y ) + (y)/(z) , ( z)/(x) + (z)/(x) + (x)/(y)then the area of the triangle is

The locus of the point P such that PA^2+PB^2=2PC^2 where A=(1,3,2),B=(2,4,-3),C=(-2,1,3) is

Kavita draws a card from a pack of cards . What is the probability that she drawsa heart or a spade ?

Find the principal solutions of the equation sinx=sqrt(3)/(2).

Find the component statement of the compound statement given below :Rekha is studying in class eleven and she has to offer 5 subjects.

For each of the following compound statements first identify the connecting words and then break it into component statements: Gandhiji was born in Porbandar and Porbandar is in Gujarat.

The point of intersection of the curves y=cosh(x) and y=sech(x) is

For each of the following compound statements first identify the connecting words and then break it into component statements: (1)^(2)=1 or (1)^(3)=1

For each of the following compound statements first identify the connecting words and then break it into component statements: Triangle has three sides and three angles.

If sin A+sin 2A+sin ^(3) A=cos A+cos 2A+cos 3A, then tan 2A is equal to

For each of the following compound statements first identify the connecting words and then break it into component statements: 3+4=7 and 2+2=4

For each of the following compound statements first identify the connecting words and then break it into component statements: There are 5 days in a week or there are 24 hours ina day.

If -1 lt x lt 0," then "cos^(-1)x is equal to

Domain of the function sqrt(log {(5x-x ^(2))//6}) is

Insert three numbers between 1 and 256 so that the resulting sequence is a G.P.

Let h(x) be differentiable for all x and let f(x) = (kx+e^(x)),h(x) where k is some constant . If h(0) = 5 , h'(0) =- 2 and f'(0)= 18 , then the value of k is

The sum of the first three terms of a G.P. is (13)/(12) and their product is -1. Find the G.P.

Two vertical poles 20m and 80m heigh stand apart on a horizontal plane. The height of the point of intersection of the lines joining the top of each pole to the foot of the other is

If the letters of the word REGULATIONS bearranged at random, find the probability that there will be exactly fourletters between the Rand the E.

lim_(xto1)(x^(365)-365x+364)/((x-1)^(2)) =………..

One of the solution of |y-cosa|lex, where x and a are values that satisfy the given equation is

Let {{:(x^(3)+x^(2)+3x+sinx|(3+"sin"(1)/(x)),x ne0),(0,x=0):} Then the number of points where f(x) attrains its minimum value is ___________

Find the difference of slopes of the lines represented by y^2- 2xy sec^2 alpha+(3+tan^2 alpha)(-1+tan^2 alpha)x^2=0

The middle point of line segment joining (3,-1) and (1,1) is shifted by 2units (increasing y) perpendicular to line segment. Coordinates of point in new position is

Statement 1: If the quadrilateral Q_(1)formed by joining midpoints of sides of another quadrilateral Q_(2) is cyclic, then Q_(1) is necessarily a rectangle. Statement 2 : The quadrilateral Q_(1) formed by joining midpoints of sides of another quadrilateral Q_(2) is always a parallelogram.

If |vec(a)| = |vec(b)|=2, then (vec(a) xx vec(b))^(2) + (vec(a).vec(b))^(2)=

Determine the x- intercept 'a' and the y-intercept 'b' of the following lines. Sketch each. x-y-7=0