14949 + Interview Questions in Maths in Class 11 Page 213 InterviewSolution

10601.	The minimum value of f(x)=x^(2)+(250)/(x) is
Answer» 15 25 45 75 Answer :D

Discussion

10602.	Find the mean variance and standard deviation using short-cut method
Answer» SOLUTION : Let assumed mean `A=92.5` and `h=5` Mean `barx=A+(sumf_(i)d_(i))/(sumf_(i))xxh=62.5+(6xx5)/60=93` VARIANCE `sigma^(2)=h^(2)[((sumf_(i)d_(i)^(2)))/N-((sumf_(i)d_(i))/N)^(2)]` `=5^(2)[254/60-(6/60)^(2)]` `=25/(60^(2))[15240-36]` `=1/144xx15204=105.58` STANDARD deviation `=SQRT(105.58)` `=10.28`

Discussion

10603.	If bara,barc,bard are coplaner then the value of (bard+bara).[baraxx{barbxx(barcxxbard)}]=
Answer» 0 1 `[BARA BARB barc]` NONE of them Answer :A

Discussion

10604.	One of the general solutions of sqrt(3) cos theta - 3 sin theta = 4 sin 2 theta cos 3 thetais
Answer» `n pi + pi //18 , n in Z` `n pi // 2 + pi // 6, AA n in Z` `n pi // 3 + pi // 18 , n in Z` `(n pi)/( 3) + (pi)/( 9) , n in Z` ANSWER :C

Discussion

10605.	If alpha+beta+gamma =2pi, then
Answer» `"tan"(ALPHA)/(2)+"tan"(beta)/(2)+"tan"(GAMMA)/(2)="tan"(alpha)/(2)"tan"(beta)/(2)"tan"(gamma")/(2)` `"tan"(alpha)/(2)"tan"(beta)/(2)+"tan"(beta)/(2)"tan"(gamma)/(2)+"tan"(gamma)/(2)"tan"(alpha)/(2)=1` `"tan"(alpha)/(2)+"tan"(beta)/(2)+"tan"(gamma)/(2)=-"tan"(alpha)/(2)"tan"(beta)/(2)"tan"(gamma)/(2)` `sum tan((alpha)/(2))tan((beta)/(2))=-1` Answer :A

Discussion

10606.	Find the 10^(th) and n^(th) terms of the G.P . 5, 25,125 ...............
Answer» ANSWER :`a_(10)= 5^(10), a_(N)= 5^(n)`

Discussion

10607.	What is the area of a sector of circle with radius r and central angle theta?
Answer» ANSWER :`(1)/(2)RR^(2)THETA`

Discussion

10608.	Using Binomial Theorem, indicate which number is larger (1.1)^10000 or 1000.
Answer» ANSWER :` :. ( 1.1)^(10000) ` is a LARGER .

Discussion

10609.	Solve sqrt(2)(sinx+cosx)=sqrt(3)
Answer» ANSWER :`2NPI+(5PI)/(12),2npi+(PI)/(12)`

Discussion

10610.	Find the points on the line 3x-4y-1=0 which are at a distance of 5 units from the point (3,2).
Answer» ANSWER :`(7,5),(-1,-1)`

Discussion

10611.	If \|z-3+ i\|=4, then the locus of z is
Answer» `x^(2) + y^(2)- 6= 0` `x^(2) + y^(2) - 3x + y-6= 0` `x^(2) + y^(2)- 6X - 2= 0` `x^(2) + y^(2)- 6x + 2Y -6= 0` Answer :D

Discussion

10612.	Show that the straight line x + y=1 touches the hyperbola 2x ^(2) - 3y ^(2)= 6. Also find the coordinates of the point of contact.
Answer» ANSWER :`(3, -2)`

Discussion

10613.	Write down all the subsets of the following sets {1,2,3}
Answer» ANSWER :`PHI, {1, 2, 3}, {1}, {2}, {3}, {1, 2}, {2, 3}, {1, 3}`

Discussion

10614.	Prove that 3 sin ""pi/6 sec ""pi/3 -4 sin ""(5pi)/(6) cot"" (pi)/(4) = 3 -4 xx 1/2 =1=R.H.S.
Answer» ANSWER :`=2-4 XX 1/2 =1 =R.H.S.`

Discussion

10615.	The values of b and c for which the identity f(x+1)-f(x)=8x+3 is satisfied, where f(x)=bx^(2)+cx+d, are
Answer» `B=2, C=1` `b=4, c= -1` `b= -1, c=4` `b = -1, c = 1` ANSWER :B

Discussion

10616.	The plane x - 2y + 7z + 21=0
Answer» contains the LINE `(x+1)/(-3) = (y-3)/(2) = (z+2)/(1) ` contains the point `(0,7,-1)` is PERPENDICULAR to the line `x/1 = (y)/(-2) = z/7` is parallel to the plane `x - 2Y +7z =0` Answer :A::B::C::D

Discussion

10617.	Determine the slope and y- intercept of the following lines: y=sqrt(3)x-7
Answer» ANSWER :7

Discussion

10618.	A flag-staff stands on a tower which is on level ground. The total height of the flag-staff and tower taaken together is 300 metres. The flag-staff subtends an angle of Tan^(-1)(1/5) at a point P on the level ground at a distance 300 metres from the foot of the tower. The heightof the tower is
Answer» 100 metres 200 metres 250 metres 300 metres Answer :C

Discussion

10619.	Two line from the family of lines (1+2lambda)x-(1+lambda)y+1=0 and the line x+y=5 form an equilateral triangle. The equation of the two lines can be
Answer» `y-2=(2+sqrt3)(x-1)` `y-2=(2-sqrt3)(x-1)` `y-2=(-SQRT2)(x-1)` `y-1=(3-sqrt2)(x-1)` ANSWER :A::B

Discussion

10620.	Find the range of the following function f(x)= \|x-1\|, x in R
Answer» ANSWER :`[0, OO)`

Discussion

10621.	If veca=xveci+vecj-veck,vecb=veci-vecj-veck,vecc=veci-2vecj+3veck and veca.vecb X vecc =7 then x is :
Answer» 2 -2 1 -1 Answer :B

Discussion

10622.	Determine real values of x and y for which each statement is true (3-4i) (x+yi)=1 + 0i
Answer» ANSWER :`X= (3)/(25), y= (4)/(25)`

Discussion

10623.	Prove bymathematical induction that 1!+ (2xx2!)+ ( 3 xx 3!) + …+ ( n xx n!)= ( n + 1)! -1
Answer» ANSWER :` ( K + 2)! -1`

Discussion

10624.	The minimum and maximum values of 8 cos 3x - 15 sin3x are
Answer» `-7, 7` `-23, 23` `-17, 17` `-15, 8` Answer :C

Discussion

10625.	The P.V.'s of A, B, C are bar(i)+bar(j)+bar(k), 4bar(i)+bar(j)+bar(k), 4bar(i)+5bar(j)+bar(k), then the P.V. of the incentre of DeltaABC is
Answer» `1/3bar(i)+1/3bar(J)+1/3bar(K)` `(BAR(i)+bar(j)-bar(k))/3` `bar(i)+bar(j)-bar(k)` `(bar(i)-bar(j)-bar(k))/3` ANSWER :A

Discussion

10626.	If a, b and c are in GP, then the value of (a-b)/(b-c) is equal to……..
Answer» ANSWER :`(B)/(C )`

Discussion

10627.	The volume of a parallelopiped whose edges are represented by -12bari+lamdabark,3barj-barkand 2bari + barj -15bark is 546, then lamda =
Answer» `-3` `-2` 2 3 Answer :A

Discussion

10628.	The sum of interior angles of a triangle is 180^(@). Show that the sum of the interior angles of polygons with 3,4,5,6…..sides form an arithmetic progression. Find the sum of the interior angles for a 21 sided polygon.
Answer» ANSWER :`3420^(@)`

Discussion

10629.	AM, GM, HM denote the arithmetic, geometric and harmonic means of a and b then,
Answer» `AM GE GM` `GM ge HM` `AM ge GM ge HM` `AM GT GM gt HM` ANSWER :d

Discussion

10630.	Assertion (A) : if 2sin^(2)((pi)/(2)cos^(2)x)=1-cos(pisin2x), xne(2n+1)(pi)/(2),n is a integer, then sin2x+cos2x=(1)/(5) Reason (R ) : sin2x+cos2x=(2-(tanx-1)^(2))/(1+tan^(2)x). Then the true statement among the following is
Answer» A is true, R is false A is false, R is true A is true, R is true, R implies A A is false, R is false ANSWER :B

Discussion

10631.	Find all pairs of consecutive odd natural numbers, both of which are larger than 10, such that their sum is less than 40.
Answer» Answer :(11, 13), (13, 15), (15, 17), (17, 19)

Discussion

10632.	x= {1, 2, 3, 4}, y= {1, 5, 9, 11, 15, 16} which of the following relations are functions from x to y ? (1) f_(1)= {(1, 1) (2,11) (3,1) (4, 15)} (2) f_(2)= {(1, 1) (2,7)(3,5)} (3) f_(3)= {(1, 5) (2,9) (3, 1) (4, 5) (2, 11)}
Answer» ANSWER :Only `f_(1) is a FUNCTION

Discussion

10633.	Using truth table , prove that :(ptoq)to[(~ptoq)toq]is a tautology.
Answer» Answer :(i)Some circles are not round . (ii) The SET of prime NUMBERS is FINITE.

Discussion

10634.	sech^(2)("tan"h^(-1)1/2)+cosech^(2)(coth^(-1)3)=
Answer» `(35)/(9)` `(43)/(4)` `(35)/(4)` `(43)/(9)` ANSWER :C

Discussion

10635.	The triangle formed by the pair of lines x^(2)-4y^(2)=0 and x-a=0 is always
Answer» EQUILATERAL Isosceles Right ANGLED scalane ANSWER :B

Discussion

10636.	Let h(x)=f(x)-[f(x)]^(2)+[f(x)]^(3) for every real number 'x' then
Answer» ANSWER :a

Discussion

10637.	If alpha,beta are the roots of the equation x^(2)+x+1=0, find the value of alpha^(3)-beta^(3).
Answer» ANSWER :2

Discussion

10638.	(i) Find the equation of a circle passes through the origin and cuts the intercepts of 6 units and 8 units on X-axis and Y-axis respectively. (ii) Find the equation of a circle which passes through the two points on y-aixs whose distance from origin is 4 units and radius is 5 units.
Answer» ANSWER :`X^(2)+y^(2)-6x-8y=0`

Discussion

10639.	If tr(A)=3,tr(B)=5 then tr(AB)=
Answer» 15 8 `3//5` cannot SAY ANSWER :D

Discussion

10640.	If bx+cy=a, where a,b,c are of the same sign, be a line such that the area enclosed by the line and the axes of reference is 1/8unit^2, then : (A) b,a,c are in G.P. (B) b,2a,c are in G.P. (C) b,a/2,c are in A.P. (D) b,-2a,c are in G.P.
Answer» B,a,C are in GP b,2A,c are in GP b,a/2,c are in AP b, -2a, c are in GP Answer :B

Discussion

10641.	Find the values of lamda and mu if both the roots of the equation (3lamda+1)x^(2)=(2lamda+3mu)x-3 are infinite.
Answer» ANSWER :`LAMBDA= - 1/3 , MU = 2/9`

Discussion

10642.	Write the truth value of the following statement: 80 is the multiple of 5 and 4.
Answer» ANSWER :1

Discussion

10643.	In Delta ABC , if x=tan((B-C)/(2))tan.(A)/(2),y=tan((C-A)/(2))tan.(B)/(2) and z=tan((A-B)/(2))tan.(C)/(2) then (x+y+z)=.
Answer» `-2XYZ` `2xyz` `XYZ` `-xyz` ANSWER :D

Discussion

10644.	Let f(x)=Sec^(-1)[1+cos^(2)x] where [.] denotes the greatest integer function I : Domain of f(x) is R II : Range of f(x) is {Sec^(-1)1, Sec^(-1)2}
Answer» DOMAIN of F is R domain of f is [1, 2] domain of f is [2, 1] range of f is `{SEC^(-1)1, sec^(-1)2}` ANSWER :A::D

Discussion

10645.	Find the angle in radians 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 :`(7)/(25)` RADIAN.

Discussion

10646.	Iftwobalanced diceare tossedonce,the probabiltiy of the eventthesumof the integerscomingon the uppersidesof the twodice is 9 is .
Answer» `(7)/(18)` `(5)/(36)` `(1)/(9)` `(1)/(6)` ANSWER :C

Discussion

10647.	A= {1, 2, 3, 4, 5}, B= {4, 5, 6, 7, 8}, C= {7, 8, 9, 10, 11}, D= {10, 11, 12, 13, 14}. Find the following sets. B cup C
Answer» ANSWER :`={4, 5, 6, 7, 8, 9, 10, 11}`

Discussion

10648.	period of cos"" (pix)/(4) - 2 cosec (pix)/( 6) + 5 tan"" (pix)/(3) is
Answer» 12 24 48 6 Answer :B

Discussion

10649.	A spherical balloon of radius 5 subtends an angle 60^(@) at a point on the horzontal. If the angle of elevation of its centre is 30^(@), the height of the centre of the balloon is
Answer» `5sqrt2 UNITS` 10 units 15 units 20 units Answer :B

Discussion

10650.	Evaluate the limits. Lt_(xto0)(sqrt(x+4)-2)/x
Answer» ANSWER :`1/4`

Discussion

Explore topic-wise InterviewSolutions in .

The minimum value of f(x)=x^(2)+(250)/(x) is

Find the mean variance and standard deviation using short-cut method

If bara,barc,bard are coplaner then the value of (bard+bara).[baraxx{barbxx(barcxxbard)}]=

One of the general solutions of sqrt(3) cos theta - 3 sin theta = 4 sin 2 theta cos 3 thetais

If alpha+beta+gamma =2pi, then

Find the 10^(th) and n^(th) terms of the G.P . 5, 25,125 ...............

What is the area of a sector of circle with radius r and central angle theta?

Using Binomial Theorem, indicate which number is larger (1.1)^10000 or 1000.

Solve sqrt(2)(sinx+cosx)=sqrt(3)

Find the points on the line 3x-4y-1=0 which are at a distance of 5 units from the point (3,2).

If |z-3+ i|=4, then the locus of z is

Show that the straight line x + y=1 touches the hyperbola 2x ^(2) - 3y ^(2)= 6. Also find the coordinates of the point of contact.

Write down all the subsets of the following sets {1,2,3}

Prove that 3 sin ""pi/6 sec ""pi/3 -4 sin ""(5pi)/(6) cot"" (pi)/(4) = 3 -4 xx 1/2 =1=R.H.S.

The values of b and c for which the identity f(x+1)-f(x)=8x+3 is satisfied, where f(x)=bx^(2)+cx+d, are

The plane x - 2y + 7z + 21=0

Determine the slope and y- intercept of the following lines: y=sqrt(3)x-7

A flag-staff stands on a tower which is on level ground. The total height of the flag-staff and tower taaken together is 300 metres. The flag-staff subtends an angle of Tan^(-1)(1/5) at a point P on the level ground at a distance 300 metres from the foot of the tower. The heightof the tower is

Two line from the family of lines (1+2lambda)x-(1+lambda)y+1=0 and the line x+y=5 form an equilateral triangle. The equation of the two lines can be

Find the range of the following function f(x)= |x-1|, x in R

If veca=xveci+vecj-veck,vecb=veci-vecj-veck,vecc=veci-2vecj+3veck and veca.vecb X vecc =7 then x is :

Determine real values of x and y for which each statement is true (3-4i) (x+yi)=1 + 0i

Prove bymathematical induction that 1!+ (2xx2!)+ ( 3 xx 3!) + …+ ( n xx n!)= ( n + 1)! -1

The minimum and maximum values of 8 cos 3x - 15 sin3x are

The P.V.'s of A, B, C are bar(i)+bar(j)+bar(k), 4bar(i)+bar(j)+bar(k), 4bar(i)+5bar(j)+bar(k), then the P.V. of the incentre of DeltaABC is

If a, b and c are in GP, then the value of (a-b)/(b-c) is equal to……..

The volume of a parallelopiped whose edges are represented by -12bari+lamdabark,3barj-barkand 2bari + barj -15bark is 546, then lamda =

The sum of interior angles of a triangle is 180^(@). Show that the sum of the interior angles of polygons with 3,4,5,6…..sides form an arithmetic progression. Find the sum of the interior angles for a 21 sided polygon.

AM, GM, HM denote the arithmetic, geometric and harmonic means of a and b then,

Assertion (A) : if 2sin^(2)((pi)/(2)cos^(2)x)=1-cos(pisin2x), xne(2n+1)(pi)/(2),n is a integer, then sin2x+cos2x=(1)/(5) Reason (R ) : sin2x+cos2x=(2-(tanx-1)^(2))/(1+tan^(2)x). Then the true statement among the following is

Find all pairs of consecutive odd natural numbers, both of which are larger than 10, such that their sum is less than 40.

x= {1, 2, 3, 4}, y= {1, 5, 9, 11, 15, 16} which of the following relations are functions from x to y ? (1) f_(1)= {(1, 1) (2,11) (3,1) (4, 15)} (2) f_(2)= {(1, 1) (2,7)(3,5)} (3) f_(3)= {(1, 5) (2,9) (3, 1) (4, 5) (2, 11)}

Using truth table , prove that :(ptoq)to[(~ptoq)toq]is a tautology.

sech^(2)("tan"h^(-1)1/2)+cosech^(2)(coth^(-1)3)=

The triangle formed by the pair of lines x^(2)-4y^(2)=0 and x-a=0 is always

Let h(x)=f(x)-[f(x)]^(2)+[f(x)]^(3) for every real number 'x' then

If alpha,beta are the roots of the equation x^(2)+x+1=0, find the value of alpha^(3)-beta^(3).

(i) Find the equation of a circle passes through the origin and cuts the intercepts of 6 units and 8 units on X-axis and Y-axis respectively. (ii) Find the equation of a circle which passes through the two points on y-aixs whose distance from origin is 4 units and radius is 5 units.

If tr(A)=3,tr(B)=5 then tr(AB)=

If bx+cy=a, where a,b,c are of the same sign, be a line such that the area enclosed by the line and the axes of reference is 1/8unit^2, then : (A) b,a,c are in G.P. (B) b,2a,c are in G.P. (C) b,a/2,c are in A.P. (D) b,-2a,c are in G.P.

Find the values of lamda and mu if both the roots of the equation (3lamda+1)x^(2)=(2lamda+3mu)x-3 are infinite.

Write the truth value of the following statement: 80 is the multiple of 5 and 4.

In Delta ABC , if x=tan((B-C)/(2))tan.(A)/(2),y=tan((C-A)/(2))tan.(B)/(2) and z=tan((A-B)/(2))tan.(C)/(2) then (x+y+z)=.

Let f(x)=Sec^(-1)[1+cos^(2)x] where [.] denotes the greatest integer function I : Domain of f(x) is R II : Range of f(x) is {Sec^(-1)1, Sec^(-1)2}

Find the angle in radians 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.

Iftwobalanced diceare tossedonce,the probabiltiy of the eventthesumof the integerscomingon the uppersidesof the twodice is 9 is .

A= {1, 2, 3, 4, 5}, B= {4, 5, 6, 7, 8}, C= {7, 8, 9, 10, 11}, D= {10, 11, 12, 13, 14}. Find the following sets. B cup C

period of cos"" (pix)/(4) - 2 cosec (pix)/( 6) + 5 tan"" (pix)/(3) is

A spherical balloon of radius 5 subtends an angle 60^(@) at a point on the horzontal. If the angle of elevation of its centre is 30^(@), the height of the centre of the balloon is

Evaluate the limits. Lt_(xto0)(sqrt(x+4)-2)/x