14949 + Interview Questions in Maths in Class 11 Page 204 InterviewSolution

10151.	Which of the following functions is periodic ?
Answer» `F(x)=x-[x]`, where [x] DENOTES the largest integer LESS than or equal to the real number x `f(x)=sin"" 1/2` for `x != 0, f(0)=0` `f(x)=x COS x` `f(x)= (tan x)/(x)` Answer :A

Discussion

10152.	The straight line 2x+3y =24 meets the x-axis at P and the y-axis at Q. The perpendicular bisector of PQ meets the line through (-2,0) parallel to the y-axis at R. Find the area of the DeltaPQR.
Answer» SOLUTION :N/A

Discussion

10153.	If A,B,C,D are four angles then sin (A-B) cos (A+B) + sin B (B-C) .cos (B+C) + sin (C-D) cos (C+D)+ sin (D-A) cos (D+A)=
Answer» 0 1 `4 SIN A.sinB sin C sin D` `4 COS A cos B cos C cos D` ANSWER :A

Discussion

10154.	A straight pole A subtend a right angle at a point B of another pole at a distance of 30 metres from A the top of A being 60^(@) above the horizontal line joining the point B to the pole A. The length of the pole A is in metres.
Answer» `20sqrt(3)` `40sqrt(3)` `60sqrt(3)` `(40)/(SQRT(3))` ANSWER :B

Discussion

10155.	Two parallel chords of a circle of radius 2 are at a distance sqrt3 + 1apart. If the chord subtend angles pi/k "and " (2pi)/k at the center, whore k gt 0, then the value of [k] is ........... Note : [k] denotes the largest integer less than or equal to k)
Answer» 3 `3.104` `-3.001` `2.999` ANSWER :A

Discussion

10156.	If the lines x+y=0, x-y=0 and 2x+3y-6=0 are the sides of a triangle and (-2, a) is an interior point of the triangle then a lies
Answer» `2 LT a lt 10//3` `-2 lt a lt 10//3` `-1 lt a lt 9//2` `-3 gt a gt 9//2` Answer :A

Discussion

10157.	Find the sum to n terms of the series .3 xx 1^(2) + 5 xx 2^(2) + 7 xx 3^(2) +. . . . . .
Answer» ANSWER :`n/6(n+1)(3n^2+5n+1)`

Discussion

10158.	Statement 1 : If x in [1, sqrt(3)] then the range of f(x)=tan^(-1)xis [pi//4, pi//3]. Statement 2 : If x in [1, b] then the range of f(x) is [f(a), f(b)]
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 is not a correct explanation for statement 1. Statement 1 is true, statement 2 is FALSE Statement 1 is false, statement 2 is true Answer :C

Discussion

10159.	The periodof cos (x+ 4 x+ 9x…. +n^(2) x) is
Answer» `( 2pi)/( N ( n+1)(2n+1))` `(4pi)/( n (n+1) (2n+1) )` `(6pi)/(n (n+1) (2n+1))` `(8pi)/( n (n+1) (2n+1))` ANSWER :C

Discussion

10160.	Express the following in the form of a+ib: (3-sqrt(-16))/(1-sqrt(-9))
Answer» ANSWER :`(3)/(2)+(1)/(2)i`

Discussion

10161.	Find the mean and variance for the following frequency distributions in
Answer» ANSWER :27, 132

Discussion

10162.	Find the mean and variance for the following frequency distributions in
Answer» ANSWER :107, 2276

Discussion

10163.	The product of two consecutive positive integers is always divisible by ..........
Answer» ANSWER :TRUE STATEMENT

Discussion

10164.	Let A={1,2,3....14}. Define a relation R from A to A by R={(x,y) : 3x-y=0," where "x, y in A}. Write down its domain, condomain and range.
Answer» Answer :R={(1,3),(2,6),(3,9),(4,12)} Domain of R ={1,2,3,4} Range of R={3,6,9,12} CO domain of R={1,2,....14}

Discussion

10165.	If sin^(-1)x +sin^(-1)y+sin^(-1)z=pi then x^(4)+y^(4)+z^(4)+4x^(2)y^(2)z^(2)=
Answer» 1 2 4 none of these Answer :B

Discussion

10166.	The value of sin""(pi)/(10)sin""(13pi)/(10) is
Answer» `(1)/(2)` `-(1)/(2)` `-(1)/(4)` 1 Answer :C

Discussion

10167.	If [y]=sinx(x) and y=cosx are two given equations then the number of solutions is (where [.] denotes the greatest integer function)
Answer» 2 3 4 infinitely MANY solutions Answer :D

Discussion

10168.	(a ) Find the values of k so that the equationx^(2)= 2x (1+3k) +7 (3+2k) = 0has real and equal roots. (b ) If the roots of the equation (q-r) x^(2) +(r-p)x +(p-q) = 0are equal then show that p,qand r are inA. P .
Answer» ANSWER :`-(10)/9`

Discussion

10169.	If 2bar(i)+3bar(j)+5bar(k), 2bar(i)+4bar(j)+5bar(k) and 2bar(i)+4bar(j)+7bar(k) are the vertices of DeltaABC, then its circum-centre is
Answer» `2BAR(i)+7bar(J)+6bar(k)` `2bar(i)+7/2bar(j)+6bar(k)` `2bar(i)+bar(j)+3/2bar(k)` `2bar(i)+1/2bar(j)+bar(k)` ANSWER :B

Discussion

10170.	The area of the triangle formed by the linea joining the vertex of th parabola x^(2) = 12y to the ends of Latus rectum is
Answer» ANSWER :`18` SQ UNITS

Discussion

10171.	x^(2)-y^(2)=1
Answer» ANSWER :(i) 2 units , 2 units (ii) `A(-1,0) ,B(1,0)` (iii) `F_(1)(-SQRT(2),0),F_(2) (sqrt(2),0)` (iv)`e=sqrt(2)` (V)2 units

Discussion

10172.	The value of cosec^(-1)sqrt(5)+cosec^(-1)sqrt(65)+cosec^(-1)sqrt((325))+….. infty=(kpi)/4 then k =
Answer» ANSWER :1

Discussion

10173.	Letf(x ) =cos sqrt(p) x. wherep = [a](integralpart ). If the periodof f(x )is pithen a E
Answer» `[4,5]` `[4,5]` `(4,5]` `(4.5)` ANSWER :2

Discussion

10174.	Equation of the sidesoverset(harr)("BC"), overset(harr)("CA"), overset(harr)("AB") of a triangle ABC are U_(r ) = a_(r )x+b_(r )y+c_(r )=0, r=1,2,3 respectively then equation of line parallel to overset(harr)("BC") and passing through A is
Answer» `(a_(3)b_(1)-a_(1)b_(3))U_(2)+(a_(2)b_(1)-a_(1)b_(2))U_(3)=0` `(a_(3)b_(1)-a_(1)b_(3))U_(2)-(a_(2)b_(1)-a_(1)b_(2))U_(3)=0` `(a_(3)b_(1)+a_(1)b_(3))U_(2)+(a_(2)b_(1)+a_(1)b_(2))U_(3)=0` `(a_(3)b_(1)+a_(1)b_(3))U_(2)-(a_(2)b_(1)+a_(1)b_(2))U_(3)=0` Answer :B

Discussion

10175.	............ is the equation of lines passes from (2,4) and makes equal intercept an axis.
Answer» ANSWER :`x+y-6=0`

Discussion

10176.	Rolle's theorem holds for the function x^(3) + bx^(2) + cx,1 le x le2 at the point (4)/(3) , then vaue of b and c are
Answer» B=8,C = - 5 b = -5,c=8 b=5,c=-8 b=-5,c = 8 Answer :B

Discussion

10177.	Write the first five terms of each of the sequences whose n^(th) terms are as following a_(n)= (n)/(n^(2)+1)
Answer» ANSWER :`(1)/(2), (2)/(5), (3)/(10), (4)/(17), (5)/(26)`

Discussion

10178.	Find the values of theta lying between 0^(@) and 360^(@) when tan theta=-1
Answer» ANSWER :`135^(@),315^(@)`

Discussion

10179.	Consider the system of equations x cos ^(3) y + 3 x cosy sin^(2) y = 14 t o (1) and x sin^(3) y + 3 x cos^(2) y sin y = 13 to (2) The number of values of y in [0, 6 pi] are
Answer» 5 3 4 6 Answer :D

Discussion

10180.	A group consists of 4 girls and 7 boys .In how many wayscan a team of 5 members be selected , if the term has (i) no girls (ii)atleast one boy and one girl ?
Answer» Answer :Total number of SELECTION : 378 WAYS .

Discussion

10181.	The work done by the force barF = abari+barj+bark in moving a particle from (1,1,1) to (2,2,2) along a straight line is 5 units. Then a =
Answer» 1 2 3 4 Answer :C

Discussion

10182.	If f(x)=(t+3x-x^(2))/(x-4),where t is a parameter that has a minimum and maximum , then the range of values of t is
Answer» (0,4) `(0,OO)` `(-oo,4)` `(4,oo)` ANSWER :C

Discussion

10183.	A student tunes his guitar by striking a 120 Hertz with a tuning fork, and simultaneously plays the 4^(th) string on his guitar. By keen observation, he hears the amplitude of the combined sound oscillating thrice per second. Which ofthe following frequency is the most likely the frequency of the 4^(th) string on his guitar ?
Answer» 130 117 110 120 Solution :117

Discussion

10184.	Solve the general vlaue. sin 7 theta + sin 4 theta + sin theta =0
Answer» ANSWER :`(NPI)/(4) or (2)/(3)`

Discussion

10185.	cos(pi/3)cos(pi/4) + sin(pi/3) sin(pi/4) .................
Answer» ANSWER :`=(sqrt3+1)/(2SQRT2)`FUNDAMENTAL VALUE

Discussion

10186.	Prove that 2222^(5555)+5555^(2222) is divisible by 7
Answer» Solution :When 2222 is divided by 7 it leaves a reminder 3 So adding & SUBTRACTING `3^(5555)` we get For `E_(1)` : Now since 2222-3 =2219 is divideble by 7 thefore `E_(1)` is dividible by 7 ` (`thereforex^n - a^n ` is divisible by x - a) For `E_2:555 when devided by 7 leaves remainder 4ltbegt Soadding and subtracting `4^(2222)` we get `E_(2)=3^(5555)+4^(2222)+5555^(2222)-4^(2222)` `= (243)^(1111)+(16)^(1111)+5555^(2222)- 4^(2222)` `=(243)^(1111)+(16)^(1111)+(5555)^2222-4^(2222)` are divisible by7

Discussion

10187.	If B,A+B are acute angle , sin(A+B)=12/13, sin B=5/13 then sin A =
Answer» `-(119)/(169)` `(119)/(169)` `(169)/(119)` `(-169)/(119)` ANSWER :B

Discussion

10188.	Find (dy)/(dx) in the following : y= cos^(-1) ((2x)/(1+x^(2))), -1 lt x lt1.
Answer» ANSWER :`(-2)/(1 + X ^(2))`

Discussion

10189.	If z in z and \|z+3\| le 8 then find the maximum and minimum value of \|z-2\|.
Answer» ANSWER :MAXIMUM 13, MINIMUM 0

Discussion

10190.	Show that the following statement is true by the method of contrapositive. p: If x is an integer and x2 is even, then x is also even.
Answer» ANSWER :1

Discussion

10191.	Find the value of cos (-1710^(@)).
Answer» ANSWER :`=0`

Discussion

10192.	Let bara,barb are two unit vectors such that bara.barb=0. If barc=xbara+ybarb+z(baraxxbarb) then x+y+z=
Answer» 0 1 `{bara+barb+(BARAXXBARB)}.BARC` `bara.barc` ANSWER :C

Discussion

10193.	underset(x to o) (Lt) (x(1-sqrt(1-x^(2))))/(sqrt(1-x^(2)).sin^(-1)(x^(3)))
Answer» 1 `(1)/(2)` `(-1)/(2)` `-1` ANSWER :B

Discussion

10194.	If cot theta=-3//4and thetais not in the second quadrant, then5 sin theta + 10 cos theta + 9 sec theta + 16 " cosec" theta - 4 cot theta =
Answer» 0 -1 1 2 Answer :A

Discussion

10195.	The value of 'c' in Rolle's theorem for f(x) = log ((x^(2)+ ab)/(x(a+b))) in (a,b) where a gt 0 is
Answer» A.M. of a,B G.M. of a,b H.M. of a,b `(1)/(a) + ( 1)/(b)` ANSWER :B

Discussion

10196.	One possible representation of points (x, y) on x^(2)y^(2) =x^(2) +y^(2) is
Answer» `(sin theta, COS theta)` `(SEC theta, tan theta)` `(sec theta, cosec theta)` `(cos theta, tan theta)` ANSWER :C

Discussion

10197.	A vector of magnitude 6 which is perpendicular to both 4vec(i) - vec(j) + 3vec(k) and -2vec(i) + vec(j) - 2vec(k) is
Answer» `+- (2vec(i) -VEC(J)-vec(K))` `+- (vec(i) + 2vec(j) + vec(k))` `+- (vec(i) -2vec(j) + 3vec(k))` `vec(i) + vec(j) + vec(k)` ANSWER :A

Discussion

10198.	Find the sum of the first n terms of the series (1)/(1+sqrt(2))+(1)/(sqrt(2)+sqrt(3))+(1)/(sqrt(3)+sqrt(4))+….
Answer» ANSWER :`=SQRT(n+1)-1`

Discussion

10199.	Find the number of solutions of the equation tan x + sec x = 2 cos x, cos x ne 0 lying in the interval (0, pi)
Answer» ANSWER :`npipm(PI)/(3)`

Discussion

10200.	Number of values of p for which equation sin ^(3) x + 1 + p^(3) - 3 p sin x = 0 (p gt 0)has a root is
Answer» ANSWER :1

Discussion

Explore topic-wise InterviewSolutions in .

Which of the following functions is periodic ?

The straight line 2x+3y =24 meets the x-axis at P and the y-axis at Q. The perpendicular bisector of PQ meets the line through (-2,0) parallel to the y-axis at R. Find the area of the DeltaPQR.

If A,B,C,D are four angles then sin (A-B) cos (A+B) + sin B (B-C) .cos (B+C) + sin (C-D) cos (C+D)+ sin (D-A) cos (D+A)=

A straight pole A subtend a right angle at a point B of another pole at a distance of 30 metres from A the top of A being 60^(@) above the horizontal line joining the point B to the pole A. The length of the pole A is in metres.

Two parallel chords of a circle of radius 2 are at a distance sqrt3 + 1apart. If the chord subtend angles pi/k "and " (2pi)/k at the center, whore k gt 0, then the value of [k] is ........... Note : [k] denotes the largest integer less than or equal to k)

If the lines x+y=0, x-y=0 and 2x+3y-6=0 are the sides of a triangle and (-2, a) is an interior point of the triangle then a lies

Find the sum to n terms of the series .3 xx 1^(2) + 5 xx 2^(2) + 7 xx 3^(2) +. . . . . .

Statement 1 : If x in [1, sqrt(3)] then the range of f(x)=tan^(-1)xis [pi//4, pi//3]. Statement 2 : If x in [1, b] then the range of f(x) is [f(a), f(b)]

The periodof cos (x+ 4 x+ 9x…. +n^(2) x) is

Express the following in the form of a+ib: (3-sqrt(-16))/(1-sqrt(-9))

Find the mean and variance for the following frequency distributions in

Find the mean and variance for the following frequency distributions in

The product of two consecutive positive integers is always divisible by ..........

Let A={1,2,3....14}. Define a relation R from A to A by R={(x,y) : 3x-y=0," where "x, y in A}. Write down its domain, condomain and range.

If sin^(-1)x +sin^(-1)y+sin^(-1)z=pi then x^(4)+y^(4)+z^(4)+4x^(2)y^(2)z^(2)=

The value of sin""(pi)/(10)sin""(13pi)/(10) is

If [y]=sinx(x) and y=cosx are two given equations then the number of solutions is (where [.] denotes the greatest integer function)

(a ) Find the values of k so that the equationx^(2)= 2x (1+3k) +7 (3+2k) = 0has real and equal roots. (b ) If the roots of the equation (q-r) x^(2) +(r-p)x +(p-q) = 0are equal then show that p,qand r are inA. P .

If 2bar(i)+3bar(j)+5bar(k), 2bar(i)+4bar(j)+5bar(k) and 2bar(i)+4bar(j)+7bar(k) are the vertices of DeltaABC, then its circum-centre is

The area of the triangle formed by the linea joining the vertex of th parabola x^(2) = 12y to the ends of Latus rectum is

x^(2)-y^(2)=1

The value of cosec^(-1)sqrt(5)+cosec^(-1)sqrt(65)+cosec^(-1)sqrt((325))+….. infty=(kpi)/4 then k =

Letf(x ) =cos sqrt(p) x. wherep = [a](integralpart ). If the periodof f(x )is pithen a E

Equation of the sidesoverset(harr)("BC"), overset(harr)("CA"), overset(harr)("AB") of a triangle ABC are U_(r ) = a_(r )x+b_(r )y+c_(r )=0, r=1,2,3 respectively then equation of line parallel to overset(harr)("BC") and passing through A is

............ is the equation of lines passes from (2,4) and makes equal intercept an axis.

Rolle's theorem holds for the function x^(3) + bx^(2) + cx,1 le x le2 at the point (4)/(3) , then vaue of b and c are

Write the first five terms of each of the sequences whose n^(th) terms are as following a_(n)= (n)/(n^(2)+1)

Find the values of theta lying between 0^(@) and 360^(@) when tan theta=-1

Consider the system of equations x cos ^(3) y + 3 x cosy sin^(2) y = 14 t o (1) and x sin^(3) y + 3 x cos^(2) y sin y = 13 to (2) The number of values of y in [0, 6 pi] are

A group consists of 4 girls and 7 boys .In how many wayscan a team of 5 members be selected , if the term has (i) no girls (ii)atleast one boy and one girl ?

The work done by the force barF = abari+barj+bark in moving a particle from (1,1,1) to (2,2,2) along a straight line is 5 units. Then a =

If f(x)=(t+3x-x^(2))/(x-4),where t is a parameter that has a minimum and maximum , then the range of values of t is

Solve the general vlaue. sin 7 theta + sin 4 theta + sin theta =0

cos(pi/3)cos(pi/4) + sin(pi/3) sin(pi/4) .................

Prove that 2222^(5555)+5555^(2222) is divisible by 7

If B,A+B are acute angle , sin(A+B)=12/13, sin B=5/13 then sin A =

Find (dy)/(dx) in the following : y= cos^(-1) ((2x)/(1+x^(2))), -1 lt x lt1.

If z in z and |z+3| le 8 then find the maximum and minimum value of |z-2|.

Show that the following statement is true by the method of contrapositive. p: If x is an integer and x2 is even, then x is also even.

Find the value of cos (-1710^(@)).

Let bara,barb are two unit vectors such that bara.barb=0. If barc=xbara+ybarb+z(baraxxbarb) then x+y+z=

underset(x to o) (Lt) (x(1-sqrt(1-x^(2))))/(sqrt(1-x^(2)).sin^(-1)(x^(3)))

If cot theta=-3//4and thetais not in the second quadrant, then5 sin theta + 10 cos theta + 9 sec theta + 16 " cosec" theta - 4 cot theta =

The value of 'c' in Rolle's theorem for f(x) = log ((x^(2)+ ab)/(x(a+b))) in (a,b) where a gt 0 is

One possible representation of points (x, y) on x^(2)y^(2) =x^(2) +y^(2) is

A vector of magnitude 6 which is perpendicular to both 4vec(i) - vec(j) + 3vec(k) and -2vec(i) + vec(j) - 2vec(k) is

Find the sum of the first n terms of the series (1)/(1+sqrt(2))+(1)/(sqrt(2)+sqrt(3))+(1)/(sqrt(3)+sqrt(4))+….

Find the number of solutions of the equation tan x + sec x = 2 cos x, cos x ne 0 lying in the interval (0, pi)

Number of values of p for which equation sin ^(3) x + 1 + p^(3) - 3 p sin x = 0 (p gt 0)has a root is