14949 + Interview Questions in Maths in Class 11 Page 279 InterviewSolution

13901.	If the period of (sin nx)/( sin"" (x)/(n) ) is 4pi then n=
Answer» 2 3 4 5 Answer :A

Discussion

13902.	A coin is tossed. If it shows tail, we draw a ball from a box contains of 2 red and 3 black balls. If it shows heads, we throw a die. Find the sample space of this experiment.
Answer» Answer :`{TR_(1), TR_(2), TB_(1), TB_(2), TB_(3), H1, H2, H3, H4, H5, H6}`

Discussion

13903.	If a, b, c and d are in G.P. show that (a^2+b^2+c^2)(b^2+c^2+d^2) = (ab+bc+cd)^2
Answer» ANSWER :`(AB+ BC+ CD)^(2)`

Discussion

13904.	(d)/(dx) {Tan ^(-1) (sqrt(1+ x ^(2))-1)/( x)}=
Answer» ANSWER :`((1)/( 1 + X ^(2)))`

Discussion

13905.	If the cosines of angles of a triangle areproportional to opposite sides then the triangle is
Answer» isosceles RIGHT ANGLED equilateral isoceles or right angled ANSWER :C

Discussion

13906.	Write the solution set of the equation x^(2)+x -2=0 in roster form.
Answer» ANSWER :`{1, -2}`

Discussion

13907.	If Costheta=5/13 and 270^(@)ltthetalt360^(@). Evaluate "Sin"theta/2 and "Cos"theta/2
Answer» ANSWER :`2/SQRT13, (-3)/sqrt13`

Discussion

13908.	If bare_(1) = (1,1,1), bare_(2) = (1,1,-1) and bara, barb " are two vectors such that " bare_(1)=2bara+barb and bare_(2)= bara+2barb, " then " (bara,barb)=
Answer» `COS^(-1)(7//9)` `cos^(-1)(7//11)` `cos^(-1)(-7//11)` `cos^(-1)(6sqrt2//11)` ANSWER :C

Discussion

13909.	x^(2)-2x + 3/2=0
Answer» ANSWER :`1+- SQRT(2)/2I`

Discussion

13910.	Out of 9 outstanding students in a college, thereare 4 boys and 5 girls. A team of four students is to be selected for a quizprogramme. Find the probability that two are boys and two are girls.
Answer» Answer :`(""^(4)C_(2)xx^(5)C_(2))/(""^(9)C_(4))=(10)/(21)`

Discussion

13911.	In the given figure, what is the radius of the inscribed circle?
Answer» `3//2` `5//2` `7//5` NONE of these Answer :A

Discussion

13912.	If 2lexle4then the max value of f(x)=(x-2)^(6)(4-x)^(5)is
Answer» `((11)/(12))^(5)((11)/(10))^(5)` `((2)/(11))^(6)((10)/(9))^(5)` `((12)/(11))^(6)((10)/(11))^(5)` `((2)/(11))^(6)((10)/(11))^(5)` Answer :C

Discussion

13913.	Draw force-displacement graph for a spring and find an expression for the potential energy of an elastic spring.
Answer» Solution :(i) According to Hooke's law the restoring spring FORCE and displacement are linearly related as F =- kx, and are opposite in direction, the GRAPH between F and x is a straight line with dwelling only in the second and fourth quadrant as SHOWNIN Figure. (ii) The elastic potential energy can be easily CALCULATED by drawing a F-x graph. The shaded area (triangle) is the work done by the spring force. (iii) Area (base) (height) `= 1/2 xx (x) xx (kx)` . `= 1/2 kx^2` (iv) Work done is stored as the potential energy of the spring. ` therefore U = 1/2 kx^2`

Discussion

13914.	The product of the perpendiculars from (-1, 2) to the pair of lines 2x^(2)-5xy+2y^(2)=0
Answer» 4 3 8 `5//2` ANSWER :A

Discussion

13915.	Find the specified term of the expression in each of the following binomials: (ii) Sixth term of (2x - (1)/( x^2) )^7.
Answer» ANSWER :`(-84)/(8)`

Discussion

13916.	If f(x){:{(x^(2)+4," for "x lt 2 ),(x^(3)," for " x gt 2 ):} , find Lim_(x to 2) f(x)
Answer» ANSWER :8

Discussion

13917.	Express each of the following decimals in the p/q form 11.55
Answer» ANSWER :WEIGHT

Discussion

13918.	Find the area of the triangle formed by the lines joining the vertex of the parabola x^(2)=12y to the ends of its latus rectum.
Answer» ANSWER :`18` SQ UNITS

Discussion

13919.	A straight line through the origin O meets the parallel lines 4x+2y=9 and 2x+y+6=0 at points P and Q respectively. Then the point O dividesthe segment PQin the ratio
Answer» `1:2` `3:4` `2:1` `4:3` ANSWER :B

Discussion

13920.	If f(x) and g(x)are two functions with g(x) = x -1/x and fog (x) = x^3 -x/x^3 then f^(1)(x)=
Answer» `x^2-1/x^2` `x^2+1/x^2` `3(x^2+1)` `3x^2+3//x^4` ANSWER :C

Discussion

13921.	If the product of two + ve numbers is 256 then the least value of their sumis
Answer» 32 16 48 40 Answer :A

Discussion

13922.	r, R are radii of incircle and circum circle of a regular polygon for 7-sides such that (R)/(r)= sqrt(5)-1 then n=
Answer» 5 6 10 7 Answer :A

Discussion

13923.	How many 4-digit numbers can be formed by using the digits 1 to 9 if repetition of digits is not allowed?
Answer» ANSWER :3024

Discussion

13924.	If the eqaution ax^(2)+2hxy +by^(2) +2g x +2fy+c=0represents a pair of straigtht lines, then the square of the distance of their point of intersection from the origin is
Answer» `(C(a+b)-af^2-bg^2)/(ab-h^2)` `(c(a+b)+f^2-g^2)/(ab-h^2)` `(c(a+b)-f^2-g^2)/(ab-h^2)` `(c(a+b)-f^2-g^2)/(ab-h^2)^2` ANSWER :C

Discussion

13925.	Show that the complex number z, satisfying the condition arg((z-1)/(z+1))=(pi)/(4) lie son a circle.
Answer» ANSWER :which REPRESENTS a CIRCLE.

Discussion

13926.	21x^(2) - 28x + 10=0
Answer» ANSWER :`2/3 +- SQRT(14)/21 i`

Discussion

13927.	If A and B are two events such thatP(A uu B) = P(A nn B) thenthe truerealtionis
Answer» `P(A) +P(B) =0` `P(A) +P(B) = P(A)P((B)/(A))` `P(A) +P(B) = 2P(A) P((B)/(A))` NONEOF these Answer :C

Discussion

13928.	arg((1-isqrt(3))/(1+isqrt(3)))=.....
Answer» `60^(@)` `120^(@)` `210^(@)` `240^(@)` ANSWER :D

Discussion

13929.	A match can be won , drawn or lost One week a school it to play two matches .Draw a tree diagram to show all the possible outcomes and list them . Ifthe outcomes are equally likely ,calculate the probability that ,no match is lost ,
Answer» ANSWER :`(4)/(9)`

Discussion

13930.	A line passes through a fixed point A(h, k). The locus of the foot of the perpendicular on it from origin is
Answer» 1)`x^(2)+y^(2)+hx+ky=0` 2)`x^(2)+y^(2)-hx-ky=0` `3)x^(2)+y^(2)-kx-hy=0` 4)`x^(2)+y^(2)+kx+hy=0` ANSWER :2

Discussion

13931.	A match can be won , drawn or lost One week a school it to play two matches .Draw a tree diagram to show all the possible outcomes and list them . Ifthe outcomes are equally likely ,calculate the probability that ,at least one match is drawn ,
Answer» ANSWER :`(5)/(9)`

Discussion

13932.	A bag contains 7 white, 5 black and 4 red balls. Four balls are drawnwithout replacement find the probability that t least three balls are black.
Answer» ANSWER :`(23)/(364)`

Discussion

13933.	Find lim_(xrarr0)f(x), where f(x)={{:((x)/(\|x\|)",", x ne0),(0",",x=0):}
Answer» ANSWER :LIMIT does not EXIST at `X = 0`

Discussion

13934.	A match can be won , drawn or lost One week a school it to play two matches .Draw a tree diagram to show all the possible outcomes and list them . Ifthe outcomes are equally likely ,calculate the probability that ,both matches are won ,
Answer» ANSWER :`(1)/(9)`

Discussion

13935.	If the product of perpendiculars from (k,k) to the pair of lines x^2+4xy+3y^2=0 is 4sqrt5 then k is
Answer» `PM4` `PM3` `PM2` `pm1` ANSWER :D

Discussion

13936.	A coin is tossed four times.
Answer» Answer :{HHHH, HHHT, HHTH, HTHH, THHH, HHTT, HTHT, HTTH, THHT, THTH, TTHH, HTTT, THTT, TTHT, TTTH, TTTT}

Discussion

13937.	Obtain equation of circle in Centre (a,a) and radius sqrt(2a).
Answer» ANSWER :`X^(2) + y^(2) - 2ax - 2ay = 0`

Discussion

13938.	Let A(1,-1,3), B(2,3,5) is divided by p in the ratio 3:2 internally then harmonic conjugate of P w.r.t to A, B is
Answer» (2,13,3) (2,-13,3) (-2,13,-3) (-2,-13,-3) ANSWER :D

Discussion

13939.	A line which makes an acute angle theta with the positive dirction of the x-axis is drown through the point P(3,4) to meet the line x=6 at R and y=8 at S. Then.
Answer» `PR=3sec THETA` `PS=4cosectheta` `PR+PS=(2(sintheta+4costheta))/(SIN 2theta)` `9/(PR)^2+16/(PS)^2=1` Answer :A::B::C::D

Discussion

13940.	Let ABC be a triangle with integer sides a,b,c and angle C = 90^(@) The greatest perimeter of triangle of r = 4
Answer» 60 90 96 112 Answer :B

Discussion

13941.	Consider a circle with centre (2,-1) and which passes through (3,6).Find the equation of the circle
Answer» SOLUTION :`x^2+y^2-4x+2y-45 = 0`

Discussion

13942.	If one vertex of an equilateral triangle of side a lies at the origin and the other lies on the line x=sqrt(3)y then the third vertex is
Answer» (a,0) (-a,0) (0,a) (a,a) ANSWER :C

Discussion

13943.	Let S={x in (-pi,pi),x!=0+-(pi)/2}. The sum of all distinct solution is of the equation sqrt(3)secx+(cosecx+2(tanx-cotx)=0 in the set S=
Answer» `-7pi//9` `-2pi//9` `0` `5pi//9` ANSWER :C

Discussion

13944.	Find the mean deviation about the mean for the data in 38, 70, 48, 40, 42, 55, 63, 46, 54, 44
Answer» ANSWER :8.4

Discussion

13945.	The no of solution of the equation log_(2)(sinx)+log_(e)(tanx)=log_(4)(cos^(2)x)+log_(5)(cotx) in (-2pi, 2pi).
Answer» `(PI)/4,-(7pi)/4` `(pi)/4, (5PI)/4` `(pi)/4, (3PI)/4` `(3pi)/4, (5pi)/4` ANSWER :A

Discussion

13946.	Ifp_1,p_2,P_3 are the lengths ofthe altitudesfrom theverticesofDelta ABCto the oppositesides
Answer» ` (1)/ ( R ) ` ` (1)/( R) ` ` (1)/( r^(2))` ` ( 1)/(r_2) ` ANSWER :D

Discussion

13947.	Find the modulus and the arguments of the following complex numbers : ((2+i)/(3-))^(2)
Answer» ANSWER :Modulus `=(1)/(2)` ARGUMENT `=(PI)/(2)`

Discussion

13948.	Find the square roots of the following : i
Answer» ANSWER :`+-(1)/(SQRT(2)) (1-i)`

Discussion

13949.	Consider a plane x + y - z= 1 and point A (1,2,-3). A line L has the equation x =1 + 3r ,y =2- r and z =3 + 4r The coordinate of a point B of line L such that AB is parallel to the plane is
Answer» `(10, -1,15)` `(-5,4,-5)` `(4,1,7)` `(-8,5,-9)` ANSWER :D

Discussion

13950.	A(6,4) and B(2,12) are given points . Then slope of line perpendicular to {:(harr),(AB):}is ...........
Answer» ANSWER :`1/2`

Discussion

Explore topic-wise InterviewSolutions in .

If the period of (sin nx)/( sin"" (x)/(n) ) is 4pi then n=

A coin is tossed. If it shows tail, we draw a ball from a box contains of 2 red and 3 black balls. If it shows heads, we throw a die. Find the sample space of this experiment.

If a, b, c and d are in G.P. show that (a^2+b^2+c^2)(b^2+c^2+d^2) = (ab+bc+cd)^2

(d)/(dx) {Tan ^(-1) (sqrt(1+ x ^(2))-1)/( x)}=

If the cosines of angles of a triangle areproportional to opposite sides then the triangle is

Write the solution set of the equation x^(2)+x -2=0 in roster form.

If Costheta=5/13 and 270^(@)ltthetalt360^(@). Evaluate "Sin"theta/2 and "Cos"theta/2

If bare_(1) = (1,1,1), bare_(2) = (1,1,-1) and bara, barb " are two vectors such that " bare_(1)=2bara+barb and bare_(2)= bara+2barb, " then " (bara,barb)=

x^(2)-2x + 3/2=0

Out of 9 outstanding students in a college, thereare 4 boys and 5 girls. A team of four students is to be selected for a quizprogramme. Find the probability that two are boys and two are girls.

In the given figure, what is the radius of the inscribed circle?

If 2lexle4then the max value of f(x)=(x-2)^(6)(4-x)^(5)is

Draw force-displacement graph for a spring and find an expression for the potential energy of an elastic spring.

The product of the perpendiculars from (-1, 2) to the pair of lines 2x^(2)-5xy+2y^(2)=0

Find the specified term of the expression in each of the following binomials: (ii) Sixth term of (2x - (1)/( x^2) )^7.

If f(x){:{(x^(2)+4," for "x lt 2 ),(x^(3)," for " x gt 2 ):} , find Lim_(x to 2) f(x)

Express each of the following decimals in the p/q form 11.55

Find the area of the triangle formed by the lines joining the vertex of the parabola x^(2)=12y to the ends of its latus rectum.

A straight line through the origin O meets the parallel lines 4x+2y=9 and 2x+y+6=0 at points P and Q respectively. Then the point O dividesthe segment PQin the ratio

If f(x) and g(x)are two functions with g(x) = x -1/x and fog (x) = x^3 -x/x^3 then f^(1)(x)=

If the product of two + ve numbers is 256 then the least value of their sumis

r, R are radii of incircle and circum circle of a regular polygon for 7-sides such that (R)/(r)= sqrt(5)-1 then n=

How many 4-digit numbers can be formed by using the digits 1 to 9 if﻿ repetition of digits is not allowed?

If the eqaution ax^(2)+2hxy +by^(2) +2g x +2fy+c=0represents a pair of straigtht lines, then the square of the distance of their point of intersection from the origin is

Show that the complex number z, satisfying the condition arg((z-1)/(z+1))=(pi)/(4) lie son a circle.

21x^(2) - 28x + 10=0

If A and B are two events such thatP(A uu B) = P(A nn B) thenthe truerealtionis

arg((1-isqrt(3))/(1+isqrt(3)))=.....

A match can be won , drawn or lost One week a school it to play two matches .Draw a tree diagram to show all the possible outcomes and list them . Ifthe outcomes are equally likely ,calculate the probability that ,no match is lost ,

A line passes through a fixed point A(h, k). The locus of the foot of the perpendicular on it from origin is

A match can be won , drawn or lost One week a school it to play two matches .Draw a tree diagram to show all the possible outcomes and list them . Ifthe outcomes are equally likely ,calculate the probability that ,at least one match is drawn ,

A bag contains 7 white, 5 black and 4 red balls. Four balls are drawnwithout replacement find the probability that t least three balls are black.

Find lim_(xrarr0)f(x), where f(x)={{:((x)/(|x|)",", x ne0),(0",",x=0):}

A match can be won , drawn or lost One week a school it to play two matches .Draw a tree diagram to show all the possible outcomes and list them . Ifthe outcomes are equally likely ,calculate the probability that ,both matches are won ,

If the product of perpendiculars from (k,k) to the pair of lines x^2+4xy+3y^2=0 is 4sqrt5 then k is

A coin is tossed four times.

Obtain equation of circle in Centre (a,a) and radius sqrt(2a).

Let A(1,-1,3), B(2,3,5) is divided by p in the ratio 3:2 internally then harmonic conjugate of P w.r.t to A, B is

A line which makes an acute angle theta with the positive dirction of the x-axis is drown through the point P(3,4) to meet the line x=6 at R and y=8 at S. Then.

Let ABC be a triangle with integer sides a,b,c and angle C = 90^(@) The greatest perimeter of triangle of r = 4

Consider a circle with centre (2,-1) and which passes through (3,6).Find the equation of the circle

If one vertex of an equilateral triangle of side a lies at the origin and the other lies on the line x=sqrt(3)y then the third vertex is

Let S={x in (-pi,pi),x!=0+-(pi)/2}. The sum of all distinct solution is of the equation sqrt(3)secx+(cosecx+2(tanx-cotx)=0 in the set S=

Find the mean deviation about the mean for the data in 38, 70, 48, 40, 42, 55, 63, 46, 54, 44

The no of solution of the equation log_(2)(sinx)+log_(e)(tanx)=log_(4)(cos^(2)x)+log_(5)(cotx) in (-2pi, 2pi).

Ifp_1,p_2,P_3 are the lengths ofthe altitudesfrom theverticesofDelta ABCto the oppositesides

Find the modulus and the arguments of the following complex numbers : ((2+i)/(3-))^(2)

Find the square roots of the following : i

Consider a plane x + y - z= 1 and point A (1,2,-3). A line L has the equation x =1 + 3r ,y =2- r and z =3 + 4r The coordinate of a point B of line L such that AB is parallel to the plane is

A(6,4) and B(2,12) are given points . Then slope of line perpendicular to {:(harr),(AB):}is ...........

How many 4-digit numbers can be formed by using the digits 1 to 9 if repetition of digits is not allowed?