14949 + Interview Questions in Maths in Class 11 Page 235 InterviewSolution

11701.	The periodof sin x cos x is
Answer» `(PI)/(2)` `pi` `2PI` `(3PI)/(2)` ANSWER :2

Discussion

11702.	Find the sum of the following series up to n terms: 1^3/1+(1^3+2^3)/(1+3)+(1^3+2^3+3^3)/(1+3+5)+.......
Answer» ANSWER :`n/24 (2n^2+9n+13)`

Discussion

11703.	If the line joining the points (2,k,5), (0,1,6) is parallel to the line joining the points (3,-1,2), (-1,2,4) then find k,
Answer» ANSWER :`-1//2`

Discussion

11704.	Two dice are thrown together , what is the probabability that the sum of the numbers on the two faces is neither divisible by 3 nor by 5.
Answer» ANSWER :`(17)/(36)`

Discussion

11705.	If a,b,c are arithmeticprogression then show that the equation ax+by+c=0 represents a family of concurrent lines and find the point of concurrency.
Answer» ANSWER :(1-2)

Discussion

11706.	If tan theta_(1), tan theta_(2) tan theta_(3) and tan theta_(4) are the roots of the equation x^(4) - x^(3) sin 2 beta + x^(2) cos 2 beta - x cos beta - sin beta = "0 then tan" (theta_(1) + theta_(2) + theta_(3) + theta_(4)) is equal to
Answer» `SIN BETA` `cos beta` `tan beta` `cot beta` ANSWER :D

Discussion

11707.	Evaluate : (i) 5 ! (ii) 7 ! (iii) 7 ! - 5 !
Answer» ANSWER :(i) 120, (II) 5040, (III) 4920

Discussion

11708.	AB=12cm. Ab sides with A on x-axis, B on y-axis respectively. Then the radius of the circle which is the locus of DeltaAOB,where O is origin is:
Answer» 36 4 16 9 Answer :B

Discussion

11709.	The minute hand of a watch is 1.5 cm long. How far does its tip move in 40 minutes ? (Use pi = 3.14).
Answer» ANSWER :`6.28 CM`

Discussion

11710.	Prove that tanalpha=(Sin2alpha)/(1+cos2alpha) and hence deduce the value of tan15^(@) and tan22 1^(@)/2
Answer» ANSWER : `2-sqrt3,sqrt2-1`

Discussion

11711.	(1.2^2+ 2.3^2 + 3.4^2+ .... + n(n+1)^2)/( 1^2. 2 +2^2. 3+ 3^2. 4+ ..... + n^2 (n+1) ) =
Answer» `(3n+1)/( 3n+5)` `(3n+5)/( 3n+1)` `(3n+1)/(3n+5)` `( 3n+5)/( 3n+7)` ANSWER :B

Discussion

11712.	No. of solutions of \|cosx\|=sinx,0lexle4pi, is
Answer» 8 4 2 6 Answer :B

Discussion

11713.	Assertion (A) sum _(r=1)^(n-1) cos^2((rpi)/(n))=(n)/(2)-1 Reasion (R) : cos alpha+ cos (alpha+ beta)+cos(alpha+2 beta)+....+cos (alpha(n-1) beta)=(sin(n beta//2))/(sin(beta//2)). Cos ((2 alpha+(n-1) beta)/(2))
Answer» A is TRUE, R is true and R is CORRECT explanation of A A is true, R is true and R is not correct explanation of A A is true, R is false A is false, R is true Answer :A

Discussion

11714.	If abgt0 find th area of the rhombus enclosed by the four straight lines ax+-by+-c=0
Answer» ANSWER :`(2C^(2))/(AB)`

Discussion

11715.	Let ABC be a triangle whose circumcentre is at P. If the position vectors of A, B, C and P are bar(a), bar(b), bar(c) and (bar(a)+bar(b)+bar(c))/4 respectively, then the position vector of the orthocentre of this triangle is
Answer» `-((bar(a)+bar(B)+bar(C))/2)` `bar(a)+bar(b)+bar(c)` `(bar(a)+bar(b)+bar(c))/2` `bar(0)` Answer :D

Discussion

11716.	Numbers of elements in power set of the given set A={"x"in N \|x^2
Answer» ANSWER :16

Discussion

11717.	A triangle has sides that measure 13, 14, 15. A line perpendicular to the side of measure 14 divides the interior of the triangle in to two regions of equal area. Length of this perpendicular with in the triangle
Answer» `3sqrt(7)` `4sqrt(7)` `2sqrt(7)` None Answer :B

Discussion

11718.	Show that the feet of the perpendicular from (-2,-8) to the lines x-2y+6=0,x-7y+6=0 and x+3y-4=0 are collinear.
Answer» ANSWER :are colinear.

Discussion

11719.	Which value of theta listed below leads to 2 ^(sin theta) gt 1 and 3^(cos theta) lt 1 ?
Answer» `70^(0)` `140^(0)` `210^(0)` `280^(0)` ANSWER :B

Discussion

11720.	If f(x) = [x - 8] " & " g(x) = f(f(x)) AA x > 16 then g^1(x) equals
Answer» `1` `-1` `0` `2` ANSWER :A

Discussion

11721.	If ‘f' isgiven by f(x)={{:(ax-b,if xlt-1),(3x^(2)-4ax+2b,if-1ltxlt1 "is continous function on Rthen find the values"),(10,if x ge1):} is continuous function on R then find the values of a and b
Answer» Answer : ` underset -a - b = 3 + 4a + 2b rArr 5A + 3b = - 3 ` ...(2) From (1) & (2); ` a = - (27)/(22), b = (23)/(22)` .

Discussion

11722.	Through a point A on the x-axis, a staight line is drawn parallel to the y-axis so as to meet the pair of straight lines ax^2+2hxy+by^2=0 at B and C. If AB=BC, then
Answer» `h^2=4ab` `8h^2=9ab` `9h^2=8ab` `4h^2=ab` ANSWER :B

Discussion

11723.	Change the following complex numbers into polar form (1+ 2i)/(1-(1-i)^(2))
Answer» ANSWER :`COS 0^(@) + i "SIN" 0^(@)`

Discussion

11724.	Find the derivative of w.r.to x 20 ^(log (tan x ))
Answer» Answer :`20 ^( LOG (tan X )) , 2 cos EC 2 x log 20`

Discussion

11725.	Find the mean deviation about median for the following data :
Answer» ANSWER :7.35

Discussion

11726.	If z = (x,-y) then point (x,y) with respect to real axis is called.
Answer» ANSWER :MIRROR IMAGE

Discussion

11727.	The variance of the given data 2,4,5,6,8,17 is 23.33 . Then find the variance of the data 4,8,10,12,16,34.
Answer»

Discussion

11728.	If a=6 , b=5 ,c=9then angle A .
Answer» ANSWER :` COS ^(-1) ((7)/(9))`

Discussion

11729.	If f(x+y,x-y) =xy, then the arithmetic mean of f(x,y) and f(y,-x) is
Answer» x y 0 1 Answer :C

Discussion

11730.	Find the derivative of the function (sqrtx -3x) (x + (1)/(x))
Answer» ANSWER :`3/2 SQRTX - 6X - (1)/(2X sqrtx)`

Discussion

11731.	Find the value of cos(-1710^(@))
Answer» ANSWER :`=0`

Discussion

11732.	The sum of algebraic distances from the points (n,n^2) where n=1,2,3 …….,2013, to a straightline is zero and if such a line always passes through the point (alpha,beta) and 1/alpha(beta-1007/3)=abcd then b+d=(abcd is four digited number)
Answer» ANSWER :5

Discussion

11733.	A group consists of 4 girls and 7 boys. In how many ways can a team of 5 members be selected, if the team has (i) no girls (ii) atleast one boy and one girl (iii) at least three girls
Answer» Answer :(i) 21 (II) 441 (iii) 91

Discussion

11734.	Iff:R to N UU {0}where f (area of triangle joining points P( 0,5) , Q( 8,4)and R(x,y ) such that angle PRQis a right angle) = number of triangle , then which of the following is true?
Answer» `F(5)=4` `f(7)-0` `f(6.25)=2` `f(x)` is into Answer :A::B::C::D

Discussion

11735.	Evaluate the following limits : Lim_( n to oo) (1+2/n)^(2n)
Answer» ANSWER :`E^(4)`

Discussion

11736.	A lamp post is sittuated at the middle point M of the side AC of a triangular plot ABC with BC=m CA =8 m and AB =9 m. Lamp post subleds an anlgle 15^(@) at the point B. The height of the lamp post is
Answer» `7(2+sqrt3) m` `7(2-sqrt3) m` `14(2-sqrt3) m` `14(2+sqrt3) m` ANSWER :C

Discussion

11737.	From a rectangular sheet of a cm xx bcm,four equal square pieces of side x cm are removed at the corners and the sides are then turned up so as to form an open rectangular box. Find the value of x so that the volume of the box is greatest.
Answer» ANSWER :`x=1/6[(a+b)-SQRT(a^2-ab+b^2)]`

Discussion

11738.	Usingthe mathematicalinduction , show that forany naturalnumbern le 2 1/ (1 +2) + 1/( 1 + 2+3) + 1/( 1 + 2+3+4)+ ….+ 1/( 1+2+3+….+n)= ( n -1)/(n+1)
Answer» ANSWER :RHS

Discussion

11739.	Show that the function f (x) = (x)/(1 + \|x\| ) , x in R, is differentiable at x =0. Hence find f '(0).
Answer» ANSWER :1

Discussion

11740.	Function and g defined on RrarrR" as "f(x)=x^2+7 and g(x)=3x+5. Then f(3) + g(-5) = ….. .
Answer» ANSWER :6

Discussion

11741.	The pointcollinearwith (1, -2 -3 ) and (2, 0, 0 ) among the following is
Answer» (0, 4, 6) (0, -4, -5) (0, -4, -6) (0, -4, 6) ANSWER :c

Discussion

11742.	Statement I : The ratio in which L=ax+by+c=0 divides the line segment joining A(x_(1),y_(1))B(x_(2),y_(2)) is -(L_(11))/(L_(22)) Statement II: The equation of the line in which (x_(1),y_(1)) divides the line segment between the coordinate axes in the ratio m:n is (nx)/(x_(1))+(my)/(y_(1))=m+n Then which of the following is true
Answer» only I onlyII both I and Ii neither I nor II Answer :B

Discussion

11743.	For a cubic function y=f(x),f(x)=4x at each point (x,u=y) on it crosses the x-axis at (-2,0) at an angle of 45^(@) with positive direction of thex- axis . Then the value of \|(f(1))/(5)\| is ________
Answer» ANSWER :3

Discussion

11744.	Let z_(1)=2 -I, z_(2)= -2 +i, find (i) Re ((z_(1)z_(2))/(bar(z)_(1))), (ii) Im ((1)/(z_(1)bar(z)_(2)))
Answer» ANSWER :(i) `-(2)/(5)`, (II) 0

Discussion

11745.	If f(x)=[x], g(x)=x-[x] then which of the following functions is the zero function
Answer» `(f+g)(X)` `(FG)(x)` `(f-g)(x)` `(FOG)(x)` ANSWER :D

Discussion

11746.	The periodof the functionf( theta ) = sin""(theta )/(3) + cos""(theta )/(2)is
Answer» `3PI` `6PI` `9pi` `12pi` ANSWER :4

Discussion

11747.	If the radius of a circle is 2.1 cm, then the approximate area of the circle is
Answer» `0.125pi` SQ. CM `4.4pi` sq.cm `0.4pi` sq. cm `3.6pi` sq. cm ANSWER :B

Discussion

11748.	Let A = {1, 2, 3}, B = { 2, 3, 4} , then which of the following is a function form A to B ?(a){(1,2),(1,3),(2,3),(3,3)}(b){(1,3),(2,4)}(c){(1,3),(2,2),(3,3)}(d){(1,2),(2,3),(3,2),(3,4)}
Answer» {(1,2),(1,3),(2,3),(3,3)} {(1,3),(2,4)} {(1,3),(2,2),(3,3)} {(1,2),(2,3),(3,2),(3,4)} ANSWER :C

Discussion

11749.	If the anglesof a right angled trianglesare in A.P.Then the sides are in the ratio
Answer» `1:SQRT(3):2` `1:1:sqrt(2)` `2:3:sqrt(13)` `1:2:3` ANSWER :A

Discussion

11750.	If C is the mid point of AB and P is any point outside AB, then
Answer» `bar(PA)+bar(PB)+bar(PC)=bar(0)` `bar(PA)+bar(PB)+2bar(PC)=bar(0)` `bar(PA)+bar(PB)=bar(PC)` `bar(PA)+bar(PB)=2bar(PC)` ANSWER :D

Discussion

Explore topic-wise InterviewSolutions in .

The periodof sin x cos x is

Find the sum of the following series up to n terms: 1^3/1+(1^3+2^3)/(1+3)+(1^3+2^3+3^3)/(1+3+5)+.......

If the line joining the points (2,k,5), (0,1,6) is parallel to the line joining the points (3,-1,2), (-1,2,4) then find k,

Two dice are thrown together , what is the probabability that the sum of the numbers on the two faces is neither divisible by 3 nor by 5.

If a,b,c are arithmeticprogression then show that the equation ax+by+c=0 represents a family of concurrent lines and find the point of concurrency.

If tan theta_(1), tan theta_(2) tan theta_(3) and tan theta_(4) are the roots of the equation x^(4) - x^(3) sin 2 beta + x^(2) cos 2 beta - x cos beta - sin beta = "0 then tan" (theta_(1) + theta_(2) + theta_(3) + theta_(4)) is equal to

Evaluate : (i) 5 ! (ii) 7 ! (iii) 7 ! - 5 !

AB=12cm. Ab sides with A on x-axis, B on y-axis respectively. Then the radius of the circle which is the locus of DeltaAOB,where O is origin is:

The minute hand of a watch is 1.5 cm long. How far does its tip move in 40 minutes ? (Use pi = 3.14).

Prove that tanalpha=(Sin2alpha)/(1+cos2alpha) and hence deduce the value of tan15^(@) and tan22 1^(@)/2

(1.2^2+ 2.3^2 + 3.4^2+ .... + n(n+1)^2)/( 1^2. 2 +2^2. 3+ 3^2. 4+ ..... + n^2 (n+1) ) =

No. of solutions of |cosx|=sinx,0lexle4pi, is

Assertion (A) sum _(r=1)^(n-1) cos^2((rpi)/(n))=(n)/(2)-1 Reasion (R) : cos alpha+ cos (alpha+ beta)+cos(alpha+2 beta)+....+cos (alpha(n-1) beta)=(sin(n beta//2))/(sin(beta//2)). Cos ((2 alpha+(n-1) beta)/(2))

If abgt0 find th area of the rhombus enclosed by the four straight lines ax+-by+-c=0

Let ABC be a triangle whose circumcentre is at P. If the position vectors of A, B, C and P are bar(a), bar(b), bar(c) and (bar(a)+bar(b)+bar(c))/4 respectively, then the position vector of the orthocentre of this triangle is

Numbers of elements in power set of the given set A={"x"in N |x^2

A triangle has sides that measure 13, 14, 15. A line perpendicular to the side of measure 14 divides the interior of the triangle in to two regions of equal area. Length of this perpendicular with in the triangle

Show that the feet of the perpendicular from (-2,-8) to the lines x-2y+6=0,x-7y+6=0 and x+3y-4=0 are collinear.

Which value of theta listed below leads to 2 ^(sin theta) gt 1 and 3^(cos theta) lt 1 ?

If f(x) = [x - 8] " & " g(x) = f(f(x)) AA x > 16 then g^1(x) equals

If ‘f' isgiven by f(x)={{:(ax-b,if xlt-1),(3x^(2)-4ax+2b,if-1ltxlt1 "is continous function on Rthen find the values"),(10,if x ge1):} is continuous function on R then find the values of a and b

Through a point A on the x-axis, a staight line is drawn parallel to the y-axis so as to meet the pair of straight lines ax^2+2hxy+by^2=0 at B and C. If AB=BC, then

Change the following complex numbers into polar form (1+ 2i)/(1-(1-i)^(2))

Find the derivative of w.r.to x 20 ^(log (tan x ))

Find the mean deviation about median for the following data :

If z = (x,-y) then point (x,y) with respect to real axis is called.

The variance of the given data 2,4,5,6,8,17 is 23.33 . Then find the variance of the data 4,8,10,12,16,34.

If a=6 , b=5 ,c=9then angle A .

If f(x+y,x-y) =xy, then the arithmetic mean of f(x,y) and f(y,-x) is

Find the derivative of the function (sqrtx -3x) (x + (1)/(x))

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

The sum of algebraic distances from the points (n,n^2) where n=1,2,3 …….,2013, to a straightline is zero and if such a line always passes through the point (alpha,beta) and 1/alpha(beta-1007/3)=abcd then b+d=(abcd is four digited number)

A group consists of 4 girls and 7 boys. In how many ways can a team of 5 members be selected, if the team has (i) no girls (ii) atleast one boy and one girl (iii) at least three girls

Iff:R to N UU {0}where f (area of triangle joining points P( 0,5) , Q( 8,4)and R(x,y ) such that angle PRQis a right angle) = number of triangle , then which of the following is true?

Evaluate the following limits : Lim_( n to oo) (1+2/n)^(2n)

A lamp post is sittuated at the middle point M of the side AC of a triangular plot ABC with BC=m CA =8 m and AB =9 m. Lamp post subleds an anlgle 15^(@) at the point B. The height of the lamp post is

From a rectangular sheet of a cm xx bcm,four equal square pieces of side x cm are removed at the corners and the sides are then turned up so as to form an open rectangular box. Find the value of x so that the volume of the box is greatest.

Usingthe mathematicalinduction , show that forany naturalnumbern le 2 1/ (1 +2) + 1/( 1 + 2+3) + 1/( 1 + 2+3+4)+ ….+ 1/( 1+2+3+….+n)= ( n -1)/(n+1)

Show that the function f (x) = (x)/(1 + |x| ) , x in R, is differentiable at x =0. Hence find f '(0).

Function and g defined on RrarrR" as "f(x)=x^2+7 and g(x)=3x+5. Then f(3) + g(-5) = ….. .

The pointcollinearwith (1, -2 -3 ) and (2, 0, 0 ) among the following is

For a cubic function y=f(x),f(x)=4x at each point (x,u=y) on it crosses the x-axis at (-2,0) at an angle of 45^(@) with positive direction of thex- axis . Then the value of |(f(1))/(5)| is ________

Let z_(1)=2 -I, z_(2)= -2 +i, find (i) Re ((z_(1)z_(2))/(bar(z)_(1))), (ii) Im ((1)/(z_(1)bar(z)_(2)))

If f(x)=[x], g(x)=x-[x] then which of the following functions is the zero function

The periodof the functionf( theta ) = sin""(theta )/(3) + cos""(theta )/(2)is

If the radius of a circle is 2.1 cm, then the approximate area of the circle is

Let A = {1, 2, 3}, B = { 2, 3, 4} , then which of the following is a function form A to B ?(a){(1,2),(1,3),(2,3),(3,3)}(b){(1,3),(2,4)}(c){(1,3),(2,2),(3,3)}(d){(1,2),(2,3),(3,2),(3,4)}

If the anglesof a right angled trianglesare in A.P.Then the sides are in the ratio

If C is the mid point of AB and P is any point outside AB, then