14949 + Interview Questions in Maths in Class 11 Page 17 InterviewSolution

801.	In DeltaABC" prove that " (r_(1))/(bc)+(r_(2))/(ca)+(r_(3))/(ab)=(1)/(r)-(1)/(2R)
Answer» `(1)/(R)-(1)/(2R)` `1+(r)/(R)` `2+(r)/(2R)` `1-(r)/(2R)` ANSWER :A

Discussion

802.	Find the distance between each of pair of point: (2,5,3 and (-3,2,1),
Answer» ANSWER :7

Discussion

803.	If x+y=(2pi)/(3)andsinx+siny=(3)/(2)" then find"x ,y
Answer» ANSWER :`x=2NPI+(PI)/(2),y=(pi)/(6)-2npi;x=2npi+(pi)/(6),y=(pi)/(2)-2npi`

Discussion

804.	If a=5, b=6, sin A=5//A then B=
Answer» `PI` `pi//2` `pi//3` `pi//4` ANSWER :B

Discussion

805.	In a triangle ABC, fi Tan A + Tan B + Tan C = 6 and Tan A Tan B = 2 then the triangle is
Answer» RIGHT angled triange equilateral triangle obtuse angled ACUTE angled triangle ANSWER :D

Discussion

806.	Find the values of k for which the line (k - 3) x - (4 - k^(2)) y +k^(2) - 7k + 6 = 0 is (a) Parallel to the x-axis,(b) Parallel to the y-axis, (c) Passing through the origin.
Answer» Answer :`(a)3, (B) pm 2, (C ) 6 " or " 1`

Discussion

807.	The orthocentre of the triangle formed by the lines x+y+1=0,x-y-1=0,3x+4y+5=0 is
Answer» (0,-1) (0,0) (1,10 (-1,0) ANSWER :A

Discussion

808.	Find the solution of sin x =-sqrt3/2.
Answer» ANSWER :`X = N PI + (-1)^(n) (4PI)/(3),` where `n in Z`

Discussion

809.	If f(x)=x^(2)," find "(f(1.1)-f(1))/((1.1-1))
Answer» ANSWER :2.1

Discussion

810.	Write each sentence in the " If ................Then " form. All ducks are birds.
Answer» ANSWER :If the CREATURE is a DUCK, then it is a BIRD.

Discussion

811.	The trigonometric equationsin 2 x + sin 3 x + sin 4 x + . . . . + sin n x = n - 1( n is a natural number greater than2)
Answer» has unique SOLUTION for any N has no solution for any n has INFINITE SOLUTIONS has no solutions in `[ 2 , n pi`] Answer :B::D

Discussion

812.	Find the approximations of the following sin (62^(@))
Answer» ANSWER :0.8834

Discussion

813.	Solve the following systems of homogeneous equations. x+y-2z=0 2x+y-3z=0 5x+4y-9z=0
Answer» ANSWER :`x=y=z=K` for any REAL NUMBER k

Discussion

814.	I : The function f(x)=9x^(2)-15x-x^(3)+10is increasing in (1,5) II :The function f(x)=9x^(2)-15x-x^(3)+10 is deresing in (1,5)which of the above statements are true
Answer» only I only II Both I and II NEITHER I nor II ANSWER :A

Discussion

815.	Findlimit of the following if it exists: lim_(xto3)(e^(x)-e^(3))/(x-3)
Answer» ANSWER :`E^(3)`

Discussion

816.	If A = {x : x is a natural number },B = {x : x is an even natural number} C = {x : x is an odd natural number} and D = {x : x is a prime number }, find A ∩ C
Answer» ANSWER :C

Discussion

817.	Find the sum to n terms of the series 1xx2+2xx3+3xx4+.. ?1xx2+2xx3+3xx4+.. ?
Answer» ANSWER :`n/3(n+1)(n+2)`

Discussion

818.	Find the position of the following points with respect to the parabola y^(2)=16x (i) (4,-8) , (ii) (2,4) (iii) (0,1) , (iv) (-2,8)
Answer» Answer :(i) (4,-8) LIES on PARABOLA, (ii) (2,4) lies inside the parabola (iii) (0,1) lies outside the parabola , (IV) (-2,8) lies outside the parabola

Discussion

819.	If x_1,y_1 " are roots of" x^2+8x-20=0, x_1,y_1" are the roots of " 4x^2+32x-57=0 and x_3,y_3 " are the roots of "9x^2+72x-112=0,then the points (x_1,y_1 )(x_2,y_2) and (x_3,y_3) where x_1 lt y_1 for i=1,2,3
Answer» are COLLINEAR form an equitateral triangle form a RIGHT ANGLED isosceles triangle are concyclic Answer :A

Discussion

820.	A coin is tossed three times.
Answer» Answer :{HHH, HHT, HTH, TTH, HTT, THT, TTT}

Discussion

821.	If 0lttheta ltpi/2,sin2theta=cos3theta then sintheta=
Answer» `(sqrt5-1)/4` `(1-sqrt5)/4` `(sqrt5+1)/4` `-((sqrt5+1)/4)` ANSWER :A

Discussion

822.	Calculate the mean deviation about median for the following data:
Answer» ANSWER :10.16

Discussion

823.	Find the derivative of f (x) w.r.t. g(x) for the f(x) = e ^(sinx), g (x) = sin x
Answer» ANSWER :`E ^(SIN X)`

Discussion

824.	Find the 12th term of a G.P . Whose 8th terms is 192 and the common ratio is 2.
Answer» ANSWER :3072

Discussion

825.	Find the sum of the series : 5^(2)+6^(2)+7^(2)+…+20^(2).
Answer» SOLUTION :N/a

Discussion

826.	Seven persons are to be seated in a row. The probability that two particular persons sit next to each other is
Answer» `(1)/(3)` `(1)/(6)` `(2)/(7)` `(1)/(2)` Answer :C

Discussion

827.	There are 5 red , 4 white and 3 blue marbles in a bag. They are drawn one by one and arranged in a row . Assuming that all the 12 marbles are drawn , determine the number of different arrangements.
Answer» ANSWER :` (12!)/( 5!XX 4!xx 3!)` = 27720 `

Discussion

828.	Show that f(x)=sin^(m)x.cos^(n)x has maximum value at x=Tan^(-1)sqrt(m/n)(m,ngt0)
Answer» ANSWER :F(X) has MAXIMUM

Discussion

829.	Ifsin ^(2) A+ sin ^(2) B + sin ^(2) Cthenangle C =
Answer» ` 45 ^(@) ` ` 60^(@) ` ` 30 ^(@) ` ` 90 ^(@) ` ANSWER :D

Discussion

830.	O(0,0), A(4,0), B(0, 6) are the points. If P is a point such that the area of DeltaPOB is twice the area of DeltaPOA, then the locus of P is
Answer» 1)`2X^(2)=3y^(2)` 2)`3x^(2)=4Y^(2)` 3)`9x^(2)=16y^(2)` 4)`4x^(2)=9Y^(2)` Answer :3

Discussion

831.	If the coordiantes of a point P are transformed to (2,-4sqrt(3)) when the axes are rotated through an angle 60^(@), then P=
Answer» ANSWER :`- SQRT(3)`

Discussion

832.	Which of the following is the quadratic equation whose roots are cosec^(2) theta and sec^(2)theta when θ = π/4?
Answer» `X^(2) - 6x + 6 = 0 ` `x^(2) - 7X + 7 = 0` `x^(2) - 4X + 4 = 0` none of these Answer :A::B::C::D

Discussion

833.	Statement-1: The fucntion x^(2)(e^(x)+e^(-x)) is increasing for all x gt 0. Statement-2 : The function x^(2)e^(x) and x^(2)e^(-x) are increasing for all x gt 0 and the sum of two increasing functions in any interval (a,b) is an increasing function in (a,b)
Answer» STATEMENT-1 is FALSE and the Statement-2 is true Statement-1 is true, Statement-2 is true and the Statement 2 is not the correct EXPLANATION of the Statement 1. Statement-I is true and the Satement-2 is false Statement-1 is true, Statement -2 is true and the Statement 2 is true explanation of the Statement 1. Answer :C

Discussion

834.	Let alpha,beta be the roots of the equation x^(2)-px+r=0 and alpha//2,2beta be the roots of the equation x^(2)-qx+r=0, then the value of r is(1)(2)/(9)(p-q)(2q-p)(2) (2)/(9)(q-p)(2p-q)(3)(2)/(9)(q-2p)(2q-p)(4)(2)/(9)(2p-q)(2q-p)
Answer» `(2)/(9)(p-q)(2q-p)` `(2)/(9)(q-p)(2p-q)` `(2)/(9)(q-2p)(2q-p)` `(2)/(9)(2p-q)(2q-p)` ANSWER :D

Discussion

835.	If tanh(x)=(3)/(5) then cosh(2x)=
Answer» `(15)/(8)` `(15)/(17)` `(8)/(17)` `(17)/(8)` ANSWER :D

Discussion

836.	The vector equation of the line passing through the point 2bar(i)+bar(j)-3bar(k) and parallel to bar(i)+2bar(j)+bar(k) is
Answer» `BAR(r)=2BAR(i)+bar(j)+bar(k)+t(-bar(i)+5bar(j)-6bar(k))` `bar(r)=2bar(i)-bar(j)+bar(k)+t(bar(i)+5bar(j)-6bar(k))` `bar(r)=2bar(i)+bar(j)-bar(k)+t(-bar(i)+5bar(j)+6bar(k))` `bar(r)=2bar(i)+bar(j)-bar(k)+t(bar(i)-5bar(j)+6bar(k))` ANSWER :A

Discussion

837.	If A(bar(i)+2bar(j)+3bar(k)), B(-bar(i)-bar(j)+8bar(k)), C(-4bar(i)+4bar(j)+6bar(k)) are the vertices of a triangle then the equation of the line passing through the circumcentre and parallel to bar(AB) is
Answer» `BAR(R)=(-4/3BAR(i)+5/3bar(J)+17/3bar(k))+t(2bar(i)+3bar(j)-5bar(k))` `bar(r)=(2bar(i)+3bar(j)+5bar(k))+t(2bar(i)-3bar(j)-5bar(k))` `bar(r)=(4/3bar(i)-5/3bar(j)-17/3bar(k))+t(2bar(i)-3bar(j)+5bar(k))` `bar(r)=(-4/3bar(i)-5/3bar(j)-17/3bar(k))+t(2bar(i)+3bar(j)+5bar(k))` Answer :A

Discussion

838.	A(2,3) B (-3,4)are two points P moves such that the area of DeltaPAB is 8.5 square units, thenfind the locus of P
Answer» ANSWER :`X^(2)+10xy+25y^(2)-34x-170y=0`

Discussion

839.	The point A(0, 0), B(1, 7), C(5, 1) are the vertices of a triangle. Find the length of the perpendicular from A to BC and hence the area of the DeltaABC.
Answer» ANSWER : `17/sqrt(13)UNITS;17sq. Units`

Discussion

840.	If""^(n)C_(3) + ""^(n)C_4 gt ""^(n+1) C_3 ,then.
Answer» ` n gt 6` ` n gt 7 ` `n lt 6` NONE of these ANSWER :a

Discussion

841.	Write out the expansions of the following: (c ) (x- (y)/(2) )^(4)
Answer» ANSWER :`x^4 - 2x^3y + (3)/(2) x^(2) y^(2) - (1)/(2) xy^(3) + (1)/(16) y^(4)`

Discussion

842.	If the length of side of an equilateral triangle is 10cm , then R =
Answer» ` ( 10 )/(SQRT3) ` ` 10 sqrt3` ` 10 + sqrt3` ` ( 20 )/(sqrt3) ` ANSWER :A

Discussion

843.	The parabola y^(2) = 4px passes through the point (3, -2). The length of the latus-rectum is …………..
Answer» ANSWER :`(4)/(3)`

Discussion

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

Discussion

845.	If y = (tan x-1)/(sec x) then dy/dx=?
Answer» ANSWER :` COS X + SIN x `

Discussion

846.	The ratio in which zx-plane divides the line segment joining (-2,3,5),(3,-2,1) is
Answer» " 1 :2 " " 2:1 " " 2: 3 " " 3 : 2 " ANSWER :D

Discussion

847.	If f(x)=x^(5)-5x^(4)+5x^(3)-10 has local maximum and minimum at x=p and x=q , respectively , then (p,q)=
Answer» (0,1) (1,3) (1,0) (1,2) ANSWER :B

Discussion

848.	The rate of change of sin t is n, then the rate of change of tan t is
Answer» `N^(2)` `1//n^(2)` 1/n `n^(3)` ANSWER :B

Discussion

849.	Evaluate (8492 xx 3.72)/(47.8 xx 52.24).
Answer» SOLUTION :Let `X = (8492 xx 3.72)/(47.8 xx 52.24).` Then, log x = log 8492 + log 3.72 - log 47.8 - log 52.24 = 3.9290 + 0.5705 - 1.6794 - 1.7180 = 4.4995 - 3.3974 = 1.1021 `rArr x =` antilog (1.1021) = 12.65. Hence, the value of the GIVEN EXPRESSION is 12.65.

Discussion

850.	Solve the following equations and write general solutions sec 4 x - sec 2x = 2
Answer» Answer :`(2NPI)/(5) pm (PI)/(10), 2npi pm (pi)/(2)`

Discussion

Explore topic-wise InterviewSolutions in .

In DeltaABC" prove that " (r_(1))/(bc)+(r_(2))/(ca)+(r_(3))/(ab)=(1)/(r)-(1)/(2R)

Find the distance between each of pair of point: (2,5,3 and (-3,2,1),

If x+y=(2pi)/(3)andsinx+siny=(3)/(2)" then find"x ,y

If a=5, b=6, sin A=5//A then B=

In a triangle ABC, fi Tan A + Tan B + Tan C = 6 and Tan A Tan B = 2 then the triangle is

Find the values of k for which the line (k - 3) x - (4 - k^(2)) y +k^(2) - 7k + 6 = 0 is (a) Parallel to the x-axis,(b) Parallel to the y-axis, (c) Passing through the origin.

The orthocentre of the triangle formed by the lines x+y+1=0,x-y-1=0,3x+4y+5=0 is

Find the solution of sin x =-sqrt3/2.

If f(x)=x^(2)," find "(f(1.1)-f(1))/((1.1-1))

Write each sentence in the " If ................Then " form. All ducks are birds.

The trigonometric equationsin 2 x + sin 3 x + sin 4 x + . . . . + sin n x = n - 1( n is a natural number greater than2)

Find the approximations of the following sin (62^(@))

Solve the following systems of homogeneous equations. x+y-2z=0 2x+y-3z=0 5x+4y-9z=0

I : The function f(x)=9x^(2)-15x-x^(3)+10is increasing in (1,5) II :The function f(x)=9x^(2)-15x-x^(3)+10 is deresing in (1,5)which of the above statements are true

Findlimit of the following if it exists: lim_(xto3)(e^(x)-e^(3))/(x-3)

If A = {x : x is a natural number },B = {x : x is an even natural number} C = {x : x is an odd natural number} and D = {x : x is a prime number }, find A ∩ C

Find the sum to n terms of the series 1xx2+2xx3+3xx4+.. ?1xx2+2xx3+3xx4+.. ?

Find the position of the following points with respect to the parabola y^(2)=16x (i) (4,-8) , (ii) (2,4) (iii) (0,1) , (iv) (-2,8)

If x_1,y_1 " are roots of" x^2+8x-20=0, x_1,y_1" are the roots of " 4x^2+32x-57=0 and x_3,y_3 " are the roots of "9x^2+72x-112=0,then the points (x_1,y_1 )(x_2,y_2) and (x_3,y_3) where x_1 lt y_1 for i=1,2,3

A coin is tossed three times.

If 0lttheta ltpi/2,sin2theta=cos3theta then sintheta=

Calculate the mean deviation about median for the following data:

Find the derivative of f (x) w.r.t. g(x) for the f(x) = e ^(sinx), g (x) = sin x

Find the 12th term of a G.P . Whose 8th terms is 192 and the common ratio is 2.

Find the sum of the series : 5^(2)+6^(2)+7^(2)+…+20^(2).

Seven persons are to be seated in a row. The probability that two particular persons sit next to each other is

There are 5 red , 4 white and 3 blue marbles in a bag. They are drawn one by one and arranged in a row . Assuming that all the 12 marbles are drawn , determine the number of different arrangements.

Show that f(x)=sin^(m)x.cos^(n)x has maximum value at x=Tan^(-1)sqrt(m/n)(m,ngt0)

Ifsin ^(2) A+ sin ^(2) B + sin ^(2) Cthenangle C =

O(0,0), A(4,0), B(0, 6) are the points. If P is a point such that the area of DeltaPOB is twice the area of DeltaPOA, then the locus of P is

If the coordiantes of a point P are transformed to (2,-4sqrt(3)) when the axes are rotated through an angle 60^(@), then P=

Which of the following is the quadratic equation whose roots are cosec^(2) theta and sec^(2)theta when θ = π/4?

Statement-1: The fucntion x^(2)(e^(x)+e^(-x)) is increasing for all x gt 0. Statement-2 : The function x^(2)e^(x) and x^(2)e^(-x) are increasing for all x gt 0 and the sum of two increasing functions in any interval (a,b) is an increasing function in (a,b)

Let alpha,beta be the roots of the equation x^(2)-px+r=0 and alpha//2,2beta be the roots of the equation x^(2)-qx+r=0, then the value of r is(1)(2)/(9)(p-q)(2q-p)(2) (2)/(9)(q-p)(2p-q)(3)(2)/(9)(q-2p)(2q-p)(4)(2)/(9)(2p-q)(2q-p)

If tanh(x)=(3)/(5) then cosh(2x)=

The vector equation of the line passing through the point 2bar(i)+bar(j)-3bar(k) and parallel to bar(i)+2bar(j)+bar(k) is

If A(bar(i)+2bar(j)+3bar(k)), B(-bar(i)-bar(j)+8bar(k)), C(-4bar(i)+4bar(j)+6bar(k)) are the vertices of a triangle then the equation of the line passing through the circumcentre and parallel to bar(AB) is

A(2,3) B (-3,4)are two points P moves such that the area of DeltaPAB is 8.5 square units, thenfind the locus of P

The point A(0, 0), B(1, 7), C(5, 1) are the vertices of a triangle. Find the length of the perpendicular from A to BC and hence the area of the DeltaABC.

If""^(n)C_(3) + ""^(n)C_4 gt ""^(n+1) C_3 ,then.

Write out the expansions of the following: (c ) (x- (y)/(2) )^(4)

If the length of side of an equilateral triangle is 10cm , then R =

The parabola y^(2) = 4px passes through the point (3, -2). The length of the latus-rectum is …………..

Evaluate the following limits. Lt_(xto0)(x-1)/(x^(2)+4)

If y = (tan x-1)/(sec x) then dy/dx=?

The ratio in which zx-plane divides the line segment joining (-2,3,5),(3,-2,1) is

If f(x)=x^(5)-5x^(4)+5x^(3)-10 has local maximum and minimum at x=p and x=q , respectively , then (p,q)=

The rate of change of sin t is n, then the rate of change of tan t is

Evaluate (8492 xx 3.72)/(47.8 xx 52.24).

Solve the following equations and write general solutions sec 4 x - sec 2x = 2