14949 + Interview Questions in Maths in Class 11 Page 30 InterviewSolution

1451.	If the pair of lines given by (x^(2)+y^(2))cos^(2) theta=(x cos theta+ y sin theta)^(2) are perpendicular to each other, then theta=
Answer» 0 `pi/4` `pi/3` `(3PI)/4` ANSWER :B

Discussion

1452.	vec(a) is perpendicular to both vec(b) and vec(c ). The angle between vec(b) and vec(c ) is (2pi)/(3). If \|vec(a)\|=2, \|vec(b)\|=3, \|vec(c )\|=4 then vec(a ).(vec(b) xx vec(c))=
Answer» `18 SQRT3` `12 sqrt3` `8sqrt3` `6sqrt3` ANSWER :B

Discussion

1453.	Maximum area of the rectangle incribedin a circle of radius 10 cms is
Answer» 100 200 400 1600 Answer :B

Discussion

1454.	If sin(theta+alpha)=a and sin (theta+ beta) , then cos2(alpha-beta)-4ab cos(alpha -beta) =
Answer» `1-a^2-B^2` `1-2a^2-2b^2` `2+a^2-b^2` `2-a^2-b^2` ANSWER :B

Discussion

1455.	The sum up to n terms of the series 1/(sqrt(1) + sqrt(3)) + 1/(sqrt(3) + sqrt(5)) + 1/(sqrt(5) + sqrt(7)) +… is:
Answer» `SQRT(2n+1)` `sqrt(2n+1)/2` `sqrt(2n+1) -1` `(sqrt(2n+1) -1)/2` ANSWER :D

Discussion

1456.	Resolve the following rational expressions into partial fractions.(1)(1)/(x^(2)-(a^(2))
Answer» ANSWER :`(1)/(2A(X + a))`

Discussion

1457.	Length of transverse axis and conjugate axis in hyperbola are equal then its eccentricity e =…….
Answer» `sqrt(3)` `sqrt(2)` `(1)/(sqrt(2))` 2 Answer :B

Discussion

1458.	One vertex of the equilateral triangle with centroid at the origin and one side as x+y -2 =0 is
Answer» `(-1,-1) ` `(2,2)` `(-2,-2)` `(2,-2)` ANSWER :C

Discussion

1459.	Represent the complex numbers z= 1 + sqrt3i into polar form
Answer» ANSWER :`2("COS"(pi)/(3) + I"SIN" (pi)/(3))`

Discussion

1460.	Use the first derivative test to find the local extrema of f(x) =x^(3) - 12x on R.
Answer» Answer :POINT of local minimum = x = 2, local minimum= -16 Point of local MAXIMUM x = -2, local maximum = 16

Discussion

1461.	5 sin x + 4 cos x =3 rArr 4 sin x - 5 cos x=
Answer» 4 `4sqrt(2)` `3sqrt(2)` `SQRT(2)` ANSWER :B

Discussion

1462.	If the function f(x) and phi (x) are continuous in [a,b] and differentiable in (a,b) , then the value of 'c' for the pair of functions f(x) = e^(x), phi (x) = e^(-x)is
Answer» `(a)/(2)` `(a-b)/(2)` `(a+b)/(2)` `(-a+b)/(2)` ANSWER :C

Discussion

1463.	For what real values of a, will the expression x^(2)-ax+1-2a^(2), for the real x, be always positive ?
Answer» ANSWER :`-(2)/(3) LT a lt (2)/(3)`.

Discussion

1464.	If 13 vec(a)= 3vec(i) + 4vec(j)+ 12vec(k), 13vec(b)= 4vec(i)-12vec(j) + 3vec(k), 13vec(c )=12vec(i) + 3vec(j)-4vec(k), then vec(a) xx vec(b)=
Answer» `VEC(C )` `5 vec(c )` `13 vec(c )` `169 vec(c )` ANSWER :A

Discussion

1465.	If the d.c's of a line are proportional to (1, -2, 1) find its d.c's
Answer» ANSWER :d.c's of the line are `PM((1)/(sqrt(6)),(-2)/(sqrt(6)),(1)/(sqrt(6)))`

Discussion

1466.	If sin theta+cos theta=sqrt(2)cos A then theta=
Answer» `2N pi +(pi)/3+-A,AA n in Z` `2NPI+(pi)/2+-A, AA n in Z` `2 n pi+(pi)/4+-A, AA n INZ` `2npi+(pi)/6+-A, AA n in Z` Answer :C

Discussion

1467.	Find the perpendicular distance from the origin to the plane passing through the points (1, 0,5), (1, - 5, -1) and (-3, 5, 0).
Answer» ANSWER :`45/(SQRT(4001))`

Discussion

1468.	Given the meaning and value of the symbol in the following ""^(10) P_4
Answer» ANSWER :` 5040 `

Discussion

1469.	If tan ((A -B)/( 2)) = (1)/(3)tan ((A+B)/( 2))then a : b is
Answer» ` 2: 1 ` ` 3: 1` ` 4: 1` ` 1: 3` ANSWER :A

Discussion

1470.	Solve the following equations and write general solutions4 cos^(2)x + sqrt(3) = 2(sqrt(3) +1) cos x
Answer» Answer :`2NPI pm (PI)/(3), 2npi pm(pi)/(6)`

Discussion

1471.	A tangent to the parabola y^(2)=8x makes an angle of45^(@)with the straight liney=3x+5. The equation of tangent is:
Answer» `x+2y+1=0` `2x+y +1=0` `x+y +2=0` `x+y +1=0` SOLUTION : EQUATION of any tangent to the PARABOLA `y^(2)=8x` is `y=mx +(a)/(m)=mx +(2)/(m)` `L: y=3x+5` `:.tan45^(@)=\|(m-3)/(1+3m)\|` `rArr (m-3)/(1+3m)=pm1` `rArr m-3=1+3m rArr m-3= -1-3m` `rArr m-3m=4 rArr 4m=2 rArr m=(4)/(-2)= -2 rArr m=(1)/(2)` Equation of tangent is `y= -2x-1` `y=(1)/(2)x +4 rArr y+2x+1=0 rArr 2y-x-8=0`

Discussion

1472.	The point P(1,3) undergoes the following transformations successively : (i) Reflection with respect to the line y = x (ii) Translation through 3 units along the positivedirection of the X-axis (iii) Rotation through an angle of (pi)/(6) aboutthe origin in theclockwise direction. The final position of the point P is
Answer» `((6sqrt(3))/(2),(-6 sqrt(3))/(2))` `((6 sqrt(3)-1)/(2),(6+ sqrt(3))/(2))` `((6 sqrt(3)+1)/(2),( sqrt(3)-6)/(2))` `((7)/(sqrt(2)),(-5)/(sqrt(2)))` ANSWER :B

Discussion

1473.	Evaluate the following limits : Lt_(xto0)(3^(-x)-1)/x
Answer» ANSWER :`-LOG3`

Discussion

1474.	If sin theta_(1)sin theta_(2)-cos theta_(1)cos theta_(2)+1=0, then the value of tan(theta_(1)//2)cot(theta_(1)//2) is equal to
Answer» `-1` 1 2 `-2` ANSWER :A

Discussion

1475.	In Delta ABC, if r_1=8, r_2=12, r_3=24, then a=
Answer» ` 10 ` ` 11` ` 16` ` 12` ANSWER :D

Discussion

1476.	If the points whose position vectors are 2bar(i)+bar(j)+bar(k), 6bar(i)-bar(j)+2bar(k)" and "14bar(i)-5bar(j)+pbar(k) are collinear, then the value of p is
Answer» 2 4 6 8 Answer :B

Discussion

1477.	Evaluate : sum_(i=1)^(10){(1/2)^(j-1)+(1/5)^(j+1)}
Answer» ANSWER :`=1(1-1/(2^(10)))+1/20(1-1/(5^(10)))`

Discussion

1478.	If 1+ tan^(2) theta = sec^(2) theta then find (sec theta + tan theta)
Answer» Answer :`rArr SEC THETA - TAN theta = (1)/(sec theta + tan theta)`

Discussion

1479.	find general solution sin x + sin 3x + sin 5x =0
Answer» ANSWER :`X = (npi)/(3), or N pi PM (pi)/(3) , n in Z`

Discussion

1480.	(a+bsinx)/(c+dcosx)
Answer» ANSWER :`(bccosx+ad SIN x+bd)/((c+d COSX)^(2)) (because COS^(2)x+sin^(2)x=1)`

Discussion

1481.	Find the locus of the point such that its distance from the y-axis is equal to its distance from the point (1, 1).
Answer» ANSWER : `y^(2)-2x-2y+2=0`

Discussion

1482.	If sinx+cosx=a, then (i) sin^(6)x+cos^(6)x = …………. (ii) \|sinx-cosx\| = …………….
Answer» ANSWER :`SQRT(2-a^(2))`

Discussion

1483.	Find the distance from the origin to A(6, 6, 7).
Answer» ANSWER :11 UNIT

Discussion

1484.	Find the value of a for which one root of the quadratic equation (a^(2)-5a+3)x^(2)+(3a-1) x+2=0 is twice as large as the other.
Answer» ANSWER :`(2)/(3)`

Discussion

1485.	If (-2 + sqrt-3) (-3 + 2 sqrt-3) = a + bi, find the real numbers a and b. With these values of a and b, also find the modulus of a+ bi
Answer» ANSWER :a=0, `B= - 7 SQRT3`, MODULUS = `7 sqrt3`

Discussion

1486.	The periodof (cot (x//4)+ tan(x//4))/(1+tan(x//2)-tanx) is
Answer» `(PI)/(2) ` `(pi)` `4pi` `2PI ` ANSWER :3

Discussion

1487.	Convert the sums or differences into products: sin 4x + cos 2x
Answer» ANSWER :`2 sin (45 ^(@) -x) cos (45 6(@) - 3x)`

Discussion

1488.	Which of the following is not statement.
Answer» `2xx3=6` `2xx4!=8` Let the TRUTH WIN ! Square of an ODD number of odd Answer :C

Discussion

1489.	barc.(barb+barc)xx(bara+barb+barc)=
Answer» `barc.barbxxbarc` `BAR0` `barc.baraxxbarb` `bara.barcxxbarb` ANSWER :D

Discussion

1490.	Find the equation of parabola if it's vertexis at (0,0) and the focus at (0,1).
Answer» ANSWER :`X^(2)=4Y`

Discussion

1491.	Differentiate the following function w.r.t. x. f(x) = sqrt( 3 x + 4), x gt -1
Answer» ANSWER :`(3)/(2). (1)/( SQRT (3 x+4) )`

Discussion

1492.	The point P(-1,0) lies on the circle x^(2)+y^(2)-4x+8y+k=0. Find the radius of the circle Also determine the equation of the circle of equal radius which touches the given circle at P.
Answer» ANSWER :`(x+4)^(2)=(y-4)^(2)=25`

Discussion

1493.	The solution set of the equation sin^(-1)sqrt(1-x^(2))+cos^(-1)x=cot^(-1)""sqrt(1-x^(2))/x-sin^(-1)x is
Answer» `[-1, 1]-{0}` `(0,1)U{-1}` `[-1,0)U{1}` `[-1, 1]` ANSWER :C

Discussion

1494.	For a paricle moving on a straight line it is observed that the distance 'S' at time 't' is given by S=6t-(t^(2))/(2) , the maximum velocity during the motion is
Answer» 3 units/sec 6units/sec 9units/sec 12units/sec Answer :B

Discussion

1495.	With the help of tables, find the values, correct to places of decimals, of each of the following : cos116^(@)
Answer» ANSWER :`-0.4384`

Discussion

1496.	sin10^(@) is greater than cos10^(@).
Answer» ANSWER :FALSE

Discussion

1497.	Find the coefficient of x^(4) in the expansion of (1+x+x^(2)+x^(3))^(11)
Answer» ANSWER :990

Discussion

1498.	alpha, beta, gamma are the root of x^(3)-2x^(2)-x+2=0. Centroidof triangle with verties alpha, beta, gamma, (beta, gamma, alpha), (gamma, alpha, beta) is
Answer» `(-(2)/(3), (2)/(3), -(2)/(3))` `(-(2)/(3), (1)/(3), (2)/(3))` `((2)/(3), (2)/(3), (2)/(3))` `((4)/(5), (2)/(3), (2)/(3))` Answer :c

Discussion

1499.	How many 9- digits numbers of different digits can be formed?
Answer» Answer :` 9 xx 9 8 xx 7 xx 6 xx 15 xx 4 xx 3 xx 2 = 3265920 `

Discussion

1500.	Solve the inequalities (2x-1) lt x + 5, 3(x+2) gt 2-x
Answer» ANSWER :`(-1,7)` `(##NCERT_TAM_MAT_XI_C06_E04_008_A01##)`

Discussion

Explore topic-wise InterviewSolutions in .

If the pair of lines given by (x^(2)+y^(2))cos^(2) theta=(x cos theta+ y sin theta)^(2) are perpendicular to each other, then theta=

vec(a) is perpendicular to both vec(b) and vec(c ). The angle between vec(b) and vec(c ) is (2pi)/(3). If |vec(a)|=2, |vec(b)|=3, |vec(c )|=4 then vec(a ).(vec(b) xx vec(c))=

Maximum area of the rectangle incribedin a circle of radius 10 cms is

If sin(theta+alpha)=a and sin (theta+ beta) , then cos2(alpha-beta)-4ab cos(alpha -beta) =

The sum up to n terms of the series 1/(sqrt(1) + sqrt(3)) + 1/(sqrt(3) + sqrt(5)) + 1/(sqrt(5) + sqrt(7)) +… is:

Resolve the following rational expressions into partial fractions.(1)(1)/(x^(2)-(a^(2))

Length of transverse axis and conjugate axis in hyperbola are equal then its eccentricity e =…….

One vertex of the equilateral triangle with centroid at the origin and one side as x+y -2 =0 is

Represent the complex numbers z= 1 + sqrt3i into polar form

Use the first derivative test to find the local extrema of f(x) =x^(3) - 12x on R.

5 sin x + 4 cos x =3 rArr 4 sin x - 5 cos x=

If the function f(x) and phi (x) are continuous in [a,b] and differentiable in (a,b) , then the value of 'c' for the pair of functions f(x) = e^(x), phi (x) = e^(-x)is

For what real values of a, will the expression x^(2)-ax+1-2a^(2), for the real x, be always positive ?

If 13 vec(a)= 3vec(i) + 4vec(j)+ 12vec(k), 13vec(b)= 4vec(i)-12vec(j) + 3vec(k), 13vec(c )=12vec(i) + 3vec(j)-4vec(k), then vec(a) xx vec(b)=

If the d.c's of a line are proportional to (1, -2, 1) find its d.c's

If sin theta+cos theta=sqrt(2)cos A then theta=

Find the perpendicular distance from the origin to the plane passing through the points (1, 0,5), (1, - 5, -1) and (-3, 5, 0).

Given the meaning and value of the symbol in the following ""^(10) P_4

If tan ((A -B)/( 2)) = (1)/(3)tan ((A+B)/( 2))then a : b is

Solve the following equations and write general solutions4 cos^(2)x + sqrt(3) = 2(sqrt(3) +1) cos x

A tangent to the parabola y^(2)=8x makes an angle of45^(@)with the straight liney=3x+5. The equation of tangent is:

Evaluate the following limits : Lt_(xto0)(3^(-x)-1)/x

If sin theta_(1)sin theta_(2)-cos theta_(1)cos theta_(2)+1=0, then the value of tan(theta_(1)//2)cot(theta_(1)//2) is equal to

In Delta ABC, if r_1=8, r_2=12, r_3=24, then a=

If the points whose position vectors are 2bar(i)+bar(j)+bar(k), 6bar(i)-bar(j)+2bar(k)" and "14bar(i)-5bar(j)+pbar(k) are collinear, then the value of p is

Evaluate : sum_(i=1)^(10){(1/2)^(j-1)+(1/5)^(j+1)}

If 1+ tan^(2) theta = sec^(2) theta then find (sec theta + tan theta)

find general solution sin x + sin 3x + sin 5x =0

(a+bsinx)/(c+dcosx)

Find the locus of the point such that its distance from the y-axis is equal to its distance from the point (1, 1).

If sinx+cosx=a, then (i) sin^(6)x+cos^(6)x = …………. (ii) |sinx-cosx| = …………….

Find the distance from the origin to A(6, 6, 7).

Find the value of a for which one root of the quadratic equation (a^(2)-5a+3)x^(2)+(3a-1) x+2=0 is twice as large as the other.

If (-2 + sqrt-3) (-3 + 2 sqrt-3) = a + bi, find the real numbers a and b. With these values of a and b, also find the modulus of a+ bi

The periodof (cot (x//4)+ tan(x//4))/(1+tan(x//2)-tanx) is

Convert the sums or differences into products: sin 4x + cos 2x

Which of the following is not statement.

barc.(barb+barc)xx(bara+barb+barc)=

Find the equation of parabola if it's vertexis at (0,0) and the focus at (0,1).

Differentiate the following function w.r.t. x. f(x) = sqrt( 3 x + 4), x gt -1

The point P(-1,0) lies on the circle x^(2)+y^(2)-4x+8y+k=0. Find the radius of the circle Also determine the equation of the circle of equal radius which touches the given circle at P.

The solution set of the equation sin^(-1)sqrt(1-x^(2))+cos^(-1)x=cot^(-1)""sqrt(1-x^(2))/x-sin^(-1)x is

For a paricle moving on a straight line it is observed that the distance 'S' at time 't' is given by S=6t-(t^(2))/(2) , the maximum velocity during the motion is

With the help of tables, find the values, correct to places of decimals, of each of the following : cos116^(@)

sin10^(@) is greater than cos10^(@).

Find the coefficient of x^(4) in the expansion of (1+x+x^(2)+x^(3))^(11)

alpha, beta, gamma are the root of x^(3)-2x^(2)-x+2=0. Centroidof triangle with verties alpha, beta, gamma, (beta, gamma, alpha), (gamma, alpha, beta) is

How many 9- digits numbers of different digits can be formed?

Solve the inequalities (2x-1) lt x + 5, 3(x+2) gt 2-x