14949 + Interview Questions in Maths in Class 11 Page 128 InterviewSolution

6351.	Find the angle between the lines whose direction cosines satisfy the equaitons l + m + n = 0, l^(2) + m^(2) - n^(2) = 0.
Answer» ANSWER :`(PI)/(3)`

Discussion

6352.	(iii) Find the modulus and argument of the complex numbers. (a) (1+i)/(1-i), (b) 1/(1+i)
Answer» ANSWER :(i) modulus of `(1+i)/(1-i)` is 1 and the ARGUMENT is `pi/2`. (II) modulus of `1/(1+i)` is `1/sqrt(2)`,argument is `-pi/4`.

Discussion

6353.	Expand ((2)/( x) - (x)/(2))^(5), x ne 0.
Answer» ANSWER :`32X^(-5) - 40x^(-3) + 20x^(-4) - 5X + (5)/(8) x^(3) - (1)/(32) x^(5)`

Discussion

6354.	Find the second derivative of the function (Find y" or (d ^(2) y)/(dx ^(2)) of the x ^(4) + tan x
Answer» ANSWER :`12 x ^(2) + 2 SEC ^(2) x TAN x`

Discussion

6355.	Differentiate w.r.t xx^(4)(5sin x-3 cos x)
Answer» ANSWER :`X^(3)[5xcosx+3xsinx+20sinx-12cosx]`

Discussion

6356.	If 3, 10 and 15 are the altitudes of a triangle then area of incircle is
Answer» `2PI` `9pi` `4PI` `16pi` ANSWER :C

Discussion

6357.	If f: R rarr Rand g: R rarr R are defined by f(x)=\|x\| and g(x)=[x-3] for x in R, then {g(f(x)):-8//5 lt x lt 8//5}=
Answer» `{0, 1}` `{1,2}` `{-3, -2}` `{2, 3}` ANSWER :C

Discussion

6358.	If cos h x = sec theta then tan h^(2) ((x)/(2))=
Answer» `TAN^(2)""(THETA)/(2)` `COT^(2)""(theta)/(2)` `-tan^(2)""(theta)/(2)` `-cot^(2)""(theta)/(2)` ANSWER :A

Discussion

6359.	Let f(x)= a X^(2013)+b X^(1011) + c sin^(3) X + 20 where a, b, c are non-zero constants. If f(-2014)=36, then the value of (2014) is equal to _____
Answer» ANSWER :D

Discussion

6360.	Construct the truth table for[(~p)^^q]implies(pvvq)
Answer» ANSWER :`(##VVA_ISC_MAT_XI_MTP_04_E01_040_A01##)`

Discussion

6361.	Find the component statements of the following compound statements: A rectangle is a quadrilateral or a 5 sided polygon.
Answer» ANSWER :p: A RECTANGLE is a QUADRILATERIAL. Q: A rectangle is 5 sided polygon.

Discussion

6362.	The point on the line (x-2)/(1) = (y+3)/(-2) = (z+5)/(-2) at a distance of 6 from the point (2, -3, -5) is
Answer» `(3,-5,-3)` `(4,-7,-9)` `(0,2,-1)` `(-3,5,3)` Answer :B

Discussion

6363.	In triangle ABC, medians AD and CE are drawn. If AD = 5, angle DAC = pi//8 " and " angle ACE = pi//4, then the area of the triangle ABC is equal to
Answer» `25/9` `25/3` `25/18` `10/3` ANSWER :B

Discussion

6364.	Solve 2 cos ^(2) x + 3 sin x =0
Answer» ANSWER :`X = NPI + (-1) ^(N)`

Discussion

6365.	For an data if n = 10, sumx_1=40,sumx_i^2=250 then standard deviation s = ....
Answer» ANSWER :TRUE STATEMENT

Discussion

6366.	A point is moving on y = 4 - 2x^(2). The x-coordinate of the point is decreasint at the rate of 5 units/sec. Then the rate at which y - coordinate of the point is changing when the point is at (1,2) is
Answer» 5 units/sec 10unit/sec 15unit/sec 20unit/sec Answer :D

Discussion

6367.	1^(3)- 2^(3) + 3^(3) - 4^(3) + …….+9^(3) =
Answer» `425` `-425` `475` `-475` ANSWER :A

Discussion

6368.	The locus of the point (2sec alpha cos beta, 2 sec alpha sin beta, 2tanalpha) is
Answer» `X^(2)+y^(2)-Z^(2)=R^(2)` `x^(2)+y^(2)+z^(2)=r^(2)` `x^(2)+y^(2)-z^(2)=2r^(2)` `x^(2)-y^(2)+z^(2)=r^(2)` ANSWER :a

Discussion

6369.	Statement-I : If side BC and radiu of r_(2)a nd r_(3) of an acute angled triangle is given, then the locus of A is hyperbola. Statement-2 : If the base of a triangle is given and difference of two variable sides is constant, less than the base. Then locus of variable vertex is a hyperbola.
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 NOT a correct explanation for Statement-1. Statement-1 is True, Statement-2 is FALSE Statement -1 is False, Statement-2 is True. Answer :A

Discussion

6370.	f_(n)(x)=e^(f_(n-1^(x))) for all n inN and f_0(x) = x , then (d)/(dx){f_(n)(x)} is
Answer» `f_(n)(X)(d)/(dx){f_(n-1)(x)}` `f_(n)(x)f_(n-1)` `f_(n)(x)f_(n-1)(x)....f_(2)(x).f_(1)(x)` none of these Answer :A::C

Discussion

6371.	P (a, b) is the mid-point of a line segment between axes. Show that equation of the line is (x)/(a) + (y)/(b) =2.
Answer» Answer :`(x)/(2) + (y)/(b) =2` Which is required equation of the LINE.

Discussion

6372.	If the letters of the word ALGORITHM are arranged at random in a row what is the probability the letters GOR must remain together as a unit ?
Answer» ANSWER :`(1)/(72)`

Discussion

6373.	Find the eccentricity, coordinates of the foci and the equations of the directrices of the hyperbolas:
Answer» ANSWER :(i) `E = (5)/(3), (PM5, 0), 5x = pm9` (ii) `e = (sqrt(13))/(3) ,(pmsqrt(13,0), sqrt(13x) = pm19`

Discussion

6374.	A triangle is inscribed in a circle. The vertices of the triangle divide the circle into three arcs of length 3, 4 and 5 units, then area of the triangle is equal to
Answer» `(9 SQRT3(1 + sqrt3))/PI^(2)` `(9sqrt3(sqrt3 - 1))/pi^(2)` `(9sqrt3(1 + sqrt3))/(2pi^(2))` `(9sqrt3 (sqrt3 - 1))/(2 pi^(2)) ` ANSWER :A

Discussion

6375.	Solve the system of homogenous equations x+y-z=0,x-2y+z=0,3x+6y-5z=0.
Answer» ANSWER :`x=K,y=2k,z=3k`for any REAL NUMBER k.

Discussion

6376.	Consider the points A(-5,6,8), B(1,8,11),C(4,2,9) and D(-2,0,6).Find the mid points of AC and the mid point of BD and prove that ABCD is a parallelogram
Answer» SOLUTION :`(-1/2,4,17/2), (-1/2,4,17/2)`

Discussion

6377.	When two dies are thrown , calculate the probability of throwing a total of (i) a 7 or an 11 , (ii) a doublet or a total of 6.
Answer» ANSWER :`=(5)/(18)`.

Discussion

6378.	If forces of magnitude 6 and 7 units acting in the direction bari-2barj +2bark and 2bari -3barj -6bark respectively act on particle which is displaced from P (2,-1,-3) to Q(5,-1,1) then the work done by the forces is
Answer» 4 UNITS `-4 units` 7 units `-7 units Answer :A

Discussion

6379.	Evaluate the following limits : Lt_(xtooo)(1+1/x)^(2x)
Answer» ANSWER :`E^(2)`

Discussion

6380.	Show that for any sets A and B, A = ( A ∩B )∪ ( A – B ) and A ∪ ( B – A ) =( A ∪ B )
Answer» ANSWER :`= A CUP B`

Discussion

6381.	If A and B are matrices such that AB = O then
Answer» `A=O,B!=O` `A!=O,B=O` `A=O,B=O` A, B NEED not be NULL MATRICES ANSWER :D

Discussion

6382.	At time t, the distance s of a particle moving in a straight line is given by s= 4t^2+ 2t. Find the average velocity between t= 2sec and t= 8 sec.
Answer» ANSWER :`-38` unit/sec

Discussion

6383.	If A=[(5,4),(1,2)] and if (A+2I)^(-1)=k_(1)A+k_(2)I then find (k_(1),k_(2)).
Answer» ANSWER :`((-1)/(24),(3)/(8))`

Discussion

6384.	Find the multiplicative inverse of each of the following complex numbers when it exists. -16
Answer» ANSWER :`-(1)/(16) + 0I`

Discussion

6385.	Write each sentence in the " If ................Then " form. Roses are vegetables if carrots are flowers.
Answer» ANSWER :If CARROTS are FLOWERS, then ROSES are VEGETABLES.

Discussion

6386.	The period of the function f(theta) = sin ((theta)/( 3)) + cos ((theta)/(2)) is
Answer» `3PI` `6PI` `9pi` `12pi` ANSWER :D

Discussion

6387.	If bar(a)=bar(i)+bar(j)+bar(k) and bar(b)=2bar(i)-3bar(j)-bar(k), find the unit vector in the direction of bar(a)+bar(b).
Answer» ANSWER :`1/sqrt(13)(3BAR(i)-2BAR(J))`

Discussion

6388.	Find the sixth term of the expansion (y^(1/2) +x^(1/3))^(n) , if the Binomial coefficient of the third term from the end is 45.
Answer» ANSWER :` :. T_(6) = 252 XX X^(5/3) xx y^(5/2)`

Discussion

6389.	Which of the following are sets ? Justify your answer. The collection of all boys in your class.
Answer» ANSWER :VI

Discussion

6390.	If the circles x^(2) + y^(2) = a^(2) and x^(2) + y^(2) - 6x - 8y + 9 = 0 touches each other externally, then a = …….
Answer» 1 -1 21 16 Answer :A

Discussion

6391.	lim_(xrarr2)[x]=……...
Answer» 2 3 0 does not exist Answer :D

Discussion

6392.	If \|x\| lt 1 and (1 - 2x)/(1 - x + x^2) + (2x - 4x^3)/(1 - x^2 + x^4) + (4x^3 - 8x^7)/(1 - x^4 + x^8) + ….. oo = (1 + ax)/(1 + bx + cx^2) then a + b - c is
Answer» ANSWER :B

Discussion

6393.	theminutehandof a watchis 1.5 cmlong. Findthe distancecoveredby its tipin 40minutes( usepi =3.14
Answer» ANSWER :`6.28 CM`

Discussion

6394.	IfA = (pi )/(4) , B = ( 5pi )/(12)"then " a + sqrt( 2 ) c=
Answer» ` 2B` ` B ` ` 3B ` ` 4B` ANSWER :A

Discussion

6395.	Find the sum to n terms of 3 (3)/(8) + 2 (1)/(4) + 1 (1)/(2)+ .....
Answer» Answer :`(81)/(8) {1-((2)/(3))^(N)}`

Discussion

6396.	Find the slope of the lines : Passing through the points (3, -2) " and " (-1, 4)
Answer» ANSWER :`- 3/2`

Discussion

6397.	A die is thrown. Describe the following events : (i) A: a number less then 7 (ii) B : a number greater then 7 (iii) C: a multiple of 3. (iv) D : a number less then 4 (v) E : an even number greater then 4 (vi) F : a number not less then 3 Also find AuuB,AnnB,BuuC,EnnF,DnnE,A-C,D-E,EnnF',F'.
Answer» Answer :(i) `{1, 2, 3, 4, 5, 6}` (ii) `phi` (iii) `{3, 6}` (IV) `{1, 2, 3}` (v) `{6}` (VI) `{3, 4, 5, 6}, A uu B = {1, 2, 3, 4, 5, 6}, A nn B = phi, B uu C = {3, 6}, E nn F = {6}, D nn E = phi`.

Discussion

6398.	The set of values 'x' for which f(x)=x^(3)+6x^(2)+27x+10 is increasisngin
Answer» (1,2) `(-OO,1)U(2,oo)` `(-oo,oo)` `(-oo,1)` ANSWER :C

Discussion

6399.	Fill in the blanks to make each of the following a true statement : (A')'"………"
Answer» ANSWER :`= A`

Discussion

6400.	Find the perpendicular distance between the lines. 3x+4y-5=0 ...(1) and 6x+8y-45=0 ...(2)
Answer» ANSWER : `7/(2)`

Discussion

Explore topic-wise InterviewSolutions in .

Find the angle between the lines whose direction cosines satisfy the equaitons l + m + n = 0, l^(2) + m^(2) - n^(2) = 0.

(iii) Find the modulus and argument of the complex numbers. (a) (1+i)/(1-i), (b) 1/(1+i)

Expand ((2)/( x) - (x)/(2))^(5), x ne 0.

Find the second derivative of the function (Find y" or (d ^(2) y)/(dx ^(2)) of the x ^(4) + tan x

Differentiate w.r.t xx^(4)(5sin x-3 cos x)

If 3, 10 and 15 are the altitudes of a triangle then area of incircle is

If f: R rarr Rand g: R rarr R are defined by f(x)=|x| and g(x)=[x-3] for x in R, then {g(f(x)):-8//5 lt x lt 8//5}=

If cos h x = sec theta then tan h^(2) ((x)/(2))=

Let f(x)= a X^(2013)+b X^(1011) + c sin^(3) X + 20 where a, b, c are non-zero constants. If f(-2014)=36, then the value of (2014) is equal to _____

Construct the truth table for[(~p)^^q]implies(pvvq)

Find the component statements of the following compound statements: A rectangle is a quadrilateral or a 5 sided polygon.

The point on the line (x-2)/(1) = (y+3)/(-2) = (z+5)/(-2) at a distance of 6 from the point (2, -3, -5) is

In triangle ABC, medians AD and CE are drawn. If AD = 5, angle DAC = pi//8 " and " angle ACE = pi//4, then the area of the triangle ABC is equal to

Solve 2 cos ^(2) x + 3 sin x =0

For an data if n = 10, sumx_1=40,sumx_i^2=250 then standard deviation s = ....

A point is moving on y = 4 - 2x^(2). The x-coordinate of the point is decreasint at the rate of 5 units/sec. Then the rate at which y - coordinate of the point is changing when the point is at (1,2) is

1^(3)- 2^(3) + 3^(3) - 4^(3) + …….+9^(3) =

The locus of the point (2sec alpha cos beta, 2 sec alpha sin beta, 2tanalpha) is

Statement-I : If side BC and radiu of r_(2)a nd r_(3) of an acute angled triangle is given, then the locus of A is hyperbola. Statement-2 : If the base of a triangle is given and difference of two variable sides is constant, less than the base. Then locus of variable vertex is a hyperbola.

f_(n)(x)=e^(f_(n-1^(x))) for all n inN and f_0(x) = x , then (d)/(dx){f_(n)(x)} is

P (a, b) is the mid-point of a line segment between axes. Show that equation of the line is (x)/(a) + (y)/(b) =2.

If the letters of the word ALGORITHM are arranged at random in a row what is the probability the letters GOR must remain together as a unit ?

Find the eccentricity, coordinates of the foci and the equations of the directrices of the hyperbolas:

A triangle is inscribed in a circle. The vertices of the triangle divide the circle into three arcs of length 3, 4 and 5 units, then area of the triangle is equal to

Solve the system of homogenous equations x+y-z=0,x-2y+z=0,3x+6y-5z=0.

Consider the points A(-5,6,8), B(1,8,11),C(4,2,9) and D(-2,0,6).Find the mid points of AC and the mid point of BD and prove that ABCD is a parallelogram

When two dies are thrown , calculate the probability of throwing a total of (i) a 7 or an 11 , (ii) a doublet or a total of 6.

If forces of magnitude 6 and 7 units acting in the direction bari-2barj +2bark and 2bari -3barj -6bark respectively act on particle which is displaced from P (2,-1,-3) to Q(5,-1,1) then the work done by the forces is

Evaluate the following limits : Lt_(xtooo)(1+1/x)^(2x)

Show that for any sets A and B, A = ( A ∩B )∪ ( A – B ) and A ∪ ( B – A ) =( A ∪ B )

If A and B are matrices such that AB = O then

At time t, the distance s of a particle moving in a straight line is given by s= 4t^2+ 2t. Find the average velocity between t= 2sec and t= 8 sec.

If A=[(5,4),(1,2)] and if (A+2I)^(-1)=k_(1)A+k_(2)I then find (k_(1),k_(2)).

Find the multiplicative inverse of each of the following complex numbers when it exists. -16

Write each sentence in the " If ................Then " form. Roses are vegetables if carrots are flowers.

The period of the function f(theta) = sin ((theta)/( 3)) + cos ((theta)/(2)) is

If bar(a)=bar(i)+bar(j)+bar(k) and bar(b)=2bar(i)-3bar(j)-bar(k), find the unit vector in the direction of bar(a)+bar(b).

Find the sixth term of the expansion (y^(1/2) +x^(1/3))^(n) , if the Binomial coefficient of the third term from the end is 45.

Which of the following are sets ? Justify your answer. The collection of all boys in your class.

If the circles x^(2) + y^(2) = a^(2) and x^(2) + y^(2) - 6x - 8y + 9 = 0 touches each other externally, then a = …….

lim_(xrarr2)[x]=……...

If |x| lt 1 and (1 - 2x)/(1 - x + x^2) + (2x - 4x^3)/(1 - x^2 + x^4) + (4x^3 - 8x^7)/(1 - x^4 + x^8) + ….. oo = (1 + ax)/(1 + bx + cx^2) then a + b - c is

theminutehandof a watchis 1.5 cmlong. Findthe distancecoveredby its tipin 40minutes( usepi =3.14

IfA = (pi )/(4) , B = ( 5pi )/(12)"then " a + sqrt( 2 ) c=

Find the sum to n terms of 3 (3)/(8) + 2 (1)/(4) + 1 (1)/(2)+ .....

Find the slope of the lines : Passing through the points (3, -2) " and " (-1, 4)

A die is thrown. Describe the following events : (i) A: a number less then 7 (ii) B : a number greater then 7 (iii) C: a multiple of 3. (iv) D : a number less then 4 (v) E : an even number greater then 4 (vi) F : a number not less then 3 Also find AuuB,AnnB,BuuC,EnnF,DnnE,A-C,D-E,EnnF',F'.

The set of values 'x' for which f(x)=x^(3)+6x^(2)+27x+10 is increasisngin

Fill in the blanks to make each of the following a true statement : (A')'"………"

Find the perpendicular distance between the lines. 3x+4y-5=0 ...(1) and 6x+8y-45=0 ...(2)