14949 + Interview Questions in Maths in Class 11 Page 201 InterviewSolution

10001.	LetA = { 1, 2, { 3, 4 }, 5 }. Which of the following statements are incorrect and why? {{3, 4}} ⊂A
Answer» ANSWER :1

Discussion

10002.	If x = log p and y = 1/p then
Answer» `(d^2y)/(dx^2) - 2p = 0 ` `(d^2y)/(dx^2) + y= 0 ` `(d^2y)/(dx^2) + (DY)/(dx)=0` `(d^2y)/(dx^2)-(dy)/(dx)=0` ANSWER :C

Discussion

10003.	The sum of first three terms of a G.P is 16 and the sum of the next three terms is 128 Determine the first term, the common ratio and the sum to n terms of the G.P.
Answer» ANSWER :`16/7;2;16/7(2^(N)-1)`

Discussion

10004.	\|{:(x+y,0,0),(0,x-y,0),(0,0,x^(2)+y^(2)):}\|=
Answer» `x^(4)-y^(4)` `x^(4)+y^(4)` `x^(9)-y^(8)` `x^(6)-y^(6)` ANSWER :A

Discussion

10005.	If the radius of a sphere ia equal to the height and radius of the cylinder then the ratio of the rates of increases of the volumes of the sphere and cylinder is
Answer» `4:3` `3:4` `4:3pi` `3pi:4` ANSWER :A

Discussion

10006.	Find the position vector of two points on the line through P(bar(i)+bar(j)-2bar(k)) at a distance 6 units from P, if the line is parallel to 2bar(i)+2bar(j)+bar(k).
Answer» ANSWER :`5bar(i)+5bar(J) and -3BAR(i)-3bar(j)-4bar(K)`

Discussion

10007.	sec h^(2)[tan h^(-1)((1)/(2))] + "cosec " h^(2) (cot h^(-1)(3)) =
Answer» `(35)/(9)` `(43)/(4)` `(35)/(4)` `(43)/(9)` Answer :C

Discussion

10008.	A (3,4,5), C(-1,6,1) are the vetrices of a triangle then Statement-I : The circumcentre of Delta ABC is (1,5,3) Statement -II : The orthocentre of Delta ABC is (2,3,1)
Answer» Only I Only II Both I and II Neither I nor II Answer :C

Discussion

10009.	Eccentricity of hyperbola 16y^2-9x^2=144 is ...........
Answer» ANSWER :`5/3`

Discussion

10010.	A function 'f' well defined AA x , y in R is such that f(1)=2, f(2)=8 and f(x+y)-kxy= f(x)+2y^(2), where 'k' is some constant then f(x) is
Answer» `X^(2)` `3X^(2)` `2x^(2)` `4x^(2)` ANSWER :C

Discussion

10011.	If tan""((theta)/(2))=sqrt([(1-e)/(1+e)]) tan""((alpha)/(2)) thencos alpha=
Answer» `(1 - E COS THETA)/(cos theta + e)` `(1 + e cos theta)/(cos theta + e)` `(1-e cos theta)/(cos theta - e)` `(cos theta - e)/(1 - e cos theta)` ANSWER :D

Discussion

10012.	The value of tan6^@ tan42^@ tan66^@ tan78^@ is
Answer» 1 `1//2` `1//4` `1//8` ANSWER :A

Discussion

10013.	Assertion (A): The sum of the distances of a point from two perpendicular lines is 1, then its locus is a square Reason (R): The locus of a point which is at a distance 'p' from the given point is a circle
Answer» A TRUE, R true and R is CORRECT explanation of A A true, R true but R is not a correct explanation of A A true, R FALSE A false, R true Answer :2

Discussion

10014.	If (1)/(6) sin theta, cos theta and tan theta are in geometric progression, then the solution set of theta is
Answer» `2 N pi PM(pi)/(3)` `2 n pi pm (pi)/(6)` `n pi + (-1)^(n) (pi)/(3)` `n pi + (pi)/(3)` Answer :A

Discussion

10015.	The negation of the statement 101 is not a multiple of 3" is….
Answer» 101 is a multiple od 3 101 is a multiple of 2 101 is an ODD number 101 is an EVEN number Answer :A::C::D

Discussion

10016.	Solve: sqrt(x + 5) + sqrt(x + 21) = sqrt(6x + 40)
Answer» ANSWER :`therefore X = (-14)/(3) ` is not a ROOT . `therefore ` The only root is 4 .

Discussion

10017.	The solution set of (5+4Costheta)(2costheta+1)=0 in the interval [0,2pi] is
Answer» `{(pi)/(3),(2PI)/(3)}` `{(2pi)/(3),pi}` `{(2pi)/(3),(4PI)/(3)}` `{(2pi)/(3),(5PI)/(3)}` Answer :C

Discussion

10018.	Let bara =4bari+5barj-bark, barb = bari - 4barj+5bark and c= 3bari +barj-bark. Find the vector which is perpendicular to both bara and barb whose magnitude is twenty one times the magnitude of barc.
Answer» ANSWER :`pm7sqrt33(bari-barj-bark)`

Discussion

10019.	Compute the derivative of f(x)=sin^(2)x
Answer» ANSWER :`2sinx COS x=sin2.`

Discussion

10020.	Evaluate the following limits : Lim_(x to 0 ) (1-cosmx)/(1- cos nx)
Answer» ANSWER :`(m^(2))/(N^(2))`

Discussion

10021.	ax+b(sec(tan^(-1)x))=c and ay+b(sec(tan^(-1)y))=c The value of x + y is
Answer» `(2AC)/(a^(2)-b^(2))` `(C^(2)-b^(2))/(a^(2)-b^(2))` `(c^(2)-b^(2))/(a^(2)+b^(2))` NONE of these Answer :A

Discussion

10022.	If f(theta)=(1-sin2theta+cos2theta)/(2cos2theta) , then value of 8f(11^(0)).f(34^0) is _____
Answer» ANSWER :4

Discussion

10023.	For all value of theta, the lines represented by the equation (2costheta+3sin theta)x+(3costheta-5sintheta)y-(5costheta-2sintheta)=0
Answer» PASS through a fixed POINT pass through the point (1,1) pass through a fixed point whose REFLECTION in the LINE `x+y=sqrt2 is (sqrt2-1,sqrt2-1)` pass through the origin Answer :sqrt2-1,sqrt2-1

Discussion

10024.	If the constant term in expansion of (sqrt(x)-k/(x^(2)))^(10) is 405 then find the value of k .
Answer» ANSWER :` PM 3 `

Discussion

10025.	If a+b+c=0 the straight line 2ax+3by+4c=0 passes through the fixed point
Answer» `[2,4/3]` `(2,2)` `[4/3,4/3]` `(1,1)` ANSWER :A

Discussion

10026.	If A = { 3, 5, 7, 9, 11 }, B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}, find B ∩ D
Answer» ANSWER :`PHI`

Discussion

10027.	Evaluate the following limits in Exercises lim_(xto2)(3x^(2)-x-10)/(x^(2)-4)
Answer» ANSWER :`(11)/(4)`

Discussion

10028.	If the vector -bar(i)+bar(j)-bar(k) bisects the angles between the vector bar(c) and the vector 3bar(i)+4bar(j), then the unit vector in the direction of bar(c) is
Answer» `11bar(i)+10bar(J)+2BAR(K)` `-(11bar(i)+10bar(j)+2bar(k))` `-1/15(11bar(i)+10bar(j)+2bar(k))` `1/15(11bar(i)+10bar(j)+2bar(k))` ANSWER :C

Discussion

10029.	Function f and g defined on R-{0}rarrRas f(x)=x and g(x)=1/x" then "f.g(x) = ...... .
Answer» ANSWER :1

Discussion

10030.	Insert three geometric means between 1 and 256.
Answer» ANSWER :4,16,64

Discussion

10031.	A line is drawn through the point A(4,-1) and parallel to the line 3x-4y+7=0. Find the coordinates of two points on this line which are at distance of 5 units from A.
Answer» ANSWER :(8,2) or (0,-4)

Discussion

10032.	If theta in [pi/2, (3pi)/2]" then "Sin^(-1)(sintheta)=
Answer» `theta` `PI-theta` `2PI -theta` `-pi +theta` ANSWER :B::C::D

Discussion

10033.	Find the value of ""^6P_1
Answer»

Discussion

10034.	How many automobiles licence plates can be made if the inscriptions on each contains two different letters followed by three differents digits ?
Answer» Answer :Number of plates ` = 26 XX 25 xx 9 xx 9 xx 8 = 4,21,200`

Discussion

10035.	If cos x + cos y - cos (x + y ) =3/2, the
Answer» `X + y=0` `x = 2Y ` `x=y` `2X =y` ANSWER :C

Discussion

10036.	The perpendicular distance from the point (1,-1) to the line x+5y-9=0 is equal to
Answer» `SQRT(2/13)` `sqrt(13)/2` `2/13` `13/2` ANSWER :B

Discussion

10037.	Let a = 6, b = 3 , " and " cos (A - B) = 4/5 Value of sin A is equal to
Answer» `1/(2SQRT5)` `1/sqrt3` `1/sqrt5` `2/sqrt5` ANSWER :D

Discussion

10038.	Evaluate the following limits in Exercises lim_(xto-1)(x^(10)+x^(5)+1)/(x-1)
Answer» ANSWER :`-(1)/(2)`

Discussion

10039.	Find the equation of locus of the point whose distance from the coordinate axes are in the ratio 2:3
Answer» ANSWER :`9Y^(2)=4X^(2)`

Discussion

10040.	A and B are events such that P(A) = 0. 42, P(B) = 0. 48and P(A a n d B) = 0. 16. Determine(i) P(not A), (ii) P(not B) and (iii) P(A or B)
Answer» ANSWER :(i) 0.58,(II) 0.52 ,(III) 0.74

Discussion

10041.	cosec(-1410^(@))= ………….
Answer» `-2` 2 `(SQRT(3))/(2)` `(2)/(sqrt(3))` ANSWER :B

Discussion

10042.	Cos^(2)20^(@)+Cos^(2)40^(@)+cos^(2)80^(@)=
Answer» `1/2` 1 `3/2` 2 Answer :C

Discussion

10043.	If the point A(3, -2, 4), B(1, 1, 1) and C(-1, 4, -2) are collinear then (C:AB)=
Answer» `1:2` `-2:1` `-1:2` `4:0` ANSWER :B

Discussion

10044.	Prove that (1+sec 2 theta) (1+sec 4 theta)........(1+sec 2^(n) theta)=tan 2^(n) theta cot theta
Answer» Answer :`tan 2^(n)THETA CDOT COT theta`

Discussion

10045.	If f^(3)(x)-3f^(2)(x)+3f(x)-1=x^(6) then the value of f(0) is
Answer» ANSWER :1

Discussion

10046.	Find the acute angle between the diagonals of a parallelogram whose adjacent sides are bar(AB)= 3bari - 2barj +2bark and bar(BC)=-bari-2bark.
Answer» ANSWER :`COS^(-1)SQRT(2/10)`

Discussion

10047.	Write the negation of the following statements: Chenai is the capital of Tamil Nadu.
Answer» ANSWER :CHENNAI is not the CAPITAL of TAMIL NADU.

Discussion

10048.	If (2, 5, 1) and (9, 10, 5) are the ends of a diagonal ofa rectangular parallelopiped whose faces are parallel to the coordinate planes, then the lengths of edges are
Answer» ANSWER :7,5,3

Discussion

10049.	The value of expression (1+ sin 2 alpha)/(cos (2 alpha -2pi) tan (alpha -(3pi)/(4)))- 1/2 sin 2 alpha (cot ""(alpha)/(2) + cot ((3pi)/(2)+(alpha)/(2))) is
Answer» 0 1 `SIN ^(2) "" (ALPHA)/(2)` `sin ^(2) alpha` ANSWER :D

Discussion

10050.	If0 lt (2x -5) / (2) lt 7 and x is integer then sum of its maxi and minimum value is .................
Answer» ANSWER :12

Discussion

Explore topic-wise InterviewSolutions in .

LetA = { 1, 2, { 3, 4 }, 5 }. Which of the following statements are incorrect and why? {{3, 4}} ⊂A

If x = log p and y = 1/p then

The sum of first three terms of a G.P is 16 and the sum of the next three terms is 128 Determine the first term, the common ratio and the sum to n terms of the G.P.

|{:(x+y,0,0),(0,x-y,0),(0,0,x^(2)+y^(2)):}|=

If the radius of a sphere ia equal to the height and radius of the cylinder then the ratio of the rates of increases of the volumes of the sphere and cylinder is

Find the position vector of two points on the line through P(bar(i)+bar(j)-2bar(k)) at a distance 6 units from P, if the line is parallel to 2bar(i)+2bar(j)+bar(k).

sec h^(2)[tan h^(-1)((1)/(2))] + "cosec " h^(2) (cot h^(-1)(3)) =

A (3,4,5), C(-1,6,1) are the vetrices of a triangle then Statement-I : The circumcentre of Delta ABC is (1,5,3) Statement -II : The orthocentre of Delta ABC is (2,3,1)

Eccentricity of hyperbola 16y^2-9x^2=144 is ...........

A function 'f' well defined AA x , y in R is such that f(1)=2, f(2)=8 and f(x+y)-kxy= f(x)+2y^(2), where 'k' is some constant then f(x) is

If tan""((theta)/(2))=sqrt([(1-e)/(1+e)]) tan""((alpha)/(2)) thencos alpha=

The value of tan6^@ tan42^@ tan66^@ tan78^@ is

Assertion (A): The sum of the distances of a point from two perpendicular lines is 1, then its locus is a square Reason (R): The locus of a point which is at a distance 'p' from the given point is a circle

If (1)/(6) sin theta, cos theta and tan theta are in geometric progression, then the solution set of theta is

The negation of the statement 101 is not a multiple of 3" is….

Solve: sqrt(x + 5) + sqrt(x + 21) = sqrt(6x + 40)

The solution set of (5+4Costheta)(2costheta+1)=0 in the interval [0,2pi] is

Let bara =4bari+5barj-bark, barb = bari - 4barj+5bark and c= 3bari +barj-bark. Find the vector which is perpendicular to both bara and barb whose magnitude is twenty one times the magnitude of barc.

Compute the derivative of f(x)=sin^(2)x

Evaluate the following limits : Lim_(x to 0 ) (1-cosmx)/(1- cos nx)

ax+b(sec(tan^(-1)x))=c and ay+b(sec(tan^(-1)y))=c The value of x + y is

If f(theta)=(1-sin2theta+cos2theta)/(2cos2theta) , then value of 8f(11^(0)).f(34^0) is _____

For all value of theta, the lines represented by the equation (2costheta+3sin theta)x+(3costheta-5sintheta)y-(5costheta-2sintheta)=0

If the constant term in expansion of (sqrt(x)-k/(x^(2)))^(10) is 405 then find the value of k .

If a+b+c=0 the straight line 2ax+3by+4c=0 passes through the fixed point

If A = { 3, 5, 7, 9, 11 }, B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}, find B ∩ D

Evaluate the following limits in Exercises lim_(xto2)(3x^(2)-x-10)/(x^(2)-4)

If the vector -bar(i)+bar(j)-bar(k) bisects the angles between the vector bar(c) and the vector 3bar(i)+4bar(j), then the unit vector in the direction of bar(c) is

Function f and g defined on R-{0}rarrRas f(x)=x and g(x)=1/x" then "f.g(x) = ...... .

Insert three geometric means between 1 and 256.

A line is drawn through the point A(4,-1) and parallel to the line 3x-4y+7=0. Find the coordinates of two points on this line which are at distance of 5 units from A.

If theta in [pi/2, (3pi)/2]" then "Sin^(-1)(sintheta)=

Find the value of ""^6P_1

How many automobiles licence plates can be made if the inscriptions on each contains two different letters followed by three differents digits ?

If cos x + cos y - cos (x + y ) =3/2, the

The perpendicular distance from the point (1,-1) to the line x+5y-9=0 is equal to

Let a = 6, b = 3 , " and " cos (A - B) = 4/5 Value of sin A is equal to

Evaluate the following limits in Exercises lim_(xto-1)(x^(10)+x^(5)+1)/(x-1)

Find the equation of locus of the point whose distance from the coordinate axes are in the ratio 2:3

A and B are events such that P(A) = 0. 42, P(B) = 0. 48and P(A a n d B) = 0. 16. Determine(i) P(not A), (ii) P(not B) and (iii) P(A or B)

cosec(-1410^(@))= ………….

Cos^(2)20^(@)+Cos^(2)40^(@)+cos^(2)80^(@)=

If the point A(3, -2, 4), B(1, 1, 1) and C(-1, 4, -2) are collinear then (C:AB)=

Prove that (1+sec 2 theta) (1+sec 4 theta)........(1+sec 2^(n) theta)=tan 2^(n) theta cot theta

If f^(3)(x)-3f^(2)(x)+3f(x)-1=x^(6) then the value of f(0) is

Find the acute angle between the diagonals of a parallelogram whose adjacent sides are bar(AB)= 3bari - 2barj +2bark and bar(BC)=-bari-2bark.

Write the negation of the following statements: Chenai is the capital of Tamil Nadu.

If (2, 5, 1) and (9, 10, 5) are the ends of a diagonal ofa rectangular parallelopiped whose faces are parallel to the coordinate planes, then the lengths of edges are

The value of expression (1+ sin 2 alpha)/(cos (2 alpha -2pi) tan (alpha -(3pi)/(4)))- 1/2 sin 2 alpha (cot ""(alpha)/(2) + cot ((3pi)/(2)+(alpha)/(2))) is

If0 lt (2x -5) / (2) lt 7 and x is integer then sum of its maxi and minimum value is .................