14949 + Interview Questions in Maths in Class 11 Page 218 InterviewSolution

10851.	If cottheta+tantheta=2cosectheta, then find the general value of theta.
Answer» ANSWER :`2npipm(PI)/(3);NINZ`

Discussion

10852.	Write T before each true statement and write F before each false statement. Then give the truth value of the conditionalexpressed. Water is dry implies snow is hot .
Answer» ANSWER :T

Discussion

10853.	Write T before each true statement and write F before each false statement. Then give the truth value of the continent, expressed. If monkeys climb trees, then 6 is divisible by 2
Answer» ANSWER :T

Discussion

10854.	Write T before each true statement and write F before each false statement. Then give the truth value of the conditional expressed. If oxygen is a gas, then gold is a compound.
Answer» ANSWER :F

Discussion

10855.	Write T before each true statement and write F before each false statement. Then give the truth value of the continent, expressed. If Asia is a continent, then Delhi is in Japan.
Answer» ANSWER :F

Discussion

10856.	Find the equation of the circle passing through the points (4,1) and (6,5) and whose centre is on the line 4x+y=16
Answer» ANSWER :`X^(2)+y^(2)-6x-8y+15=0`

Discussion

10857.	A,B,C,D are 4 complanar points and A:B:C:D are their projectioins on any plane. If alpha is the angle between plane of ABCD and plane of projections then ("Volume of tetrahedron AB'C'D' ")/("Volume of tetrahedronA'BCD")=
Answer» 1 2 `2COS ALPHA` `COS alpha` ANSWER :a

Discussion

10858.	If A(1,0), B(0,1) and P(x,y) are points such that xygt0 and x+ylt1, then
Answer» p LIES EITHER inside the triangle OAB or in the third quadrant p can not LIE insde the triangle OAB P lies inside the triangle OAB P lies in the first quadrant ony Answer :B

Discussion

10859.	AB is a vertical pole with B at the ground level and and A at the top .A man finds that the angle of elevation of the point A from a certain point C on the ground is 60^(@) . He moves away from the pole along the line BC to a point D such that CD = 7 m .From D . the angle of elevation of the point A is 45^(@) .Find the height of the pole .
Answer» ANSWER :` (7sqrt3)/( 2) (sqrt3+1) `

Discussion

10860.	Find the mean deviation about the median for the data in 13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17
Answer» ANSWER :2.33

Discussion

10861.	If the pair of lines 6x^(2)-5xy-6y^(2)=0, 6x^(2)-5xy-6y^(2)+x+5y-1=0 form a square then area of square is
Answer» `(1)/(3)` 13 `(13)/(4)` `(1)/(13)` ANSWER :D

Discussion

10862.	If sin^(-1)(3/x)+sin^(-1)(4/x)=(pi)/2 then x=
Answer» 6 7 8 5 Answer :D

Discussion

10863.	The value of 'c' by Rolle's Theorem for which f(x) =1-root(3)(x^(4)in [-1,1] is
Answer» 0 1 2 `-1` ANSWER :A

Discussion

10864.	Which of the following sentences are statement? Give reason for your answer: What is your name?
Answer» ANSWER :Not a STATEMENT

Discussion

10865.	If y=\|cosx\|+\|sinx\|, then (dy)/(dx)at x = (2pi)/3 is
Answer» `(1-sqrt3)/2` 0 `1/2(sqrt3-1)` `(1)/2 (sqrt3+1)` ANSWER :C

Discussion

10866.	Let A (5,2), B (3,-3) and C (-4,3) be the vertices of a Delta ABC Find the length of the altitude from A to BC
Answer» SOLUTION :`47/sqrt 85`

Discussion

10867.	If [sin x] + [ sqrt(2)cos x] = -3, x in [ 0, 2pi]( [*] denotes the greatest integer function), then x belongs to
Answer» `(PI, (5 pi)/(4))` `[pi, (5 pi)/(4)]` `((5 pi)/(4), 2 pi)` `[(5 pi)/(4), 2 pi]` ANSWER :A

Discussion

10868.	sin((pi)/(16))sin((3pi)/(16))sin((5pi)/(16))sin((7pi)/(16))= ………..
Answer» `(1)/(16)` `(sqrt(2))/(16)` `(1)/(8)` `(sqrt(2))/(8)` ANSWER :B

Discussion

10869.	Find the centroid of the triangle whose vertices are (5,4,6),(1,-1,3) and (4, 3, 2).
Answer» ANSWER :`=((10)/(3),2,(11)/(3))`

Discussion

10870.	sin ""(pi)/(14).sin""(3pi)/(14).sin""(5pi)/(14).sin""(7pi)/(14).sin""(9pi)/(14).sin""(11pi)/(14).sin""(13pi)/(14)=
Answer» `1//64` `3//64` `5//64` `7//64` ANSWER :A

Discussion

10871.	If alt0 the function e^(ax)+e^(-ax) is a monotonically decreasing function for values of 'x' given by
Answer» `XGT0` `xlt0` `XGT1` `xlt1` ANSWER :B

Discussion

10872.	If 0 lt a lt b lt ( pi )/(2) and f(a,b) = ( tan b - tan a )/( b-a), then which of the following are not correct .
Answer» `F(a,B) ge 2` `f(a,b) gt 1` `f(a,b) le1` `f(a,b) =0` Answer :A::C::D

Discussion

10873.	If A(a,0), B(-a,0) and angleAPB=45^(@), then the locus of P is
Answer» `X^(2)+y^(2)+2ax+a^(2)=0` `x^(2)+y^(2)-2ax-a^(2)=0` `x^(2)+y^(2)+2yx+a^(2)=0` `x^(2)+y^(2)-2ay-a^(2)=0` ANSWER :4

Discussion

10874.	f(x)= sin alpha + cos alpha -1, where alpha= sin^(-1) sqrt({x}), {.} is the fractional part of x, then f(x) is
Answer» an EVEN function an odd functions a periodic function zero, `X in Z` Answer :A::C::D

Discussion

10875.	If the distance between the points (x,-2,-3) and (3,1,-9) is 7 units, find the values of x
Answer» SOLUTION :x=5 or a]

Discussion

10876.	If tan^(-1)x+tan^(-1)y+tan^(-1)z=pi then x+y+z=
Answer» `xy+yz+zx=1` `X^(2)+y^(2)+Z^(2)+2xyz=1` `x+y+z=xyz` `Sigmax+Sigmayz=1+xyz` ANSWER :A

Discussion

10877.	The roots of the quadratic equation 4x^(2)-(5a+1)x+5a=0, are p and q. if q=1+p, calculate the possible values of a,p and q.
Answer» Answer :(i) `a=3,p=(3)/(2),q=(5)/(2);a=(-1)/(5),p=(-1)/(2),q=(1)/(2)` (ii) (a) `6,-2,` (B) `p lt -2 or p GT 6,` (C) `p lt -3`.

Discussion

10878.	If Tan theta + Cot theta = 3 then Tan^(4)theta+Cot^(4)theta =
Answer» 24 47 55 81 Answer :B

Discussion

10879.	The point (4,1) undergoes the following transformations successively I. Reflection about the line y =x II. Translation through a distance 2 units in the direction of positive X-axis. III. Rotation through an angle pi/4 about origin in the anticlock wise direction. Then, the final position of the point is
Answer» `(- SQRT(18), sqrt(18))` (-2,3) `(0, sqrt(18))` (0,3) ANSWER :C

Discussion

10880.	Write T before each true statement and write F before each false statement. Then give the truth value of the conditional expressed. Ifsqrt(5) is an integer, then 3 is an integer.
Answer» ANSWER :T

Discussion

10881.	Write T before each true statement and write F before each false statement. Then give the truth value of the conditional expressed. If a triangle is a rectangle, then a circle is a rhombus.
Answer» ANSWER :T

Discussion

10882.	Write T before each true statement and write F before each false statement. Then give the truth value of the conditional expressed. If 51 is theproduct of 17 and -3, then lions can fly in the air.
Answer» ANSWER :T

Discussion

10883.	Write T before each true statement and write F before each false statement. Then give the truth value of the conditional expressed. If 3=5, then 7 is a prime number :
Answer» ANSWER :T

Discussion

10884.	Write T before each true statement and write F before each false statement. Then give the truth value of the conditional expressed. 5x6-4=21 implies 2 (5 -: 15+3)=20/3
Answer» ANSWER :T

Discussion

10885.	Write T before each true statement and write F before each false statement. Then give the truth value of the conditionalexpressed. Snow is cold implies water is wet
Answer» ANSWER :T

Discussion

10886.	Find the square root of the following complex numbers -8+ 6i
Answer» ANSWER :`+- (1+ 3I)`

Discussion

10887.	If cos(alpha - beta) + cos(beta - gamma)+ cos(gamma-alpha)=-3/2, then
Answer» `SUM COS ALPHA =0` `sum sin alpha = 0` `sum (cos alpha +sin alpha)=0` `sum cos alpha sin alpha = 0` Answer :A::B::C

Discussion

10888.	Find the mean and variance for the following frequency distribution :
Answer» ANSWER :27, 132

Discussion

10889.	Find the mean and variance for the following frequency distributions in
Answer» ANSWER :107, 2276

Discussion

10890.	Find the slope of a line perpendicular to the line whose slope is -5/(6)
Answer» ANSWER : `6/(5)`

Discussion

10891.	If f(x)=int_(0)^(x)e^(t^(2))(t-2)(t-3)dt for all x in(0,oo), then
Answer» F has a local maximum at x=2 f is DECREASING on (2,3) there EXISTS some `c in(0,oo)` such that f''(c ) =0 f has a local minimum at x=3 Answer :A::B::C::D

Discussion

10892.	Let f(x)= x^(2)+ (1)/(x^(2)) and g(x)= x- (1)/(x), x in R -{-1, 0,1}. If h(x)= (f(x))/(g(x)) then the minimum local value of h(x) is…….
Answer» 3 `-3` `-2 SQRT2` `2 sqrt2` ANSWER :D

Discussion

10893.	Assertion (A) :The value of "tan"^(-1)+"tan"^(-1)3=(3pi)/(4) Reason (R) : If x gt 0, y gt , 0, xy gt 1 then tan^(-1)x+tan^(-1)y=pi +tan^(-1)((x+y)/(1-xy))
Answer» Both A and R are TRUE and R is CORRECT EXPLANATION of A Both A and R are true but R is not the correct explanation of A A is FALSE, R is true A is true, R is false Answer :A

Discussion

10894.	For all natural numbers n, statementp(n)= 1+2+3+ 4....+n = (n(n+1))/2 is truefind p(n+1)
Answer» `(N(n+1))/2` `((n+1)(n+2))/2` `(n(n-1))/2` `((n+1)(n+1))/2` Solution :Let `P (n) : 1+2+3+â€¦. +N` `=1/2 n(n+1)` For n=1 `L.H.S =1` `R.H.S =1/2 .1 (1+1) =1/2 .1.2=1` `L.H.S. =R.H.S` Therefore p (n) is TRUE for n=1 Let P (n) is true for n=K `:. P (K) :1+2+3+â€¦.+K =1/2 K(k+1)` Adding(k+1) on both sides `1+2+3+.....+K+(K+1)` `=1/2 K(k+1) +(K+1)` `=1/2 (K+1) (K+2)` `=1/2 (K+1){(K+1)+1}` `rArr ""P (n)" is also true for" n=K +1 ` Hence by the principle of mathematical induction, GIVEN STATEMENT is true for all natural NUMBER 'n'

Discussion

10895.	The ratio between the sum of n terms of two A.P.'s is (7n + 1) : (4n+27). Find the ratio of their 11 th terms.
Answer» ANSWER :`148 : 111`

Discussion

10896.	If non zero numers a,b,c are in harmonic progression, the show that the equation x/a+y/b+1/c=0 represents a family of concurrent lines and find the point of concurrency.
Answer» ANSWER :(1,-2)

Discussion

10897.	Evaluate the following limits in lim_(xrarr0)(cos2x-1)/(cosx-1)
Answer» ANSWER :4

Discussion

10898.	A ray makes angles pi//3, pi//3 with bar(OX) and bar(OY) respectively. Find the angle made by it with bar(OZ)
Answer» ANSWER :`(PI)/(4) or (3PI)/(4)`

Discussion

10899.	If fifth term of a G.P. is 2, then the product of its first 9 terms is
Answer» 256 512 1024 none of these ANSWER :B

Discussion

10900.	What is the distance of the point (h,k) from the line 9x + 40y + 21 = 0?
Answer» SOLUTION :`abs (9H + 40K + 21)/14`

Discussion

Explore topic-wise InterviewSolutions in .

If cottheta+tantheta=2cosectheta, then find the general value of theta.

Write T before each true statement and write F before each false statement. Then give the truth value of the conditionalexpressed. Water is dry implies snow is hot .

Write T before each true statement and write F before each false statement. Then give the truth value of the continent, expressed. If monkeys climb trees, then 6 is divisible by 2

Write T before each true statement and write F before each false statement. Then give the truth value of the conditional expressed. If oxygen is a gas, then gold is a compound.

Write T before each true statement and write F before each false statement. Then give the truth value of the continent, expressed. If Asia is a continent, then Delhi is in Japan.

Find the equation of the circle passing through the points (4,1) and (6,5) and whose centre is on the line 4x+y=16

A,B,C,D are 4 complanar points and A:B:C:D are their projectioins on any plane. If alpha is the angle between plane of ABCD and plane of projections then ("Volume of tetrahedron AB'C'D' ")/("Volume of tetrahedronA'BCD")=

If A(1,0), B(0,1) and P(x,y) are points such that xygt0 and x+ylt1, then

Find the mean deviation about the median for the data in 13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17

If the pair of lines 6x^(2)-5xy-6y^(2)=0, 6x^(2)-5xy-6y^(2)+x+5y-1=0 form a square then area of square is

If sin^(-1)(3/x)+sin^(-1)(4/x)=(pi)/2 then x=

The value of 'c' by Rolle's Theorem for which f(x) =1-root(3)(x^(4)in [-1,1] is

Which of the following sentences are statement? Give reason for your answer: What is your name?

If y=|cosx|+|sinx|, then (dy)/(dx)at x = (2pi)/3 is

Let A (5,2), B (3,-3) and C (-4,3) be the vertices of a Delta ABC Find the length of the altitude from A to BC

If [sin x] + [ sqrt(2)cos x] = -3, x in [ 0, 2pi]( [*] denotes the greatest integer function), then x belongs to

sin((pi)/(16))sin((3pi)/(16))sin((5pi)/(16))sin((7pi)/(16))= ………..

Find the centroid of the triangle whose vertices are (5,4,6),(1,-1,3) and (4, 3, 2).

sin ""(pi)/(14).sin""(3pi)/(14).sin""(5pi)/(14).sin""(7pi)/(14).sin""(9pi)/(14).sin""(11pi)/(14).sin""(13pi)/(14)=

If alt0 the function e^(ax)+e^(-ax) is a monotonically decreasing function for values of 'x' given by

If 0 lt a lt b lt ( pi )/(2) and f(a,b) = ( tan b - tan a )/( b-a), then which of the following are not correct .

If A(a,0), B(-a,0) and angleAPB=45^(@), then the locus of P is

f(x)= sin alpha + cos alpha -1, where alpha= sin^(-1) sqrt({x}), {.} is the fractional part of x, then f(x) is

If the distance between the points (x,-2,-3) and (3,1,-9) is 7 units, find the values of x

If tan^(-1)x+tan^(-1)y+tan^(-1)z=pi then x+y+z=

The roots of the quadratic equation 4x^(2)-(5a+1)x+5a=0, are p and q. if q=1+p, calculate the possible values of a,p and q.

If Tan theta + Cot theta = 3 then Tan^(4)theta+Cot^(4)theta =

Write T before each true statement and write F before each false statement. Then give the truth value of the conditional expressed. Ifsqrt(5) is an integer, then 3 is an integer.

Write T before each true statement and write F before each false statement. Then give the truth value of the conditional expressed. If a triangle is a rectangle, then a circle is a rhombus.

Write T before each true statement and write F before each false statement. Then give the truth value of the conditional expressed. If 51 is theproduct of 17 and -3, then lions can fly in the air.

Write T before each true statement and write F before each false statement. Then give the truth value of the conditional expressed. If 3=5, then 7 is a prime number :

Write T before each true statement and write F before each false statement. Then give the truth value of the conditional expressed. 5x6-4=21 implies 2 (5 -: 15+3)=20/3

Write T before each true statement and write F before each false statement. Then give the truth value of the conditionalexpressed. Snow is cold implies water is wet

Find the square root of the following complex numbers -8+ 6i

If cos(alpha - beta) + cos(beta - gamma)+ cos(gamma-alpha)=-3/2, then

Find the mean and variance for the following frequency distribution :

Find the mean and variance for the following frequency distributions in

Find the slope of a line perpendicular to the line whose slope is -5/(6)

If f(x)=int_(0)^(x)e^(t^(2))(t-2)(t-3)dt for all x in(0,oo), then

Let f(x)= x^(2)+ (1)/(x^(2)) and g(x)= x- (1)/(x), x in R -{-1, 0,1}. If h(x)= (f(x))/(g(x)) then the minimum local value of h(x) is…….

Assertion (A) :The value of "tan"^(-1)+"tan"^(-1)3=(3pi)/(4) Reason (R) : If x gt 0, y gt , 0, xy gt 1 then tan^(-1)x+tan^(-1)y=pi +tan^(-1)((x+y)/(1-xy))

For all natural numbers n, statementp(n)= 1+2+3+ 4....+n = (n(n+1))/2 is truefind p(n+1)

The ratio between the sum of n terms of two A.P.'s is (7n + 1) : (4n+27). Find the ratio of their 11 th terms.

If non zero numers a,b,c are in harmonic progression, the show that the equation x/a+y/b+1/c=0 represents a family of concurrent lines and find the point of concurrency.

Evaluate the following limits in lim_(xrarr0)(cos2x-1)/(cosx-1)

A ray makes angles pi//3, pi//3 with bar(OX) and bar(OY) respectively. Find the angle made by it with bar(OZ)

If fifth term of a G.P. is 2, then the product of its first 9 terms is

What is the distance of the point (h,k) from the line 9x + 40y + 21 = 0?