14949 + Interview Questions in Maths in Class 11 Page 255 InterviewSolution

12701.	Evaluate the following limits in Exercises lim_(rto1)pir^(2)
Answer» ANSWER :`PI`

Discussion

12702.	Find the domain and range of the following real functions: (i) f(x)=-\|x\| (ii) f(x)=sqrt(9-x^(2))
Answer» Answer :(i) DOMAIN =R , RANGE `=(-oo, 0]` (ii) Domain of function `={x: -3 LE x le 3}` Range of function `={x : 0 le x le 3}`

Discussion

12703.	(d)/(dx)(tan^(2)x)=……..
Answer» 2TAN x `SEC^(2)x` `COT^(2)x` `2tanx sec^(2)x` Answer :D

Discussion

12704.	Find the eccentricity of the ellipse, 4x^(2)+9y^(2)-8x-36y+4=0.
Answer» ANSWER :`SQRT(5)/3`

Discussion

12705.	{:("Column-I", "Column-II"), ("A) "sin^(-1)x+x gt 0", for","p) "x lt 0), ("B) "cos^(-1)x-x ge 0", for", "q) "x in (0,1]),("C) "tan^(-1)x+x lt 0", for", "r) "x in [-1,0)), ("D) "cot^(-1)x+x gt 0", for","s) "x gt 0):}
Answer» ANSWER :A-q,B-r,C-pr,D-qrs

Discussion

12706.	Match the percentage error of the following and choose correct ansere
Answer» A, D, C C, E,B B, E, C B, D, C Answer :C

Discussion

12707.	If inside a big circle exactly n(n ge3) small circles, each of radius r, can be drawn in such a way that each small circle touches the big circle and also touches both its adjacent small circles, then the radius of big circle is
Answer» `R(1+"cosec"(pi)/(N))` `((1+"TAN"(pi)/(n))/(cospi//n))` `[1+"cosec"(2pi)/(n)]` `r(["sin"(pi)/(2n)+"COS"(pi)/(2n)])^2/(sinpi//n)` Answer :A::D

Discussion

12708.	If the angle subtended at the centre of a circle of diameter 50 cm by an arc of length 11 cm is theta radians find theta
Answer» SOLUTION :`theta=11/25 RADIANS`

Discussion

12709.	Find the angle between the lines y- sqrt(3) x - 5 = 0 and sqrt(3) y - x+6=0.
Answer» ANSWER :`30^(@)` OR `150^(@)`

Discussion

12710.	Find the number of terms in the following expansions. (x+y)^(100) + (x-y)^(100)
Answer» ANSWER :`=51`

Discussion

12711.	Find the derivative of x^2 at x = 1.
Answer» ANSWER :2

Discussion

12712.	(0,2) . (0,2) = (0,4)
Answer» ANSWER :FALSE STATEMENT

Discussion

12713.	Find the multiplicative inverse ofsqrt 5 + 3i
Answer» ANSWER :`SQRT(5)/14 -i3/14`

Discussion

12714.	Which term of the series 5, 8, 11...... is 320 ?
Answer» ANSWER :106 TH TERM

Discussion

12715.	cot x = 3/4,x lies in third quadrant. Find all trignometric ratios
Answer» Answer :`SIN X =- 4/5, cosec x =- 5/4, cos x =- 3/5, SEC x =- 5/3, TAN x =- 4/3`

Discussion

12716.	sin^(4) theta + cos ^(4) theta + 2sin^(2) theta cos ^(2) theta has value 1.
Answer» ANSWER :TRUE STATEMENT

Discussion

12717.	If A, B and C be sets. Then, show that, A cap (B cup C) = (A cap B) cup (A cap C).
Answer» ANSWER :`A CAP (B CUP C) = (A cap B) cup (A cap C)`.

Discussion

12718.	cos(2cos^(-1)(7//25))=
Answer» `527/625` `-527/625` `pi-527/625` `24/25` ANSWER :B

Discussion

12719.	Range of the function f(x)=sqrt([x]-x) is
Answer» R {1} {0} `(0, OO)` Answer :C

Discussion

12720.	Evaluate the following limits : Lim_( xto0) (x sin 5x)/(sin^(2) 4x)
Answer» ANSWER :`5/16`

Discussion

12721.	Given that \|z+4\| le 3 then greatest & least values of \|z + 1\| are
Answer» ANSWER :3

Discussion

12722.	If theta is th angle between the vector 2i - 2j + 4k and 3i + j + 2k, then sin theta =
Answer» `(2)/(7)` `(2)/(sqrt7)` `(sqrt2)/(7)` `SQRT((2)/(7))` ANSWER :B

Discussion

12723.	(1)/(2) tan"" ((x)/(2) ) + (1)/( 4) (tan"" (x)/(4) ) + ...... + (1)/(2^(n) ) tan"" ((x)/( 2^n) ) =
Answer» `(1)/( 2^n) COT ((X)/( 2^n) )` `(1)/( 2^n) cot((x)/( 2^n) ) + cot x` `(1)/( 2^n) cot ( (x)/( 2^n) ) - cot x` `cot ((x)/( 2^n) ) -cot x` ANSWER :C

Discussion

12724.	List all the elements of the following sets : F = {x : x is a consonant in the English alphabet which precedes k }.
Answer» Answer :`F = {B, c, d, f, G, h, j }`

Discussion

12725.	The total number of words formed by 2 vowels and 3 consonanats taken from 4 vowels and 5 consonants is
Answer» 60 120 7200 720 Answer :B

Discussion

12726.	Locus ofx/a+y/b=1 and z = 0 is
Answer» Any STRAIGHT LINE Straight line in xy-plane Plane z-axis Answer :A

Discussion

12727.	Find the sum to n terms of the series : 5+11+19+29+41..........
Answer» ANSWER :`=(N(n+2)(n+4))/3`

Discussion

12728.	Find the mean deviation about the mean for the given data:
Answer» ANSWER :2.3

Discussion

12729.	5x+1 gt - 24, 5x-1 lt 24
Answer» ANSWER :`(-5,5)` `(##NCERT_TEL_MAT_XI_C06_E04_007_A01##)`

Discussion

12730.	Statement - 1 : For all n in N x^(n) - y^(n) is divisible by x-y Statement - 2: x^(n) + y^(n) is divisible by x+y if n is even natural number Which of the above statement is true :
Answer» only 1 only 2 both 1 & 2 neither 1 nor 2 Answer :A

Discussion

12731.	Which of the following sentences are statements? Give reasons for your answer: The sides of a quadrilateral have equal length.
Answer» ANSWER :It is not a STATEMENT.

Discussion

12732.	S.T the equation 2x^2-13xy-7y^2+x+23y-6=0 represents a pair of straight lines. Also find the angle between them and the coordinates of the point of intersection of the lines.
Answer» ANSWER :`((19)/(15),(7)/(15)), tan^(-1)3`

Discussion

12733.	If (sin(x+y))/(sin(x-y))=(a+b)/(a-b), then show that (tanx)/(tany)=(a)/(b).
Answer» ANSWER :`(a)/(B)`

Discussion

12734.	If "cosec"theta = (p+q)/(p-q) " then " cot((pi)/4+( theta )/(2))=
Answer» `SQRT(p/q)` `sqrt(q/p)` `sqrt(PQ)` pq Answer :B

Discussion

12735.	Prove that (sin 5x - 2 sin 3x + sin x)/(cos 5 x - cos x)= tan x
Answer» ANSWER :`TAN X = R.H.S`

Discussion

12736.	The value of cot""(7pi)/16 + 2 cos""(3pi)/8 + cot""(15pi)/16 is
Answer» 4 2 `-2` `-4` ANSWER :D

Discussion

12737.	If the points where position vector 5veci+3vecj,2veci-vecj and xveci+3vecj are collinear then x is :
Answer» 5 3 3 2 Answer :A

Discussion

12738.	Ifc^(2)= a^(2)+ b^(2)then write the value of 4s ( s- a)(s-b)(s-c)in terms of a,b.
Answer» ANSWER :` a^(2) B^(2) `

Discussion

12739.	If 7 theta = (2n +1) pi,where n = 0 , 1, 2, 3, 4,5, 6 then on the basis of above information, answer the following questions The equation whose roots are cos pi//7 , cos 3pi//7, cos 5pi//7 is
Answer» `8x^(3) + 4X^(2) + 4x + 1 = 0` `8x^(3) - 4x^(2) - 4x + 1 = 0` `8x^(3) - 4x^(2) - 4x - 1 = 0` `8x^(3) + 4x^(2) + 4x - 1 = 0` Answer :B

Discussion

12740.	If f(x)=lambdax^(2)+mux+12, f'(4)=15 and f'(2)=11, then find the value of lambda+mu.
Answer» ANSWER :`lambda+mu=8`

Discussion

12741.	Find the sum to n terms of the series whose nth term is n (n+2)
Answer» ANSWER :`(N)/(6) (n+1)(2n+7)`

Discussion

12742.	Find the values of k for which the line (k-3) x-(4-k^2) y+k^2 -7k+6=0 is (iii) Passing through the origin.
Answer» ANSWER :`k=1` OR `k=6`

Discussion

12743.	If the A.M. and G.M. between two numbers are in the ratio x:y, then prove that the numbers are in the ratio (x+sqrt(x^(2)-y^(2))):(x-sqrt(x^(2)-y^(2))).
Answer» ANSWER :`(X+sqrt(x^(2)-y^(2))):(x-sqrt(x^(2)-y^(2)))`

Discussion

12744.	Which of the following function /functions has /have point of inflection ?
Answer» `F(X)=x^(6//7)` `f(x)=x^(6)` `f(x)=cosx+2x` `f(x)=x\|x\|` ANSWER :C::D

Discussion

12745.	Find the domain of the real function f(x)=(1)/(sqrt([x]^(2)-[x]-2).
Answer» `R-[-1, 3)` `(-oo, -3) NN[3, oo)` `[2, oo)` `(-oo, 3]` Answer :A

Discussion

12746.	Given that P(3, 2, -4), Q(5, 4, -6) and R(9, 8, -10) are collinear. Find the ratio in which Q divides PR.
Answer» ANSWER :`1:2`

Discussion

12747.	The plane2x - y + 4z = 5 and 5x - (2.5) y + 10 z =6 are
Answer» PERPENDUCULAR parallel INTERSECT Y-axis PASSES through `(0.0, 5//4)` ANSWER :B

Discussion

12748.	If X= { a, b, c, d } and Y = { f, b, d, g}, find Y – X
Answer» ANSWER :`{F, G }`

Discussion

12749.	If A,B, C and D are four points, then show that \|bar(AB) xx bar(CD) + bar(BC) xx bar(AD) + bar(CA) xx bar(BD)\| is four times the area of Delta ABC
Answer» ANSWER :4 AREA of `DELTA ABC`

Discussion

12750.	If cos h (x)=(5)/(4), then cos h (3x)=
Answer» `(61)/(16)` `(63)/(16)` `(61)/(63)` `(65)/(16)` ANSWER :D

Discussion

Explore topic-wise InterviewSolutions in .

Evaluate the following limits in Exercises lim_(rto1)pir^(2)

Find the domain and range of the following real functions: (i) f(x)=-|x| (ii) f(x)=sqrt(9-x^(2))

(d)/(dx)(tan^(2)x)=……..

Find the eccentricity of the ellipse, 4x^(2)+9y^(2)-8x-36y+4=0.

{:("Column-I", "Column-II"), ("A) "sin^(-1)x+x gt 0", for","p) "x lt 0), ("B) "cos^(-1)x-x ge 0", for", "q) "x in (0,1]),("C) "tan^(-1)x+x lt 0", for", "r) "x in [-1,0)), ("D) "cot^(-1)x+x gt 0", for","s) "x gt 0):}

Match the percentage error of the following and choose correct ansere

If inside a big circle exactly n(n ge3) small circles, each of radius r, can be drawn in such a way that each small circle touches the big circle and also touches both its adjacent small circles, then the radius of big circle is

If the angle subtended at the centre of a circle of diameter 50 cm by an arc of length 11 cm is theta radians find theta

Find the angle between the lines y- sqrt(3) x - 5 = 0 and sqrt(3) y - x+6=0.

Find the number of terms in the following expansions. (x+y)^(100) + (x-y)^(100)

Find the derivative of x^2 at x = 1.

(0,2) . (0,2) = (0,4)

Find the multiplicative inverse ofsqrt 5 + 3i

Which term of the series 5, 8, 11...... is 320 ?

cot x = 3/4,x lies in third quadrant. Find all trignometric ratios

sin^(4) theta + cos ^(4) theta + 2sin^(2) theta cos ^(2) theta has value 1.

If A, B and C be sets. Then, show that, A cap (B cup C) = (A cap B) cup (A cap C).

cos(2cos^(-1)(7//25))=

Range of the function f(x)=sqrt([x]-x) is

Evaluate the following limits : Lim_( xto0) (x sin 5x)/(sin^(2) 4x)

Given that |z+4| le 3 then greatest & least values of |z + 1| are

If theta is th angle between the vector 2i - 2j + 4k and 3i + j + 2k, then sin theta =

(1)/(2) tan"" ((x)/(2) ) + (1)/( 4) (tan"" (x)/(4) ) + ...... + (1)/(2^(n) ) tan"" ((x)/( 2^n) ) =

List all the elements of the following sets : F = {x : x is a consonant in the English alphabet which precedes k }.

The total number of words formed by 2 vowels and 3 consonanats taken from 4 vowels and 5 consonants is

Locus ofx/a+y/b=1 and z = 0 is

Find the sum to n terms of the series : 5+11+19+29+41..........

Find the mean deviation about the mean for the given data:

5x+1 gt - 24, 5x-1 lt 24

Statement - 1 : For all n in N x^(n) - y^(n) is divisible by x-y Statement - 2: x^(n) + y^(n) is divisible by x+y if n is even natural number Which of the above statement is true :

Which of the following sentences are statements? Give reasons for your answer: The sides of a quadrilateral have equal length.

S.T the equation 2x^2-13xy-7y^2+x+23y-6=0 represents a pair of straight lines. Also find the angle between them and the coordinates of the point of intersection of the lines.

If (sin(x+y))/(sin(x-y))=(a+b)/(a-b), then show that (tanx)/(tany)=(a)/(b).

If "cosec"theta = (p+q)/(p-q) " then " cot((pi)/4+( theta )/(2))=

Prove that (sin 5x - 2 sin 3x + sin x)/(cos 5 x - cos x)= tan x

The value of cot""(7pi)/16 + 2 cos""(3pi)/8 + cot""(15pi)/16 is

If the points where position vector 5veci+3vecj,2veci-vecj and xveci+3vecj are collinear then x is :

Ifc^(2)= a^(2)+ b^(2)then write the value of 4s ( s- a)(s-b)(s-c)in terms of a,b.

If 7 theta = (2n +1) pi,where n = 0 , 1, 2, 3, 4,5, 6 then on the basis of above information, answer the following questions The equation whose roots are cos pi//7 , cos 3pi//7, cos 5pi//7 is

If f(x)=lambdax^(2)+mux+12, f'(4)=15 and f'(2)=11, then find the value of lambda+mu.

Find the sum to n terms of the series whose nth term is n (n+2)

Find the values of k for which the line (k-3) x-(4-k^2) y+k^2 -7k+6=0 is (iii) Passing through the origin.

If the A.M. and G.M. between two numbers are in the ratio x:y, then prove that the numbers are in the ratio (x+sqrt(x^(2)-y^(2))):(x-sqrt(x^(2)-y^(2))).

Which of the following function /functions has /have point of inflection ?

Find the domain of the real function f(x)=(1)/(sqrt([x]^(2)-[x]-2).

Given that P(3, 2, -4), Q(5, 4, -6) and R(9, 8, -10) are collinear. Find the ratio in which Q divides PR.

The plane2x - y + 4z = 5 and 5x - (2.5) y + 10 z =6 are

If X= { a, b, c, d } and Y = { f, b, d, g}, find Y – X

If A,B, C and D are four points, then show that |bar(AB) xx bar(CD) + bar(BC) xx bar(AD) + bar(CA) xx bar(BD)| is four times the area of Delta ABC

If cos h (x)=(5)/(4), then cos h (3x)=