14949 + Interview Questions in Maths in Class 11 Page 286 InterviewSolution

14251.	A - (B capC) = (A - B) cap (A-C) .
Answer» ANSWER :FALSE STATEMENT

Discussion

14252.	Evaluatesum_(k-1)^11(2+3^k)
Answer» ANSWER :`22+3/2(3^(11)-1)`

Discussion

14253.	Find the equation of tangents to the curve y = cos(x+y), -2pi le x le 2pi that are parallel to the line x + 2y = 0
Answer» ANSWER :`2x+4y + 3PI = 0`

Discussion

14254.	If in an AP, S_(n)= q n^(2) and S_(m)= qm^(2), where S_(r ) denotes the sum of r terms of the AP, then S_(q) equals to,
Answer» `(q^(3))/(2)` MNQ `q^(3)` `(m+ N)q^(2)` Answer :C

Discussion

14255.	If 10^n + 3.4^(n+2) + kis divisible by 9 , for all n in N , then the least positive integral value of k is
Answer» 5 3 7 1 Answer :A

Discussion

14256.	Differentiate the following functions w.r.t. x: sin 5x
Answer» ANSWER :`5 COS 5X`

Discussion

14257.	Find all possible 'b' for which f(x)=sin2x-8(b+2)cosx-(4b^(2)+16b+6)x is monotoic decreasing for xhatIRandhas nocritical point .
Answer» `(-1,-2)` (2,3) `(sqrt(3)-1,OO)` `(sqrt(3)+1,oo)` Answer :C

Discussion

14258.	If f(x)=2tan^(-1)x+sin^(-1)((2x)/(1+x^(2))),xgt1 then f(5) is equal to
Answer» `(PI)/2` `pi` `4tan^(-1)(5)` `TAN^(-1)(65/156)` ANSWER :C

Discussion

14259.	Simplify : i^(15)
Answer» ANSWER :`-i`

Discussion

14260.	If sinbeta is geometric mean between sin alpha and cos alpha ,then cos 2beta =
Answer» `2sin^2(pi/4-alpha)" or " 2 cos^2(pi/4+alpha)` `2sin^2(pi/3-alpha)" or " 2 cos^2(pi/3+alpha)` `sin^2(pi/4-alpha)" or "cos^2(pi/4+alpha)` `sin^2(pi/3-alpha)" or " 2 cos^2(pi/3+alpha)` ANSWER :A

Discussion

14261.	Check the continuity of the function f defined by f(x)={{:(x+1,if xle1),(2x,if 1 lt x lt 2x),(1+xA^(2),if x ge 2):} at x=1 and 2
Answer» ANSWER :CONTINOUS

Discussion

14262.	theperiodof tan (4 x)+ sec(4 x)is
Answer» `2PI` `(3PI)/(2)` `PI` `(pi)/(2)` ANSWER :D

Discussion

14263.	Out of the following which is a function?
Answer» `{(X,y): x, y in R " " y^(2)= x}` `{(x,y): y = \|x\|, x y in R}` `{(x,y): x^(2) + y^(2)=1, x, y in R}` `{(x, y): x^(2)-y^(2)=1, x, y INR}` Answer :B

Discussion

14264.	Express each of the complex number given in the form of a+ib i^(-39)
Answer» ANSWER :0 + I1

Discussion

14265.	Third term of G.P. is 3 then product of its first 5 terms is .............
Answer» ANSWER :243

Discussion

14266.	Match from List-I to List-II {:("List-I","List-II"),("(Function)","(Domain)"),(I.sechx,(a)R-[-1,1]),(II.coth^(-1)x,(b)R-{0}),(III.cosh^(-1)x,(c )R),(IV.cothx,(d)[1,oo)),(,(e )[2,oo)):}
Answer» C,a,B,d a,c,b,d a,c,d,b c,a,d,b ANSWER :D

Discussion

14267.	A fair coin is tossed four times, and a person win Re 1 for each head and lose Rs 1.50 for each tail that turns up. From the sample space calculate how many different amounts of money you can have after four tosed once. Find the probability of getting.
Answer» ANSWER :RS 4.00 GAIN, Rs 1.50 gain, Re 1.00 LOSS, Rs 3.50 loss, Rs 6.00 loss.

Discussion

14268.	If cos alpha + cos beta = 3/2 and sin alpha + sin beta = 1/2 and thetais the arithmetic mean of alpha and beta then sin 2 theta + cos 2 theta
Answer» `3/5` `4/5` `7/5` `8/5` ANSWER :C

Discussion

14269.	The sum of the first n terms of the arithmetical progression 3, 5(1)/(2),8,.... is equal to the 2nth term of the arithmetical progression 16(1)/(2),28(1)/(2),40(1)/(2) . Calculate the value of n.
Answer» ANSWER :N = 18

Discussion

14270.	Evaluate the following limits : Lim_(x to 1) (x^(2)-1)/(x-1)
Answer» Answer :` Lim_(x to 1) (x+1) = 1+1 = 2 "" [:' x != 1 rArr x - 1 != 0]`

Discussion

14271.	Iff : R to is definedbyf(x )=7+ cos (5x+3) for x E Rthen theperiodof f is
Answer» `2PI` `PI` `(pi)/(5)` `(2pi)/(5)` ANSWER :4

Discussion

14272.	The perpendicular distance from A(1, 4, -2) to BC, where B= (2, 1, -2), C= (0, -5, 1) is
Answer» `(3 sqrt26)/(7)` `(3)/(7)` `(sqrt26)/(7)` 2 Answer :A

Discussion

14273.	If l^(2)+m^(2)=1 then the max value of l+m is
Answer» 1 `SQRT2` `1/sqrt2` `sqrt2` ANSWER :B

Discussion

14274.	If 5^(th),6^(th) and 7^(th) terms in the expansion of (1+y)^(n) are in A.P . Then the value of n is ………..
Answer» 7,11 7,14 8,16 None of these ANSWER :B

Discussion

14275.	Which one of the following sentences is a statement?A) 275 is a perfect square.B)Mathematics is a difficult subjectC)Answer this questionD)Today is a rainy day
Answer» 275 is PERFECT square. Mathematics is a DIFFICULT subject Answer this question Today is a RAINY day. Answer :A

Discussion

14276.	3x-7 gt 2 (x-6), 6-x gt 11 -2x
Answer» ANSWER :`(5,OO)` `(##NCERT_TAM_MAT_XI_C06_E04_009_A01##)`

Discussion

14277.	Evaluate Lt_(x to 3)(x^2 + 3x + 2)/(x^2 - 6x + 9)
Answer» ANSWER :`+OO`

Discussion

14278.	Ifa,b,c arep^(th),q^(th),r^(th) " terms of an H.P and" baru=(q-r)bari+(r-p)barj+(p-q)bark, barv=bari/a+barj/b+bark/c, then
Answer» `BARU,BARV` are othoganal VECTORS `baru,barv` are PARALLEL can not be determined none of these Answer :A

Discussion

14279.	Evaluate the following limits : Lim_(x to oo )( sqrt(x^(2)+5x+4)-sqrt(x^(2)-3x+4))
Answer» ANSWER :4

Discussion

14280.	Two dice are thrown and the sum of the number which come up on the dice is noted. Let us consider the following events associated with the experiment A: 'the sum is even'. B: 'the sum is a multiple of 3'. C: 'the sum is less than 4'. D: 'the sum is greater than 11'. Which pairs of these events are mutually exclusive?
Answer» ANSWER :`A NN B = PHI, A nn C = phi` and `B nn C = phi`

Discussion

14281.	If tan^(-1)((x-1)/(x-2))+tan^(-1)((x+1)/(x+2))=(pi)/4 then x=
Answer» `1/sqrt(2)` `pm1/sqrt(2)` `pm1/sqrt(3)` `1/sqrt(3)` ANSWER :B

Discussion

14282.	If tan^(-1)x+2cot^(-1)x=(2pi)/3, then x is equal to
Answer» `(SQRT(3)-1)/(sqrt(3)+1)` `3` `sqrt(3)` `sqrt(2)` ANSWER :C

Discussion

14283.	Find the derivative of y = sin [cos (x)^(2)]
Answer» Answer :`-2x SIN X ^(2) COS (cos x ^(2))`

Discussion

14284.	If A+B=225^(@) then (cotA)/(1+cotA).(cotB)/(1+cotB) = ………….
Answer» 1 `-1` 0 `(1)/(2)` ANSWER :D

Discussion

14285.	If sinh(x+y) cosh(x-y)=k (sinh2x+sinh2y) then k =
Answer» 1 `1//2` 2 `-1//2` ANSWER :B

Discussion

14286.	Derive section formula in 3-D for internal division . Also find the co-ordinates of mid points of the line joining thepoints A(1,-2,3) and B (3,4,8)?
Answer» ANSWER :`= [2,1,(11)/(2)]`

Discussion

14287.	LetE and Fbe two independentevents . Theprobabilitythatneither happensis (1)/(2) . Then
Answer» <P>`P(E ) = (1)/(13), P(F ) = (1)/(4)` `P(E ) = (1)/(2), P(F ) = (1)/(6)` `P(E ) = (1)/(6),P( E) = (1)/(12)` `P( E) = (1)/(4),PE =(1)/(3)` Answer :D

Discussion

14288.	The period of f(x) = sin""(pi x)/(n!)-cos""(pi x)/((n+1)!) is
Answer» `(N+1)!` `2(n+1)!` `2(n)!` `((n+1))/(2!)` ANSWER :B

Discussion

14289.	Prove that sin20^(@)sin40^(@)sin80^(@)=(sqrt(3))/(8)
Answer» ANSWER :`(SQRT(3))/(8)`

Discussion

14290.	Expandthe expression (2/x - x/2)^5
Answer» ANSWER :`32/x^5` - `40/x^3` + `20/x` - 5X + `5/8`x^3` - `x^5/32`

Discussion

14291.	Find the derivative of x^(-4)(3-4x^(-5))
Answer» ANSWER :`(-12)/(x^(5))+(36)/(x^(10))`

Discussion

14292.	If the sum of the slopes of the lines given by x^(2)-2cxy-7y^(2)=0 is four times their product, then 'c' has the value
Answer» `-2` `-1` 2 1 Answer :C

Discussion

14293.	Cos15^(@) - Cos75^(@) =
Answer» `SQRT((3)/(2))` `(sqrt(3))/(2)` `(1)/(2)` `(1)/(sqrt(2))` ANSWER :D

Discussion

14294.	The values of Sin^(-1)(cos{Cos^(-1)(cosx)+Sin^(-1)(sinx)})" where "x in (pi/2, pi) is
Answer» `PI/2` `-pi` `pi` `-pi/2` ANSWER :D

Discussion

14295.	Light from a point source at A(7,0,0) strikes a small mirror at the origin the normal to which has direction ratios (2,1,2). Find the actual direction cosines of the reflected ray.
Answer» ANSWER :`((-1)/(9),(4)/(9),(8)/(9))`

Discussion

14296.	Show that thelines form an equilateral triangle and find its area x^(2)-4xy+y^(2)=0, x+y-3=0
Answer» ANSWER :`(3sqrt(3))/(2)` SQ UNITS

Discussion

14297.	A die is thrown once . Find P(a number lt7),
Answer» ANSWER :`(6)/(6),i.e,1`

Discussion

14298.	The sum of terms equidistant from the beginning and end in an AP is equal to……..
Answer» ANSWER :`a_(1)+ a_(N)`

Discussion

14299.	Solve the general vlaue. 2 sin ^(2) x + sqrt3 cos x + 1 =0
Answer» ANSWER :`2n PI PM (5pi)/(6)`

Discussion

14300.	Reduce the following equations in intercept form and find their intercepts on axis. (ii) 4x-3y=6
Answer» ANSWER :`(X)/( (3)/(2) ) + (y)/( -2) = 1`

Discussion

Explore topic-wise InterviewSolutions in .

A - (B capC) = (A - B) cap (A-C) .

Evaluatesum_(k-1)^11(2+3^k)

Find the equation of tangents to the curve y = cos(x+y), -2pi le x le 2pi that are parallel to the line x + 2y = 0

If in an AP, S_(n)= q n^(2) and S_(m)= qm^(2), where S_(r ) denotes the sum of r terms of the AP, then S_(q) equals to,

If 10^n + 3.4^(n+2) + kis divisible by 9 , for all n in N , then the least positive integral value of k is

Differentiate the following functions w.r.t. x: sin 5x

Find all possible 'b' for which f(x)=sin2x-8(b+2)cosx-(4b^(2)+16b+6)x is monotoic decreasing for xhatIRandhas nocritical point .

If f(x)=2tan^(-1)x+sin^(-1)((2x)/(1+x^(2))),xgt1 then f(5) is equal to

Simplify : i^(15)

If sinbeta is geometric mean between sin alpha and cos alpha ,then cos 2beta =

Check the continuity of the function f defined by f(x)={{:(x+1,if xle1),(2x,if 1 lt x lt 2x),(1+xA^(2),if x ge 2):} at x=1 and 2

theperiodof tan (4 x)+ sec(4 x)is

Out of the following which is a function?

Express each of the complex number given in the form of a+ib i^(-39)

Third term of G.P. is 3 then product of its first 5 terms is .............

Match from List-I to List-II {:("List-I","List-II"),("(Function)","(Domain)"),(I.sechx,(a)R-[-1,1]),(II.coth^(-1)x,(b)R-{0}),(III.cosh^(-1)x,(c )R),(IV.cothx,(d)[1,oo)),(,(e )[2,oo)):}

A fair coin is tossed four times, and a person win Re 1 for each head and lose Rs 1.50 for each tail that turns up. From the sample space calculate how many different amounts of money you can have after four tosed once. Find the probability of getting.

If cos alpha + cos beta = 3/2 and sin alpha + sin beta = 1/2 and thetais the arithmetic mean of alpha and beta then sin 2 theta + cos 2 theta

The sum of the first n terms of the arithmetical progression 3, 5(1)/(2),8,.... is equal to the 2nth term of the arithmetical progression 16(1)/(2),28(1)/(2),40(1)/(2) . Calculate the value of n.

Evaluate the following limits : Lim_(x to 1) (x^(2)-1)/(x-1)

Iff : R to is definedbyf(x )=7+ cos (5x+3) for x E Rthen theperiodof f is

The perpendicular distance from A(1, 4, -2) to BC, where B= (2, 1, -2), C= (0, -5, 1) is

If l^(2)+m^(2)=1 then the max value of l+m is

If 5^(th),6^(th) and 7^(th) terms in the expansion of (1+y)^(n) are in A.P . Then the value of n is ………..

Which one of the following sentences is a statement?A) 275 is a perfect square.B)Mathematics is a difficult subjectC)Answer this questionD)Today is a rainy day

3x-7 gt 2 (x-6), 6-x gt 11 -2x

Evaluate Lt_(x to 3)(x^2 + 3x + 2)/(x^2 - 6x + 9)

Ifa,b,c arep^(th),q^(th),r^(th) " terms of an H.P and" baru=(q-r)bari+(r-p)barj+(p-q)bark, barv=bari/a+barj/b+bark/c, then

Evaluate the following limits : Lim_(x to oo )( sqrt(x^(2)+5x+4)-sqrt(x^(2)-3x+4))

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

If tan^(-1)x+2cot^(-1)x=(2pi)/3, then x is equal to

Find the derivative of y = sin [cos (x)^(2)]

If A+B=225^(@) then (cotA)/(1+cotA).(cotB)/(1+cotB) = ………….

If sinh(x+y) cosh(x-y)=k (sinh2x+sinh2y) then k =

Derive section formula in 3-D for internal division . Also find the co-ordinates of mid points of the line joining thepoints A(1,-2,3) and B (3,4,8)?

LetE and Fbe two independentevents . Theprobabilitythatneither happensis (1)/(2) . Then

The period of f(x) = sin""(pi x)/(n!)-cos""(pi x)/((n+1)!) is

Prove that sin20^(@)sin40^(@)sin80^(@)=(sqrt(3))/(8)

Expandthe expression (2/x - x/2)^5

Find the derivative of x^(-4)(3-4x^(-5))

If the sum of the slopes of the lines given by x^(2)-2cxy-7y^(2)=0 is four times their product, then 'c' has the value

Cos15^(@) - Cos75^(@) =

The values of Sin^(-1)(cos{Cos^(-1)(cosx)+Sin^(-1)(sinx)})" where "x in (pi/2, pi) is

Light from a point source at A(7,0,0) strikes a small mirror at the origin the normal to which has direction ratios (2,1,2). Find the actual direction cosines of the reflected ray.

Show that thelines form an equilateral triangle and find its area x^(2)-4xy+y^(2)=0, x+y-3=0

A die is thrown once . Find P(a number lt7),

The sum of terms equidistant from the beginning and end in an AP is equal to……..

Solve the general vlaue. 2 sin ^(2) x + sqrt3 cos x + 1 =0

Reduce the following equations in intercept form and find their intercepts on axis. (ii) 4x-3y=6