14949 + Interview Questions in Maths in Class 11 Page 130 InterviewSolution

6451.	Evaluate the following limits. Lt_(xto1)(x^(3)-1)/(x^(4)-1)
Answer» ANSWER :`3/4`

Discussion

6452.	Use the graph to find the limits (if it exists).If the limit does not exist ,explain why? lim_(xrarr5) [\|x-5\|/(x-5)]
Answer» ANSWER :LIMIT does not EXIST

Discussion

6453.	If p_1,p_2 are the perpendicular distance from the origin to the two perpendicular to each other, then the locus of the point of intersection of the perpendicularlines is
Answer» `x^2+y^2=p_1^2+p_2^2` `x+y=p_1+p_2` `x^2-y^2=p_1^2-p_2^2` `x-y=p_1-p_2` ANSWER :C

Discussion

6454.	If sin x sinhy= cos theta, cos x coshy = sin thetathen cosh^2 y + cos^2 x=
Answer» `-1` 0 1 2 Answer :D

Discussion

6455.	Let a and b be the intercepts made by a line on the x-axes and y-axes respectively If the area of the triangle formed by the co-ordinate axes and the line is 6 sq. units and the lenght of the hypotenuse of this triangle is 5 units, derive two equations in a and b
Answer» SOLUTION :`AB = 12, a^2 + b^2 = 25`

Discussion

6456.	Find the value of a and b: (a +1, 1) = (3, b-a)
Answer» ANSWER :a=2, B= 3

Discussion

6457.	If (bara xx barb).(barc xx bard) = (bara.barc)(barb.bard) + k(bara.bard)(barb.barc) then the value of k is
Answer» 1 0 `-2` `-1` ANSWER :D

Discussion

6458.	Solution of cot^(2)theta+[sqrt(3)+1/(sqrt(3))]cot theta+1=0 is
Answer» `{-(pi)/(3),(pi)/(4)}` `{(pi)/(3),-(pi)/(4)}` `{(pi)/(6),(pi)/(3)}` `{(pi)/(12),(pi)/(12)}` ANSWER :B

Discussion

6459.	The mean and standard deviation of a set of n_(1)observation are barx_(1)and s_(1) respectively while the mean and standard deviation of another set of n_(2) observations are barx_(2) and s_(2) respectively . Show that the standard deviation of the combined set of (n_(1)+n_(2)) observations is given bySD=sqrt((n_(1)(s_(1))^(2)+n_(2)(s_(2))^(2))/(n_(1)+n_(2))+(n_(1)n_(2)(barx_(1)-barx_(2))^(2))/((n_(1)-n_(2))^(2)))
Answer» Solution :LET`x_(i),i=1,2,3 ….., and y_(J),j=1,2,3…..n_(2)` `thereforebarx_(1)=(1)/(n_(1))overset(n_(1))underset(i=1)Sigmax_(i) and barx_(2)=(1)/(n_(2))overset(n_(2))underset(i=1)Sigmay_(i)` `rArrsigma_(1)^(2)=(1)/(n_(1))overset(n_(1))underset(i=1)(x_(i)-barx_(1))^(2)` and`sigma_(2)^(2)=(1)/(n_(2))overset(n_(1))underset(i=1)(y_(i)-barx_(2))^(2)` Now , mean `barx`of the COMBINED series is given by `barx=(1)/(n_(1)+n_(2))[overset(n_(1))underset(i=1)Sigmax_(i)+overset(n_(2))underset(i=1)Sigmay_(i)]=(n_(1)barx_(1)+n_(2)barx_(2))/(n_(1)+n_(2))` The variance `sigma^(2)` of the combined series is given by `sigma ^(2)=(1)/(n_(2)+n_(2))[overset(n_(1))underset(i=1)Sigmax_(i(x_(1)-barx)^(2))+overset(n_(2))underset(i=1)Sigmay_(i(y_(1)-barx)^(2))]` Now`overset(n_(1))underset(i=1)Sigmax_(i(x_(1)-barx)^(2))=overset(n_(1))underset(i=1)Sigmax_(i(x_(1)-barx_(j)+barx_(j)-barx)^(2)` `=overset(n_(1))underset(i=1)Sigma(x_(i)-barx_(j))^(2)+n_(1)(barx_(j)-barx)^(2)+2(barx_(j)-barx)underset(i=1)overset(n_(1))Sigma(x_(i)-barx)^2` But`overset(n_(1))underset(i=1)Sigma(x_(i)-barx_(i))=0` [algbraic SUM of the deviation of VALUES of first series from their mean is zero] Also`overset(n_(1))underset(i=1)Sigma(x_(i)-barx_(i))^(2)=n_(1)s_(1)^2+n_(1)(barx_(1)-barx)^2=n_1s_1^2+n_1d_1^2` Where,`d_1=(barx_1-barx)` Similarly, `overset(n_2)underset(j=1)Sigma(y_1-barx)^2=overset(n_2)underset(j=1)Sigma(y_1-barx_i+barx_i-barx)^2=n_2s_2^2+n_2d_2^2` Where, `d_2=barx_2-barx` `sigma=sqrt(([n_1(s_1^2+d_1^2)+n_2(s_2^2+d_2^2)])/(n_1+n_2))` where, `d_1=barx_1-barx=barx_1-((n_1barx_1+n_2barx_2)/(n_1+n_2))=((n_2barx_1-barx_2))/(n_1+n_2)` `d_2=barx_2-barx=barx_2-(n_1barx_1+n_2barx_2)/(n_1+n_2)=(n_1(barx_2-barx_1))/(n_1+n_2)` `thereforesigma^2=(1)/(n_1+n_2)[n_1s_1^2+n_2s_2^2+(n_1n_2(barx_1-barx_2)^2)/(n_1+n_2)^2+(n_2n_1(barx_2-x_1)^2)/((n_1+n_2)^2)]` Also`sigma=sqrt((n_1s_1^2+n_2s_2^2)/(n_1+n_2)+(n_1n_2(barx_1-barx_2)^2)/((n_1+n_2)^2))`

Discussion

6460.	Find the angle between the lines whose direction ratios are (1,1,2)(sqrt(3), -sqrt(3),0)
Answer» ANSWER :`(PI)/(2)`

Discussion

6461.	"cos"^(2)pi/10+"cos"^(2)(2pi)/5+"cos"^(2)(3pi)/5+"cos"^(2)(9pi)/10=
Answer» 1 2 4 6 Answer :B

Discussion

6462.	Let f : [2,7] rarr [ 0 , oo) bea continuous and differentiable function. Then, the value of (f (7) - f(2)) ((f(7))^(2)+ (f(2))^(2) + f(2). f(7))/(3) is ( where c in ( 2, 7 ))
Answer» `3F^(2) .( c ) F'( c ) ` `5F^(2) ( c ) . f( c )` `5f^(2) ( c ) . f'( c ) ` `3f^(2)(c ) .f(c )` ANSWER :C

Discussion

6463.	Evaluate (n!)/(r!(n-r)!), when n = 5, r = 2.
Answer» ANSWER :10

Discussion

6464.	If the equation 9x^(2)+24xy+by^(2)-12x+2fy-12=0 represents a pair of parallel lines, the f=
Answer» `-4` `-3` `-8` `-12` ANSWER :C

Discussion

6465.	If y is infinite and tan^(-1)y=4tan^(-1)x then
Answer» `x^(2)=3+2sqrt(2)` `x^(2)=3-2sqrt(2)` `x^(4)=6X^(2)-1` `x^(4)=6x^(2)+1` Answer :A::B::C

Discussion

6466.	A fair coin is tossed four times and a person win R1 for each head and lose R1.50 for each tail that turns up. From the sample space calculate how manydifferent amounts of money you can have after four tosses and the probability of having each of the amounts.
Answer» ANSWER :`(1)/(16)`

Discussion

6467.	Lt_(xto0)(xcosx-ln(1+x))/x^(2)
Answer» ANSWER :`1/2`

Discussion

6468.	Let f(x)=n x + n - [n x + n] tan"" (pi x)/(2), where [x] is the greatest integer le x and n in N. It is
Answer» a periodic FUNCTION of PERIOD 1 a periodic function of period 4 not periodic a periodic function of period 2 Answer :D

Discussion

6469.	The three coordinate planes divide the space into ____ parts.
Answer» ANSWER :EIGHT

Discussion

6470.	If d.c's of the line joining the origin and a point unit distance from the origin are (1)/(sqrt(3)),(1)/-(2),lambda then the point is
Answer» `((1)/(SQRT(3)),(1)/(sqrt(2)),(1)/(2)sqrt((5)/(3)))` `((2)/(sqrt(3)),-1,sqrt((5)/4))` `((-2)/(sqrt(3)),1-sqrt((5)/(4)))` `((1)/(2),(1)/(3),sqrt((5)/(3)))` ANSWER :A

Discussion

6471.	If f (x) is a function such that (x - y) f (x + y)- (x + y) f (x - y) 4xy (x ^(2) - y ^(2)) AA x, y in R and f (1) =1 then find f (x).
Answer» ANSWER :`F (X) = x ^(3)`

Discussion

6472.	Find the area of the parallelogram whose diagonals are 3bar(i) + bar(j) - 2bar(k), bar(i) - 3bar(j) + 4bar(k)
Answer» ANSWER :`5 SQRT3` sq.units

Discussion

6473.	The radius of a closed cylinder is half of its height. If an error of 0.5% is made in measuring the radius, the percentage error in the surface area is
Answer» 1 2 3 4 Answer :A

Discussion

6474.	Write the following sets in roster form : D= {x : x is integers x^(2)-9 =0}
Answer» ANSWER :`D= {3, -3}`

Discussion

6475.	If A, B, C are the angles of a triangle, then the determinant Delta = \|(sin 2 A,sin C,sin B),(sin C,sin 2B,sin A),(sin B,sin A,sin 2 C)\| is equal to
Answer» 1 `-1` `sin A + sin B + sin C` none of these Answer :D

Discussion

6476.	If f(1)=1, f(n+1)=2f(n)+1, n ge1, then f(n) is
Answer» `2^(N+1)` `2^(n)` `2^(n)-1` `2^(n+1)-1` ANSWER :C

Discussion

6477.	Given the f (n theta) = ( 2 sin 2 theta)/( cos 2 theta - cos 4 n theta) and f (theta) + f ( 2 theta) + f (3 theta) +…+ f (n theta) = (sin gamma thea)/(sin theta sin mu theta)the the value of mu - gamma , is
Answer» ANSWER :1

Discussion

6478.	(i) Find the cosinefunctionwith period7 (ii)finda simefunctionwhoseperiodis 2//3
Answer» ANSWER :B::C

Discussion

6479.	If 3 is spinning at 2 radians/ second. How seconds will it take to make 10 complete rotations………………
Answer» 5 7 6 9 Answer :B

Discussion

6480.	For that value of 'x' the line joining A(4,1,2), B(5,x,0) is perpendicular to the line joining C(1,2,3), D(3,5,7) ?
Answer» ANSWER :3

Discussion

6481.	Find the points of local extrema (if any) and local extrema of the following functions each of whose domain is shown against the function. f(x) = -(x-1)^(3)(x+1)^(2) AA x in R
Answer» Answer :POINT of local minimum X = -1, local minimum = 0 Point of local maximum `x = -(1)/(5)`, local maximum `= (3456)/(3125)`

Discussion

6482.	Two dice are tossed once . Find the probability of getting an even number on first die or a total of 8.
Answer» ANSWER :`(5)/(9)`

Discussion

6483.	Ifthetais acute and (1-a^(2)) sin theta =(1+ a^(2)) cos theta, thensin theta =
Answer» `(1-a^(2))/(SQRT(2(1+a^(4))))` `(sqrt(2(1+a^(4))))/(1-a^(2))` `(1+a^(2))/(sqrt(2(1+a^(4))))` `(sqrt(2(1+a^(4))))/(1+a^(2))` ANSWER :C

Discussion

6484.	(1+sinA)(1+sinB)(1+sinC) = (1-sinA)(1-sinB)(1-sinC) = k rArr k=
Answer» `pm SIN A sin B sin C` `pm cos A cos B cos C` `pm SEC A sec B sec C` `pm cosec A cosec B COSECC` Answer :B

Discussion

6485.	The vector equation of the plane which contains the point (1,1,8) and is normal to the line barr = 2bari +3barj+5bark+t(3bari-2barj+2bark) is
Answer» 1)`BARR.(2bari+3barj+5bark) =45` 2)`barr.(3bari-2barj+2bark) =17` 3)`barr.(2bari+3barj+5bark) =10` 4)`barr.(3bari-2barj+2bark) = 10` ANSWER :B

Discussion

6486.	Find the points of local extrema (if any) and local extrema of the following functions each of whose domain is shown against the function. (x) =sin x, [0, 4pi]
Answer» ANSWER :Pointof local minimum `X = (3PI)/(2)`, local minimum = -1 Point of local minimum `x = (7pi)/(2)`, local minimum = -1 Point of local maximum `x = (pi)/(2)`, local maximum = 1 Point of local maximum `x = (5pi)/(2)`, local maximum = 1

Discussion

6487.	Find the points of local extrema (if any) and local extrema of the following functions each of whose domain is shown against the function. f(x) = x^(3) - 3x AA x in R
Answer» ANSWER :Point of LOCAL minimum X=1, local minimum = -2Point of local maximum x = 01, local maximum = 2

Discussion

6488.	Find the points of local extrema (if any) and local extrema of the following functions each of whose domain is shown against the function. f(x) = x^(2), AA x in R
Answer» ANSWER :Point of local MINIMUM X = 0, local minimum = 0

Discussion

6489.	Find the points of local extrema (if any) and local extrema of the following functions each of whose domain is shown against the function. f(x) = 1//(x^(2) + 2) AA x in R
Answer» Answer :POINT of LOCAL maximum x = 0, local maximum `= (1)/(2)`

Discussion

6490.	Find the points of local extrema (if any) and local extrema of the following functions each of whose domain is shown against the function. f(x) = x^(2) e^(3x)AA x in R
Answer» Answer :Point of local minimum X = 0, local minimum = 0 Point of local MAXIMUM `x = -(2)/(3)`, local maximum`= (4)/(9e^(2))`

Discussion

6491.	Find the points of local extrema (if any) and local extrema of the following functions each of whose domain is shown against the function. f(x) = xsqrt((1-x)) AA x in (0, 1)
Answer» ANSWER :Point of local maximum `x = (2)/(3)`, local maximum `= (2sqrt(3))/(9)`

Discussion

6492.	Find the points of local extrema (if any) and local extrema of the following functions each of whose domain is shown against the function. f(x) = (x)/(2) + (2)/(x) AA x in R (0, oo)
Answer» ANSWER :Point of local minimum `x = (5pi)/(2)`, local maximum = 1

Discussion

6493.	Find the points of local extrema (if any) and local extrema of the following functions each of whose domain is shown against the function. f(x) = (x-1)(x+2)^(2) AA x in R
Answer» Answer :POINT of the local minimum x = 0, local minimum = -4 Point of local maximumx = -2, local maximum = 0

Discussion

6494.	P_1 and P_2 are the length of perpendicular from origin to the line x sec theta + y cosec theta =a and x cos theta - y sin theta = a cos 2 theta then ….... of the following is valid.
Answer» `4P_1^2 + P_2^2 = a^2` `P_1^2 + 4P_2^2 = a^2` `P_1^2 + P_2^2 = a^2` NONE of these Answer :A

Discussion

6495.	Locus of mirror image of (4,3) about the variable (2-3m)x+(1+4m)y+(2-m)=0(m is varying) (x+9/11)^2=(y+4/11)^2 =k then k=
Answer» `121/4178` `4178/121` 1 none Answer :B

Discussion

6496.	Find local maximum or local minimum of f(x) = -sin 2x - x defined o [-pi//2, pi//2].
Answer» Answer :LOCAL MINIMUM = `= -(sqrt(3))/(2) - (PI)/(3)`, local maximum `= (sqrt(3))/(2) + (pi)/(3)`

Discussion

6497.	Solve the equation 1 + sin^(2) theta = 3 sin theta cos theta.
Answer» ANSWER :`{NPI + (pi)/(4) : n in Z} cup {n pi + alpha : n in Z}` where `0 lt alpha lt pi//2` and `TAN alpha = 1//2`

Discussion

6498.	Find the derivative of (x^(2)-cosx)/(sinx)
Answer» Answer :`(-X^(5)cosx+5x^(4)sinx+1)/((sinx)^(2))`

Discussion

6499.	Write the following as interval. {x : x in R, 5 le x le 12}
Answer» ANSWER :`(5, 12)`

Discussion

6500.	If the direction rations of two lines are given by 3lm-4ln+mn = 0 and l + 2m + 3n = 0 then the angle between the lines is
Answer» `(PI)/(2)` `(pi)/(3)` `(pi)/(4)` `(pi)/(6)` ANSWER :A

Discussion

Explore topic-wise InterviewSolutions in .

Evaluate the following limits. Lt_(xto1)(x^(3)-1)/(x^(4)-1)

Use the graph to find the limits (if it exists).If the limit does not exist ,explain why? lim_(xrarr5) [|x-5|/(x-5)]

If p_1,p_2 are the perpendicular distance from the origin to the two perpendicular to each other, then the locus of the point of intersection of the perpendicularlines is

If sin x sinhy= cos theta, cos x coshy = sin thetathen cosh^2 y + cos^2 x=

Let a and b be the intercepts made by a line on the x-axes and y-axes respectively If the area of the triangle formed by the co-ordinate axes and the line is 6 sq. units and the lenght of the hypotenuse of this triangle is 5 units, derive two equations in a and b

Find the value of a and b: (a +1, 1) = (3, b-a)

If (bara xx barb).(barc xx bard) = (bara.barc)(barb.bard) + k(bara.bard)(barb.barc) then the value of k is

Solution of cot^(2)theta+[sqrt(3)+1/(sqrt(3))]cot theta+1=0 is

Find the angle between the lines whose direction ratios are (1,1,2)(sqrt(3), -sqrt(3),0)

"cos"^(2)pi/10+"cos"^(2)(2pi)/5+"cos"^(2)(3pi)/5+"cos"^(2)(9pi)/10=

Let f : [2,7] rarr [ 0 , oo) bea continuous and differentiable function. Then, the value of (f (7) - f(2)) ((f(7))^(2)+ (f(2))^(2) + f(2). f(7))/(3) is ( where c in ( 2, 7 ))

Evaluate (n!)/(r!(n-r)!), when n = 5, r = 2.

If the equation 9x^(2)+24xy+by^(2)-12x+2fy-12=0 represents a pair of parallel lines, the f=

If y is infinite and tan^(-1)y=4tan^(-1)x then

A fair coin is tossed four times and a person win R1 for each head and lose R1.50 for each tail that turns up. From the sample space calculate how manydifferent amounts of money you can have after four tosses and the probability of having each of the amounts.

Lt_(xto0)(xcosx-ln(1+x))/x^(2)

Let f(x)=n x + n - [n x + n] tan"" (pi x)/(2), where [x] is the greatest integer le x and n in N. It is

The three coordinate planes divide the space into ____ parts.

If d.c's of the line joining the origin and a point unit distance from the origin are (1)/(sqrt(3)),(1)/-(2),lambda then the point is

If f (x) is a function such that (x - y) f (x + y)- (x + y) f (x - y) 4xy (x ^(2) - y ^(2)) AA x, y in R and f (1) =1 then find f (x).

Find the area of the parallelogram whose diagonals are 3bar(i) + bar(j) - 2bar(k), bar(i) - 3bar(j) + 4bar(k)

The radius of a closed cylinder is half of its height. If an error of 0.5% is made in measuring the radius, the percentage error in the surface area is

Write the following sets in roster form : D= {x : x is integers x^(2)-9 =0}

If A, B, C are the angles of a triangle, then the determinant Delta = |(sin 2 A,sin C,sin B),(sin C,sin 2B,sin A),(sin B,sin A,sin 2 C)| is equal to

If f(1)=1, f(n+1)=2f(n)+1, n ge1, then f(n) is

Given the f (n theta) = ( 2 sin 2 theta)/( cos 2 theta - cos 4 n theta) and f (theta) + f ( 2 theta) + f (3 theta) +…+ f (n theta) = (sin gamma thea)/(sin theta sin mu theta)the the value of mu - gamma , is

(i) Find the cosinefunctionwith period7 (ii)finda simefunctionwhoseperiodis 2//3

If 3 is spinning at 2 radians/ second. How seconds will it take to make 10 complete rotations………………

For that value of 'x' the line joining A(4,1,2), B(5,x,0) is perpendicular to the line joining C(1,2,3), D(3,5,7) ?

Find the points of local extrema (if any) and local extrema of the following functions each of whose domain is shown against the function. f(x) = -(x-1)^(3)(x+1)^(2) AA x in R

Two dice are tossed once . Find the probability of getting an even number on first die or a total of 8.

Ifthetais acute and (1-a^(2)) sin theta =(1+ a^(2)) cos theta, thensin theta =

(1+sinA)(1+sinB)(1+sinC) = (1-sinA)(1-sinB)(1-sinC) = k rArr k=

The vector equation of the plane which contains the point (1,1,8) and is normal to the line barr = 2bari +3barj+5bark+t(3bari-2barj+2bark) is

Find the points of local extrema (if any) and local extrema of the following functions each of whose domain is shown against the function. (x) =sin x, [0, 4pi]

Find the points of local extrema (if any) and local extrema of the following functions each of whose domain is shown against the function. f(x) = x^(3) - 3x AA x in R

Find the points of local extrema (if any) and local extrema of the following functions each of whose domain is shown against the function. f(x) = x^(2), AA x in R

Find the points of local extrema (if any) and local extrema of the following functions each of whose domain is shown against the function. f(x) = 1//(x^(2) + 2) AA x in R

Find the points of local extrema (if any) and local extrema of the following functions each of whose domain is shown against the function. f(x) = x^(2) e^(3x)AA x in R

Find the points of local extrema (if any) and local extrema of the following functions each of whose domain is shown against the function. f(x) = xsqrt((1-x)) AA x in (0, 1)

Find the points of local extrema (if any) and local extrema of the following functions each of whose domain is shown against the function. f(x) = (x)/(2) + (2)/(x) AA x in R (0, oo)

Find the points of local extrema (if any) and local extrema of the following functions each of whose domain is shown against the function. f(x) = (x-1)(x+2)^(2) AA x in R

P_1 and P_2 are the length of perpendicular from origin to the line x sec theta + y cosec theta =a and x cos theta - y sin theta = a cos 2 theta then ….... of the following is valid.

Locus of mirror image of (4,3) about the variable (2-3m)x+(1+4m)y+(2-m)=0(m is varying) (x+9/11)^2=(y+4/11)^2 =k then k=

Find local maximum or local minimum of f(x) = -sin 2x - x defined o [-pi//2, pi//2].

Solve the equation 1 + sin^(2) theta = 3 sin theta cos theta.

Find the derivative of (x^(2)-cosx)/(sinx)

Write the following as interval. {x : x in R, 5 le x le 12}

If the direction rations of two lines are given by 3lm-4ln+mn = 0 and l + 2m + 3n = 0 then the angle between the lines is