14949 + Interview Questions in Maths in Class 11 Page 290 InterviewSolution

14451.	Evaluate the following limits in Exercises lim_(xto0)(ax+xcosx)/(b sin x)
Answer» ANSWER :`(a+1)/(B)`

Discussion

14452.	If x=sin^(-1)(a^(6)+1)+cos^(-1)(a^(4)+1)-tan^(-1)(a^(2)+1),a in R then the value of sec^(2)x is
Answer» ANSWER :2

Discussion

14453.	A point equidistant from the lines 4x + 3y + 10 = 0, 5 x - 12y + 26 =0 and 7 x + 24y - 50 = 0 is,
Answer» `(1,-1)` `(1,1)` `(0,0)` `(0,1)` ANSWER :C

Discussion

14454.	An ellipse is desrcibed by using an endless string which is passed over two pins. If the axes are 6 cm and 4 cm, the leght of the string and distance between the pins are ……..
Answer» ANSWER :`6 + 2sqrt(5)`

Discussion

14455.	Find the derivative of : sinx+1
Answer» ANSWER :`COS(x+1)`

Discussion

14456.	The sum of two positive numbers is equal to '2' and if the sum of their cubes is least , the numbers are
Answer» `2//3,2//3` 1,1 `1//2,1//2` `2,1//2` ANSWER :B

Discussion

14457.	Determine the number of 5 cardcombinationsoutof a deck of 52 cards if there is exactlythree acesin eachcombination .
Answer» ANSWER :778320

Discussion

14458.	If ex[ [(sin ^(2) x + sin ^(4) x + sin^(6) x + . . .. " to "infty) " In " 2 ]is a root of the equation y ^(2) - 9 y + 8 = 0 , then the valueof (cos x)/( cos x + sin x), 0 lt x lt (pi)/(2) is
Answer» `sqrt(2) - 1` `(sqrt(2) - 1)/(2)` `(sqrt(3) - 1)/(2)` `(sqrt(3) - sqrt(2))/(2)` Answer :C

Discussion

14459.	If bari,barj,bark are orthogonal unit vector triad, then bari xx(barrxxbari)+ barjxx(barrxxbarj)+bark xx(barrxxbark) =
Answer» `BARR` `-barr` `-2barr` `2barr` ANSWER :D

Discussion

14460.	If the pairs of straight lines x^(2)-2pxy-y^(2)=0 and x^(2)-2qxy-y^(2)=0 be such that each pair bisects the angle between the other pair, then
Answer» p=q pq=1 pq=-1 p=-q Answer :C

Discussion

14461.	Let f be the greatest integer function and g be the modulous functions, then
Answer» `(gof-fog)(- 5/3) = 1` `(f+2g)(-1)=1` `(gof-fog)(5/3)=0` `(f+2g)(1)=1` ANSWER :A::B::C

Discussion

14462.	f(x) = {{:((3)/(x^(2))Sin 2x^(2) " , if" x lt 0),((x^(2) + 2x + c)/(1-3x^(2) ) " , if " x ge 0 " , " x ne (1)/(sqrt(3))),(0 " , if " x = (1)/(sqrt(3))):} then in order that 'f' be a continuous at x =0 , the value of 'c' is
Answer» 2 4 6 8 Answer :C

Discussion

14463.	If the coefficients of a^r-1, a^r and a^r+1 in the expansion of (1+a)^n are in arithmetic progression, prove that n^2 - n(4r+1)+4r^2 - 2 =0.
Answer» ANSWER :`n^2 - n (4R + 1) + 4r^2 - 2 = 0`

Discussion

14464.	Find the co-ordinates of a point on Y-axis which are at a distance of 5sqrt2 from the point P(3, -2, 5).
Answer» ANSWER :POINT is (0, -6, 0) OR (0, 2, 0).

Discussion

14465.	(sin 3 alpha)/(cos 2 alpha) lt 0 ifalpha lies in
Answer» `((13 pi)/(48), (14 pi)/(48))` `((14 pi)/(48), (18 pi)/(48))` `((18 pi)/(48),(23 pi)/(48))` `(0, (pi)/(2))` ANSWER :A

Discussion

14466.	Write the first five terms of each of the sequencesand obtain the corresponding series: a_(1) =a_(2) =2 , a_(n) =a_(n-1) -1, n gt 2
Answer» ANSWER :2, 2, 1, 0, –1; 2 + 2 + 1 + 0 + (–1) + ...

Discussion

14467.	Find modulus and argument of the complex numbers z=-sqrt(3)+i
Answer» ANSWER :`2,(5PI)/6`

Discussion

14468.	For non null sete A and B ,Acap(B-A) = ….
Answer» ANSWER :`PHI`

Discussion

14469.	cos5x=16 cos^(5) x -20 cos^(3) x +5 cos x in
Answer» [-1, 1] `[-(1)/(4), (1)/(4)]` `[-(3)/(4), (3)/(4)]` [-2, 2] ANSWER :A

Discussion

14470.	Inclination of a vertical line is
Answer» Not defined 0 `(PI)/2` `pi` ANSWER :C

Discussion

14471.	Convert the sums or differences into products: sin 12 A + sin 4 A
Answer» ANSWER :`2 sin8A COS 4 A`

Discussion

14472.	If p is a real number and if the middle term in the expansion of ((p)/(2)+2)^(8) is 1120, find p.
Answer» <P> ANSWER :`p= PM 2`

Discussion

14473.	If alpha , beta , gamma , deltaare the smallest positive angles in ascending order of magnitude which have their sines equal to the positive quantity K the value of 4 sin(alpha/2)+3sin(beta/2)+2sin(gamma/2)+sin(delta/2)=
Answer» `2sqrt(1-K)` `2sqrt(1+K)` `2sqrtK` `SQRT(K+1)` ANSWER :B

Discussion

14474.	Derive Projection formula from (i) Law of sines, (ii) Law of cosines.
Answer» ANSWER :`(2A^(2))/(2a)`

Discussion

14475.	Examine the continuity of the following: x. ln x
Answer» Answer :` therefore F(X) ` is CONTINUOUS is `(0, OO) ` .

Discussion

14476.	The rank of the matrix [(-1,2,5),(2,-4,a-4),(1,-2,a+1)] is
Answer» 3 if a = 6 1 if`a=-6` 3 if `a=2` 2 if `a=-6` Answer :B

Discussion

14477.	If P(A)=(1)/(4),P(B)=(1)/(2)andP(AcapB)=(1)/(8), find (a) P(AuuB).
Answer» ANSWER :`=(5)/(8)`.

Discussion

14478.	Iff: R to Ris an invertible functions such that f(x) and f^(-1)(x)are symmetric about the line y = -x , then
Answer» `F(X)` is odd `f(x)` and `f^(-1)(x)` may not be symmetric about the LINE `y=x` `f(x)` may not be odd `f^(-1)(x)` may be odd Answer :A

Discussion

14479.	If, absbara = 3, absbarb = 4 abs(bara+barb) = 1 " ,then " abs(bara-barb)=
Answer» 5 6 7 8 Answer :C

Discussion

14480.	If cosh 2 x= 99, then tanh x =
Answer» `(5)/(7 SQRT(2))` `(7)/(5 sqrt(2))` `(5 sqrt(7))/(2)` `(7 sqrt(5))/(2)` Answer :B

Discussion

14481.	Find the number of real solutions of (pi)/2+cos^(-1)(cosx)=\|tanx\|,0lexle2pi
Answer» 1 2 3 4 Answer :D

Discussion

14482.	Find the mean and variance for the following frequency distributions in
Answer» ANSWER :107, 2276

Discussion

14483.	Point (2,4) is transtated through a distance 3sqrt2 units measured parallelto the line y-x=1, in the direction on decreasing ordinates, to reach, to reach at Q. If R is the image of Q with respect to the line y-x=0 the coordinates of R are
Answer» (0,0) (-1,1) (6,6) (5,7) ANSWER :C

Discussion

14484.	Find the mean and variance for the following frequency distributions in
Answer» ANSWER :27, 132

Discussion

14485.	Evaluate 8!
Answer» ANSWER :40320

Discussion

14486.	The temperature in Celsius in the particular day in city is given by t(c)=(9c)/5+32. if c = - 10 then value of t(c) = …. .
Answer» ANSWER :14

Discussion

14487.	Findthe volumeof the tetrahedron, whosevertices are(1,2,1),(3,2,5) , (2,-1,0) and (-1,0,1).
Answer» ANSWER :6

Discussion

14488.	Write the contrapositive and converse of the following statements. You cannot comprehend geometry if you do not know how to reason deductively.
Answer» ANSWER :The contrapositive is If you KNOW how to REASON deductively, then you can COMPREHEND geometry. The converse is If you do not know how to reason deductively, then you can not comprehend geometry.

Discussion

14489.	Find the value of sin15^(@)
Answer» ANSWER :`SIN 30^(@)`

Discussion

14490.	The value of 'c' of Lagrange's mean value theorem for f(x) = (x-a)^(m) ( x - b)^(n)in [a,b] is
Answer» `(mb+na)/( m + N ) ` `(ma+nb)/( m + n ) ` `(a+b)/( m+n)` `(a+b)/( 2)` ANSWER :A

Discussion

14491.	If :"Tan"^(-1)(2x)/(1-x^(2))+Cot^(-1)((1-x^(2))/(2x))=(pi)/3,xgt0 then
Answer» `2+sqrt(3)` `2-sqrt(3)` `3-sqrt(2)` `3+sqrt(2)` ANSWER :B

Discussion

14492.	Let f(x) = (1+b^(2))x^(2) + 2bx + 1 and let m (b) be the minimum value of f(x). As b varies, find the range of m(b).
Answer» ANSWER :(0, 1)

Discussion

14493.	Let bara be perpendicular to both barb,barc. If \|bara\|=2, \|barb\|=3, \|barc\|=4" and "(barb,barc)= (2pi)/(3), compute \|[bara barb barc]\|.
Answer» ANSWER :`12sqrt3`

Discussion

14494.	In Delta ABC,if 3a=b+c, then cot""B/2.cot""C/2=
Answer» `1` `2` `3` `4` ANSWER :B

Discussion

14495.	Find the value of tan""(13pi)/(12)
Answer» ANSWER :`2-sqrt(3)`

Discussion

14496.	Find the coordinates of the point which divides the line segement joining the points (-2,3,5) and (1,-4,6) in the ratio (i) 2:3 internally ,(ii) 2:3 externally
Answer» ANSWER :`(i)(-4/5,1/5,27/5)` (II)-8,17,3)

Discussion

14497.	Show that the middle term in the expansion of (x-1/x)^(2n) is (1xx3xx5xx....xx(2n-1))/(n!) xx(-2)^(n)
Answer» ANSWER :MIDDLE TERM = `(-2)^(N){(1xx3xx5xx7...(2n-1))/(n!)}`

Discussion

14498.	If the lines ax^(2) + 2hxy + by^(2)= 0 are equally inclined with the coordinate axes then
Answer» `H^(2)=AB` `h=0, ab gt 0` `h=0 ab lt 0` `h NE 0 ab lt 0` Answer :C

Discussion

14499.	If n in N, sum_(k=1)^(n)sin^(-1(x_(k))=(npi)/2 then the value of sum_(k=1)^(n)x_(k)=
Answer» N K `(k(k+1))/2` `(n(n+1))/2` ANSWER :A

Discussion

14500.	If f: C to R such that f(z) =Re(z), then f is:
Answer» one-one ONTO bijection neither one-one nor onto ANSWER :B

Discussion

Explore topic-wise InterviewSolutions in .

Evaluate the following limits in Exercises lim_(xto0)(ax+xcosx)/(b sin x)

If x=sin^(-1)(a^(6)+1)+cos^(-1)(a^(4)+1)-tan^(-1)(a^(2)+1),a in R then the value of sec^(2)x is

A point equidistant from the lines 4x + 3y + 10 = 0, 5 x - 12y + 26 =0 and 7 x + 24y - 50 = 0 is,

An ellipse is desrcibed by using an endless string which is passed over two pins. If the axes are 6 cm and 4 cm, the leght of the string and distance between the pins are ……..

Find the derivative of : sinx+1

The sum of two positive numbers is equal to '2' and if the sum of their cubes is least , the numbers are

Determine the number of 5 cardcombinationsoutof a deck of 52 cards if there is exactlythree acesin eachcombination .

If ex[ [(sin ^(2) x + sin ^(4) x + sin^(6) x + . . .. " to "infty) " In " 2 ]is a root of the equation y ^(2) - 9 y + 8 = 0 , then the valueof (cos x)/( cos x + sin x), 0 lt x lt (pi)/(2) is

If bari,barj,bark are orthogonal unit vector triad, then bari xx(barrxxbari)+ barjxx(barrxxbarj)+bark xx(barrxxbark) =

If the pairs of straight lines x^(2)-2pxy-y^(2)=0 and x^(2)-2qxy-y^(2)=0 be such that each pair bisects the angle between the other pair, then

Let f be the greatest integer function and g be the modulous functions, then

f(x) = {{:((3)/(x^(2))Sin 2x^(2) " , if" x lt 0),((x^(2) + 2x + c)/(1-3x^(2) ) " , if " x ge 0 " , " x ne (1)/(sqrt(3))),(0 " , if " x = (1)/(sqrt(3))):} then in order that 'f' be a continuous at x =0 , the value of 'c' is

If the coefficients of a^r-1, a^r and a^r+1 in the expansion of (1+a)^n are in arithmetic progression, prove that n^2 - n(4r+1)+4r^2 - 2 =0.

Find the co-ordinates of a point on Y-axis which are at a distance of 5sqrt2 from the point P(3, -2, 5).

(sin 3 alpha)/(cos 2 alpha) lt 0 ifalpha lies in

Write the first five terms of each of the sequencesand obtain the corresponding series: a_(1) =a_(2) =2 , a_(n) =a_(n-1) -1, n gt 2

Find modulus and argument of the complex numbers z=-sqrt(3)+i

For non null sete A and B ,Acap(B-A) = ….

cos5x=16 cos^(5) x -20 cos^(3) x +5 cos x in

Inclination of a vertical line is

Convert the sums or differences into products: sin 12 A + sin 4 A

If p is a real number and if the middle term in the expansion of ((p)/(2)+2)^(8) is 1120, find p.

If alpha , beta , gamma , deltaare the smallest positive angles in ascending order of magnitude which have their sines equal to the positive quantity K the value of 4 sin(alpha/2)+3sin(beta/2)+2sin(gamma/2)+sin(delta/2)=

Derive Projection formula from (i) Law of sines, (ii) Law of cosines.

Examine the continuity of the following: x. ln x

The rank of the matrix [(-1,2,5),(2,-4,a-4),(1,-2,a+1)] is

If P(A)=(1)/(4),P(B)=(1)/(2)andP(AcapB)=(1)/(8), find (a) P(AuuB).

Iff: R to Ris an invertible functions such that f(x) and f^(-1)(x)are symmetric about the line y = -x , then

If, absbara = 3, absbarb = 4 abs(bara+barb) = 1 " ,then " abs(bara-barb)=

If cosh 2 x= 99, then tanh x =

Find the number of real solutions of (pi)/2+cos^(-1)(cosx)=|tanx|,0lexle2pi

Find the mean and variance for the following frequency distributions in

Point (2,4) is transtated through a distance 3sqrt2 units measured parallelto the line y-x=1, in the direction on decreasing ordinates, to reach, to reach at Q. If R is the image of Q with respect to the line y-x=0 the coordinates of R are

Find the mean and variance for the following frequency distributions in

Evaluate 8!

The temperature in Celsius in the particular day in city is given by t(c)=(9c)/5+32. if c = - 10 then value of t(c) = …. .

Findthe volumeof the tetrahedron, whosevertices are(1,2,1),(3,2,5) , (2,-1,0) and (-1,0,1).

Write the contrapositive and converse of the following statements. You cannot comprehend geometry if you do not know how to reason deductively.

Find the value of sin15^(@)

The value of 'c' of Lagrange's mean value theorem for f(x) = (x-a)^(m) ( x - b)^(n)in [a,b] is

If :"Tan"^(-1)(2x)/(1-x^(2))+Cot^(-1)((1-x^(2))/(2x))=(pi)/3,xgt0 then

Let f(x) = (1+b^(2))x^(2) + 2bx + 1 and let m (b) be the minimum value of f(x). As b varies, find the range of m(b).

Let bara be perpendicular to both barb,barc. If |bara|=2, |barb|=3, |barc|=4" and "(barb,barc)= (2pi)/(3), compute |[bara barb barc]|.

In Delta ABC,if 3a=b+c, then cot""B/2.cot""C/2=

Find the value of tan""(13pi)/(12)

Find the coordinates of the point which divides the line segement joining the points (-2,3,5) and (1,-4,6) in the ratio (i) 2:3 internally ,(ii) 2:3 externally

Show that the middle term in the expansion of (x-1/x)^(2n) is (1xx3xx5xx....xx(2n-1))/(n!) xx(-2)^(n)

If the lines ax^(2) + 2hxy + by^(2)= 0 are equally inclined with the coordinate axes then

If n in N, sum_(k=1)^(n)sin^(-1(x_(k))=(npi)/2 then the value of sum_(k=1)^(n)x_(k)=

If f: C to R such that f(z) =Re(z), then f is: