14949 + Interview Questions in Maths in Class 11 Page 180 InterviewSolution

8951.	Number of solution of 2^(\|sinx\|)=\|cosx\|x in [0,2pi] is ________
Answer» 1 2 3 4 Answer :C

Discussion

8952.	Find the standard deviation of the following set of numbers: 25, 50, 45, 30, 70, 42, 36, 48, 34, 50
Answer» ANSWER :13.1

Discussion

8953.	Find the derivative with respect to x of the following: (2x +x^4)/( x^2)
Answer» ANSWER :`(2)/(x^2) + 2X`

Discussion

8954.	State which of the following statements are true and which are false. Justify your answer. 35 in {x\|x has exactly four positive factors}.
Answer» ANSWER :1

Discussion

8955.	Obtain equation of circle inTouches both axis and radius 5 unit.
Answer» Answer :`x^(2) + y^(2) pm 10X pm 10y + 25 = 0`

Discussion

8956.	If bara = 6bari+2barj+3bark and barb = 2bari - 9barj+6bark , " then find " bara.barb " and the angle between " bara and barb .
Answer» ANSWER :`12 and COS^(-1)(12/77)`

Discussion

8957.	Differentiate the following functions w.r.t. x. f(x) = sqrt( 4-x), x lt 4
Answer» ANSWER :`(1)/( 2 sqrt( 4 -x ) )`

Discussion

8958.	Find the domain of each of the following functions given by f(x)= (1)/(sqrt(1-cos x))
Answer» ANSWER :`R- {2N PI: n in Z}`

Discussion

8959.	Find the standard deviation from the following datas, using assumed mean:
Answer» SOLUTION :NA

Discussion

8960.	Find the standard deviation from the following datas, using assumed mean:
Answer» SOLUTION :NA

Discussion

8961.	IF (1+i)z=(1-i)z, then show that z=-barz.
Answer» ANSWER :`-ibarz`

Discussion

8962.	Let f(x) = {(""x e^(a x), x le 0),(x + a x^(2) - x^(3) , x gt 0):}, where a is a positive constant. Find theintervals in whichf'(x) in increasing and decreasing.
Answer» Answer :INCREASES in `((-2)/(a), (a)/(3))`, DECREASES in `R -[(-2)/(a), (a)/(3)]`

Discussion

8963.	Sum of the cubes of three successive natural number is divisible by
Answer» `9` `27` `54` 99 Answer :A

Discussion

8964.	Show that 2xltln((1+x)/(1-x))lt2x[1+x^2/(2(1-x^2))]" for all "x in(0,1)
Answer» ANSWER :`2xlt((1+x)/(1-x))lt2x(1+x^2/(2(1-x^2)))AAX in(0,1)`

Discussion

8965.	Which of the following are sets ? Justify your answer. The collection of all natural numbers less than 100.
Answer» ANSWER :it is a SET

Discussion

8966.	The value of 'x' for which the angle between bara=2x^(2)bari+4barxj+bark and barb=7bari -2barj+xbark is obtuse and the angle between barb and Z-axis is acute and less then pi//6, are
Answer» `0ltxlt1/2` `1/2ltxlt15` `xgt1/2 or XLT0` No VALUE of x Answer :D

Discussion

8967.	Statement - I : Thepoint to which the origin has to be shifted to eliminate x and y term in the equation a(x + alpha)^(2) + b (y + beta)^(2) = c " is " (- alpha, - beta) Statement - II : The point to which the origin has to be shifted to eliminate x and y terms in ax^(2) + by^(2)+ 2gx + 2fy + c = 0 " is " ((-g)/(a),(-f)/(b)) Statement - III : If the axes are rotated through an angle 90^(0) then transformed equation of x^(2) - y^(2) = 1 " is " x^(2) - y^(2) = - 1 whichof the above statements are true
Answer» I, II are true II, III are true III, I are true All are true Answer :D

Discussion

8968.	Evaluate the following limits : Lim_( xto 0) (sqrt(1+x) -sqrt(1-x))/(2x)
Answer» ANSWER :`1/2`

Discussion

8969.	Find the centre of the inscribed circle of the triangle the equations, of whose sides are y-15=0, 12y+5x=0 and 4y-3x=0.
Answer» ANSWER : `(-1, 8)`

Discussion

8970.	Sum of integer obtain on two dice have sum 14 is impossible event.
Answer» ANSWER :TRUE STATEMENT

Discussion

8971.	In which of the following sets the inequality sin^(6) x + cos^(6) x gt 5//8 holds good?
Answer» `( - pi//8, pi//8)` `( 3PI //8, 5pi//8)` `(pi//4,3pi//4)` `(7pi//8, 9pi//8)` ANSWER :A::B::D

Discussion

8972.	Write the contrapositive and converse of the statement. If two lines are parallel, then they do not intersect in the same plane.
Answer» Answer :The CONTRAPOSITIVE is If two lines intersect in the same plane, then they are not PARALLEL The CONVERSE is If two lines do not interesect in the same plane, then they are parallel

Discussion

8973.	Find the sum of the series whose n^(th) term is as following: 2n^(2)-3n+ 5
Answer» ANSWER :`(N)/(6)(4N^(2)-3n+23)`

Discussion

8974.	Events E and F are such that P( not E or not F) =0.25, State whether E and F are mutually exclusive.
Answer» ANSWER :`:.` E and F are not MUTUALLY exclusive EVENTS.

Discussion

8975.	Prove that r+ r_3 + r_1-r_2= 4 R cos B
Answer» `4R cos A ` ` 4R cos B ` ` 4 R cos C ` ` 4R ` ANSWER :B

Discussion

8976.	Find the mean and variance for the following frequency distribution :
Answer» ANSWER :2276

Discussion

8977.	If vec(c ) is a unit vector perpendicular to both vec(a)= vec(i) + 5vec(j) + vec(k) and vec(b)= 2vec(i) - vec(j) + vec(k) such that vec(a), vec(b), vec(c ) form right handed system then find vec(c ).
Answer» ANSWER :`(6vec(i) + VEC(J) -11vec(K))/(sqrt158)`

Discussion

8978.	If cos theta + cos 2theta + cos 3theta = 0 then theta =
Answer» `(2n+1)(PI)/4, 2n pi +-(2PI)/3, n inZ` `(2n+1)(pi)/3, 2npi +-(pi)/4, n in Z` `(2n+1)(pi)/6, 2n pi +-(2pi)/3, n in Z` `(2n+1)(pi)/3, 2n pi +-(2pi)/3, n in Z` Answer :A

Discussion

8979.	A parallelopiped is formed by planes drawn through the points (2,3,5) and (5,9,7), parallel to the coordinate planes. The length of a diagonal of the parallelopiped is
Answer» 7 `sqrt38` `sqrt155` `SQRT7` ANSWER :A

Discussion

8980.	Findthe periodof sin (x+3x+5x) (ii)sin (x+2x+3x+…. Nx )VV x EE R , n EE Z^(+) (iii) tan (x+4x + 9x + …… + n^(2) x)
Answer» ` ANSWER :A::B::D

Discussion

8981.	Evaluate the following limits : Lim_(xto3) (x^(3)-6x-9)/(x^(4)-81)
Answer» ANSWER :`7/36`

Discussion

8982.	Find the point to which the origin has to be shifted to eliminate x and y terms (to remove first degree terms) in the following equations. x^(2)+y^(2)-2ax-4ay+a^(2) = 0
Answer» ANSWER :(a,2a)

Discussion

8983.	If the lines represented by h(x^(2)-y^(2))+txy=0 bisects the angle between (a-b)(x^(2)-y^(2))+4hxy=0 then t=
Answer» `a-b` `a+b` `b-a` `AB` ANSWER :C

Discussion

8984.	The value of the expression Sin^(-1)(Sin""(22pi)/7)+Cos^(-1)(Cos""(5pi)/3)+Tan^(-1)(Tan""(5pi)/7)+Sin^(-1)(Cos2) is
Answer» `(17pi)/42-2` -2 `-pi/21-2` `pi/21` ANSWER :A

Discussion

8985.	A coin is tossed. If the out come is a head, a die is thrown. If the die shows up an even number, the die is thrown again. What is the sample space for the experiment ?
Answer» ANSWER :`S={T,H1,H3,H5,H21,H22,H23,H24,H25,H26,H41,H42,H43,H44,H45,H46,H61,H62,H63,H64,H65,H66}`

Discussion

8986.	If B an idempotent matrix and A=I-B then AB =
Answer» I 0 `-I` B Answer :B

Discussion

8987.	Function f defined on Z to Z as f = {(1,1),(2,3),(3,5),(4,7)} and f(x) = ax + b then a + b = …… .
Answer» ANSWER :1

Discussion

8988.	If the angles of the DeltaABC are in A.P., then a^(2)+c^(2)-ac=
Answer» bc `b^(2)c` ABC `b^(2)` ANSWER :D

Discussion

8989.	A man running a racecourse notes that the sum of the distancesfrom the two flag posts from him is always 10 m and the distance between theflag posts is 8 m. Find the equation of the posts traced by the man.
Answer» Answer :`(X^(2))/(25)+(y^(2))/(9)=1`

Discussion

8990.	Write each of the statements in the form ''if p, then q'' r: You can access the website only if you pay a subsciption fee.
Answer» ANSWER :If you can ACCESS the WEBSITE, then you PAY a SUBSCRIPTION fee.

Discussion

8991.	A plane passing through the line joining the points A(1, -3, 5) and B(4, 1, -1) is turned about AB till it passes through the origin. The equation of the plane in the new position is
Answer» `3x+4y-6z=0` `2x-21y+13z=0` `2x-21y-13z=0` `2x-21y-3z=0` ANSWER :C

Discussion

8992.	The number of terms common between the series 1+2+4+8+ .......to 100terms and 1+4+7+10 +...... to 100 terms is
Answer» ANSWER :`(N)/(2)(n^(2)+6n-1)`

Discussion

8993.	Evaluatelim_(x rarr 1) (x^2 -1)/(x-1) if it exist by (i) tabulation method
Answer» ANSWER :2

Discussion

8994.	Solve the system of equation Re(z^(2))=0,\|z\|=2.
Answer» ANSWER :`SQRT(2)+-I sqrt(2), -sqrt(2)+-sqrt(2)`

Discussion

8995.	If p and q are the prependicular distance from the origin to the straight lines xsectheta-ycosectheta=a and xcostheta+ysin theta =acos2theta then
Answer» `4p^2+q^2=a^2` `p^2+q^2=a^2` `p^2+q^2=a^2` `4p^2+q^2= 2a^2` ANSWER :A

Discussion

8996.	The period of f(x) = sin x + [x], where [x] is fractional part of x is
Answer» 0 1 `2PI` Does not exist Answer :D

Discussion

8997.	Find the coordinate of the foci, vertice eccentricity and the length of the latus rectum of the hyperbola 49y ^(2) - 16x ^(2) = 784
Answer» Answer :foci `(0, pm sqrt65),` Vertices `(0, pm 4) , E = (sqrt65)/(4),` LATUS rectum `= (49)/(2)`

Discussion

8998.	Find the coordinate of the foci, vertices, eccentricity and the length of the latus rectum of the hyperbola 9y ^(2) - 4x ^(2) = 36
Answer» ANSWER :FOCI (0, pm sqrt13) , ` Vertices `(0, pm 2) , e = (sqrt13)/(2),` Latus rectum = 9

Discussion

8999.	Find the centroid of the triangle whose vertices are (3, -5), (-7, 4) and (10, -2).
Answer» ANSWER :THIRD vertex A(x, y, z) = (-2, -2, -1).

Discussion

9000.	Find the coordinate of the foci, vertice eccentricity and the length of the latus rectum of the hyperbola (y ^(2))/(9) - (x ^(2))/(27) =1
Answer» Answer :foci `(0, pm 6),` Vertices `(0, pm 3) e = 2,` LATUS RECTUM = 18

Discussion

Explore topic-wise InterviewSolutions in .

Number of solution of 2^(|sinx|)=|cosx|x in [0,2pi] is ________

Find the standard deviation of the following set of numbers: 25, 50, 45, 30, 70, 42, 36, 48, 34, 50

Find the derivative with respect to x of the following: (2x +x^4)/( x^2)

State which of the following statements are true and which are false. Justify your answer. 35 in {x|x has exactly four positive factors}.

Obtain equation of circle inTouches both axis and radius 5 unit.

If bara = 6bari+2barj+3bark and barb = 2bari - 9barj+6bark , " then find " bara.barb " and the angle between " bara and barb .

Differentiate the following functions w.r.t. x. f(x) = sqrt( 4-x), x lt 4

Find the domain of each of the following functions given by f(x)= (1)/(sqrt(1-cos x))

Find the standard deviation from the following datas, using assumed mean:

Find the standard deviation from the following datas, using assumed mean:

IF (1+i)z=(1-i)z, then show that z=-barz.

Let f(x) = {(""x e^(a x), x le 0),(x + a x^(2) - x^(3) , x gt 0):}, where a is a positive constant. Find theintervals in whichf'(x) in increasing and decreasing.

Sum of the cubes of three successive natural number is divisible by

Show that 2xltln((1+x)/(1-x))lt2x[1+x^2/(2(1-x^2))]" for all "x in(0,1)

Which of the following are sets ? Justify your answer. The collection of all natural numbers less than 100.

The value of 'x' for which the angle between bara=2x^(2)bari+4barxj+bark and barb=7bari -2barj+xbark is obtuse and the angle between barb and Z-axis is acute and less then pi//6, are

Evaluate the following limits : Lim_( xto 0) (sqrt(1+x) -sqrt(1-x))/(2x)

Find the centre of the inscribed circle of the triangle the equations, of whose sides are y-15=0, 12y+5x=0 and 4y-3x=0.

Sum of integer obtain on two dice have sum 14 is impossible event.

In which of the following sets the inequality sin^(6) x + cos^(6) x gt 5//8 holds good?

Write the contrapositive and converse of the statement. If two lines are parallel, then they do not intersect in the same plane.

Find the sum of the series whose n^(th) term is as following: 2n^(2)-3n+ 5

Events E and F are such that P( not E or not F) =0.25, State whether E and F are mutually exclusive.

Prove that r+ r_3 + r_1-r_2= 4 R cos B

Find the mean and variance for the following frequency distribution :

If vec(c ) is a unit vector perpendicular to both vec(a)= vec(i) + 5vec(j) + vec(k) and vec(b)= 2vec(i) - vec(j) + vec(k) such that vec(a), vec(b), vec(c ) form right handed system then find vec(c ).

If cos theta + cos 2theta + cos 3theta = 0 then theta =

A parallelopiped is formed by planes drawn through the points (2,3,5) and (5,9,7), parallel to the coordinate planes. The length of a diagonal of the parallelopiped is

Findthe periodof sin (x+3x+5x) (ii)sin (x+2x+3x+…. Nx )VV x EE R , n EE Z^(+) (iii) tan (x+4x + 9x + …… + n^(2) x)

Evaluate the following limits : Lim_(xto3) (x^(3)-6x-9)/(x^(4)-81)

Find the point to which the origin has to be shifted to eliminate x and y terms (to remove first degree terms) in the following equations. x^(2)+y^(2)-2ax-4ay+a^(2) = 0

If the lines represented by h(x^(2)-y^(2))+txy=0 bisects the angle between (a-b)(x^(2)-y^(2))+4hxy=0 then t=

The value of the expression Sin^(-1)(Sin""(22pi)/7)+Cos^(-1)(Cos""(5pi)/3)+Tan^(-1)(Tan""(5pi)/7)+Sin^(-1)(Cos2) is

A coin is tossed. If the out come is a head, a die is thrown. If the die shows up an even number, the die is thrown again. What is the sample space for the experiment ?

If B an idempotent matrix and A=I-B then AB =

Function f defined on Z to Z as f = {(1,1),(2,3),(3,5),(4,7)} and f(x) = ax + b then a + b = …… .

If the angles of the DeltaABC are in A.P., then a^(2)+c^(2)-ac=

A man running a racecourse notes that the sum of the distancesfrom the two flag posts from him is always 10 m and the distance between theflag posts is 8 m. Find the equation of the posts traced by the man.

Write each of the statements in the form ''if p, then q'' r: You can access the website only if you pay a subsciption fee.

A plane passing through the line joining the points A(1, -3, 5) and B(4, 1, -1) is turned about AB till it passes through the origin. The equation of the plane in the new position is

The number of terms common between the series 1+2+4+8+ .......to 100terms and 1+4+7+10 +...... to 100 terms is

Evaluatelim_(x rarr 1) (x^2 -1)/(x-1) if it exist by (i) tabulation method

Solve the system of equation Re(z^(2))=0,|z|=2.

If p and q are the prependicular distance from the origin to the straight lines xsectheta-ycosectheta=a and xcostheta+ysin theta =acos2theta then

The period of f(x) = sin x + [x], where [x] is fractional part of x is

Find the coordinate of the foci, vertice eccentricity and the length of the latus rectum of the hyperbola 49y ^(2) - 16x ^(2) = 784

Find the coordinate of the foci, vertices, eccentricity and the length of the latus rectum of the hyperbola 9y ^(2) - 4x ^(2) = 36

Find the centroid of the triangle whose vertices are (3, -5), (-7, 4) and (10, -2).

Find the coordinate of the foci, vertice eccentricity and the length of the latus rectum of the hyperbola (y ^(2))/(9) - (x ^(2))/(27) =1