14949 + Interview Questions in Maths in Class 11 Page 78 InterviewSolution

3851.	Find the absolute maximum and absolute minimum values of f(x)=x^(40)-x^(20)" on "[0,1]
Answer» ANSWER :`-1/4`

Discussion

3852.	The perpendicular distance from origin to the plane passing through the point bara = 2bari +3barj -bark " and perpendicular to the vector " 3bari -2barj-2bark is
Answer» `1/sqrt17` `2/sqrt17` `3/sqrt17` `4/sqrt17` ANSWER :B

Discussion

3853.	Solve the inequality-14 lt (3(x-2))/( 5) le 0
Answer» ANSWER :`(-23,2]`

Discussion

3854.	A coin and a die are tossed . Describe the following events . C :getting a tail and an even number ,
Answer» ANSWER :`C=(T1,T3,T5}`

Discussion

3855.	In the following table, the mean and S.D. of the income of the employees of two factories are given. Find the variability of their average income.
Answer» SOLUTION :NA

Discussion

3856.	Values of x and y satisfying the equationsin ^(7)y = \|x^(2) - x^(2) - 9 x + 9\|+. \|x^(3) - x^(2) - 4 x + 4 \| + sec^(2) 2 y + cos ^(4) yare
Answer» ` X = 1, y = N pi, n in I` ` x = 1, y = 2 n pi + (pi)/(2), n in I` ` x = 1 , y = 2 n pi, n in I` `x = 1 , y = n pi + (pi)/( 2), n in I` Answer :B

Discussion

3857.	If alpha, beta, gamma, delta are 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)) + 3 sin ((beta)/(2)) + 2 sin ((gamma)/(2)) + sin ((delta)/(2))=
Answer» `2 SQRT(1-K)` `2 sqrt(1+K)` `2 sqrt(K)` `sqrt(K + 1)` Answer :B

Discussion

3858.	Write the following sets in roster form : E= {x : x is a positive factor of 18}
Answer» Answer :`E= {1, 2, 3, 6, 9, 18}`

Discussion

3859.	Which of the following pairs of sets are disjoint {x : x is an even integer } and {x : x is an odd integer}
Answer» ANSWER :A and B are DISJOINT SET

Discussion

3860.	Let f= {(2,4), (5,6), (8, -1), (10, -3) and g{(2, 5) (7, 1), (8, 4), (10, 13), (11,5)} be two real functions. Then, match the following. The domain of f-g, f+ g, f.g, (f)/(g) is domain of f nn domain of g. Then, find their images.
Answer» Answer :`(i) RARR (c ), (ii) rarr (d), (III) rarr (B), (IV) rarr (a)`

Discussion

3861.	Find the derivative of Sin^(-1)((2x)/(1+x^(2))).
Answer» ANSWER :`(2)/( 1 +X ^(2))`

Discussion

3862.	Focus and directrix of parabola x^(2) = - 8ay are …….., …….. Respectivel.
Answer» (0, -2A) and y = 2a (0, 2a) and y = -2a (2a, 0) and X = -2a (-2a, 0) and x = 2a Answer :A

Discussion

3863.	sinx+cosx=y^(2)-y+a has no value of x for any value of y if a belongs to
Answer» `(0,SQRT(3))` `(-sqrt(3),0)` `(-OO,sqrt(3))` `(sqrt(3),oo)` ANSWER :D

Discussion

3864.	Write each of the following statements in the form of if then: To get sweets Ram has to take lunch.
Answer» ANSWER :If RAM GETS SWEET then he takes lunch.

Discussion

3865.	Find the value of x for which the points (x,-1), (2,1) and (4,5) are collinear.
Answer» ANSWER :`x=1`

Discussion

3866.	lim_( x to 0)(xsqrt(y^(2)-(y-x)^(2)))/({sqrt((8xy-4x^(2))+sqrt(8xy))}^(3))=
Answer» `(1)/(4Y)` `(1)/(2)` `(1)/(3sqrt(2))` `(1)/(128y)` ANSWER :D

Discussion

3867.	If P is a poit (x,y) on the line y=-3x such that P and the point (3,4) are on the opposite sides of the line 3x-4y =8, then
Answer» `XGT 8//15` `xgt8/5` `ylt-8/5` `ylt-8//15` ANSWER :A::C

Discussion

3868.	If cos theta + cos 7 theta + cos 3 theta + cos 5 theta = 0" then " theta=
Answer» `(N pi)/(8), n in Z` `(n pi)/( 4), n in Z` `(n pi)/( 2), n in Z` `(n pi)/( 6) , n in Z` Answer :A

Discussion

3869.	Given n is a positive integer for the function f(x) = 5x(x-2)^(n), x in [ 0,2].By Rolle's theorem the value of c is 1//5 then n is equal to
Answer» 3 6 9 10 Answer :C

Discussion

3870.	A railway emgine is travellings alongs a circular railway track of radius 1500 metres with aa speed of66 km/hour. Find the angle truned by the engine in 10 seconds.
Answer» ANSWER :`7^(@)`

Discussion

3871.	If tan theta = (cos 11^(@)+sin11^(@))/(cos11^(@)-sin11^(@)) and theta is the third quadrant find theta.
Answer» ANSWER :`236^(@)`

Discussion

3872.	If vec(a)-vec(i)-2vec(j)-3vec(k), vec(b)=2vec(i)+vec(j)-vec(k) and vec(c )=vec(i)+3vec(j)-2vec(k), verify that vec(a) xx (vec(b) xx vec(c )) = (vec(a).vec(c ))vec(b)-(vec(a).vec(b))vec(c ).
Answer» Answer :`120 vec(i) + 304 vec(J) + 424 vec(K)`

Discussion

3873.	Using quotient rule differentiate tan x w.r.t.x
Answer» SOLUTION :`sec^2 X`

Discussion

3874.	The vertex at the origin, the axis along the x-axis, and passes through (-3,6).
Answer» ANSWER :`y^(2)=-12X`

Discussion

3875.	Find the sum of n terms of the series 1+4+10+20+35+…
Answer» Solution :Let nth term and sum of n terms of the SERIES be `T_(n)" and "S_(n)` respectively. `S_(n)=1+4+10+20+35+...+T_(n-1)+T_(n)` `underline(S_(n)=""1+4+10+20+...+T_(n-1)+T_(n))` On SUBTRACTING `0=1+3+6+10+15+...+t_(n)-T_(n)` `rArr" "T_(n)=1+3+6+10+15+...+t_(n)` `underline(T_(n)=""1+3+6+10+...+t_(n-1)+t_(n))` On subtracting `0=[1+2+3+4+5+..."nth term"]-t_(n)` `rArr" "t_(n)=Sigman=(n(+1))/(2)` `=(1)/(2)(n^(2)+n)` `rArr" "T_(n)=(1)/(2)(Sigman^(2)+Sigman)` `=(1)/(2)[(1)/(6)n(n+1)(2n+1)+(1)/(2)n(n+1)]` `=(1)/(2)n(n+1)[(2n+1+3)/(6)]` `=(1)/(6)n(n+1)(n+2)` `rArr" "T_(n)=(1)/(6)[n^(2)+3n^(2)+2n]` `rArr" "S_(n)=(1)/(6)[Sigman^(2)+3Sigman^(2)+2Sigman]` `=(1)/(6)[(1)/(4)n^(2)(n+1)^(2)+(3)/(6)n(n+1)(2n+1)+(2)/(2)n(n+1)]` `=(1)/(6)n(n+1)[(1)/(4)n(n+1)+(1)/(2)(2n+1)+1]` `=(1)/(6)n(n+1)[(n(n+1)+2(2n+1)+4)/(4)]` `=(1)/(24)n(n+1)(n^(2)+n+4n+2+4)` `=(1)/(24)n(n+1)(n^(2)+5n+6)` `=(1)/(24)n(n+1)(n+2)(n+3)`

Discussion

3876.	Which among the following is the interval corresponding to the inequality-2ltxle3.
Answer» [-2,3] [-2,3) (-2,3] (-2,3) ANSWER :C

Discussion

3877.	If n(xi) = 40 and n((A uu B)) = 31, then find n(A' nn B')
Answer» ANSWER :9

Discussion

3878.	Solve (5-2x)/(3) le (x)/(6)-5.
Answer» ANSWER :the SOLUTIONS of the given INEQUALITY, `i.e.` x in [8,oo)`.

Discussion

3879.	Mean deviation for n observation x_1,x_2,……….,x_n from their mean barx is given by…….
Answer» `sum_(i=1)^(n) (x_i = BARX)` `1/n sum_(i=1)^(n) \|x_i - barx\|` `sum_(i=1)^(n) \|x_i - barx\|` `1/n sum_(i=1)^(n) (x_i - barx)^2` ANSWER :B

Discussion

3880.	Find the medianfor the following data
Answer» ANSWER :`26.5`

Discussion

3881.	The sides of a rhombus are parallel to the lines x+y-1=0 and 7x-y-5=0. It is given that the diagonals of the rhombus intersect at (1,3) and one vertex, A of the rhombus lies on the line y=2x.Then the coordinates of vertex A are.
Answer» `(8//5,16//5)` `(7//15,14//15)` `(6//5,12//5)` `(4//15,8//15)` ANSWER :A::C

Discussion

3882.	Using binomial theorem , Evaluate the following : (98)^(5)
Answer» ANSWER :`9039207968`

Discussion

3883.	If the roots of the quadratic equation x^(2)+px+q=0 are tan 30^(@) and tan15^(@), then value of 2+q-p is
Answer» 1 2 3 0 Answer :C

Discussion

3884.	Which of the following statements are true Statement-I : If y=x^(2)+2x,x=3, deltax=0.01 then dy=0.08 Statement-II : If y=x^(2)+2x,x=3,deltax=0.01 then deltay=0.0801
Answer» only I only II both I and II neither I nor II Answer :C

Discussion

3885.	baraxx(barbxxbarc) is parallel to barb then
Answer» `baraabs()BARC` `barbabs()barc` `baraabs()BARB` `BARA,barb,barc` are PARALLEL to each other Answer :B

Discussion

3886.	If sin^(-1)a+sin^(-1)b+sin^(-c)=pi, then the value of asqrt((1-a^(2)))+bsqrt((1-b^(2)))+csqrt((1-c^(2))) will be
Answer» 2abc abc `1/2abc` `1/3abc` ANSWER :A

Discussion

3887.	Convert the following into simplest form (iv) sec ( 4pi - theta)
Answer» ANSWER :`SEC THETA`

Discussion

3888.	Find the values of m for which the quadratic equation x^(2)-m(2x-8)-15=0 has (i) equal roots, (ii) both roots positive.
Answer» ANSWER :(i) m=3,5, (II) `m GT 0, m gt (15)/(8)`

Discussion

3889.	If f(x) = {:{(x/(\|x\|)" for "x != 0 ),(0 "for " x = 0 ):} , find Lim_(x to 0 ) f(x)
Answer» ANSWER :Does not EXIST

Discussion

3890.	If 3a+2b+4c=0 then the lines ax+by+c=0 pass through the fixed point
Answer» `(3//4,1//2)` `(-3//4,1//2)` `(3//4,-1//2)` `(-3//4,-1//2)` ANSWER :A

Discussion

3891.	A line is such that its segment between the lines 5x-y + 4=0 and 3x + 4y - 4 =0 is bisected at the point (1,5). Obtain its equation.
Answer» ANSWER :`107 x - 3y - 92 =0`

Discussion

3892.	If function f satisfies the relation f(x) xx f'(-x) = f(-x) xx f'(x) for all x. and f'(3) = -3 . Then the value of f(-3) is ……
Answer» ANSWER :C

Discussion

3893.	If A= {-1, 3,4} and B={2,3} then find A xx B, B xx A and A xx A
Answer» ANSWER :`A xx B= {(-1, 2)(-1, 3)(3,2)(3,3) (4,2)(4,3)}` `B xx A = {(2, -1) (3, -1) (2,3) (3,3) (2,4) (3,4)}` `A xx A= {(-1, -1) (-1, 3)(-1, 4) (3,-1) (3,3) (3,4) (4, -1) (4,3) (4,4)}`

Discussion

3894.	Angle between the lines x^(2)+2xysecalpha+y^(2)=0 is
Answer» `pi/2` `ALPHA` `2ALPHA` `alpha/2` ANSWER :B

Discussion

3895.	Two cards are drawn at random from a pack of 52 cards. The probability that both the cards are kings is ........
Answer» `(1)/(221)` `(5)/(221)` `(4)/(13)` `(1)/(21)` ANSWER :A

Discussion

3896.	For what values of x, the numbers -2/7 , x, -7/2 are in G.P ?
Answer» ANSWER :`pm1`

Discussion

3897.	If the matrix [(cos theta, sin theta, 0),(sin theta, cos theta, 0),(0,0,1)] is singular then theta=
Answer» `PI` `pi/2` `pi/3` `pi/4` ANSWER :D

Discussion

3898.	For complex number z =3 -2i,z + bar z = 2i Im(z) .
Answer» ANSWER :FALSE STATEMENT

Discussion

3899.	If (vec(a) xx vec(b))^(2) + (vec(a).vec(b))^(2)=144 and \|vec(a)\|=4" then " \|vec(b)\|=
Answer» 16 9 3 2 Answer :C

Discussion

3900.	The range of f(x)=sin^(2)x-5 sin x-6 is
Answer» `[-10, 0]` `[-1, 1]` `[0, PI]` `[ (-49)/(4), 0]` ANSWER :A

Discussion

Explore topic-wise InterviewSolutions in .

Find the absolute maximum and absolute minimum values of f(x)=x^(40)-x^(20)" on "[0,1]

The perpendicular distance from origin to the plane passing through the point bara = 2bari +3barj -bark " and perpendicular to the vector " 3bari -2barj-2bark is

Solve the inequality-14 lt (3(x-2))/( 5) le 0

A coin and a die are tossed . Describe the following events . C :getting a tail and an even number ,

In the following table, the mean and S.D. of the income of the employees of two factories are given. Find the variability of their average income.

Values of x and y satisfying the equationsin ^(7)y = |x^(2) - x^(2) - 9 x + 9|+. |x^(3) - x^(2) - 4 x + 4 | + sec^(2) 2 y + cos ^(4) yare

If alpha, beta, gamma, delta are 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)) + 3 sin ((beta)/(2)) + 2 sin ((gamma)/(2)) + sin ((delta)/(2))=

Write the following sets in roster form : E= {x : x is a positive factor of 18}

Which of the following pairs of sets are disjoint {x : x is an even integer } and {x : x is an odd integer}

Let f= {(2,4), (5,6), (8, -1), (10, -3) and g{(2, 5) (7, 1), (8, 4), (10, 13), (11,5)} be two real functions. Then, match the following. The domain of f-g, f+ g, f.g, (f)/(g) is domain of f nn domain of g. Then, find their images.

Find the derivative of Sin^(-1)((2x)/(1+x^(2))).

Focus and directrix of parabola x^(2) = - 8ay are …….., …….. Respectivel.

sinx+cosx=y^(2)-y+a has no value of x for any value of y if a belongs to

Write each of the following statements in the form of if then: To get sweets Ram has to take lunch.

Find the value of x for which the points (x,-1), (2,1) and (4,5) are collinear.

lim_( x to 0)(xsqrt(y^(2)-(y-x)^(2)))/({sqrt((8xy-4x^(2))+sqrt(8xy))}^(3))=

If P is a poit (x,y) on the line y=-3x such that P and the point (3,4) are on the opposite sides of the line 3x-4y =8, then

If cos theta + cos 7 theta + cos 3 theta + cos 5 theta = 0" then " theta=

Given n is a positive integer for the function f(x) = 5x(x-2)^(n), x in [ 0,2].By Rolle's theorem the value of c is 1//5 then n is equal to

A railway emgine is travellings alongs a circular railway track of radius 1500 metres with aa speed of66 km/hour. Find the angle truned by the engine in 10 seconds.

If tan theta = (cos 11^(@)+sin11^(@))/(cos11^(@)-sin11^(@)) and theta is the third quadrant find theta.

If vec(a)-vec(i)-2vec(j)-3vec(k), vec(b)=2vec(i)+vec(j)-vec(k) and vec(c )=vec(i)+3vec(j)-2vec(k), verify that vec(a) xx (vec(b) xx vec(c )) = (vec(a).vec(c ))vec(b)-(vec(a).vec(b))vec(c ).

Using quotient rule differentiate tan x w.r.t.x

The vertex at the origin, the axis along the x-axis, and passes through (-3,6).

Find the sum of n terms of the series 1+4+10+20+35+…

Which among the following is the interval corresponding to the inequality-2ltxle3.

If n(xi) = 40 and n((A uu B)) = 31, then find n(A' nn B')

Solve (5-2x)/(3) le (x)/(6)-5.

Mean deviation for n observation x_1,x_2,……….,x_n from their mean barx is given by…….

Find the medianfor the following data

The sides of a rhombus are parallel to the lines x+y-1=0 and 7x-y-5=0. It is given that the diagonals of the rhombus intersect at (1,3) and one vertex, A of the rhombus lies on the line y=2x.Then the coordinates of vertex A are.

Using binomial theorem , Evaluate the following : (98)^(5)

If the roots of the quadratic equation x^(2)+px+q=0 are tan 30^(@) and tan15^(@), then value of 2+q-p is

Which of the following statements are true Statement-I : If y=x^(2)+2x,x=3, deltax=0.01 then dy=0.08 Statement-II : If y=x^(2)+2x,x=3,deltax=0.01 then deltay=0.0801

baraxx(barbxxbarc) is parallel to barb then

If sin^(-1)a+sin^(-1)b+sin^(-c)=pi, then the value of asqrt((1-a^(2)))+bsqrt((1-b^(2)))+csqrt((1-c^(2))) will be

Convert the following into simplest form (iv) sec ( 4pi - theta)

Find the values of m for which the quadratic equation x^(2)-m(2x-8)-15=0 has (i) equal roots, (ii) both roots positive.

If f(x) = {:{(x/(|x|)" for "x != 0 ),(0 "for " x = 0 ):} , find Lim_(x to 0 ) f(x)

If 3a+2b+4c=0 then the lines ax+by+c=0 pass through the fixed point

A line is such that its segment between the lines 5x-y + 4=0 and 3x + 4y - 4 =0 is bisected at the point (1,5). Obtain its equation.

If function f satisfies the relation f(x) xx f'(-x) = f(-x) xx f'(x) for all x. and f'(3) = -3 . Then the value of f(-3) is ……

If A= {-1, 3,4} and B={2,3} then find A xx B, B xx A and A xx A

Angle between the lines x^(2)+2xysecalpha+y^(2)=0 is

Two cards are drawn at random from a pack of 52 cards. The probability that both the cards are kings is ........

For what values of x, the numbers -2/7 , x, -7/2 are in G.P ?

If the matrix [(cos theta, sin theta, 0),(sin theta, cos theta, 0),(0,0,1)] is singular then theta=

For complex number z =3 -2i,z + bar z = 2i Im(z) .

If (vec(a) xx vec(b))^(2) + (vec(a).vec(b))^(2)=144 and |vec(a)|=4" then " |vec(b)|=

The range of f(x)=sin^(2)x-5 sin x-6 is