14949 + Interview Questions in Maths in Class 11 Page 54 InterviewSolution

2651.	The variable x satisfying the equation \|sinxcosx\|+sqrt(2+tan^(2)x+cot^(2))x=sqrt(3) belongs to the interval
Answer» `[0,(PI)/(3)]` `(pi)/(3),(pi)/(2))` `[(3PI)/(4),pi]` non-existent Answer :D

Discussion

2652.	Let A(1,0), B(-1,0), C(2, 0) then the locus of a point P such that PB^(2)+ PC^(2) = 2PA^(2) is
Answer» a STRAIGHT line PARALLEL to X - axis a straight line parallel to y-axis parallel to x + y =2 xy=0 Answer :2

Discussion

2653.	Three students A,B,C stand one behind other in a row to take a part in a march -past.There are 5 different colour flags are there. Each student is to carry a flag such that on two students should carry the flag of the same colour.Find the probability that the first student should carry white flag where white is one of the 5 colours.
Answer» ANSWER :`(1)/(5)`

Discussion

2654.	Find the standard deviation from the following datas, using assumed mean: (a) 112,117,121,125,130 (b) 37,43,48,34,41,39,46,40
Answer» SOLUTION :NA

Discussion

2655.	If tan theta + sin theta = m and tan theta - sin theta = n, then
Answer» `m^(2) - N^(2) = 4MN` `m^(2) + n^(2) = 4mn` `m^(2) - n^(2) = 4 sqrt(mn)` `m^(2)-n^(2)=4sqrt(mn)` Answer :D

Discussion

2656.	If A and B are any two events associated with an experiment, then
Answer» `P(A uu B) = P(A) + P(B)`ifA and Bindependent `P(A uu B) =1- P(A') P(B')` if A and B are INDEPENDENT `P(A NN B)= P(A) P(B)`ifA and B are exclusie `P(ANN B) =P(A) +P(A nn B)` . Answer :B

Discussion

2657.	A and B are three mutuallyexclusive events . If P(A)=0.5and P(overline(B))=0.6,find P(A or B).
Answer» ANSWER :0.9

Discussion

2658.	Find the deviation using median of the following observations: 15,19,20,28,16.
Answer» Solution :TAKING in ascending ORDER Here `n=5` (odd) Median `M=(n+1)/2` th term `=(5+1)/2` th term `=` 3rd term `=19` Mean deviation `=(sum_(i=1)^(n)\|x_(i)-M\|)/n=17/5=3.4`

Discussion

2659.	If satisfies the relation f(x+y)+f(x-y)=2 " " f(x).f(y) AA x , y in R and f(0) != 0, then f(10)-f(-10)=
Answer» 0 1 2 3 Answer :A

Discussion

2660.	If vec(a), vec(b) are collinear, then which of the following is false?
Answer» `VEC(a) xx vec(B)= vec(0)` `vec(a).vec(b) = +-\|vec(a)\|\|vec(b)\|` `vec(a) xx vec(b)= 0` `vec(a) = t vec(b)` Answer :C

Discussion

2661.	If f(x) is a function such that f(xy)=f(x)+f(y) and f(2)=1 then f(x)=
Answer» `f(0) = 2` `f(0) = 1` `f'(4) = 7` `f'(4) = 12` ANSWER :B::D

Discussion

2662.	Show that \|(1,1,1),(x,y,z),(x^(2),y^(2),z^(2))\|=(x-y)(y-z)(z-x)
Answer» ANSWER :`-25 = VEC(a) . vec(B) + vec(b) . vec(C) + vec(c) . vec(a)`

Discussion

2663.	For each of the following compound statements, first identify the corresponding component statements. Then check whether the statements are true or not: If a triangle ABC is equilateral, then it is isosceles.
Answer» ANSWER :TRUE.

Discussion

2664.	For each of the following compound statements, first identify the correspoinding component statements. Then check whether the statements are true or not: If a and b are integers, then ab is a rational number.
Answer» ANSWER :TRUE.

Discussion

2665.	Let y=ax^(3) + bx^(2) + cx +d. Find the rate of change of y w.r.t x at x=0.
Answer» ANSWER :`=3AX^(2) + 2bx+c`.

Discussion

2666.	State true of false for the following: 2 is not a complex number.
Answer» ANSWER :TRUE

Discussion

2667.	Write down the first five terms of the sequence, whose nth term is (-1)^(n-1) , 5^(n+1)
Answer» ANSWER :25,-125,625,-3125 , 15625

Discussion

2668.	If bara,barb,barc are unit vectors equally inclined to each other at an angle pi/3 then find the value of [baraxxbarb bar bxxbarc barcxxbara]
Answer» ANSWER :`1/4`

Discussion

2669.	Write the contrapositive of the contrapositive of p implies q.
Answer» <P> ANSWER : p=> Q

Discussion

2670.	Evaluate the following limits in Exercises lim_(xto0)(cos (2x)-1)/(cosx-1)
Answer» ANSWER :4

Discussion

2671.	Find n if : ""^(2n+1) P_(n-1): ""^(2n-1) P_n = 3: 5
Answer» ANSWER :` 4`

Discussion

2672.	(d)/(dx)(sqrt(sinx))=………..(0ltxlt (pi)/(2))
Answer» `SQRT(COSX)` `sqrt(SINX)` `(cosx)/(2sqrt(sinx))` `(sinx)/(2sqrt(cosx))` ANSWER :C

Discussion

2673.	In the mean value theorem, f(b) - f(a) = (b-a) f(c ) , if a= 4, b = 9and f(x) =sqrt(x)then the value of c is
Answer» 8 1/2 6.25 4 Answer :C

Discussion

2674.	If the line (x/2+y/3-1)+lamda(2x+y-1)=0 is parallel to x-axis then lamda=
Answer» `-1/2` `1/2` `-1/4` `1/4` ANSWER :C

Discussion

2675.	If bara,barb " are noncollinear unit vectors, " abs(bara+barb) =sqrt 3 " then " (2bara+5barb).(3bara-barb)=
Answer» 1)-15 2)`-15/2` 3)15 4)`15/2` ANSWER :D

Discussion

2676.	Prove by direct method that for any real numbers x,y if x=y, then x^(2)=y^(2)
Answer» ANSWER :HENCE GIVE STATEMENT is PROVED.

Discussion

2677.	If x,y,z are chosen at random from the set (1,2,3) (repetition is allowed) .What is the probability that the equation x^(2)-yzge0 is satisfied.
Answer» ANSWER :`(5)/(9)`

Discussion

2678.	The ratio between the circumradius and invadius of a right angled isosceles triangle is
Answer» `2:1` `(SQRT(2)+1):1` `1:(sqrt(2)+1` `(sqrt(2)+1):sqrt(2)` ANSWER :B

Discussion

2679.	sqrt(-5x^(8))- sqrt(-20x^(8)) + sqrt(-45x^(8)), where x is a positive real number
Answer» ANSWER :`2 SQRT5 X^(4)i`

Discussion

2680.	If the origin is the centroid of the tetrahedron for which (2,-1,3),(-1,3,1),(3,4,-2) are three vertices then fourth vertex is
Answer» (4,6,2) (-4,-6,-2) (-4,6,-2) (4,-6,2) ANSWER :B

Discussion

2681.	A variable plane makes with the co-ordinates plane, tetrahedron of contant volume 64 k^3 Then the locus of the centroid of tetrahedron is the surface.
Answer» ANSWER :O(0, 0, 0), A(5, 0, 0), B(5, 5, 0), C(0, 5, 5), D(0, 0, 5), E(5, 0, 5) F(5, 5, 5), G(0, 5, 0)

Discussion

2682.	If A = {4,5,6,8,9}, B = {4,5,8} and C = {3,4,8,9} Find A cup B and B cup C
Answer» SOLUTION :{4,5,6,8,9},{3,4,5,8,9}

Discussion

2683.	The set S_(1) and S_(2) are solution sets of (1 + a) cos theta cos ( 2 theta - b)= (1 + a cos 2 theta ) cos (theta - b)
Answer» `{N PI , n in A} and (1)/( 2) {n pi + (-1)^(n) SIN ^(-1) (a sin b) + b, n in Z}` `{n(pi)/(2), n in Z} and { n pi + (- 1)^(n)sin ^(-1) ( a sin b) , n in Z}` `{n (pi)/( 2), n in Z} and {n pi + ( - 1)^(n) sin^(-1) ((a)/( 2) sin b) , n in Z}` None of these Answer :A

Discussion

2684.	For each of the following statements, determine whether an inclusive Or or exclusive or is used. Give reasons for your answer: Students can take French or Sanskrit as their third language.
Answer» ANSWER :EXCLUSIVE

Discussion

2685.	Find the derivative of the w.r.t.x x log x log (log x)
Answer» ANSWER :`LOG (E log X ) + log x log ( log x)`

Discussion

2686.	For each of the following statements, determine whether an inclusive Or or exclusive or is used. Give reasons for your answer: To enter a country, you need a passport or a voter registration card.
Answer» ANSWER :INCLUSIVE

Discussion

2687.	For each of the following statements, determine whether an inclusive Or or exclusive or is used. Give reasons for your answer: Two lines intersect at a point or are parallel.
Answer» ANSWER :EXCLUSIVE

Discussion

2688.	The total number of solutions of log_(e)\|sinx\|=-x^(2)+2x in [-pi/2,pi/2] is equal to
Answer» 1 2 3 4 Answer :B

Discussion

2689.	If 2( r+R ) = b+ c then A =
Answer» ` 60 ^(@) ` ` 30 ^(@) ` ` 90 ^(@) ` ` 45 ^(@) ` Answer :C

Discussion

2690.	Find the derivative of the w.r.to x. x ^(tan x ) + (sin x ) ^( cos x)
Answer» Answer :`[ (COS ^(2)X)/( sin x ) - sin x log (sin x)]`

Discussion

2691.	Write the following sets in the set-builder form : {2,4,8,16,32}
Answer» ANSWER :`={x : x = 2^(n), 1 LE n le 5, n in N}`

Discussion

2692.	Find all points of dicontinuity of f, where f(x)={{:((sinx)/(x)," if "x lt 0),(x+1," if "x ge 0):}.
Answer» ANSWER :there is no POINT of DISCONTINUITY

Discussion

2693.	If \|a_1Sinx+a_(2)sin2x+.....+a_(n)sinx\|le\|sinx\| for x in R then maimum value of \|a_(1)+2a_(2)+3a_(3)+.....+na_(n)\| is
Answer» ANSWER :1

Discussion

2694.	A particle moves along a straight line according to the equation s = 8 cos 2t + 4sint. The initial velocity is
Answer» `-5` units/sec `-4` units/sec `23^(E )` units/sec 5 units/sec Answer :C

Discussion

2695.	The sides of a triangle are the lines x+y=1, 7y=x, and sqrt3y+x=0, then which of the following are not interior points of triangle?
Answer» ORHOCENTER and circumcentre CENTROID and circumcentre Incentre and ORTHOCENTER centroid and incentre Answer :D

Discussion

2696.	Calculate the cost of living index for the following data:
Answer» ANSWER :`171.229`

Discussion

2697.	If A and B are any two sets, then A - B is equal to………….
Answer» ANSWER :`A CAP B'`

Discussion

2698.	The value of 2tan^(-1)(cosec(tan^(-1)x)-tan(cot^(-1)x)) is equal to
Answer» `cot^(-1)x` `cot^(-1)""1/x` `TAN^(-1)x` NONE of these Answer :C

Discussion

2699.	sec h^(-1)((2)/(3)) = log_(e)(((k+1) + sqrt(k^(2) +1))/(k)) then k =
Answer» 2 3 5 6 Answer :A

Discussion

2700.	If tan^(3) x + 3 gt 3 tan x + tan^(2) xthen
Answer» `X in (n pi + (pi)/(3), n pi + (pi)/(2)) cup (n pi - (pi)/(3), n pi + (pi)/(4)), n in Z` `x in (n pi + (pi)/(4), n pi + (pi)/(2)) cup (n pi - (pi)/( 4), n pi + (pi)/(4)), n in Z` `x in (n pi - (pi)/(6), n pi + (pi)/(2)) cup (n pi - (pi)/(4), n pi + (pi)/(4)), n in Z` `x in (n pi - (pi)/(3), n pi + (pi)/(2)) cup (n pi - (pi)/(4), n pi + (pi)/(4)), n in Z` ANSWER :A

Discussion

Explore topic-wise InterviewSolutions in .

The variable x satisfying the equation |sinxcosx|+sqrt(2+tan^(2)x+cot^(2))x=sqrt(3) belongs to the interval

Let A(1,0), B(-1,0), C(2, 0) then the locus of a point P such that PB^(2)+ PC^(2) = 2PA^(2) is

Find the standard deviation from the following datas, using assumed mean: (a) 112,117,121,125,130 (b) 37,43,48,34,41,39,46,40

If tan theta + sin theta = m and tan theta - sin theta = n, then

If A and B are any two events associated with an experiment, then

A and B are three mutuallyexclusive events . If P(A)=0.5and P(overline(B))=0.6,find P(A or B).

Find the deviation using median of the following observations: 15,19,20,28,16.

If satisfies the relation f(x+y)+f(x-y)=2 " " f(x).f(y) AA x , y in R and f(0) != 0, then f(10)-f(-10)=

If vec(a), vec(b) are collinear, then which of the following is false?

If f(x) is a function such that f(xy)=f(x)+f(y) and f(2)=1 then f(x)=

Show that |(1,1,1),(x,y,z),(x^(2),y^(2),z^(2))|=(x-y)(y-z)(z-x)

For each of the following compound statements, first identify the corresponding component statements. Then check whether the statements are true or not: If a triangle ABC is equilateral, then it is isosceles.

For each of the following compound statements, first identify the correspoinding component statements. Then check whether the statements are true or not: If a and b are integers, then ab is a rational number.

Let y=ax^(3) + bx^(2) + cx +d. Find the rate of change of y w.r.t x at x=0.

State true of false for the following: 2 is not a complex number.

Write down the first five terms of the sequence, whose nth term is (-1)^(n-1) , 5^(n+1)

If bara,barb,barc are unit vectors equally inclined to each other at an angle pi/3 then find the value of [baraxxbarb bar bxxbarc barcxxbara]

Write the contrapositive of the contrapositive of p implies q.

Evaluate the following limits in Exercises lim_(xto0)(cos (2x)-1)/(cosx-1)

Find n if : ""^(2n+1) P_(n-1): ""^(2n-1) P_n = 3: 5

(d)/(dx)(sqrt(sinx))=………..(0ltxlt (pi)/(2))

In the mean value theorem, f(b) - f(a) = (b-a) f(c ) , if a= 4, b = 9and f(x) =sqrt(x)then the value of c is

If the line (x/2+y/3-1)+lamda(2x+y-1)=0 is parallel to x-axis then lamda=

If bara,barb " are noncollinear unit vectors, " abs(bara+barb) =sqrt 3 " then " (2bara+5barb).(3bara-barb)=

Prove by direct method that for any real numbers x,y if x=y, then x^(2)=y^(2)

If x,y,z are chosen at random from the set (1,2,3) (repetition is allowed) .What is the probability that the equation x^(2)-yzge0 is satisfied.

The ratio between the circumradius and invadius of a right angled isosceles triangle is

sqrt(-5x^(8))- sqrt(-20x^(8)) + sqrt(-45x^(8)), where x is a positive real number

If the origin is the centroid of the tetrahedron for which (2,-1,3),(-1,3,1),(3,4,-2) are three vertices then fourth vertex is

A variable plane makes with the co-ordinates plane, tetrahedron of contant volume 64 k^3 Then the locus of the centroid of tetrahedron is the surface.

If A = {4,5,6,8,9}, B = {4,5,8} and C = {3,4,8,9} Find A cup B and B cup C

The set S_(1) and S_(2) are solution sets of (1 + a) cos theta cos ( 2 theta - b)= (1 + a cos 2 theta ) cos (theta - b)

For each of the following statements, determine whether an inclusive Or or exclusive or is used. Give reasons for your answer: Students can take French or Sanskrit as their third language.

Find the derivative of the w.r.t.x x log x log (log x)

For each of the following statements, determine whether an inclusive Or or exclusive or is used. Give reasons for your answer: To enter a country, you need a passport or a voter registration card.

For each of the following statements, determine whether an inclusive Or or exclusive or is used. Give reasons for your answer: Two lines intersect at a point or are parallel.

The total number of solutions of log_(e)|sinx|=-x^(2)+2x in [-pi/2,pi/2] is equal to

If 2( r+R ) = b+ c then A =

Find the derivative of the w.r.to x. x ^(tan x ) + (sin x ) ^( cos x)

Write the following sets in the set-builder form : {2,4,8,16,32}

Find all points of dicontinuity of f, where f(x)={{:((sinx)/(x)," if "x lt 0),(x+1," if "x ge 0):}.

If |a_1Sinx+a_(2)sin2x+.....+a_(n)sinx|le|sinx| for x in R then maimum value of |a_(1)+2a_(2)+3a_(3)+.....+na_(n)| is

A particle moves along a straight line according to the equation s = 8 cos 2t + 4sint. The initial velocity is

The sides of a triangle are the lines x+y=1, 7y=x, and sqrt3y+x=0, then which of the following are not interior points of triangle?

Calculate the cost of living index for the following data:

If A and B are any two sets, then A - B is equal to………….

The value of 2tan^(-1)(cosec(tan^(-1)x)-tan(cot^(-1)x)) is equal to

sec h^(-1)((2)/(3)) = log_(e)(((k+1) + sqrt(k^(2) +1))/(k)) then k =

If tan^(3) x + 3 gt 3 tan x + tan^(2) xthen