14949 + Interview Questions in Maths in Class 11 Page 108 InterviewSolution

5351.	Sum the series to infinity : 16 ,-8,4 , .....
Answer» ANSWER :`(32)/(3)`

Discussion

5352.	If log4=1.3868 then log(4.01)=
Answer» 1.3843 1.3893 1.3968 1.3768 Answer :B

Discussion

5353.	A survey shows that 63% of the people watch a news channel where as 76% watch another channel. If x% of the people watch both channel then,
Answer» `X= 35` `x= 63` `39 le x le 63` `x= 39` ANSWER :C

Discussion

5354.	A point P moves so that the sum of its distance from the points (ae, 0), (-ae, o) is 2a. The locus of the point P is (0ltelt1)
Answer» `(X^(2))/(a^(2))-(y^(2))/(a^(2)(1+e^(2)))=1` `(x^(2))/(a^(2))+(y^(2))/(a^(2)(1+e^(2)))=1` `(x^(2))/(a^(2))-(y^(2))/(a^(2)(1-e^(2)))=1` `(x^(2))/(a^(2))+(y^(2))/(a^(2)(1-e^(2)))=1` ANSWER :4

Discussion

5355.	Cos((pi)/(4)+A).Cos((pi)/(4)-B)-Sin((pi)/(4)+A).Sin((pi)/(4)-B)=
Answer» COS(A+B) Cos(A-B) SIN(A+B) Sin(B-A) ANSWER :D

Discussion

5356.	Let A(1, 2),B(3, 4) are two vertices of a DeltaABC. The third vertex C moves along L=7x+ 5y-10=0. The locus of the centroid of DeltaABC is
Answer» `21x+15y-68 =0` `7X + 5y -4 = 0` `7x + 5y +68=0` `7x+ 5y-17=0` ANSWER :1

Discussion

5357.	If the distance from (1,2,4) to the plane 2x+2y-z+k=0 is 3, then k =
Answer» 4 5 7 11 Answer :C

Discussion

5358.	Find the coefficient of x^10 in the expansion of (2x^2- 3/x)^11 , x ne0 Also , prove that there is no term involving x^6
Answer» ANSWER :3421440

Discussion

5359.	If sin theta + sin^(2) theta =1 then cos^(4) theta + cos^(8) theta + 2 cos^(6) theta =
Answer» 1 `1//2` `3//4` 2 Answer :A

Discussion

5360.	Find the equation of the circle which has radius 5 units and which is tangent to the line 3x+4y-16=0 at the point (4, 1).
Answer» SOLUTION :N/A

Discussion

5361.	Equation of the plane containing the lines vec(r )= vec(i) + 2vec(j) -vec(k) + lamda (vec(i) + 2vec(j)-vec(k)), vec(r )=vec(i) + 2vec(j) -vec(k)+ mu (vec(i) + vec(j) + 3vec(k)) is
Answer» `vec(r).(7vec(i)-4vec(J)-vec(k))=0` `vec( r).(vec(i)+2vec(j)-vec(k))=0` `vec( r).(vec(i) + vec(j) + 3vec(k))=0` `vec(r ).(vec(i) + vec(j))= 0` ANSWER :A

Discussion

5362.	(sin h (2x))/(1 + cos h(2x))=
Answer» TAN H(x) tan `h^(2) (x)` cot h(x) cot `h^(2) (x)` ANSWER :A

Discussion

5363.	How many numbers are tehre in all which consist of 5 digits?
Answer» ANSWER :` 9 XX 10 ^(4) = 90,000`

Discussion

5364.	If f(x) = (2x + 3 sin x)/( 3x + 2 sin x), x ne0is continuous at x = 0 , then find f(0)
Answer» ANSWER :F(0) = 1

Discussion

5365.	Let A(0,0), B (5,0), C (5,3) and D(0,3) be the vertice of rectiangle ABCD , If P is a variable point lying inside the rectangle ABCD and d (P,L) denotes perpendicular distance of point P from line L Ifle min{d(P,BC),d(P,CD),d(P,AD)}, then area of the region in which P lies is (in sq. units
Answer» `17/4` `19/4` `21/4` `23/4` ANSWER :C

Discussion

5366.	Let A(0,0), B (5,0), C (5,3) and D(0,3) be the vertice of rectiangle ABCD , If P is a variable point lying inside the rectangle ABCD and d (P,L) denotes perpendicular distance of point P from line L If(d(P,AB)-(3)/2)^2 +(d(P,AD))^2ge1, then area of region in which P lies is (in sq.units)
Answer» `15-2pi` `10-pi/2` `15-pi` `15-pi/2` ANSWER :D

Discussion

5367.	Let A(0,0), B (5,0), C (5,3) and D(0,3) be the vertice of rectiangle ABCD , If P is a variable point lying inside the rectangle ABCD and d (P,L) denotes perpendicular distance of point P from line L If d(P,AB)gemx[d(P,BC),d(P,CD),d(P,AD)], then the area of the region in which P lies (in sq. units)
Answer» 1 `1//2` `3//4` `1//4` ANSWER :D

Discussion

5368.	Prove that (1+cos(A-B)cosC)/(1+cos(A-C)cosB)=(a^(2)+b^(2))/(a^(2)+c^(2))
Answer» `(a^(2)+B^(2))/(b^(2)+C^(2))` `(a^(2)+b^(2))/(a^(2)+c^(2))` `(a^(2)-b^(2))/(b^(2)-c^(2))` `(a^(2)-b^(2))/(a^(2)-c^(2))` ANSWER :B

Discussion

5369.	Find the condition that one root of ax^(2)+bx+c=0 may be (i) three tiems the other, (ii) n times the other, (iii) more than the other by h.
Answer» Answer :(i) `3B^(2)=16ac`, (ii) `B^(2)n=ac(1+n)^(2)`, (III) `a^(2)h^(2)=b^(2)-4ac`.

Discussion

5370.	Area of the circlex^(2) + y^(2)+ 2 cos thetasin phi * x + 2 sin phi * y - cos^(2) phi = 0, is
Answer» `(PI)/(2)` `4PI` `9pi` `pi` SOLUTION :N/A

Discussion

5371.	Find the number of ways of selecting 9 ball from 6 red balls, 5 white balls and 5 blue balls if each selection consists of 3 balls of each colour.
Answer» ANSWER :2000

Discussion

5372.	2sin^(2)(8(1^(0))/(2))+4 cos 16^(0) sin(7(1^(0))/(2)) sin (8(1^(0))/(2))+cos32^(0)=
Answer» `(sqrt(3)-1)/(2 sqrt(2))` `(sqrt(3)+1)/(2 sqrt(2))` `2-sqrt(3)` `2+sqrt(3)` ANSWER :B

Discussion

5373.	Find the most general value of theta that satisfying both the equations "cosec" theta = -2, cot theta = -sqrt(3)
Answer» ANSWER :`2NPI + (11pi)/(6)`

Discussion

5374.	Show that r_1( s-a) = r_2 (s-b) =r_3 (s-c) = Delta
Answer» ANSWER :` THEREFORE r_1( s-a) = r_2 ( s-b) = r_3(s-c) = DELTA `

Discussion

5375.	sin alpha + sin beta= 1/4 and cos alpha + cos beta = 1/3 The value of sin (alpha + beta)is
Answer» `24/25` `13/25` `12/13` NONE of these ANSWER :A

Discussion

5376.	Find the multiplicative inverse of each of the following complex numbers when it exists. ((2 + 3i) (3 + 2i)i)/(5+ i)
Answer» ANSWER :`(-5-i)/(13)`

Discussion

5377.	Assertion (A) : cos x = (-1)/(2) and 0 lt x lt 2pi, "then the solutions are x" = (2pi)/(3), (4pi)/(3). Reason (R ) : cos is negative in the first and fourth quadrant only
Answer» Both A and ( R)are trueand ( R)is the correctexplantion of (A) Both A and Rare truebut ( R) is not thecorrectexplantionof A A is true R is FALSE A is falseR is true ANSWER :C

Discussion

5378.	The marks in Physics and Biology of 12 students in a public examination are as follows : {:("Physics",69,36,39,71,67,76,40,20,85,65,55,34),("Biology",33,52,71,25,79,22,83,81,24,35,46,64):} Calculate the coefficient of rank correlation. What conclusioncan be madefrom the result ?
Answer» Answer :`-0.78` , HIGH degree NEGATIVE correlation i.e., a very good student in PHYSICS a poor student in BIOLOGY.

Discussion

5379.	Find the number of point where a)f(x) = [x] + \|1- x\|, - 1 ge x ge 3 b)g(x) = a^([x^(2)]) , a gt 1, 1 lt x lt 3 c)h (x) = [ 2cos x ] , x in [ 0 , 2 pi]is discontinuous ([.] denotes the G.I.F)
Answer» Answer :`5,x=-1,0,1,2,4` (B)`7X,= SQRT(2), sqrt(3),2,.... sqrt(8)` (C) `8;x=0 (pi)/(3),(pi)/(2),(2pi)/(3),(3pi)/(2),(4pi)/(3),(5pi)/(3),2pi`.

Discussion

5380.	Find the derivative of the function from first principle x ^(4) + 4
Answer» ANSWER :`4X ^(3)`

Discussion

5381.	If (tanx)/(1)=(tany)/(2)=(tanz)/(3)(ne0)andx+y+z=pi then which of the following is false?
Answer» `tanx=pm1, tany=pm2, tanz=pm3` `tanx+tany+tanz=0` `tanx+tany+tanz`, MAXIMUM VALUE 6 `tanx+tany+tanz`, MINIMUM value `-6` ANSWER :B

Discussion

5382.	If g:[-2,2] rarr R, where g(x)=x^(3)+tan x [(x^(2)+1)/(P)] is an odd function, then the value of parametric P, where [.] denotes the greatest integer function, is
Answer» `-5 LT P lt 5` `P lt 5` `P GT 5` `P gt 5` ANSWER :C

Discussion

5383.	Find angles between the lines sqrt(3) x +y=1 and x+ sqrt(3) y=1.
Answer» ANSWER :Angle between TWO lines is `THETA= (pi)/(6)` OR `theta = (5pi)/( 6)`.

Discussion

5384.	cos h^(4) (x) - sin h^(4)(x) =
Answer» COS H x cos h 2x sin h x sin h 2x Answer :B

Discussion

5385.	Iff(x) = x -[x]then f(x) at x= 2 f(x) is
Answer» RIGHT CONTINUOUS left continuous not DETERMINED continuous ANSWER :A

Discussion

5386.	Find the slope of the lines making inclination of 60^(@) with the postive direction of x-axis ?
Answer» ANSWER :`SQRT 3`

Discussion

5387.	If [x] denote the greatest integer less than or equal to x then in order that the set of equations x - 3y = 5, 5x + y = 2, [2pi[ x - [e] y = [2a] may be consistent then 'a' should lie in
Answer» `[3, 7//2)` `(3, 7//3)` `(3, 7//3]` NONE of these Answer :A

Discussion

5388.	sin x + co x = 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)` `(- INFTY, - sqrt(3))` `( sqrt(3), infty)` ANSWER :D

Discussion

5389.	Find the equation of straight lines passing through (1,2) and making an angle 60^(@) with the line sqrt(3)x+y+2=0.
Answer» ANSWER :`y=2,SQRT(3)x-y+2-sqrt(3)=0`

Discussion

5390.	Consider the real values function 2 f(sin x ) + f(cos x) = x, then f(1/2)=
Answer» 1 2 0 4 Answer :C

Discussion

5391.	In Delta ABC, sum (a+b) tan ((A-B)/2)=
Answer» `2` ` -1` ` 1 ` ` 0` ANSWER :D

Discussion

5392.	Find the domain of definition of thefunction y(x), given by the equation 2^(x)+2^(y)=2.
Answer» `0 lt X LE 1` `0 le x le 1` `- oo lt x LE0` `-oo lt x LT1` Answer :D

Discussion

5393.	Evaluate :""((12!)-(10!)) / (9!)
Answer» ANSWER :1310

Discussion

5394.	\|z_(1)+z_(2)\|=\|z_(1)\|+\|z_(2)\| is possible, if
Answer» `z_(2)=barz_(1)` `z_(2)=(1)/(z_(1))` `ARG (z_(1))=arg(z_(2))` `\|z_(1)\|-\|z_(2)\|` Answer :C

Discussion

5395.	The centroid of the triangle with verticies A(1, 1, 1), B(2, 1, 2) and C(x, y, z) is O(0, 0, 0) then (x, y, z) = ______ .
Answer» ANSWER :`(-3,-2,-3)`

Discussion

5396.	If sinx+siny=sqrt(3)(cosy-cosx), then (sin3x+sin3y)=?
Answer» 1 `-1` 0 None of these Solution :N//A

Discussion

5397.	Evaluate Lt_(xto0)(cosx)^(cotx)
Answer» ANSWER :1

Discussion

5398.	If (sin x) (cos y) = 1//2then (d^2y)/(dx^2)at ((pi)/4"," (pi)/4) is equal to
Answer» `-4` `-2` `-6` `0` ANSWER :A

Discussion

5399.	The real solutions of the equation cos^(7)x+sin^(4)x=1 in (-pi,pi) are ………….
Answer» `0,(PI)/(3),-(pi)/(3)` `0,(pi)/(4),-(pi)/(4)` `0,(pi)/(2),-(pi)/(2)` `(pi)/(2),(pi)/(3),(pi)/(4)` ANSWER :C

Discussion

5400.	The number of ways in which we can choose a committee from four men and six women, so that the committee includes atleast two men and exactly twice as many women as men is
Answer» 94 125 128 None of these Answer :D

Discussion

Explore topic-wise InterviewSolutions in .

Sum the series to infinity : 16 ,-8,4 , .....

If log4=1.3868 then log(4.01)=

A survey shows that 63% of the people watch a news channel where as 76% watch another channel. If x% of the people watch both channel then,

A point P moves so that the sum of its distance from the points (ae, 0), (-ae, o) is 2a. The locus of the point P is (0ltelt1)

Cos((pi)/(4)+A).Cos((pi)/(4)-B)-Sin((pi)/(4)+A).Sin((pi)/(4)-B)=

Let A(1, 2),B(3, 4) are two vertices of a DeltaABC. The third vertex C moves along L=7x+ 5y-10=0. The locus of the centroid of DeltaABC is

If the distance from (1,2,4) to the plane 2x+2y-z+k=0 is 3, then k =

Find the coefficient of x^10 in the expansion of (2x^2- 3/x)^11 , x ne0 Also , prove that there is no term involving x^6

If sin theta + sin^(2) theta =1 then cos^(4) theta + cos^(8) theta + 2 cos^(6) theta =

Find the equation of the circle which has radius 5 units and which is tangent to the line 3x+4y-16=0 at the point (4, 1).

Equation of the plane containing the lines vec(r )= vec(i) + 2vec(j) -vec(k) + lamda (vec(i) + 2vec(j)-vec(k)), vec(r )=vec(i) + 2vec(j) -vec(k)+ mu (vec(i) + vec(j) + 3vec(k)) is

(sin h (2x))/(1 + cos h(2x))=

How many numbers are tehre in all which consist of 5 digits?

If f(x) = (2x + 3 sin x)/( 3x + 2 sin x), x ne0is continuous at x = 0 , then find f(0)

Let A(0,0), B (5,0), C (5,3) and D(0,3) be the vertice of rectiangle ABCD , If P is a variable point lying inside the rectangle ABCD and d (P,L) denotes perpendicular distance of point P from line L Ifle min{d(P,BC),d(P,CD),d(P,AD)}, then area of the region in which P lies is (in sq. units

Let A(0,0), B (5,0), C (5,3) and D(0,3) be the vertice of rectiangle ABCD , If P is a variable point lying inside the rectangle ABCD and d (P,L) denotes perpendicular distance of point P from line L If(d(P,AB)-(3)/2)^2 +(d(P,AD))^2ge1, then area of region in which P lies is (in sq.units)

Let A(0,0), B (5,0), C (5,3) and D(0,3) be the vertice of rectiangle ABCD , If P is a variable point lying inside the rectangle ABCD and d (P,L) denotes perpendicular distance of point P from line L If d(P,AB)gemx[d(P,BC),d(P,CD),d(P,AD)], then the area of the region in which P lies (in sq. units)

Prove that (1+cos(A-B)cosC)/(1+cos(A-C)cosB)=(a^(2)+b^(2))/(a^(2)+c^(2))

Find the condition that one root of ax^(2)+bx+c=0 may be (i) three tiems the other, (ii) n times the other, (iii) more than the other by h.

Area of the circlex^(2) + y^(2)+ 2 cos thetasin phi * x + 2 sin phi * y - cos^(2) phi = 0, is

Find the number of ways of selecting 9 ball from 6 red balls, 5 white balls and 5 blue balls if each selection consists of 3 balls of each colour.

2sin^(2)(8(1^(0))/(2))+4 cos 16^(0) sin(7(1^(0))/(2)) sin (8(1^(0))/(2))+cos32^(0)=

Find the most general value of theta that satisfying both the equations "cosec" theta = -2, cot theta = -sqrt(3)

Show that r_1( s-a) = r_2 (s-b) =r_3 (s-c) = Delta

sin alpha + sin beta= 1/4 and cos alpha + cos beta = 1/3 The value of sin (alpha + beta)is

Find the multiplicative inverse of each of the following complex numbers when it exists. ((2 + 3i) (3 + 2i)i)/(5+ i)

Assertion (A) : cos x = (-1)/(2) and 0 lt x lt 2pi, "then the solutions are x" = (2pi)/(3), (4pi)/(3). Reason (R ) : cos is negative in the first and fourth quadrant only

The marks in Physics and Biology of 12 students in a public examination are as follows : {:("Physics",69,36,39,71,67,76,40,20,85,65,55,34),("Biology",33,52,71,25,79,22,83,81,24,35,46,64):} Calculate the coefficient of rank correlation. What conclusioncan be madefrom the result ?

Find the number of point where a)f(x) = [x] + |1- x|, - 1 ge x ge 3 b)g(x) = a^([x^(2)]) , a gt 1, 1 lt x lt 3 c)h (x) = [ 2cos x ] , x in [ 0 , 2 pi]is discontinuous ([.] denotes the G.I.F)

Find the derivative of the function from first principle x ^(4) + 4

If (tanx)/(1)=(tany)/(2)=(tanz)/(3)(ne0)andx+y+z=pi then which of the following is false?

If g:[-2,2] rarr R, where g(x)=x^(3)+tan x [(x^(2)+1)/(P)] is an odd function, then the value of parametric P, where [.] denotes the greatest integer function, is

Find angles between the lines sqrt(3) x +y=1 and x+ sqrt(3) y=1.

cos h^(4) (x) - sin h^(4)(x) =

Iff(x) = x -[x]then f(x) at x= 2 f(x) is

Find the slope of the lines making inclination of 60^(@) with the postive direction of x-axis ?

If [x] denote the greatest integer less than or equal to x then in order that the set of equations x - 3y = 5, 5x + y = 2, [2pi[ x - [e] y = [2a] may be consistent then 'a' should lie in

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

Find the equation of straight lines passing through (1,2) and making an angle 60^(@) with the line sqrt(3)x+y+2=0.

Consider the real values function 2 f(sin x ) + f(cos x) = x, then f(1/2)=

In Delta ABC, sum (a+b) tan ((A-B)/2)=

Find the domain of definition of thefunction y(x), given by the equation 2^(x)+2^(y)=2.

Evaluate :""((12!)-(10!)) / (9!)

|z_(1)+z_(2)|=|z_(1)|+|z_(2)| is possible, if

The centroid of the triangle with verticies A(1, 1, 1), B(2, 1, 2) and C(x, y, z) is O(0, 0, 0) then (x, y, z) = ______ .

If sinx+siny=sqrt(3)(cosy-cosx), then (sin3x+sin3y)=?

Evaluate Lt_(xto0)(cosx)^(cotx)

If (sin x) (cos y) = 1//2then (d^2y)/(dx^2)at ((pi)/4"," (pi)/4) is equal to

The real solutions of the equation cos^(7)x+sin^(4)x=1 in (-pi,pi) are ………….

The number of ways in which we can choose a committee from four men and six women, so that the committee includes atleast two men and exactly twice as many women as men is