14949 + Interview Questions in Maths in Class 11 Page 58 InterviewSolution

2851.	If the graph of the function f(x)=(a^(x)-1)/(x^(n)(a^(x)+1)) is symmetrical about the y-axis, then 'n' equals
Answer» 2 `2/3` `1/4` `1/3` ANSWER :D

Discussion

2852.	If tanh^(2)(x)=tan^(2)theta then cosh(2x)=
Answer» `sec theta` COSEC`theta` `SIN theta` `COS theta` ANSWER :A

Discussion

2853.	x tan ( theta - (pi)/(6)) = y tan (theta + ( 2pi)/(3)) implies (x + y)/( x -y) =
Answer» `COS 2 THETA ` ` 2 cos 2 theta ` `SIN 2 theta ` `2 sin 2 theta ` ANSWER :B

Discussion

2854.	Equation of pair of lines through (0,0) and forming an equilateral triangle with the line x-3y+4=0 is
Answer» `23X^(2)+3Y^(2)-8xy=0` `13X^(2)-3y^(2)+12xy=0` `23x^(2)+3y^(2)-16xy=0` `23x^(2)+3y^(2)++48xy=0` ANSWER :D

Discussion

2855.	If A={x
Answer» 1 0 2 3 Answer :B

Discussion

2856.	whichofthefollowingsets in notfinite ? {(x,y):x^(2)+y^(2)le1lex+y,x,yin R}
Answer» `{(X,y):x^(2)+y^(2)le1le x+y, x,yin R]` `{(x,y):x^(2)=+ y^(2)le1le x+y, x,y in Z}` `{(x,y):x^(2)le yle \|x\|,x,y in Z}` `{(x,y):x^(2)le yle\|x\|,x,yin Z}` Solution :the set `{(x,y):x^(2)+y^(2)le1lex+y,x,yin R}` CONSISTS of all pointin thefirstquadrantwhichlieinsidethecircle`x^(2)+y^(2)=1`andabovethe line`x+y=1`. So it is NOTA finite set we have , `{(x,y):x^(2) +y^(2)=1,x=Z}={(0,1),(0,1),(-1,0),(0,-1)}` whichis afiniteset . hence, option(a)is correct .

Discussion

2857.	Prove that "Sin"^(-1)4/52"+Tan"^(-1)1/3=(pi)/2
Answer» ANSWER :40238

Discussion

2858.	Find the vertex and axis of the parabola x^(2)-4x-3y+7=0.
Answer» ANSWER :VERTEX (2,1), AXIS x=2

Discussion

2859.	Equation of a circle passing through (2, 8) and touching the lines 4x-3y-24=0 and4x+3y-42=0 having x-coordinates of the centre less than or equal to 8 is
Answer» `(x-2)^(2)+(y+3)^(2)=25` `(x-2)^(2)+(y-3)^(2)=16` `(x-2)^(2)+(y-3)^(2)=25` `(x+2)^(2)+(y-3)^(2)=25` Solution :Let centre of circle be C(a,b) Circle TOUCH both LINES `r= \|(4a-3b-24)/(5)\|=\|(4a+3b-42)/(5)\|= sqrt((a-2)^(2) + (b-8)^(2))` Solve these PAIR WISE b=3 and a=2, r=5 Equation of circle `(x-2)^(2) + (y-3)^(2)=25`.

Discussion

2860.	Let p be " I will marry her," and let q be " she is beautiful." Translate into symbolic form. If I will marry her, then she is beautiful.
Answer» <P> ANSWER :p => Q

Discussion

2861.	.......... is the y intersept of the line passes from point (2,2) and perpendicular to 3x+y=3.
Answer» `1/3` `2/3` `1` `4/3` ANSWER :D

Discussion

2862.	Match List - I with List II {:("List I","ListII"),("i"."" {(1,1) (2,2)(3,3)(1,2)},(b) """equivalence"),("ii"."" {(1,2) (2,1)(2,3)(3,2)},(b)"" "transitive"),("iii"."" {(1,1) (2,3)(1,3)},(c) """Symmetric"),("iv."""{(1,1) (2,2)(3,3)(1,2)(2,1)(2,3)(1,3)},(d) "" "reflexive"):}
Answer» C d B a d c b a b a d c b a b c ANSWER :A::B::C::D

Discussion

2863.	Find the sum of n terms of G.P where first term is a and common ratio is r.
Answer»

Discussion

2864.	If a dieis rolled three times then the probability of gettinha larger numberon its face the
Answer» `(15)/(216)` `(5)/(54)` `(13)/(216)` `(1)/(18)` Answer :B

Discussion

2865.	Let A_(1), A_(2), …… A_(n) be the vertices of an n-sided regular polygon such that 1/(A_(1)A_(2)) = 1/(A_(1)A_(3)) + 1/(A_(1)A_(4)). Find the value of n.
Answer» 7 8 9 10 Answer :a

Discussion

2866.	Compute the following limits. Lt_(xtooo)(3x^(5)-1)/(9x^(5)+1)
Answer» ANSWER :1/3

Discussion

2867.	Show that the line x + ny + an ^(2) =0 touches the parabola y ^(2) = 4 ax and find the point of contact.
Answer» ANSWER :`(an ^(2) , 2an)`

Discussion

2868.	Evaluate the following limits : Lim_(x to 0) (tan. 1/2x)/(3x)
Answer» ANSWER :`1/6`

Discussion

2869.	If tan^(-1)((x+1)/(x-1))+tan^(-1)((x-1)/x)=pi+tan^(-1)(-7), then x=
Answer» `2` `-2` `1` No solution Answer :A

Discussion

2870.	Is the given relation a function? Give reason for your answer. s= {(x,x^(2))\|x is a positive integer}
Answer» ANSWER :It is a FUNCTION

Discussion

2871.	What is the intercept on z - axis of the plane x+y+2z=2.
Answer» ANSWER :1

Discussion

2872.	The minimum distance of a point on the curve y=x^(2)-4 from the origin is :
Answer» `(SQRT(15))/(2)` `sqrt((19)/(2))` `sqrt((15)/(2))` `sqrt((19))/(2) ANSWER :A

Discussion

2873.	To the equation 2^(2pi//cos^(-1)x)-(a+1/2)2^(pi//cos^(-1)x)-a^(2)=0 has only real root, then
Answer» `1leale3` `bge1` `ale-3` `AGE3` ANSWER :B::C::D

Discussion

2874.	Evaluate the following limits : Lim_(xto3) (x^(2)-9) (1/(x+3)+1/(x-3))
Answer» ANSWER :6

Discussion

2875.	Write the negation of the following simple statements. Violets are blue.
Answer» ANSWER :VIOLETS are not BLUE.

Discussion

2876.	Find the sum of n terms of each of the following 1 +5 + 12 + 22+ 35+…….
Answer» ANSWER :`(N^(2) (n+1))/(2)`

Discussion

2877.	If f(x)=ax^(7)+bx^(3)+cx-5, a, b, c are real constants, and f(-7)=7, then the range of f(7)+17 cos x is
Answer» `[-34, 0]` `[0, 34]` `[-34, 34]` `[34, OO)` ANSWER :A

Discussion

2878.	Find the maximum and minimum values, if any, of the functions given by f (x) = (2x – 1)^(2)+ 3
Answer» ANSWER :MINIMUM VALUE = 0, at `x=1/2`

Discussion

2879.	Evaluate the limits : Lim_(theta to pi/6) (cot^(2) theta - 3)/(" cosec " theta - 2)
Answer» ANSWER :4

Discussion

2880.	Compute the following limits. Lt_(xtooo)(1+4x^(2))/(1-x^(2))
Answer» ANSWER :-4

Discussion

2881.	What is the (r+1)^(th) term in the expansion of(3x+2y)^8?
Answer» SOLUTION :`T_(r+1)="^8C_r3^(8-r).2^r.x^(8-r).y^r`

Discussion

2882.	Find the range of the following function h: N rarr R, h (x)= x- [x]
Answer» ANSWER :{0}

Discussion

2883.	Find the values of x for which the inequality (8x^(2)+16x-51)/((2x-3)(x+4))gt3 holds.
Answer» ANSWER :`(-OO,-4)UU(-3,3/2)uu(5/2,oo)`

Discussion

2884.	Let P(x, y) be any point on the locus then observe the following lists The correct matching is
Answer» `{:(A,B,C,D),(1,2,3,4):}` `{:(A,B,C,D),(1,5,3,4):}` `{:(A,B,C,D),(1,2,4,3):}` `{:(A,B,C,D),(2,1,3,5):}` ANSWER :1

Discussion

2885.	A(3x_(1), 3y_(1)), B(3x_(2), 3y_(2)), C(3x_(3), 3y_(3)) are vertices of a triangle with orthocentre H at (x_(1)+ x_(2)+ x_(3), y_(1)+y_(2)+y_(3)), then the angleABC=
Answer» `(PI)/(2)` `(pi)/(3)` `(pi)/(6)` `(pi)/(4)` ANSWER :B

Discussion

2886.	Show that the point (x,y) given by x = (2at)/(1 + t^(2)) and y = (a(1-t^(2)))/(1+t^(2)) lies on a circle for all real values of t such that -1 lt t lt 1 where a is any given real numbers.
Answer» ANSWER :`a^(2)`

Discussion

2887.	If the pairs of lines 3x^2-2pxy-3y^2=0 and 5x^2-2qxy-5y^2=0 are such that each pair bisects the angle between the pair, then pq equals to
Answer» -1 -7 -9 -15 Answer :D

Discussion

2888.	Let f:(-1,1) to B, be a function defined by f(x) = tan^(-1)((2x)/(1-x^(2))), then f is both one-one and onto when B is the interval.
Answer» `(0, pi/2)` `[0, pi/2)` `[ - pi/2, pi/2]` `( - pi/2, pi/2)` ANSWER :D

Discussion

2889.	( a cot A + b cot B + c cot C )/( a + b+ c)
Answer» ` ( R- R) /( 2S) ` ` ( r+ R) /( 2s) ` ` ( r- R) /( s) ` ` ( r+ R ) /( s) ` ANSWER :D

Discussion

2890.	A bag contains 8 red and 5 white balls. Three balls are drawn at random. Find the Probability that One ball is red and two balls are white
Answer» ANSWER :`(40)/(143)`

Discussion

2891.	The minimum value of 4x^2+3/x^2 is
Answer» `3sqrt4` `2SQRT3` `3sqrt2` `4sqrt3` ANSWER :D

Discussion

2892.	If f(g(x)) = x and g(f(x)) = x then g(x) is the inverse of f(x) . (g'(x))f'(x) = 1 implies g'(f(x))=1/(f'(x)) Let us consider a real value bijective function g(x)sun that g'(x) = sin^2 (x+pi/4) +2 cos (x -pi/4) and g(pi/4) =3 then value of (g^(-1))(3) is
Answer» `1/5` `1/2` `1/3` 0 Answer :D

Discussion

2893.	(sin3theta)/(1+2cos2theta)=
Answer» `COSTHETA` `SINTHETA` `-costheta` `-sintheta` ANSWER :B

Discussion

2894.	If cos h 2x = 99 then tan h x =
Answer» `(5)/(7sqrt(2))` `(7)/(5sqrt(2))` `(5sqrt(7))/(2)` `(7sqrt(5))/(2)` ANSWER :B

Discussion

2895.	Given that tan A = (1)/(5). find the values of tan 2 A, tan 4A andtan (45 ^(@) - 4A).
Answer» ANSWER :`(24)/(25)`

Discussion

2896.	If P (n) = 1+2+3+ …. + nis a perfect square N^(2) and N is less than 100, then possible values of n are
Answer» only 1 1 and 8 only 8 `1, 8, 49` ANSWER :D

Discussion

2897.	Three cards are drawn fromadeck of 52 cards . Whatis the probability thatthey are all red cards ?
Answer» ANSWER :`(""^(26)C_(3))/(""^(52)C_(3))=(2)/(17)`

Discussion

2898.	Ify = log ((x)/(a+bx)) , then x^3 (d^2y)/(dx^2)=
Answer» `x(DY)/(DX)-x` `(x(dy)/(dx)-y)^2` `y(dy)/(dx)-x` `(y(dy)/(dx)-x)^2` Answer :B

Discussion

2899.	If the sum of n terms of an A.P. is 3n^(2) + 5n and its m^(th) term is 164, find the value of m.
Answer» ANSWER :27

Discussion

2900.	Find in the blanks in following table :
Answer» ANSWER :0.15

Discussion

Explore topic-wise InterviewSolutions in .

If the graph of the function f(x)=(a^(x)-1)/(x^(n)(a^(x)+1)) is symmetrical about the y-axis, then 'n' equals

If tanh^(2)(x)=tan^(2)theta then cosh(2x)=

x tan ( theta - (pi)/(6)) = y tan (theta + ( 2pi)/(3)) implies (x + y)/( x -y) =

Equation of pair of lines through (0,0) and forming an equilateral triangle with the line x-3y+4=0 is

If A={x

whichofthefollowingsets in notfinite ? {(x,y):x^(2)+y^(2)le1lex+y,x,yin R}

Prove that "Sin"^(-1)4/52"+Tan"^(-1)1/3=(pi)/2

Find the vertex and axis of the parabola x^(2)-4x-3y+7=0.

Equation of a circle passing through (2, 8) and touching the lines 4x-3y-24=0 and4x+3y-42=0 having x-coordinates of the centre less than or equal to 8 is

Let p be " I will marry her," and let q be " she is beautiful." Translate into symbolic form. If I will marry her, then she is beautiful.

.......... is the y intersept of the line passes from point (2,2) and perpendicular to 3x+y=3.

Match List - I with List II {:("List I","ListII"),("i"."" {(1,1) (2,2)(3,3)(1,2)},(b) """equivalence"),("ii"."" {(1,2) (2,1)(2,3)(3,2)},(b)"" "transitive"),("iii"."" {(1,1) (2,3)(1,3)},(c) """Symmetric"),("iv."""{(1,1) (2,2)(3,3)(1,2)(2,1)(2,3)(1,3)},(d) "" "reflexive"):}

Find the sum of n terms of G.P where first term is a and common ratio is r.

If a dieis rolled three times then the probability of gettinha larger numberon its face the

Let A_(1), A_(2), …… A_(n) be the vertices of an n-sided regular polygon such that 1/(A_(1)A_(2)) = 1/(A_(1)A_(3)) + 1/(A_(1)A_(4)). Find the value of n.

Compute the following limits. Lt_(xtooo)(3x^(5)-1)/(9x^(5)+1)

Show that the line x + ny + an ^(2) =0 touches the parabola y ^(2) = 4 ax and find the point of contact.

Evaluate the following limits : Lim_(x to 0) (tan. 1/2x)/(3x)

If tan^(-1)((x+1)/(x-1))+tan^(-1)((x-1)/x)=pi+tan^(-1)(-7), then x=

Is the given relation a function? Give reason for your answer. s= {(x,x^(2))|x is a positive integer}

What is the intercept on z - axis of the plane x+y+2z=2.

The minimum distance of a point on the curve y=x^(2)-4 from the origin is :

To the equation 2^(2pi//cos^(-1)x)-(a+1/2)2^(pi//cos^(-1)x)-a^(2)=0 has only real root, then

Evaluate the following limits : Lim_(xto3) (x^(2)-9) (1/(x+3)+1/(x-3))

Write the negation of the following simple statements. Violets are blue.

Find the sum of n terms of each of the following 1 +5 + 12 + 22+ 35+…….

If f(x)=ax^(7)+bx^(3)+cx-5, a, b, c are real constants, and f(-7)=7, then the range of f(7)+17 cos x is

Find the maximum and minimum values, if any, of the functions given by f (x) = (2x – 1)^(2)+ 3

Evaluate the limits : Lim_(theta to pi/6) (cot^(2) theta - 3)/(" cosec " theta - 2)

Compute the following limits. Lt_(xtooo)(1+4x^(2))/(1-x^(2))

What is the (r+1)^(th) term in the expansion of(3x+2y)^8?

Find the range of the following function h: N rarr R, h (x)= x- [x]

Find the values of x for which the inequality (8x^(2)+16x-51)/((2x-3)(x+4))gt3 holds.

Let P(x, y) be any point on the locus then observe the following lists The correct matching is

A(3x_(1), 3y_(1)), B(3x_(2), 3y_(2)), C(3x_(3), 3y_(3)) are vertices of a triangle with orthocentre H at (x_(1)+ x_(2)+ x_(3), y_(1)+y_(2)+y_(3)), then the angleABC=

Show that the point (x,y) given by x = (2at)/(1 + t^(2)) and y = (a(1-t^(2)))/(1+t^(2)) lies on a circle for all real values of t such that -1 lt t lt 1 where a is any given real numbers.

If the pairs of lines 3x^2-2pxy-3y^2=0 and 5x^2-2qxy-5y^2=0 are such that each pair bisects the angle between the pair, then pq equals to

Let f:(-1,1) to B, be a function defined by f(x) = tan^(-1)((2x)/(1-x^(2))), then f is both one-one and onto when B is the interval.

( a cot A + b cot B + c cot C )/( a + b+ c)

A bag contains 8 red and 5 white balls. Three balls are drawn at random. Find the Probability that One ball is red and two balls are white

The minimum value of 4x^2+3/x^2 is

If f(g(x)) = x and g(f(x)) = x then g(x) is the inverse of f(x) . (g'(x))f'(x) = 1 implies g'(f(x))=1/(f'(x)) Let us consider a real value bijective function g(x)sun that g'(x) = sin^2 (x+pi/4) +2 cos (x -pi/4) and g(pi/4) =3 then value of (g^(-1))(3) is

(sin3theta)/(1+2cos2theta)=

If cos h 2x = 99 then tan h x =

Given that tan A = (1)/(5). find the values of tan 2 A, tan 4A andtan (45 ^(@) - 4A).

If P (n) = 1+2+3+ …. + nis a perfect square N^(2) and N is less than 100, then possible values of n are

Three cards are drawn fromadeck of 52 cards . Whatis the probability thatthey are all red cards ?

Ify = log ((x)/(a+bx)) , then x^3 (d^2y)/(dx^2)=

If the sum of n terms of an A.P. is 3n^(2) + 5n and its m^(th) term is 164, find the value of m.

Find in the blanks in following table :