14949 + Interview Questions in Maths in Class 11 Page 122 InterviewSolution

6051.	If f(x) +2f(1/x) =3x, x ne 0 and S={x in R//f (x) =f(-x)}, then S is:
Answer» contains exactly ONE element contains exactly TWO element contain more than two element is an EMPTY set Answer :B

Discussion

6052.	10 arithmetic mean between a and b are A_(1),A_(2),A_(3).........A_(10) then A_1+A_2+A_3+...........+A_(10)=........
Answer» ANSWER :6 (a +B) 5 (a + b)

Discussion

6053.	If the lines joining the origin to the points of intersection of a line L and x^(2)+y^(2)=4 are coordinate axes then equation of L is
Answer» x+y=4 x+y=1 x+y=2 x-y=1 Answer :C

Discussion

6054.	Write the following sets in roster form: E = The set of all letters in the word TRIGONOMETRY
Answer» ANSWER :`E= T, R, I, G, O, N, M, E, Y`

Discussion

6055.	If sin^(-1)x+sin^(-1)y=pi/2 , then (dy)/(dx) is equal to
Answer» `x/y` `-x/y` `y/x` `-y/x` ANSWER :B

Discussion

6056.	Solve 3tan^(4)alpha-10tan^(2)alpha+3=0
Answer» ANSWER :`{npipm(PI)/(3)}UU{npipm(pi)/(6)}`

Discussion

6057.	Define Power
Answer» Solution :POWER is defined as the RATE of work DONE or energy delivered. ` "Power" = (" work done(W)")/(" time taken (t) ") = vecF . vecv`

Discussion

6058.	The transformed eqution of x^(2)+y^(2)+z^(2)-6x-8y+2z+24 = 0 when the axes are transtated to the point (3,4,-1) is
Answer» `X^(2)+y^(2)+z^(2) =25` `x^(2)+y^(2)+z^(2) =2` `x^(2)-y^(2)+z^(2) =25` `x^(2)+y^(2)-z^(2) =50` ANSWER :B

Discussion

6059.	A system of lines is given as y=m_1x+c_1,"where " m_1can take any value out of 0,1,-1 and when m_1 is positive , then c1 can be 1 or -1 when m_1 equal 0, c_1 can be 0 or 1 and when m_1 equals to -1 c_1 can take 0 or 2. Then the area enclosed by all these staight lines is
Answer» `3/sqrt2(sqrt2-1)` squnit `3/sqrt2` SQ UNIT `3/2` sq unit `3/sqrt2(sqrt2+1)` squnit Answer :C

Discussion

6060.	If (1,2,-2) are the D.R's of a line then Statement-I: The D.C's of the are [(-1)/(3),(-2)/(3),(2)/(3)] Statement-II : The D. C's of the line are [(1)/(3),(2)/(3),(2)/(3)] Which of the above statement is correct :
Answer» Only I Only II Both I and II Neither I nor II Answer :A

Discussion

6061.	"sin"^(4)(pi)/(16) + "sin"^(4) (3pi)/(16) + "sin"^(4) (5pi)/(16) + "sin"^(4) (7pi)/(16)=
Answer» 1 `1//2` `3//2` 2 Answer :C

Discussion

6062.	Complete solution set of tan^(2)(sin^(-1)x) gt 1 is
Answer» `(-1,-1/(sqrt(2)))uu(1/(sqrt(2)),1)` `(-1/(sqrt(2)),1/(sqrt(2)))~{0}` `(-1,1)~{0}` None of these Answer :A

Discussion

6063.	P- alpha form of the line x+ sqrt(3) y - 4=0 is…......
Answer» `X cos (PI)/(6) + y sin (pi)/(6) =2` `x cos (pi)/(3) + y sin (pi)/(3) = 2` `x cos ( - (pi)/(3) ) + y sin ( - (pi)/(3)) =2` ` x cos (- (pi)/(6) ) + y sin (-(pi)/(6)) = 2` Answer :B

Discussion

6064.	Iftan theta = -4//3 " then " sin theta =
Answer» `-(4)/(5)` but not `(4)/(5)` `-(4)/(5) or (4)/(5)` `(4)/(5)` but not `-(4)/(5)` NONE of these Answer :B

Discussion

6065.	A man running around a race course notes that the sum of the distancesof two flagposts from him a always 10m and thedistance between the flag posts is 8m. Then the area of the path he enclosesin square meters is15pi (b) 20pi (c) 27pi (d) 30pi
Answer» `15pi` `12pi` `18pi` `8pi` ANSWER :A

Discussion

6066.	If Lim_(x to a) (x^(5)-a^(5))/(x-a) = 405, find all possible values of a .
Answer» ANSWER :` PM 3`

Discussion

6067.	If a, b, c are in A.P., a, x, b are in G.P. and b, y, c are in G.P. the point (x, y) lies on
Answer» `x^(2)+y^(2)=2B^(2)` `x^(2)-y^(2)=2b^(2)` `x^(2)-y^(2)=3b^(2)` `x^(2)+y^(2)=3b^(2)` ANSWER :1

Discussion

6068.	Without using tables, give the value of each of the following : cos315^(@)
Answer» ANSWER :`(1)/(SQRT(2))`

Discussion

6069.	The maximum value of f(x)=(x)/(1+4x+x^(2))is
Answer» `-(1)/(4)` `-(1)/(3)` `(1)/(6)` `(1)/(5)` ANSWER :C

Discussion

6070.	Solve 3 cos 2 theta-sin theta=2
Answer» ANSWER :`((5PI)/12)^©`

Discussion

6071.	Find the term independent of x in the expansion of (3/2x^2- 1/(3x))^6.
Answer» ANSWER :`{:((15),(5)):} (1/6)^(5)`is CONSTANT TERM .

Discussion

6072.	Write the negation of the following simple statements. All similar triangles are congruent.
Answer» ANSWER :There EXISTS a SIMILAR TRIANGLES which are not CONGRUENT.

Discussion

6073.	Find r, if 5""^(4)P_(r)=6""^(5)P_(r-1)
Answer» ANSWER :R = 8, 3.

Discussion

6074.	Differentiate (x+2)/(x^2-3) and find the value of the derivative at x =0.
Answer» ANSWER :`(-x^2 - 4X -3)/( (x^2 -3)^2) , - (1)/(3)`

Discussion

6075.	If x = a (1-cos theta) , y = a ( theta + sin theta)then (dy)/(dx)at theta = pi/2 is
Answer» 1 `1/2` 0 `(-1)/2` ANSWER :A

Discussion

6076.	The vectors baraxx(barbxxbarc),barbxx(barcxxbara).barcxx(baraxxbarb) are
Answer» coplanar non-coplanar collinear non-collinear Answer :A

Discussion

6077.	If the 3rd and the 6th terms of an A.P. are 7 and 13 respectively, find the first' term and the common difference.
Answer» ANSWER :FIRST TERM =3 COMMON difference=2

Discussion

6078.	IF alpha+beta=pi/2 and gamma+beta=alpha then find tan alpha.
Answer» `2(TAN beta + tan gamma)` `tan beta + tan gamma` `tan beta + 2TAN gamma` `2tan beta + tan gamma` ANSWER :C

Discussion

6079.	Find the co-ordinates of the mid-point of the chord intersect by the lime x-y+2=0 and the circle x^(2)+y^(2)+4x-2y=0.
Answer»

Discussion

6080.	If A is any set, then A sub A
Answer» ANSWER :1

Discussion

6081.	If A=(1, -2, -1), B= (4, 0, -3), C = (1, 2, -1), D=(2, -4, -5), then distance between AB and CD is
Answer» ANSWER :`4/3`

Discussion

6082.	phi(x) = f(x)g(x) and f'(x)g'(x) = k, then (2k)/(f(x)g(x)) =
Answer» `(PHI''(X))/(phi(x)) - (F''(x))/(f(x)) - (g''(x))/(g(x))` `(phi''(x))/(phi(x)) + (f''(x))/(f(x)) + (g''(x))/(g(x))` `(phi''(x))/(phi(x)) + (f''(x))/(f(x)) - (g''(x))/(g(x))` `(phi''(x))/(phi(x)) - (f''(x))/(f(x)) + (g''(x))/(g(x))` Answer :B

Discussion

6083.	Lines 3x + 4y = 5, 5x + 4y = 4 and lambdax + 4y = 6 passes from unique point then value of lambda = ....
Answer» `2` `1` `3` `4` Answer :B

Discussion

6084.	If the latus rectum of an ellipse is equal of half of minor axis, then find its eccentricity.
Answer» ANSWER :`e=sqrt(3)/(2)`

Discussion

6085.	Two dice are thrown simultaneously. Find the probability of getting an odd number as the sum.
Answer» ANSWER :`(18)/(36),i.e.,(1)/(2)`

Discussion

6086.	Events E and F are uch that P(not E or not F)= 0.25, State whether E and F are mutually exclusive.
Answer» ANSWER :No

Discussion

6087.	Write the first five terms of each of the sequences whose n^(th)terms are: a_(n) =(-1)^(n-1) 5^(n+1)
Answer» ANSWER :`25, -125, 625, -3125 and 15725`

Discussion

6088.	If tanA=(1-cosB)/(sinB), then tan2A=tanB.
Answer» ANSWER :TRUE

Discussion

6089.	A straight line segment of length I moves with its ends on two mutually perpendicular lines. Then the locus of the point which divides the line segment in the ratio 1 : 2 is
Answer» `9x^2+36y^2=4l^2` `9x^2+36y^2=l^2` `36x^2+9y^2=4l^2` `36x^2+9y^2=4l^2` ANSWER :B

Discussion

6090.	Find the mean deviation from median for the following tables:
Answer» SOLUTION :NA

Discussion

6091.	i^(57)+1/(i^(125)), is equal to
Answer» A. `2I` B. `-2i` C. `0` D. `2` Answer :C

Discussion

6092.	Evaluate the following limits : Lim_(x to 0) (2 sin^(2) 3x)/(x^(2))
Answer» ANSWER :18

Discussion

6093.	If the equation sin^(-1)(x^(2)+x+1)+cos^(-1)(lamdax+1)=(pi)/2 has exactly two solution for lamda in [a,b), then the value of a+b is
Answer» ANSWER :1

Discussion

6094.	Find the derivative of the following functions from first principle. x^(3)-27
Answer» ANSWER :`3X^(2)`

Discussion

6095.	Evaluate : "sin" (8 pi)/(3) "cos" (23 pi)/(6) + "cos" (13 pi)/(3) "sin" (35 pi)/(6)
Answer» ANSWER :`(1)/(2)`

Discussion

6096.	If y=(ax+b)/((x-1)(x-4)) has a maximum value at the point (2,-1) then
Answer» ANSWER :`a=1,b=0`

Discussion

6097.	Find the derivative of log(sin(logx))
Answer» ANSWER :`(1)/(X) COT (LOG x)`

Discussion

6098.	Let p be " Shruti can type," and let q be "Shruti takes shorthand." Write the following statements in Symbolic form : Shruti can type and take shorthand.
Answer» <P> ANSWER :`p ^^ Q`

Discussion

6099.	Let p be " Shruti can type," and let q be "Shruti takes shorthand." Write the following statements in Symbolic form : It is not true that Shruti can type and take shorthand .
Answer» <P> ANSWER :`~(p ^^ Q)`

Discussion

6100.	Let p be " Shruti can type," and let q be "Shruti takes shorthand." Write the following statements in Symbolic form : Shruti can neither type nor take shorthand.
Answer» <P> ANSWER :`~p ^^ ~Q`

Discussion

Explore topic-wise InterviewSolutions in .

If f(x) +2f(1/x) =3x, x ne 0 and S={x in R//f (x) =f(-x)}, then S is:

10 arithmetic mean between a and b are A_(1),A_(2),A_(3).........A_(10) then A_1+A_2+A_3+...........+A_(10)=........

If the lines joining the origin to the points of intersection of a line L and x^(2)+y^(2)=4 are coordinate axes then equation of L is

Write the following sets in roster form: E = The set of all letters in the word TRIGONOMETRY

If sin^(-1)x+sin^(-1)y=pi/2 , then (dy)/(dx) is equal to

Solve 3tan^(4)alpha-10tan^(2)alpha+3=0

Define Power

The transformed eqution of x^(2)+y^(2)+z^(2)-6x-8y+2z+24 = 0 when the axes are transtated to the point (3,4,-1) is

A system of lines is given as y=m_1x+c_1,"where " m_1can take any value out of 0,1,-1 and when m_1 is positive , then c1 can be 1 or -1 when m_1 equal 0, c_1 can be 0 or 1 and when m_1 equals to -1 c_1 can take 0 or 2. Then the area enclosed by all these staight lines is

If (1,2,-2) are the D.R's of a line then Statement-I: The D.C's of the are [(-1)/(3),(-2)/(3),(2)/(3)] Statement-II : The D. C's of the line are [(1)/(3),(2)/(3),(2)/(3)] Which of the above statement is correct :

"sin"^(4)(pi)/(16) + "sin"^(4) (3pi)/(16) + "sin"^(4) (5pi)/(16) + "sin"^(4) (7pi)/(16)=

Complete solution set of tan^(2)(sin^(-1)x) gt 1 is

P- alpha form of the line x+ sqrt(3) y - 4=0 is…......

Iftan theta = -4//3 " then " sin theta =

A man running around a race course notes that the sum of the distancesof two flagposts from him a always 10m and thedistance between the flag posts is 8m. Then the area of the path he enclosesin square meters is15pi (b) 20pi (c) 27pi (d) 30pi

If Lim_(x to a) (x^(5)-a^(5))/(x-a) = 405, find all possible values of a .

If a, b, c are in A.P., a, x, b are in G.P. and b, y, c are in G.P. the point (x, y) lies on

Without using tables, give the value of each of the following : cos315^(@)

The maximum value of f(x)=(x)/(1+4x+x^(2))is

Solve 3 cos 2 theta-sin theta=2

Find the term independent of x in the expansion of (3/2x^2- 1/(3x))^6.

Write the negation of the following simple statements. All similar triangles are congruent.

Find r, if 5""^(4)P_(r)=6""^(5)P_(r-1)

Differentiate (x+2)/(x^2-3) and find the value of the derivative at x =0.

If x = a (1-cos theta) , y = a ( theta + sin theta)then (dy)/(dx)at theta = pi/2 is

The vectors baraxx(barbxxbarc),barbxx(barcxxbara).barcxx(baraxxbarb) are

If the 3rd and the 6th terms of an A.P. are 7 and 13 respectively, find the first' term and the common difference.

IF alpha+beta=pi/2 and gamma+beta=alpha then find tan alpha.

Find the co-ordinates of the mid-point of the chord intersect by the lime x-y+2=0 and the circle x^(2)+y^(2)+4x-2y=0.

If A is any set, then A sub A

If A=(1, -2, -1), B= (4, 0, -3), C = (1, 2, -1), D=(2, -4, -5), then distance between AB and CD is

phi(x) = f(x)g(x) and f'(x)g'(x) = k, then (2k)/(f(x)g(x)) =

Lines 3x + 4y = 5, 5x + 4y = 4 and lambdax + 4y = 6 passes from unique point then value of lambda = ....

If the latus rectum of an ellipse is equal of half of minor axis, then find its eccentricity.

Two dice are thrown simultaneously. Find the probability of getting an odd number as the sum.

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

Write the first five terms of each of the sequences whose n^(th)terms are: a_(n) =(-1)^(n-1) 5^(n+1)

If tanA=(1-cosB)/(sinB), then tan2A=tanB.

A straight line segment of length I moves with its ends on two mutually perpendicular lines. Then the locus of the point which divides the line segment in the ratio 1 : 2 is

Find the mean deviation from median for the following tables:

i^(57)+1/(i^(125)), is equal to

Evaluate the following limits : Lim_(x to 0) (2 sin^(2) 3x)/(x^(2))

If the equation sin^(-1)(x^(2)+x+1)+cos^(-1)(lamdax+1)=(pi)/2 has exactly two solution for lamda in [a,b), then the value of a+b is

Find the derivative of the following functions from first principle. x^(3)-27

Evaluate : "sin" (8 pi)/(3) "cos" (23 pi)/(6) + "cos" (13 pi)/(3) "sin" (35 pi)/(6)

If y=(ax+b)/((x-1)(x-4)) has a maximum value at the point (2,-1) then

Find the derivative of log(sin(logx))

Let p be " Shruti can type," and let q be "Shruti takes shorthand." Write the following statements in Symbolic form : Shruti can type and take shorthand.

Let p be " Shruti can type," and let q be "Shruti takes shorthand." Write the following statements in Symbolic form : It is not true that Shruti can type and take shorthand .

Let p be " Shruti can type," and let q be "Shruti takes shorthand." Write the following statements in Symbolic form : Shruti can neither type nor take shorthand.