14949 + Interview Questions in Maths in Class 11 Page 205 InterviewSolution

10201.	Find the union of each of the following pairs of sets : A = {x : x is a natural number and multiple of 3} B = {x : x is a natural number less than 6}
Answer» Answer :`A CUP B= {3, 6, 9, 12, 15,…….,……,} cup {1, 2, 3, 4, 5}` `A cup B= {1, 2, 3, 4, 5, 6, 9, 12, 15, 18,……,……}`={x : x = 1, 2, 4, 5 or MULTIPLE of `3, x in N` }

Discussion

10202.	lim_(xrarr0)(1-cos(2x))/x^(2) = 0.
Answer» ANSWER :FALSE STATEMENT

Discussion

10203.	Let f(x) = x + 1/(2x + 1/(2x + 1/(2x + ....oo))) " then " sqrt((f(50) f^'(50))/(2)) =
Answer»

Discussion

10204.	Find the equation of the circle passing through the points (2,3) and (-1,-1) and whose centre is on the line x-3y-11=0.
Answer» ANSWER :`X^(2)+y^(2)-7x+5y-14=0`

Discussion

10205.	Find the derivative of y = log_(10)x with respect to x.
Answer» ANSWER :`(log_(10)E)/(X)`

Discussion

10206.	For x, y, z, t in R, sin^(-1)x+cos^(-1)y+sec^(-1)z ge t^(2)-sqrt(2pi)t+3pi The value of cos^(-1)(min{x,y,z}) is
Answer» 0 `PI/2` `pi` `pi/3` ANSWER :D

Discussion

10207.	A has 3 shares in a lottery containing 3 prizes and 9 blanks , B hastwo shares in lottery containing 2 prizes and 6 blanks , Copare their chances of success .
Answer» ANSWER :`952:715`

Discussion

10208.	Ifa_0 = x, a_( n+1) = f(a_n) , " where"n = 0,1,2……… then answer the following questions If f(x) = (1)/( 1-x)then which of the following is not true?
Answer» `a_(N) = (1)/(1-X)` if `n= 3k+1` `a_(n) = (x-1)/(x)` if `n= 3k+2` `a_(n) =x` if `n=3k` NONE of these Answer :D

Discussion

10209.	Find the sum of the series 1^(2)+3^(2)+5^(2)+...to n terms
Answer» ANSWER :`(N(2n-:1)(2n-1))/(3)`

Discussion

10210.	Find a point on the X-axis, which is equidistant from the points (7,6) and (-3,4).
Answer» <P> ANSWER :`= P( (15)/(2) ,0)`.

Discussion

10211.	Statement-I : The point A(3,1,6) is the miror image of the point B(1,3,4) in the plane x-y+z=5. Statement-II : The plane x-y+z=5 bisects the line segment joining A(3,1,6) and B(1,3,4)
Answer» STATEMENT 1 is false, statement 2 is true. Statement 1 is true, statement 2 is true, statement 2 is a CORRECT EXPLANATION for statement 1. Statement 1 is true, statement 2 is true, statement 2 is not a correct explanation for statement 2. Statement 1 is true, statement 2 is false. ANSWER :C

Discussion

10212.	If A + B + C = 90^(@) and if none of A,B,C is an odd multipl of 90^(@) then P.T. TanA Tan B + Tan B Tan C + Tan C Tan A = 1 and hence S.T.
Answer» ANSWER :1

Discussion

10213.	A= {1, 2, 3, 4, 5}, B= {1, 3, 5, 6}, C= {1, 2, 3}, then find the following sets. B- C
Answer» ANSWER :`={5, 6}`

Discussion

10214.	When the axes are rotated through an angle 60^(0)the point Q is changed as (-7,2). Find Q.
Answer» ANSWER :(i) `(2 - 7 sqrt(3))/(2)` (ii) 0 = 1

Discussion

10215.	The transformed equation of 3x^(2) + 3y^(2) + 2xy =2 when the coordinate axes are rotated through an angle of 45^(@)is
Answer» `x^(2) + 2y^(2) = 1` `2x^(2) + y^(2) = 1` `x^(2) + y^(2) = 1` `x^(2) + 3Y^(2) = 1` ANSWER :B

Discussion

10216.	If Lim_(x to a) (x^(9)-a^(9))/(x-a) = 9, find all possible values of a .
Answer» ANSWER :`1,-1`

Discussion

10217.	If sin^(2) x gt sqrt(2) sin^(2) x = ( 2 - sqrt(2)) cos ^(2) xthen
Answer» `x in ( n PI + (pi)/( 6) , n pi + (pi)/( 4)), n in Z` `x in ( n in + (pi)/( 8) , n pi + (pi)/( 4)) , n in Z` `x in ( n pi + (pi)/( 4) , n pi + (pi)/(3) ) , n in Z` `x in ( n pi + (pi)/(3), n pi +( pi)/( 2)) , n in Z` ANSWER :B

Discussion

10218.	If Lim_(x to -a) (x^(9)+a^(9))/(x+a) = 9 , find all possible values of a .
Answer» ANSWER :`=1`

Discussion

10219.	If x,y,z,t are real numbers such that x^(2) + y^(2) =9,z^(2) + t^(2)=4 and xt-yz=6, then the greatest value of xz is:
Answer» 1 2 3 4 Answer :C

Discussion

10220.	Find the coefficient of x^4 in the expansion of (1+x)^n(1-x)^n
Answer» SOLUTION :`C_0C_4-C_1C_3+C_2C_2-C_3C_1+C_4C_0=C_2`

Discussion

10221.	Let y= (x + (1)/(x))^(2)Find the rate of change of y with respect to x when x=2.
Answer» ANSWER :`=2X - (2)/( x^3)`.

Discussion

10222.	If for DeltaABC, cotA cotB cotC gt0then the triangle is
Answer» right ANGLED ACUTE angled OBTUSE angled all Answer :B

Discussion

10223.	If the position vectors of A, B, C, D are 3bar(i)+2bar(j)+bar(k), 4bar(i)+5bar(j)+5bar(k), 4bar(i)+2bar(j)-2bar(k), 6bar(i)+5bar(j)-bar(k) respectively then the position vector of the point of intersection of lines AB and CD is
Answer» `2bar(i)+BAR(J)-3BAR(K)` `2bar(i)-bar(j)+3bar(k)` `2bar(i)+bar(j)+3bar(k)` `2bar(i)-bar(j)-3bar(k)` Answer :D

Discussion

10224.	Solve: x^2+x+1=0
Answer» ANSWER :`X=(-1isqrt3)/2`

Discussion

10225.	If f(x)= \|cos x- sin x\| , then f^(1)(pi/4) =
Answer» `SQRT2` `-sqrt2` 0 does not EXIST ANSWER :D

Discussion

10226.	Write the following sets in the set-builder form : (3, 6, 9, 12}
Answer» Answer :`={X : n in N, x= 3N, 1 LE n le 4}`

Discussion

10227.	Evaluate ""^(10)C_(4).
Answer» ANSWER :210

Discussion

10228.	If the median Ad of Delta^("le") ABC makes an angle lfloorADC=45^(@) then \|cotB-cotC\|=
Answer» 1 2 3 4 Answer :B

Discussion

10229.	Consider the expansion of (3x^2-1/(2x^3))^10 Find the (r+1)^(th) term in the expansion
Answer» SOLUTION :`(-1)^R"^10C_r,(3x^2)^(10-r)(1/(2x^3))^r`

Discussion

10230.	Obtain the equation of he circle circum circle of the triangle with verticies (-2,3), (5, 2) and (6, -1).
Answer» ANSWER :`X^(2) + y^(2) - 2X + 2y - 23 = 0`

Discussion

10231.	If x_(1), x_(2), x_(3) and y_(1),y_(2), y_(3) are in arithmetic progression with the same common difference then the points (x_(1),y_(1)) (x_(2),y_(2)) (x_(3), y_(3)) are:
Answer» VERTICES of an equilateral TRIANGLE vertices of a right ANGLED triangle vertices of a right angled ISOSCELES COLLINEAR Answer :A::C

Discussion

10232.	(sin ^(3) theta - cos^(3) theta)/(sin theta - cos theta) - (cos theta)/(sqrt(1 + cot^(2)theta))-2 tan theta cot theta = - 1 , if
Answer» `THETA in (0 (pi)/2)` `theta in ((pi)/2 , pi)` `theta in (pi, (3pi)/2)` `theta in ((3pi)/2, 2 pi)` ANSWER :B

Discussion

10233.	Consider the points A(1,-1,1), B(5,-5,4), C(5,0,8) and D(1,4,5) Find AB,BC,CD and DA
Answer» SOLUTION :`sqrt41, sqrt41, sqrt41, sqrt41`

Discussion

10234.	Find the derivative of the following functions: 5secx+4cosx
Answer» ANSWER :`5secx TAN x-4sinx`

Discussion

10235.	Let h(x)=f(x)-a(f(x))^(2)+a(f(x))^(3) for all real xh(x) increases as f(x) increases for all x if
Answer» `a in(0.3)` `a in[-2,2]` `a in[3,OO)` `a in [2,oo]` ANSWER :A

Discussion

10236.	Find the orthocentre of the triangle formed by (0,0), (2,-1) (-1,3) whose circumcentre is (5/2,5/2).
Answer» ANSWER :(-4,-3)

Discussion

10237.	If det (A_(3xx3))=6, then det (Adj 2A) =
Answer» 144 `3^(2)xx2^(8)` `3^(3)xx2^(4)` `2^(2)xx3^(8)` Answer :B

Discussion

10238.	Show that the set of all points such that the difference of their distances from (4,0) and (-4,0) is alwaysequal to 2 represent a hyperbola. Find its equation.
Answer» ANSWER :`(X^(2))/(1)-(y^(2))/(15)=1`

Discussion

10239.	If the sides of a triangle are in A.P and greatest angle exceeds the least angle of the triangle by 90^(@). Then ratio of the sides .
Answer» `3 : 4 : 5` `sqrt 7 - 1 : sqrt7 : sqrt7 + 1` `sqrt2 : SQRT3 : sqrt7` `sqrt3 : sqrt7 : sqrt2` Answer :B

Discussion

10240.	In triangle ABC, if r_(1)=3, r_(2)=10, r_(3)=15 then R=
Answer» 5 12 13 `13//2` ANSWER :D

Discussion

10241.	If a = 18, b=24, c= 30and if l = r_2- r_1 , m = r_3 - r_2, n= r_3 - r_1thendescendingorder of l, m, n is
Answer» N,m,L l,m,n l,m,n n,l,m ANSWER :A

Discussion

10242.	Make correct statements by filling in the symbols ⊂ or ⊄ in the blank spaces : {x : x is a circle in the plane} . . .{x : x is a circle in the same plane with radius 1 unit}
Answer» ANSWER :`⊄`

Discussion

10243.	Given P(A)= (3)/(5) and P(B) = (1)/(5) . Find P(A or B), ifA & B are mutually exclusive events.
Answer» ANSWER :`4/5`

Discussion

10244.	Solve: 2x^(2)+2x-3=0, giving your answer correct to one decimal place.
Answer» ANSWER :`-1.8,0.8`, CORRECT to ONE DECIMAL PLACE.

Discussion

10245.	The perpendicular from the origin to a line meets it at the point (-2,9), find the equation of the line.
Answer» ANSWER :REQUIRED equation of the LINE is `2X -9Y +85=0`.

Discussion

10246.	Find the approximate value of log (2.01) give that log 2 = 0.6934
Answer» ANSWER :0.6984

Discussion

10247.	The distance of point A(-2,3,1)from the line PQ through P( 3,5,2), which make equal angles with the axes is
Answer» `2// SQRT3` `sqrt (14 //3)` `16//sqrt3` `5//sqrt3` Answer :B

Discussion

10248.	Period of cot ((5-7x)/( 2) ) is
Answer» `(pi)/(2)` `(2pi)/(7)` `(pi)/(7)` `(7pi)/(2)` Answer :B

Discussion

10249.	If barr is any vector then barr =
Answer» `(barr.BARA^(1))bara+(barr.BARB^(1))barb+(barr.BARC^(1))barc` `(barr.barc^(1))bara+(barr.barb^(1))barb+(barr.bara^(1))barc` `(barr.bara^(1))bara-(barr.barb^(1))barb+(barr.barc^(1))barc` `(bara.bara^(1))bara+(barb.barb^(1))barb+(barc.barc^(1))barc` ANSWER :A

Discussion

10250.	If x and y are acute angle such that cosx+"cos" y=(3)/(2) and sin x+"sin" y=(3)/(4) then sin (x+y)=
Answer» `(2)/(5)` `(3)/(4)` `(3)/(5)` `(4)/(5)` ANSWER :D

Discussion

Explore topic-wise InterviewSolutions in .

Find the union of each of the following pairs of sets : A = {x : x is a natural number and multiple of 3} B = {x : x is a natural number less than 6}

lim_(xrarr0)(1-cos(2x))/x^(2) = 0.

Let f(x) = x + 1/(2x + 1/(2x + 1/(2x + ....oo))) " then " sqrt((f(50) f^'(50))/(2)) =

Find the equation of the circle passing through the points (2,3) and (-1,-1) and whose centre is on the line x-3y-11=0.

Find the derivative of y = log_(10)x with respect to x.

For x, y, z, t in R, sin^(-1)x+cos^(-1)y+sec^(-1)z ge t^(2)-sqrt(2pi)t+3pi The value of cos^(-1)(min{x,y,z}) is

A has 3 shares in a lottery containing 3 prizes and 9 blanks , B hastwo shares in lottery containing 2 prizes and 6 blanks , Copare their chances of success .

Ifa_0 = x, a_( n+1) = f(a_n) , " where"n = 0,1,2……… then answer the following questions If f(x) = (1)/( 1-x)then which of the following is not true?

Find the sum of the series 1^(2)+3^(2)+5^(2)+...to n terms

Find a point on the X-axis, which is equidistant from the points (7,6) and (-3,4).

Statement-I : The point A(3,1,6) is the miror image of the point B(1,3,4) in the plane x-y+z=5. Statement-II : The plane x-y+z=5 bisects the line segment joining A(3,1,6) and B(1,3,4)

If A + B + C = 90^(@) and if none of A,B,C is an odd multipl of 90^(@) then P.T. TanA Tan B + Tan B Tan C + Tan C Tan A = 1 and hence S.T.

A= {1, 2, 3, 4, 5}, B= {1, 3, 5, 6}, C= {1, 2, 3}, then find the following sets. B- C

When the axes are rotated through an angle 60^(0)the point Q is changed as (-7,2). Find Q.

The transformed equation of 3x^(2) + 3y^(2) + 2xy =2 when the coordinate axes are rotated through an angle of 45^(@)is

If Lim_(x to a) (x^(9)-a^(9))/(x-a) = 9, find all possible values of a .

If sin^(2) x gt sqrt(2) sin^(2) x = ( 2 - sqrt(2)) cos ^(2) xthen

If Lim_(x to -a) (x^(9)+a^(9))/(x+a) = 9 , find all possible values of a .

If x,y,z,t are real numbers such that x^(2) + y^(2) =9,z^(2) + t^(2)=4 and xt-yz=6, then the greatest value of xz is:

Find the coefficient of x^4 in the expansion of (1+x)^n(1-x)^n

Let y= (x + (1)/(x))^(2)Find the rate of change of y with respect to x when x=2.

If for DeltaABC, cotA cotB cotC gt0then the triangle is

If the position vectors of A, B, C, D are 3bar(i)+2bar(j)+bar(k), 4bar(i)+5bar(j)+5bar(k), 4bar(i)+2bar(j)-2bar(k), 6bar(i)+5bar(j)-bar(k) respectively then the position vector of the point of intersection of lines AB and CD is

Solve: x^2+x+1=0

If f(x)= |cos x- sin x| , then f^(1)(pi/4) =

Write the following sets in the set-builder form : (3, 6, 9, 12}

Evaluate ""^(10)C_(4).

If the median Ad of Delta^("le") ABC makes an angle lfloorADC=45^(@) then |cotB-cotC|=

Consider the expansion of (3x^2-1/(2x^3))^10 Find the (r+1)^(th) term in the expansion

Obtain the equation of he circle circum circle of the triangle with verticies (-2,3), (5, 2) and (6, -1).

If x_(1), x_(2), x_(3) and y_(1),y_(2), y_(3) are in arithmetic progression with the same common difference then the points (x_(1),y_(1)) (x_(2),y_(2)) (x_(3), y_(3)) are:

(sin ^(3) theta - cos^(3) theta)/(sin theta - cos theta) - (cos theta)/(sqrt(1 + cot^(2)theta))-2 tan theta cot theta = - 1 , if

Consider the points A(1,-1,1), B(5,-5,4), C(5,0,8) and D(1,4,5) Find AB,BC,CD and DA

Find the derivative of the following functions: 5secx+4cosx

Let h(x)=f(x)-a(f(x))^(2)+a(f(x))^(3) for all real xh(x) increases as f(x) increases for all x if

Find the orthocentre of the triangle formed by (0,0), (2,-1) (-1,3) whose circumcentre is (5/2,5/2).

If det (A_(3xx3))=6, then det (Adj 2A) =

Show that the set of all points such that the difference of their distances from (4,0) and (-4,0) is alwaysequal to 2 represent a hyperbola. Find its equation.

If the sides of a triangle are in A.P and greatest angle exceeds the least angle of the triangle by 90^(@). Then ratio of the sides .

In triangle ABC, if r_(1)=3, r_(2)=10, r_(3)=15 then R=

If a = 18, b=24, c= 30and if l = r_2- r_1 , m = r_3 - r_2, n= r_3 - r_1thendescendingorder of l, m, n is

Make correct statements by filling in the symbols ⊂ or ⊄ in the blank spaces : {x : x is a circle in the plane} . . .{x : x is a circle in the same plane with radius 1 unit}

Given P(A)= (3)/(5) and P(B) = (1)/(5) . Find P(A or B), ifA & B are mutually exclusive events.

Solve: 2x^(2)+2x-3=0, giving your answer correct to one decimal place.

The perpendicular from the origin to a line meets it at the point (-2,9), find the equation of the line.

Find the approximate value of log (2.01) give that log 2 = 0.6934

The distance of point A(-2,3,1)from the line PQ through P( 3,5,2), which make equal angles with the axes is

Period of cot ((5-7x)/( 2) ) is

If barr is any vector then barr =

If x and y are acute angle such that cosx+"cos" y=(3)/(2) and sin x+"sin" y=(3)/(4) then sin (x+y)=