14949 + Interview Questions in Maths in Class 11 Page 15 InterviewSolution

701.	If (a+ib)(c+id)(e+if)(g+ih) = A + iB, then show that (a^(2) + b^(2))(c^(2) + d^(2))(e^(2) + f^(2)) (g^(2) + h^(2)) = A^(2) + B^(2)
Answer» ANSWER :`(A^(2)+B^(2))`

Discussion

702.	If bara = 2bari+2barj-3bark, barb=3bari -barj+3bark, " then find the angle between " 2bara+barb and bara+2barb.
Answer» ANSWER :`COS^(-1)((52)/(sqrt4810))`

Discussion

703.	If y =ax^(2)+b, y(0) = 2 and y'(1) = 2 then find y(2):
Answer» 0 2 4 6 Answer :D

Discussion

704.	Let S= set of points inside the square, T= set of points inside the triangle and C= set of points inside the circle. If the triangle and circle intersect each other and are contained in a square. Then,
Answer» `S CAP T cap C = PHI` `S CUP T cup C = C` `S cup T cup C = S` `S cup T =S cap C` ANSWER :C

Discussion

705.	Prove that the equations of concentric circles differ only in the constant term
Answer» SOLUTION :`sqrt30`, `30PI`

Discussion

706.	A= {a, b, {c, d}, e} which of the following statements are correct? {a, b, c} sub A
Answer» ANSWER :INCORRECT

Discussion

707.	The period of the function f(x) = {(1",","when x is a rational"),(0",","when x is irrational"):} is
Answer» 1 2 non - periodic periodic but having no period Answer :D

Discussion

708.	(0.09634)^(3)
Answer» ANSWER :0.0008941

Discussion

709.	A rod of 10 feet long moves with its ends A and B always on the axes of x and y respectively. If A is 8 ft from the origin and is moving away at the rate of 2ft per second, find at what rate (a) the end B is moving (b) the area formed by AB and the axes is changing.
Answer» ANSWER :(a) -8/3 ft/sec. (B) -14/3ft/sec

Discussion

710.	In three dimensions there may be more than one point, which are equidistant from three given noncolliner points A,B,C. One of these points will be circumcentre of the triangle ABC The y coordinate of orthocentre of the triangle ABC
Answer» `((3A^(2)C^(2)-a^(2)B^(2)-b^(2)c^(2))/(a^(2)b^(2)+b^(2)c^(2)+c^(2)a^(2)))` `(ab+b^(2)-AC)/(a+b+c)` `b-(2(a^(2)c^(2)-b))/(a^(3)+b^(3)+c^(3))` `(a^(2)bc^(2))/(b^(2)c^(2)+c^(2)a^(2)+a^(2)b^(2))` ANSWER :a

Discussion

711.	Evaluate : lim_(xto5^(-))(x+5)/(\|x+5\|)
Answer» ANSWER :`-1`

Discussion

712.	If z_(1)=2 + 7i and z_(2)=1- 5i, then verify that \|z_(1) + z_(2)\| le \|z_(1)\| + \|z_(2)\|
Answer» ANSWER :`SQRT13 LT sqrt53 + sqrt26`

Discussion

713.	Compute "Lt"_(x to0)(a^x-1)/(b^x-1),(a gt0,bgt0,bne1)
Answer» ANSWER :`log_(B)^(a)`

Discussion

714.	If cos(alpha+beta)=(4)/(5),sin(alpha-beta)=(5)/(13),0ltalpha,betalt(pi)/(4) then tan2alpha = …………
Answer» `(16)/(63)` `(56)/(33)` `(28)/(33)` NONE of these Answer :B

Discussion

715.	A function f is defined on the set of real numbers as follows : f(x)={:{(1+x,1lexlt2),(2x-1,2lexlt4),(3x-5,4lexlt6):} (i) Find the domain of the function. (ii) Find the range of the function. (iii) Find f(4). (iv)Is the function one-one ? Justify.
Answer» ANSWER :`D_(F)=[2,6]:R_(f)[2,13]`

Discussion

716.	OA is a crank of 2 meters long which rotates about O. AB is a connecting rod to B with AB = 5 meters long, which moves on a straight line passing through O then cosine of angle that crank OA makes with OB when
Answer» B has t RAVELLED 1 - unit from its extreame POSITION is (5/8) B has TRAVELLED 3 - units from its extreme position is `((-5)/16)` B has travelled 4 - units from its extreme position is `(-1)` When B is at RIGHT extreme position is (1). Answer :A::B::C::D

Discussion

717.	Consider the hyperbola x^2/a^2-y^2/b^2=1 If the hyperbola passes through (3,0) and (3sqrt2,2), find the eccentricity of the hyperbola
Answer» SOLUTION :`sqrt13/3`

Discussion

718.	Simplify: i^(13)
Answer» ANSWER :i

Discussion

719.	If P(A) = 0.68 and A and B are mutually exclusive events then P(AcapB') = …. .
Answer» ANSWER :`0.68`

Discussion

720.	Verify the following : (0, 7, -10), (1, 6, -6) and (4, 9, -6) are the vertices of an isosceles triangle.
Answer» ANSWER :`3sqrt2`

Discussion

721.	Compute Q_(1) and Q_(3) from the following data:
Answer» ANSWER :`Q_(1)=20,Q_(3)=40`

Discussion

722.	Two sides of triangle are x+y-1=0 and 2x-y+4=0. If its circumcentre is (2,1) the third sides is 4x+3y=6.
Answer» ANSWER :6

Discussion

723.	If alpha,beta are complementary angles and sin alpha = (3)/(5), then sin alpha cos beta - cos alpha sin beta =
Answer» `(7)/(25)` `-(7)/(25)` `(25)/(7)` `-(25)/(7)` ANSWER :B

Discussion

724.	The set of points of continuity of the function y=sqrt((1)/(2)-cos^(2)x) contains in the interval
Answer» `[(PI)/(4),(3PI)/(4)]` `[(5pi)/(4),(7pi)/(4)]` `[(21pi)/(4),(23pi)/(4)]` All the above Answer :B

Discussion

725.	Find the equation of the circle passing through (1,0),(2,-7) and (8,1). Hence prove that (1,0),(2,-7),(8,1) and (9,-6) are concyclic
Answer» SOLUTION :`x^2+y^2-10x+6y+9=0`

Discussion

726.	Check whether the following sentences are statements. Give reasons for your answer. How far is Chennai from here?
Answer» ANSWER :It is not a STATEMENT.

Discussion

727.	Which one of the following points liesin the sixth octant?
Answer» `(-4,2,-5)` `(-4,-2,-5)` `(4,-2,-5)` `(4,2,5)` ANSWER :A

Discussion

728.	A particle moves along a straight line and its velocity at a distance 'x' from the origin is ksqrt(a^(2) - x^(2)). Then accelertion of the particle is
Answer» K `-k^(2)` KX `-k^(2)X` ANSWER :D

Discussion

729.	Differentiate 1-2 tan x w.r.t.x
Answer» SOLUTION :`-2 sec^2 X`

Discussion

730.	Solve the equations: Q. x(x-1)(x+2)(x-3)+8=0.
Answer» ANSWER :2,-1,`(1pmsqrt(17))/(2)`.

Discussion

731.	Consider the expansion of (3x^2-1/(2x^3))^10 Find the term independent of x in the expansion.
Answer» SOLUTION :`76545/8]`

Discussion

732.	Write the following relation in roster from R= {(x,y) : 2x + 3y= 12, x in A, y in A} where A= {0, 1, 2,3……10}
Answer» ANSWER :R= {(0, 4), (3,2), (6,0)}

Discussion

733.	If cosec theta + cot theta = 1//3 then cosec theta - cot theta =
Answer» 3 -3 2 `1//3` ANSWER :A

Discussion

734.	Reduce the following equation in normal form. Find their perpendicular distances from origin and between perpendicular distance with positive side of X- axis : (iii) x-y=4
Answer» Answer :MEASURE of an angle MADE by perpendicular with positive side of X- AXIS is `omega = 315^(@)`.

Discussion

735.	Reduce the following equation in normal form. Find their perpendicular distances from origin and between perpendicular distance with positive side of X- axis : (ii) y-2=0
Answer» ANSWER :Measure of an ANGLE made by perpendicular with POSITIVE side of X- AXIS is `omega=90^(@)`.

Discussion

736.	Let OABC be tetrahedron, Letthe mid points of edges OA & OB and OC be Al, Bl, Cl respectively while those of edges AB, BC and AC be R, P and Q respectively. If OA is
Answer» `QB_(1)^(2)=RC_(1)^(2)` `QA_(1)^(2)=RC_(1)^(2)` `QC_(1)^(2)=RC_(1)^(2)` None Answer :a

Discussion

737.	Evaluate the limits. Lt_(xto7)(sqrt(x+2)-3)/(x-7)
Answer» ANSWER :`1/6`

Discussion

738.	How many four digit odd number are there ? (Repetition of digit is not allowed )
Answer» ANSWER :2240,

Discussion

739.	Find the derivative of (2)/(x+1)-(x^(2))/(3x-1)
Answer» ANSWER :`(-2)/((X+1)^(2))-(x(3x-2))/((3x-1)^(2))`

Discussion

740.	A line through A (-5,-4)with slopetantheta " meets the line " x+3y+2=0, 2x+y+4=0, x-y-5=0 at B,C,Drespectivelly, such that (15/AB)^2+(10/AC)^2 =(6/AD)^2 then
Answer» `15/AB=costheta+3sintheta` `10/AC=2costheta+sintheta` `6/AD= costheta-sintheta` slope of the LINE `-(2)/3` Answer :A::B::C::D

Discussion

741.	(i) Find the differentiation ofy= (x^(2) - 4x +5) (x^(3) -2)
Answer» ANSWER :`=5x^(4) - 16X^(3) + 15x^(2) -4x +8`.

Discussion

742.	Prove thatunderset(thetararr0)lim(Sintheta)/theta =1 , (theta being in radians) and henceshow thatunderset(thetararr0)lim(tantheta)/theta =1 ?
Answer» ANSWER :`(a/b)`

Discussion

743.	The number of values of y in [-2 pi, 2 pi] satisfying the equation \|sin 2 x\| + cos 2 x \| = \| sin y \| is
Answer» 3 4 5 6 Answer :B

Discussion

744.	A box contains two white, there black and four red balls. In how many ways can there balls be drawn from the box, if atleast one black ball is to be included in the draw ?
Answer» ANSWER :64

Discussion

745.	In triangle ABC, if sin A cos B = (1)/(4) and 3 tan A = tan B, then cot^(2) A is equal to
Answer» 2 3 4 5 Answer :B

Discussion

746.	The equation of the plane passing through the point (1, 2, – 3) and parallel to the plane 2x – 3y +z+5 = 0 is
Answer» `(X-1)/(-1) = (y+2)/(1) = (Z-3)/(-1)` `(x-1)/(2) = (y +2)/(3) - (z-3)/(1) ` `(x +1)/(-1) =(y-2)/(1) - (z -3)/(-1)` `(x +1)/(2) = (y-2)/(3) - (z-3)/(1)` Answer :A

Discussion

747.	Find a,b and n in the exapnsion of (a+b)^(n) ifthe first three terms of the expansion are 729 , 7290 and 30375 , respectively .
Answer» ANSWER :n=6

Discussion

748.	The mean of 5 observations is 4.4 and their varience is 8.24 . Ifthree of the observations are 1,2 and 6 , find the other two observations.
Answer» ANSWER :4 and 9

Discussion

749.	Find the derivative of x^(2)-2 at point x-10
Answer» ANSWER :20

Discussion

750.	A bag 'A' contains 2 white and 3 red balls andbag 'B' contains 4 white and 5 red balls. One ball is drawn at random from a randomlychosen bag and is found to be red. Theprobability that it was drawn from bag 'B' was
Answer» `(5)/(14)` `(5)/(16)` `(5)/(18)` `(25)/(52)` ANSWER :D

Discussion

Explore topic-wise InterviewSolutions in .

If (a+ib)(c+id)(e+if)(g+ih) = A + iB, then show that (a^(2) + b^(2))(c^(2) + d^(2))(e^(2) + f^(2)) (g^(2) + h^(2)) = A^(2) + B^(2)

If bara = 2bari+2barj-3bark, barb=3bari -barj+3bark, " then find the angle between " 2bara+barb and bara+2barb.

If y =ax^(2)+b, y(0) = 2 and y'(1) = 2 then find y(2):

Let S= set of points inside the square, T= set of points inside the triangle and C= set of points inside the circle. If the triangle and circle intersect each other and are contained in a square. Then,

Prove that the equations of concentric circles differ only in the constant term

A= {a, b, {c, d}, e} which of the following statements are correct? {a, b, c} sub A

The period of the function f(x) = {(1",","when x is a rational"),(0",","when x is irrational"):} is

(0.09634)^(3)

A rod of 10 feet long moves with its ends A and B always on the axes of x and y respectively. If A is 8 ft from the origin and is moving away at the rate of 2ft per second, find at what rate (a) the end B is moving (b) the area formed by AB and the axes is changing.

In three dimensions there may be more than one point, which are equidistant from three given noncolliner points A,B,C. One of these points will be circumcentre of the triangle ABC The y coordinate of orthocentre of the triangle ABC

Evaluate : lim_(xto5^(-))(x+5)/(|x+5|)

If z_(1)=2 + 7i and z_(2)=1- 5i, then verify that |z_(1) + z_(2)| le |z_(1)| + |z_(2)|

Compute "Lt"_(x to0)(a^x-1)/(b^x-1),(a gt0,bgt0,bne1)

If cos(alpha+beta)=(4)/(5),sin(alpha-beta)=(5)/(13),0ltalpha,betalt(pi)/(4) then tan2alpha = …………

A function f is defined on the set of real numbers as follows : f(x)={:{(1+x,1lexlt2),(2x-1,2lexlt4),(3x-5,4lexlt6):} (i) Find the domain of the function. (ii) Find the range of the function. (iii) Find f(4). (iv)Is the function one-one ? Justify.

OA is a crank of 2 meters long which rotates about O. AB is a connecting rod to B with AB = 5 meters long, which moves on a straight line passing through O then cosine of angle that crank OA makes with OB when

Consider the hyperbola x^2/a^2-y^2/b^2=1 If the hyperbola passes through (3,0) and (3sqrt2,2), find the eccentricity of the hyperbola

Simplify: i^(13)

If P(A) = 0.68 and A and B are mutually exclusive events then P(AcapB') = …. .

Verify the following : (0, 7, -10), (1, 6, -6) and (4, 9, -6) are the vertices of an isosceles triangle.

Compute Q_(1) and Q_(3) from the following data:

Two sides of triangle are x+y-1=0 and 2x-y+4=0. If its circumcentre is (2,1) the third sides is 4x+3y=6.

If alpha,beta are complementary angles and sin alpha = (3)/(5), then sin alpha cos beta - cos alpha sin beta =

The set of points of continuity of the function y=sqrt((1)/(2)-cos^(2)x) contains in the interval

Find the equation of the circle passing through (1,0),(2,-7) and (8,1). Hence prove that (1,0),(2,-7),(8,1) and (9,-6) are concyclic

Check whether the following sentences are statements. Give reasons for your answer. How far is Chennai from here?

Which one of the following points liesin the sixth octant?

A particle moves along a straight line and its velocity at a distance 'x' from the origin is ksqrt(a^(2) - x^(2)). Then accelertion of the particle is

Differentiate 1-2 tan x w.r.t.x

Solve the equations: Q. x(x-1)(x+2)(x-3)+8=0.

Consider the expansion of (3x^2-1/(2x^3))^10 Find the term independent of x in the expansion.

Write the following relation in roster from R= {(x,y) : 2x + 3y= 12, x in A, y in A} where A= {0, 1, 2,3……10}

If cosec theta + cot theta = 1//3 then cosec theta - cot theta =

Reduce the following equation in normal form. Find their perpendicular distances from origin and between perpendicular distance with positive side of X- axis : (iii) x-y=4

Reduce the following equation in normal form. Find their perpendicular distances from origin and between perpendicular distance with positive side of X- axis : (ii) y-2=0

Let OABC be tetrahedron, Letthe mid points of edges OA & OB and OC be Al, Bl, Cl respectively while those of edges AB, BC and AC be R, P and Q respectively. If OA is

Evaluate the limits. Lt_(xto7)(sqrt(x+2)-3)/(x-7)

How many four digit odd number are there ? (Repetition of digit is not allowed )

Find the derivative of (2)/(x+1)-(x^(2))/(3x-1)

A line through A (-5,-4)with slopetantheta " meets the line " x+3y+2=0, 2x+y+4=0, x-y-5=0 at B,C,Drespectivelly, such that (15/AB)^2+(10/AC)^2 =(6/AD)^2 then

(i) Find the differentiation ofy= (x^(2) - 4x +5) (x^(3) -2)

Prove thatunderset(thetararr0)lim(Sintheta)/theta =1 , (theta being in radians) and henceshow thatunderset(thetararr0)lim(tantheta)/theta =1 ?

The number of values of y in [-2 pi, 2 pi] satisfying the equation |sin 2 x| + cos 2 x | = | sin y | is

A box contains two white, there black and four red balls. In how many ways can there balls be drawn from the box, if atleast one black ball is to be included in the draw ?

In triangle ABC, if sin A cos B = (1)/(4) and 3 tan A = tan B, then cot^(2) A is equal to

The equation of the plane passing through the point (1, 2, – 3) and parallel to the plane 2x – 3y +z+5 = 0 is

Find a,b and n in the exapnsion of (a+b)^(n) ifthe first three terms of the expansion are 729 , 7290 and 30375 , respectively .

The mean of 5 observations is 4.4 and their varience is 8.24 . Ifthree of the observations are 1,2 and 6 , find the other two observations.

Find the derivative of x^(2)-2 at point x-10

A bag 'A' contains 2 white and 3 red balls andbag 'B' contains 4 white and 5 red balls. One ball is drawn at random from a randomlychosen bag and is found to be red. Theprobability that it was drawn from bag 'B' was