14949 + Interview Questions in Maths in Class 11 Page 36 InterviewSolution

1751.	Find the modulus and amplitude of the following complex numbers and hence express them into polar form -2+2 sqrt3i
Answer» ANSWER :Modulus= 4, amplitude= `(2PI)/(3), z= ("COS"(2pi)/(3) + "isin"(2pi)/(3))`

Discussion

1752.	Find the modulus and amplitude of the following complex numbers and hence express them into polar form -sqrt3+i
Answer» ANSWER :Modulus= 2, amplitude= `(5PI)/(6), z= 2 ("COS"(5pi)/(6) + "ISIN" (5pi)/(6))`

Discussion

1753.	Find the modulus and amplitude of the following complex numbers and hence express them into polar form -2i
Answer» ANSWER :MODULUS= 2, amplitude= `-(pi)/(2); Z= 2[cos (-(pi)/(2))-i " SIN" (-(pi)/(2))]`

Discussion

1754.	Find the modulus and amplitude of the following complex numbers and hence express them into polar form -1-i
Answer» ANSWER :Modulus= `sqrt2`, amplitude= `-(3pi)/(4); Z= sqrt2 [COS (-(3pi)/(4)) + "isin" (-(3pi)/(4))]`

Discussion

1755.	A function f is defined by f(x)=\|x\|^(m)\|x-1\|^(n)AAx inR . The local maximum value of the function is , (m,ninN)
Answer» 1 `m^(N)n^(m)` `(m^(m)n^(n))/((m+n)^(m+n))` `((MN)^(mn))/((m+n)^(m+n))` ANSWER :C

Discussion

1756.	If the sum of the coefficients in the expansion of (x+y)^(n) is 4096. Then find the greatest coefficient in the expansion.
Answer» ANSWER :`= 924`

Discussion

1757.	Find the modulus and amplitude of the following complex numbers and hence express them into polar form ((1+i)^(13))/((1-i)^(7))
Answer» ANSWER :MODULUS= 2, AMPLITUDE= `PI`

Discussion

1758.	Find the modulus and amplitude of the following complex numbers and hence express them into polar form -2
Answer» Answer :MODULUS= 2, amplitude= `PI, z=2 [cos pi + i SIN pi]`

Discussion

1759.	Find the slope of a line parallel to the which passes through each pair of the following points: (0, 0) and (5, 6)
Answer» ANSWER : `6/(5)`

Discussion

1760.	Find the modulus and amplitude of the following complex numbers and hence express them into polar form ((1+i)(2+i))/((3+i))
Answer» Answer :MODULUS= 1, amplitude= `53^(@)8'`

Discussion

1761.	Find the modulus and amplitude of the following complex numbers and hence express them into polar form (3+i) (4+i)
Answer» ANSWER :MODULUS= `sqrt170`, AMPLITUDE= `32^(@)29'`

Discussion

1762.	Find the modulus and amplitude of the following complex numbers and hence express them into polar form ((3+4i) (4+ 5i))/((4+3i) (6+7i))
Answer» Answer :Modulus= `SQRT((41)/(85))`, amplitude= `18^(@)12'`

Discussion

1763.	Find the modulus and amplitude of the following complex numbers and hence express them into polar form (5-i)/(2-3i)
Answer» ANSWER :Modulus= `SQRT2`, AMPLITUDE= `(pi)/(4)`

Discussion

1764.	If Sigma n = 210 " then " Sigma n^(2)=…….
Answer» 2870 2160 2970 None of these Answer :A

Discussion

1765.	If the coefficient of variation and standard deviationare 60 and 21 respectively, the arithmetic mean of distribution Is :
Answer» 30 21 60 35 Answer :D

Discussion

1766.	A straight line passing through origin and inclined at 60^(@) to the line sqrt(3)x=y=1 is
Answer» `y=0` `x=0` `x+y=0` `x-y=0` ANSWER :A

Discussion

1767.	Statemen1 : The equation x log x=2-x is satified by at least one value of x lying between 1 and 2. Statement 2: The function (f)x= x log x is an increasesing function in [1,2] and g(x)=2-xis a decreasing fucntion in [1,2] and the graphs represented by these functions intersect at a point in [1,2]
Answer» Statement-1 is TRUE, statement-2 is true, Statement-2 is CORRECT EXPLANATION for Statement-1. Statement-1 is true, statement-2 is not a correct explanation for Statement-1. Satement-1 is FALSE, Statement-2 is true Statement-1 is true Statement-2 false Answer :A

Discussion

1768.	If A+B+C=180^(@), prove that (i) sin 2A+sin 2B+sin 2C=4 sin A sin B sin C (ii) cos A+cos B-Cos C=-1 +4 cos ""A/2 cos ""B/2sin ""C/2 (iii) sin^(2) A+sin^(2) B+sin^(2) C=2+2 cos A cos B cos C (iv) sin^(2) A+sin^(2) B-sin^(2) C=2 sin A sin B cos C (v) tan ""A/2 tan""B/2 +tan""B/2 tan ""C/2+tan ""C/2 tan""A/2=1 (vi) sin A+sin B+ sin C=4 cos ""A/2 cos""B/2 cos ""C/2 (viii) sin (B+C-A) +sin (C+A-B) +sin (A+B-C)=4 sin A sin B sin C.
Answer» Answer :(i) `4 sin A sin B sin C` (ii) `-1+4 COS""A/2 cos ""B/2 sin ""C/2` (iii) `2+2 cos A cos B cos C` (iv) `2 sin A sin B cos C` (v) 1 (vi) `4 sin A sin B sin C`

Discussion

1769.	Let A= {1, 2, {3, 4}, 5}. Which of the following statemets are incorrect and why? phi in A
Answer» ANSWER :INCORRECT

Discussion

1770.	If abs(bara)=1,abs(barb)=1,abs(barc)=2 and baraxx(baraxxbarc)+barb=bar0 then find the angle between bara and barc
Answer» ANSWER :`30^(@)"(or)"150^(@)`

Discussion

1771.	Let alpha, beta and gammabe some angles in the first quadrant satisfying tan(alpha + beta)=15//8 and "cosec" gamma = 17//8, then which of the following hold(s) good ?
Answer» `ALPHA + BETA + gamma=pi` `cot alpha cot beta cotgamma = cot alpha + cotbeta + cot gamma` `TAN alpha + tan beta + tan gamma = tan alpha tan beta tan gamma` `tan alpha tan beta + tan beta tangamma + tan gamma tan alpha =1` Answer :B::D

Discussion

1772.	O is the centre and AB and AC are two diagonals of the adjacent faces of a rectangular box. If angles given by lfloorAOB=alpha,lfloorBOC=beta,lfloorCOA=lambda then find the value of cos alpha + cos beta + cos lambda.
Answer» ANSWER :-1

Discussion

1773.	If out of 6 flags any number of flags can be shown at a timefind how many different signals can be made out of them.
Answer» ANSWER :` ""^(6)P_1 ""^(6)P_1 +""^(6)P_3+""^(6) P_5+""^(6)P_6= 1956`

Discussion

1774.	Find the modulus and argument of the complex number (1+2i)/(1-3i).
Answer» ANSWER :`1/sqrt(2), (3PI)/4`

Discussion

1775.	The value of a, for which the points A,B,C with position vectors 2bari- barj+bark, bari-3barj-5bark and abari- 3barj+bark respectively are the verticesof a right angled trianglle with C=pi/2 are
Answer» 2,1 `-2,-1` `-2,1` 2,-1 Answer :A

Discussion

1776.	Define (i) f(x)=(1+2x)^(1//3x)is continuous at x = 0.
Answer» ANSWER :`E^(2//3)`

Discussion

1777.	Find point on Y-axis which is of the distance sqrt10 from point (1, 2, 3).
Answer» ANSWER :(0, 2, 0)

Discussion

1778.	Evaluate the following limits : Lim_( x to pi//6) (sin (x - pi/6))/(sqrt(3)/2 - cos x )
Answer» ANSWER :2

Discussion

1779.	A triangle of maximum area ininscribed in a circle Ifa side of the triangle is 20sqrt(3)) then theradius of the circleis
Answer» 20 30 40 60 Answer :A

Discussion

1780.	Two candidates attempt to solve a quadratic equation of the form x^(2)+px+q=0. One starts with a wrong value of p and finds the roots to be 2 and 6. the other starts with a wrong vlaue of q and finds the roots to be 2 and -9. find the correct roots and the equation.
Answer» ANSWER :`-3,-4;X^(2)+7x+12=0`.

Discussion

1781.	A coin and a die are tossed . Describe the following events . B : getting aprime number ,
Answer» Answer :`B={H2,H3,H5,T2,T3,T5}`

Discussion

1782.	Find the solution set of inequality sin theta gt (sqrt(3))/(2)
Answer» Answer :`2NPI + (PI)/(3) lt theta 2npi + (2pi)/(3)`, where `n in Z`

Discussion

1783.	Express the following expression in the form of a+lb: ((3-2i)(2+3i))/((1+2i)(2-i))
Answer» ANSWER :`(63)/(25)-(16)/(25)i`

Discussion

1784.	Differentiate the following functions: 10. (1)/( x) + (3)/( x^2)+ (2)/( x^3)
Answer» ANSWER :`(-1)/(x^2) - (6)/( x^3)- (6)/( x^4)`

Discussion

1785.	Which of the following statements are true and which are false? In each case given a valid reason forsaying so: t:sqrt(11) is a rational number.
Answer» ANSWER :IRRATIONAL NUMBER.

Discussion

1786.	Which of the following statements are true and which are false? In each case given a valid reason forsaying so: s: If x and y are integers such that xgty then -xlt-y.
Answer» ANSWER :TRUE.

Discussion

1787.	Which of the following statements are true and which are false? In each case given a valid reason forsaying so: (i) p: Each radius of a circle is a chord of the circle.
Answer» ANSWER :CHORD of the CIRCLE.

Discussion

1788.	Which of the following statements are true and which are false? In each case given a valid reason forsaying so: r: Circle is a particular case of an ellipse.
Answer» ANSWER :we GET CIRCLE.

Discussion

1789.	Which of the following statements are true and which are false? In each case given a valid reason forsaying so: q: The centre of a circle bisects each chord of the circle.
Answer» ANSWER :not the CHORD of CIRCLE.

Discussion

1790.	If S_(n) denotes the sum of n terms of an AP whose first term is a, common difference is d and n denotes the no. of terms, then S_(n)+1 - S_(n) is :
Answer» AP nd a+nd 0 Answer :C

Discussion

1791.	Complete the following table (##ANE_PMP_MAT_0XI_C11_E04_009_Q01##)
Answer» SOLUTION :LENGTH of TRANSVERSE axis: `8, 2/sqrt3,2` Eccentricity: `5/4, sqrt5/2, sqrt17/4` Latus RECTUM: `9/2, sqrt3,1/2`

Discussion

1792.	Represent the complex number 1+sqrt3i in the polar form.
Answer» ANSWER :`2(COS(PI)3/-isin(pi)/3)` or 2(cos(-pi)/3+isin(-pi)/3)`

Discussion

1793.	There are 60% students in Maths and 305 in Biology. If 10% students are in both subjects. Find the probability that a randomly selected student has Maths or Biology.
Answer» SOLUTION :N/a

Discussion

1794.	If f: C to C such that f(z) =z-barz, AA z in C, then f is:
Answer» ONE-one ONTO bijection neither one one nor onto ANSWER :D

Discussion

1795.	Find the sumof the series7 + 10 + 22 + 70 + . . . up to n terms
Answer» ANSWER :`(1)/(3)(4^(n)+18 n - 1)`

Discussion

1796.	Write the negation of the following statements: s: All students study mathematics at the elementary level.
Answer» ANSWER :ELEMENTARY LEVEL.

Discussion

1797.	If ( a^(2) + b^(2))/( a^(2) - b^(2)) = ( sin C)/( sin (A- B))then triangle ABC is
Answer» Scalene EQUILATERAL Isosceles RIGHT ANGLED ANSWER :D

Discussion

1798.	Slope of a line which cuts off intercepts of equal lengths on the axes is .........
Answer» `-1` `0` `2` `SQRT3` ANSWER :A

Discussion

1799.	Prove that the volume of the largest cone that can be inscribed in a sphere of radius R is 8/(27) times the volume of the sphere
Answer» ANSWER :`8/(27)`

Discussion

1800.	The number of values of x in the interval [0, 5 pi] satisfying the equation 3 sin^(2) x - 7 sin x + 2 = 0 is
Answer» 0 5 6 10 Answer :C

Discussion

Explore topic-wise InterviewSolutions in .

Find the modulus and amplitude of the following complex numbers and hence express them into polar form -2+2 sqrt3i

Find the modulus and amplitude of the following complex numbers and hence express them into polar form -sqrt3+i

Find the modulus and amplitude of the following complex numbers and hence express them into polar form -2i

Find the modulus and amplitude of the following complex numbers and hence express them into polar form -1-i

A function f is defined by f(x)=|x|^(m)|x-1|^(n)AAx inR . The local maximum value of the function is , (m,ninN)

If the sum of the coefficients in the expansion of (x+y)^(n) is 4096. Then find the greatest coefficient in the expansion.

Find the modulus and amplitude of the following complex numbers and hence express them into polar form ((1+i)^(13))/((1-i)^(7))

Find the modulus and amplitude of the following complex numbers and hence express them into polar form -2

Find the slope of a line parallel to the which passes through each pair of the following points: (0, 0) and (5, 6)

Find the modulus and amplitude of the following complex numbers and hence express them into polar form ((1+i)(2+i))/((3+i))

Find the modulus and amplitude of the following complex numbers and hence express them into polar form (3+i) (4+i)

Find the modulus and amplitude of the following complex numbers and hence express them into polar form ((3+4i) (4+ 5i))/((4+3i) (6+7i))

Find the modulus and amplitude of the following complex numbers and hence express them into polar form (5-i)/(2-3i)

If Sigma n = 210 " then " Sigma n^(2)=…….

If the coefficient of variation and standard deviationare 60 and 21 respectively, the arithmetic mean of distribution Is :

A straight line passing through origin and inclined at 60^(@) to the line sqrt(3)x=y=1 is

Statemen1 : The equation x log x=2-x is satified by at least one value of x lying between 1 and 2. Statement 2: The function (f)x= x log x is an increasesing function in [1,2] and g(x)=2-xis a decreasing fucntion in [1,2] and the graphs represented by these functions intersect at a point in [1,2]

Let A= {1, 2, {3, 4}, 5}. Which of the following statemets are incorrect and why? phi in A

If abs(bara)=1,abs(barb)=1,abs(barc)=2 and baraxx(baraxxbarc)+barb=bar0 then find the angle between bara and barc

Let alpha, beta and gammabe some angles in the first quadrant satisfying tan(alpha + beta)=15//8 and "cosec" gamma = 17//8, then which of the following hold(s) good ?

O is the centre and AB and AC are two diagonals of the adjacent faces of a rectangular box. If angles given by lfloorAOB=alpha,lfloorBOC=beta,lfloorCOA=lambda then find the value of cos alpha + cos beta + cos lambda.

If out of 6 flags any number of flags can be shown at a timefind how many different signals can be made out of them.

Find the modulus and argument of the complex number (1+2i)/(1-3i).

The value of a, for which the points A,B,C with position vectors 2bari- barj+bark, bari-3barj-5bark and abari- 3barj+bark respectively are the verticesof a right angled trianglle with C=pi/2 are

Define (i) f(x)=(1+2x)^(1//3x)is continuous at x = 0.

Find point on Y-axis which is of the distance sqrt10 from point (1, 2, 3).

Evaluate the following limits : Lim_( x to pi//6) (sin (x - pi/6))/(sqrt(3)/2 - cos x )

A triangle of maximum area ininscribed in a circle Ifa side of the triangle is 20sqrt(3)) then theradius of the circleis

Two candidates attempt to solve a quadratic equation of the form x^(2)+px+q=0. One starts with a wrong value of p and finds the roots to be 2 and 6. the other starts with a wrong vlaue of q and finds the roots to be 2 and -9. find the correct roots and the equation.

A coin and a die are tossed . Describe the following events . B : getting aprime number ,

Find the solution set of inequality sin theta gt (sqrt(3))/(2)

Express the following expression in the form of a+lb: ((3-2i)(2+3i))/((1+2i)(2-i))

Differentiate the following functions: 10. (1)/( x) + (3)/( x^2)+ (2)/( x^3)

Which of the following statements are true and which are false? In each case given a valid reason forsaying so: t:sqrt(11) is a rational number.

Which of the following statements are true and which are false? In each case given a valid reason forsaying so: s: If x and y are integers such that xgty then -xlt-y.

Which of the following statements are true and which are false? In each case given a valid reason forsaying so: (i) p: Each radius of a circle is a chord of the circle.

Which of the following statements are true and which are false? In each case given a valid reason forsaying so: r: Circle is a particular case of an ellipse.

Which of the following statements are true and which are false? In each case given a valid reason forsaying so: q: The centre of a circle bisects each chord of the circle.

If S_(n) denotes the sum of n terms of an AP whose first term is a, common difference is d and n denotes the no. of terms, then S_(n)+1 - S_(n) is :

Complete the following table (##ANE_PMP_MAT_0XI_C11_E04_009_Q01##)

Represent the complex number 1+sqrt3i in the polar form.

There are 60% students in Maths and 305 in Biology. If 10% students are in both subjects. Find the probability that a randomly selected student has Maths or Biology.

If f: C to C such that f(z) =z-barz, AA z in C, then f is:

Find the sumof the series7 + 10 + 22 + 70 + . . . up to n terms

Write the negation of the following statements: s: All students study mathematics at the elementary level.

If ( a^(2) + b^(2))/( a^(2) - b^(2)) = ( sin C)/( sin (A- B))then triangle ABC is

Slope of a line which cuts off intercepts of equal lengths on the axes is .........

Prove that the volume of the largest cone that can be inscribed in a sphere of radius R is 8/(27) times the volume of the sphere

The number of values of x in the interval [0, 5 pi] satisfying the equation 3 sin^(2) x - 7 sin x + 2 = 0 is