14949 + Interview Questions in Maths in Class 11 Page 117 InterviewSolution

5801.	A variable plane is at a constant distance P from the origin and meets the axes in A, B and C. The locus of the centroid of tetrahedran OABC is
Answer» `x^(-2)+y^(-2), Z^(-2)=p^(-2)` `x^(-2)+y^(-2)+z^(-2)=4p^(-2)` `x^(-2)+y^(-2)+z^(-2)=16p^(-2)` `x^(2)+y^(2)+z^(2)=p^(2)` Answer :C

Discussion

5802.	For what values of k, f(x) = x-(k)/(x) has a maximum value at x = -2.
Answer» ANSWER :`K = -4`

Discussion

5803.	Solve the equations: Q. sqrt((2x^(2)+1)/(x^(2)-1))+6sqrt((x^(2)-1)/(2x^(2)+1))=5.
Answer» ANSWER :`pmsqrt((5)/(2)),pmsqrt((10)/(7))`.

Discussion

5804.	For two events A and B P(A)=3/4 and P(B)=5/8. The false statement is:
Answer» <P>`P(AUUB)ge3/4` `1/8leP(ANNB')le3/8` `3/8leP(AnnB)le5/8` `P(AuuB)le1/2` SOLUTION :N/a

Discussion

5805.	Statement -1 : For every natural numbern ge 2, (1)/( sqrt1) + (1)/( sqrt2) + (1)/( sqrt3) + … + (1)/( sqrtn) gt sqrtn. Statement - 2 : For every natural number n ge 2, sqrt(n(n+1) ) lt n+1
Answer» STATEMENT-1 is TRUE, Statement-2 is true, Statement-2 is not a CORRECT explanation for Statement-1 Statement -, 1 is true, Statement - 2 is FALSE 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 Answer :A

Discussion

5806.	What is the probability of getting 9 cards of the same suit in one hand at a gane of bridge ?
Answer» ANSWER :`=""^(4)C_1xx""^(13)C_(9)xx""^(39)C_(4) //(""^(52)C_(13))`.

Discussion

5807.	Express sinA+sin3A and cosA+cos3A in product form
Answer» SOLUTION :sinA+sin3A=2sin2AcosA , cosA+cos3A=2cos2AcosA

Discussion

5808.	If A is the area and 2s is the sum of the sides of a triangle, then
Answer» `A LE s^(2)/4` `A le s^(2)/(3 sqrt3)` `A lt s^(2)/sqrt3` NONE of these Answer :A::B

Discussion

5809.	Letf(x)= (1)/(2)[f( xy ) + f((x)/(y)) ]AA x, y in R ^(+)such thatf(1)= 0, f^(1) (1)=2Now answer the following f(x)- f(y ) =
Answer» `F(y/x)` `f(x/y)` `f(2X)` `f(2Y)` ANSWER :B

Discussion

5810.	A box contains 8 red, 3 white and 9 black balls. If three balls are drawn at random, find the probability that: (i) All three balls are of different colour, (ii) One ball is red and two balls are white. (iii) All three balls are black.
Answer» ANSWER :(i) `(18)/(95)`(ii) `(2)/(95)`(iii) `(7)/(95)`

Discussion

5811.	The perpendicular from the origin to the line y = mx + c meets it at the point (-1, 2). Find the values of m and c.
Answer» ANSWER :`m = 1/2 , C = 5/2`

Discussion

5812.	Prove by induction the inequality (1+x)^(n) ge 1 + nx. whenever x is positive and n is a positive interger.
Answer» <P> ANSWER :p(N) is TURE for all VALUES , of n,

Discussion

5813.	If f(x)=(a-x^(n))^(1//n), where a gt 0 and n is a positive integer, then f[f(x)]=
Answer» `F(X)` x 0 1 Answer :B

Discussion

5814.	Period of tan (x + 2x + 3x +….+ n x) is
Answer» `(2pi)/(N(n+1))` `(4pi)/(n(n+1))` `(PI)/(n(n+1))` `(6PI)/(n(n+1))` Answer :A

Discussion

5815.	If sintheta-3sin2theta+sin3theta=costheta-3cos2theta+cos3theta, then one of the general value is:
Answer» `(NPI)/(2)+pi/8` `npi+pi/8` `npi-pi/8` `(npi)/(2)-pi/8` SOLUTION :N//A

Discussion

5816.	Find the approximate value of root(3)(999)
Answer» ANSWER :9.9967

Discussion

5817.	Let X= {x//x in N, 1 le x le 8}, A = {1,2,3},B={2,4,6}, C= {1,3,5,7}, then (AuuB)'=
Answer» `{5,7,8}` `{1,3,5,6,7,8}` `{2,4,6,8}` `{1,3,5,7,8}` ANSWER :A

Discussion

5818.	The system of equations 2x+6y+11=0,6y-18z+1=0,6x+20y-6z+3=0
Answer» consistent inconsistent can not be determined none Answer :B

Discussion

5819.	If the lines a_(1)x+b_(1)y=1,a_(2)x+b_(2)y=1,a_(3)x+b_(3)y=1, are concurrent then the points (a_(1),b_(1)),(a_(2),b_(2)),(a_(3),b_(3))
Answer» FORMS EQUILATERAL triangle forms RIGHT ANGLED triangle forms scalane triangle lie on a STRAIGHT line Answer :D

Discussion

5820.	For the plane pi=2x-3y+4z+5=0, the points A=(1,2,0),B=(1,2,-3)
Answer» LIE on the same side of `pi=0` lie on the OPPOSITE side of `pi=0` lie on the NORMAL to `pi=0` LIES on the plane ANSWER :B

Discussion

5821.	Find the equation of the line which passes through the point (4, -5)and is parallel to the line joining the points A(3,7) and B(-2,4) .
Answer» ANSWER : `3x+4y+8=0`

Discussion

5822.	The value of tan 6^(@) tan 42^(@) tan 66^(@) tan 78^(@) is
Answer» 1 `1//2` `1//4` `1//8` ANSWER :A

Discussion

5823.	If two coins are tossed once , what is the probability of getting (i) both heads , (ii) both heads or both talls (iii)at least one head ?
Answer» ANSWER :`=(3)/(4)`.

Discussion

5824.	Find the locus of z satisfying \|(z-3)/(z+1)\|=3 in the complex plane.
Answer» Answer :`X^(2) + y^(2)+ 3X= 0`. A circle CENTRE `(-(3)/(2), 0)` and radius `(3)/(2)` units

Discussion

5825.	If (l,m,n) are the direction cosines of a line, find the maximum value of the product lmn.
Answer» ANSWER :`(1)/(3sqrt(3))`

Discussion

5826.	If E and F are two events such that P(E)=1/4, P(E)=1/2 and P(E and F)=1/8. Find P (not E and not F).
Answer» ANSWER :(i) `5/8` (II) `3/8`

Discussion

5827.	The mean and variance of eight observation are 9 and 9.25, respectively. If six of the observation are 6,7,10,12,12 and 13, find the remaining two observations.
Answer» ANSWER :8 and 4

Discussion

5828.	The normal form of line sqrt(3)x=y+4=0 is
Answer» `x"SIN"(pi)/6+y"cos"(pi)/6=2` `x"cos"(7pi)/6+y"sin"(7pi)/6=2` `x"cos"(5PI)/6+y"sin"(5pi)/6=2` `x"cos"(11pi)/6+y"sin"(11pi)/6=2` ANSWER :B

Discussion

5829.	The value of f(0) so thatf(x) = (sqrt( 1 + x )-1)/(x)is continuous at x = 0 is
Answer» ` -(1)/(2)` `1/3` `1/2` `- (1)/(3)` ANSWER :C

Discussion

5830.	Period of sin""(3pi x)/(2) + cos""(pi x)/(2) is
Answer» 1 2 3 4 Answer :D

Discussion

5831.	cos^(2)(""(pi)/(6) + theta ) -sin^(2)""((pi)/(6) - theta ) =
Answer» `(1)/(2)COS2THETA` `-(1)/(2)COS2 THETA` 0 1 Answer :A

Discussion

5832.	The perpendicular distance of the point (2,4,-1) from line (x +5)/(1) =(y+3)/(4) = (z-6)/(-9) is
Answer» 3 5 7 9 Answer :C

Discussion

5833.	Which of the following statements is false:
Answer» if \|A\| = 0, then \|ADJ A\| = 0 adjoint of a diagonal MATRIX of order `3xx3` is a diagonal matrix product of TWO uppertriangular matrices is an upper triangular matrix adj (AB) = adj (A) adj (B) Answer :D

Discussion

5834.	Which of the following sentences are statement? Give reason for your answer: May God bless you!
Answer» ANSWER :Not a STATEMENT

Discussion

5835.	int 2 ^(3x + 5 ) dxis
Answer» `(3(2^(3x+5)))/(log 2 ) + c ` `(2^(3x+5))/( 2 log( 3 X + 5)) + c` `( 2^(3x+5))/( 2 log 3) + c` `(2^(3x +5))/(2 log 2)+ c ` ANSWER :A

Discussion

5836.	If X and Y be two events such that P(X//Y)=(1)/(2),P(Y//X)=(1)/(3) and P(X nnY)=(1)/(6) then P(XuuY) is ......
Answer» `(1)/(3)` `(2)/(3)` `(2)/(5)` `(1)/(6)` ANSWER :B::C

Discussion

5837.	Let vec(a)= 2vec(i)+ vec(j)-2vec(k), vec(b)= vec(i) + vec(j) " if " vec(c ) is a vector such that vec(a).vec(c )= \|vec(c )\|, \|vec( c)- vec(a)\|= 2 sqrt2 and the angle between vec(a) xx vec(b) and vec(c ) " is " 30^(@), then find \|(vec(a) xx vec(b)) xx vec( c)\|
Answer» ANSWER :`(3)/(2)`

Discussion

5838.	If tan A. tan B = (1)/(2),"then" (5-3 cos 2A)(5-3 cos 2B) =
Answer» 2 8 12 16 Answer :D

Discussion

5839.	Given the sets A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8}, which of the following may be considered as universal set (s) for all the three sets A, B and C {0, 1, 2, 3, 4, 5, 6}
Answer» ANSWER :III

Discussion

5840.	If the equation x^(2)+2sqrt(2)xy+2y^(2)+4x+4sqrt(2)y+1=0 represents tangents to same circle then circumference of circle is
Answer» `2PI` `3PI` `PI` `4PI` ANSWER :A

Discussion

5841.	In triangle ABC, right angle at B if s-a=3, s-c=2 then a,c are
Answer» 1,4 3,4 2,4 4,5 Answer :B

Discussion

5842.	State whether each of the following set is finite or infinite: The set of numbers which are multiple of 5
Answer» ANSWER :it is an INFINITE SET

Discussion

5843.	(Sin^(3)43^(@)-Sin^(3)17^(@))/(Sin43^(@)-Sin17^(@))=
Answer» `1/2` `3/4` 1 `3/2` ANSWER :B

Discussion

5844.	1+ 3+ 7 + 15…n terms =
Answer» `2^( N+1) -n -2` `n^(2) + n-2` `2^(n) + n^(2) -2` `n^(2) -2` ANSWER :B

Discussion

5845.	Use the graph to find the limits (if it exists).If the limit does not exist ,explain why? lim_[xrarr(pi/2)]tanx
Answer» ANSWER :LIMIT does not EXIST

Discussion

5846.	How many words with or without meaning each of 3 vowels and 2 consonants can be formed from the letters of the word INVOLUTE.
Answer» ANSWER :2880

Discussion

5847.	If the rate of change of sine and tangent of the same angle are equal then the angle
Answer» VELOCITY displacement initial velocity `AE^(t)` ANSWER :B

Discussion

5848.	Write each of the following statements in the form of if then: Tara goes to presidential house indicates that Tara is in Delhi.
Answer» Answer :I Tara is in DELHI then he GOTO PRESIDENTIAL HOUSE.

Discussion

5849.	Twoballs are selected from two black and twored balls. The probability that the two ballswill have no black balls is
Answer» `(1)/(7)` `(1)/(5)` `(1)/(4)` `(1)/(6)` ANSWER :D

Discussion

5850.	A number is selected at random from first 200 natural numbers. Find the probability that it is divisible by either 3 or 5.
Answer» SOLUTION :N/a

Discussion

Explore topic-wise InterviewSolutions in .

A variable plane is at a constant distance P from the origin and meets the axes in A, B and C. The locus of the centroid of tetrahedran OABC is

For what values of k, f(x) = x-(k)/(x) has a maximum value at x = -2.

Solve the equations: Q. sqrt((2x^(2)+1)/(x^(2)-1))+6sqrt((x^(2)-1)/(2x^(2)+1))=5.

For two events A and B P(A)=3/4 and P(B)=5/8. The false statement is:

Statement -1 : For every natural numbern ge 2, (1)/( sqrt1) + (1)/( sqrt2) + (1)/( sqrt3) + … + (1)/( sqrtn) gt sqrtn. Statement - 2 : For every natural number n ge 2, sqrt(n(n+1) ) lt n+1

What is the probability of getting 9 cards of the same suit in one hand at a gane of bridge ?

Express sinA+sin3A and cosA+cos3A in product form

If A is the area and 2s is the sum of the sides of a triangle, then

Letf(x)= (1)/(2)[f( xy ) + f((x)/(y)) ]AA x, y in R ^(+)such thatf(1)= 0, f^(1) (1)=2Now answer the following f(x)- f(y ) =

A box contains 8 red, 3 white and 9 black balls. If three balls are drawn at random, find the probability that: (i) All three balls are of different colour, (ii) One ball is red and two balls are white. (iii) All three balls are black.

The perpendicular from the origin to the line y = mx + c meets it at the point (-1, 2). Find the values of m and c.

Prove by induction the inequality (1+x)^(n) ge 1 + nx. whenever x is positive and n is a positive interger.

If f(x)=(a-x^(n))^(1//n), where a gt 0 and n is a positive integer, then f[f(x)]=

Period of tan (x + 2x + 3x +….+ n x) is

If sintheta-3sin2theta+sin3theta=costheta-3cos2theta+cos3theta, then one of the general value is:

Find the approximate value of root(3)(999)

Let X= {x//x in N, 1 le x le 8}, A = {1,2,3},B={2,4,6}, C= {1,3,5,7}, then (AuuB)'=

The system of equations 2x+6y+11=0,6y-18z+1=0,6x+20y-6z+3=0

If the lines a_(1)x+b_(1)y=1,a_(2)x+b_(2)y=1,a_(3)x+b_(3)y=1, are concurrent then the points (a_(1),b_(1)),(a_(2),b_(2)),(a_(3),b_(3))

For the plane pi=2x-3y+4z+5=0, the points A=(1,2,0),B=(1,2,-3)

Find the equation of the line which passes through the point (4, -5)and is parallel to the line joining the points A(3,7) and B(-2,4) .

The value of tan 6^(@) tan 42^(@) tan 66^(@) tan 78^(@) is

If two coins are tossed once , what is the probability of getting (i) both heads , (ii) both heads or both talls (iii)at least one head ?

Find the locus of z satisfying |(z-3)/(z+1)|=3 in the complex plane.

If (l,m,n) are the direction cosines of a line, find the maximum value of the product lmn.

If E and F are two events such that P(E)=1/4, P(E)=1/2 and P(E and F)=1/8. Find P (not E and not F).

The mean and variance of eight observation are 9 and 9.25, respectively. If six of the observation are 6,7,10,12,12 and 13, find the remaining two observations.

The normal form of line sqrt(3)x=y+4=0 is

The value of f(0) so thatf(x) = (sqrt( 1 + x )-1)/(x)is continuous at x = 0 is

Period of sin""(3pi x)/(2) + cos""(pi x)/(2) is

cos^(2)(""(pi)/(6) + theta ) -sin^(2)""((pi)/(6) - theta ) =

The perpendicular distance of the point (2,4,-1) from line (x +5)/(1) =(y+3)/(4) = (z-6)/(-9) is

Which of the following statements is false:

Which of the following sentences are statement? Give reason for your answer: May God bless you!

int 2 ^(3x + 5 ) dxis

If X and Y be two events such that P(X//Y)=(1)/(2),P(Y//X)=(1)/(3) and P(X nnY)=(1)/(6) then P(XuuY) is ......

Let vec(a)= 2vec(i)+ vec(j)-2vec(k), vec(b)= vec(i) + vec(j) " if " vec(c ) is a vector such that vec(a).vec(c )= |vec(c )|, |vec( c)- vec(a)|= 2 sqrt2 and the angle between vec(a) xx vec(b) and vec(c ) " is " 30^(@), then find |(vec(a) xx vec(b)) xx vec( c)|

If tan A. tan B = (1)/(2),"then" (5-3 cos 2A)(5-3 cos 2B) =

Given the sets A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8}, which of the following may be considered as universal set (s) for all the three sets A, B and C {0, 1, 2, 3, 4, 5, 6}

If the equation x^(2)+2sqrt(2)xy+2y^(2)+4x+4sqrt(2)y+1=0 represents tangents to same circle then circumference of circle is

In triangle ABC, right angle at B if s-a=3, s-c=2 then a,c are

State whether each of the following set is finite or infinite: The set of numbers which are multiple of 5

(Sin^(3)43^(@)-Sin^(3)17^(@))/(Sin43^(@)-Sin17^(@))=

1+ 3+ 7 + 15…n terms =

Use the graph to find the limits (if it exists).If the limit does not exist ,explain why? lim_[xrarr(pi/2)]tanx

How many words with or without meaning each of 3 vowels and 2 consonants can be formed from the letters of the word INVOLUTE.

If the rate of change of sine and tangent of the same angle are equal then the angle

Write each of the following statements in the form of if then: Tara goes to presidential house indicates that Tara is in Delhi.

Twoballs are selected from two black and twored balls. The probability that the two ballswill have no black balls is

A number is selected at random from first 200 natural numbers. Find the probability that it is divisible by either 3 or 5.