14949 + Interview Questions in Maths in Class 11 Page 230 InterviewSolution

11451.	Evaluate the following limits. Lt_(xto1)(sin(x-1))/(x^(2)-1)
Answer» ANSWER :`1/2`

Discussion

11452.	If 0lexle 2pi and \|cosx\|le sin x, then
Answer» the set of all values of x is `[(pi)/4, (3pi)/4]` the NUMBER of solutions that are integral multiple of `(pi)/4` is four the SUM of the LARGEST and the SMALLEST solution is `pi` the set of all values of `x` is `x in [(pi)/4, (pi)/2)uu((pi)/2, (3pi)/4]` ANSWER :A::C

Discussion

11453.	Common roots of the equations of cos2x+sin2x=cotx and 2cos^(2)x+ cos^(2)2x=1
Answer» `2npi` `NPI` `((2n+1)PI)/(4)` `((2n+1)pi)/(2)` ANSWER :C

Discussion

11454.	{:("Column- I ","Column-II "),("A) If " ((sin theta)/(sin phi))^(2) = (tan theta)/(tan phi)=3 "then the value of " theta and phi " are ","(p) Infinite number of solutions "),("B) The number of solutions of " (sin ^(2) x + cos ^(4) x)/(cos^(2) x + sin^(4) x ) = 1 ,"q) " theta = n pi pm (pi)/(3)"," phi = n pi pm (pi)/(6) ),("(c) Solution of " cot 2 theta = cot ^(2) theta - tan ^(2) theta ,"r) " n pi pm (pi)/(4)):}
Answer» ANSWER :A- Q; B - p; C - r

Discussion

11455.	If the image of (-7//5, -6//5) in a line is (1, 2), then the equation of the line is
Answer» 3x-y=0 4x-y=0 3x+4y=1 4x+3y=1 Answer :C

Discussion

11456.	From a committee of 8 persons, in how many ways can we choose a chairman and a vice chairman assuming one person can not hold more than one position ?
Answer» ANSWER :56

Discussion

11457.	Let f(n)=2 cos nx AA n in N, then f(1)f(n+1)-f(n) is equal to
Answer» `F (n +3)` `f (n +2)` `f ( n+1) f (2)` `f (n +1) f (2)` ANSWER :B

Discussion

11458.	Three are 4 men and 6 women in a city council.If one council member is selected for a committee at random how likely is it that it is women ?
Answer» ANSWER :`3/5`

Discussion

11459.	A box contains 1 red and 3 identical white balls. Two balls are drawn at random in succession without replacement. Write the sample space for this experiment.
Answer» ANSWER :{RW, WR, WW}

Discussion

11460.	List all the elements of the following sets : E= {x : x =(1)/(2n-1)n in N, 1 le n le 5}
Answer» ANSWER :`E= {1, (1)/(3), (1)/(5), (1)/(7), (1)/(9)}`

Discussion

11461.	If y= sin x +e^(x)then (d^2x)/(dy^2) =
Answer» `(-sinx+e^X)^(-1)` `(sinx-e^x)/((cosx+e^(x))^3)` `(sinx-e^x)/((cosx+e^x)^2)` `(sinx+e^x)/((cosx+e^x)^3)` Answer :B

Discussion

11462.	A coin is tossed thrice. If all the three times, the result is tail, a die is thrown. Otherwise the experiment become end. Write the sample space for this experiment.
Answer» Answer :`S={HHH,HHT,HTH,THH,HT T,THT,T TH,T T T1,T T T2,T T T3,T T T4,T T T5,T T T6}`

Discussion

11463.	Match the following (##ANE_PMP_MAT_0XI_C14_E01_041_Q01.png" width="80%">
Answer» <P> Solution :P is NECESSARY for Q `rarr` conditionastatement p is necessary and sufficient for q`rarr`Biconditionastatement It is not the case that p is hold `rarr`Negation .Either p or q`rarr` DISJUNCTION .

Discussion

11464.	If A=[a_(ij)]_(nxxn) and a_(ij)="A.M." of {i,j} then A is
Answer» Triangular MATRIX DIAGONAL matrix a symmertric matrix skew SYMMETRIC matrix Answer :C

Discussion

11465.	Find the radius of the circle in which a central angle of 60^(@) intercepts and arc of length 37.4cm use pi = (22)/(7).
Answer» ANSWER :`35.7 CM`

Discussion

11466.	ABCD is a rectangle in which AB=10 cmc , BC =8 cms. A point P is taken on AB such that PA =x. The the minimum value of PC^(2)+PD^(2) is obtained when x=
Answer» 10 5 8 4 Answer :B

Discussion

11467.	A factory has two Machines - I and II. Machine-I produced 60% if items and Machine - II produces 40% of the items of the total output. Further 2% of the items produced by Machine - I are defective whereas 4% produced by Machine - II are defective. If an item is drawn at random what is the probability that it is defective ?
Answer» ANSWER :`=0.028`

Discussion

11468.	Match the following: Let A -(0, 1, 2, 3) then the relations R_(1), R_(2), R_(3), R_(4), R_(5) are given and their properties are given below..
Answer» REFLEXIVE, TRANSITIVE, not SYMMETRIC Reflexive symmetric, not transitive Reflexive not symmetric, not transitive not reflexive not symmetric, not transitive

Discussion

11469.	If x in (45^(@),90^(@)), sin2x=1/2, then sin^(3)x-3/4 sinx=
Answer» `1/sqrt2` `-1/sqrt2` `1/(4sqrt2)` `-1/4sqrt2` ANSWER :D

Discussion

11470.	If 'p then q' has its converse 'q then p'.
Answer» ANSWER :TRUE STATEMENT

Discussion

11471.	A= {0, 2, 4, 6, 8, 10}. Insert the appropriate symbol in" or "notin in the blank space. 12"………"A
Answer» ANSWER :`NOTIN`

Discussion

11472.	Given the vertices A(2,-1,4), B(3,2,-6) and C(-5,0,2) of a triangle ABC Find the mid point of BC
Answer» SOLUTION :(-1,1,-2)

Discussion

11473.	If x=3cost-2cos^(3)t,y=3sint-2sin^(3)t then find dy/dx.
Answer» ANSWER : COT t

Discussion

11474.	Three numbers are chosedn from 1 to 20 . Find the probability that they are not consecutive
Answer» `(186)/(190)` `(187)/(190)` `(188)/(190)` `(18)/(""^(20)C_(3))` Answer :B

Discussion

11475.	If the d.c's of the two lines are (2)/(3),(2)/(3),(1)/(3),(5)/(13),(12)/(13),0 then the d.r.s of the line bisecting the angle between the lines are
Answer» 40, 60, 13 41, 60, 10 41, 62, 13 41, 60, 13 Answer :C

Discussion

11476.	The number of values of x in the interval [0,5pi] satisfying the equation. 3sin^(2)x -7sinx + 2=0 is-
Answer» 0 5 6 10 Solution :`3sin^(2)x-7sinx+2=0` `rArr (3sinx-1)(sinx-2)=0` `therefore sinx ne 2` `rArr sinx=1/3 =sinalpha` (SAY) Where `alpha` is the least positive VALUE of x such that `sinalpha=1/3` Clearly, `0 lt alpha lt pi/2`. We get the solution, `x=alpha, pi-alpha, 2pi+alpha, 4PI + alpha` and `5pi- alpha` Hence total six VALUES in `[0,5pi]` Ans.

Discussion

11477.	If A= {-1, 2, 3} and B= {1, 3}, the determine B xx B
Answer» ANSWER :`{(1,1),(1,3),(3,1),(3,3)}`

Discussion

11478.	An event has odds in favour 4 : 5, then the probability that event occurs, is
Answer» `(1)/(5)` `(4)/(5)` `(4)/(9)` `(5)/(9)` ANSWER :C

Discussion

11479.	Write the following as interval. {x : x in R, -2 lt x lt 5}
Answer» ANSWER :`(-2, 5)`

Discussion

11480.	A and B stand in a ring with 10 other persons . If the arrangement of the twelve persons is at random , find the chance that there are exactly three persons between A and B.
Answer» ANSWER :`=(2)/(111)`.

Discussion

11481.	If 1+sin x + sin^(2)x +….oo = 4 + 2sqrt(3), 0 lt x lt pi, x ne pi//2 then x =
Answer» `(pi)/(6)` `(pi)/(4)` `(pi)/(3)or(pi)/(6)` `(pi)/(3) or(2PI)/(3)` Answer :D

Discussion

11482.	The vertex of an equilateral triangle is (2, 3) and the equation of the opposite side is x + y = 2. Then the other two sides are y-3 =( 2 pm sqrt(3) ) ( x-2).
Answer» ANSWER :1

Discussion

11483.	Median of nine observations is 20.45 . If 2 is added in last four observations, then new median is
Answer» ANSWER :FALSE STATEMENT

Discussion

11484.	Line (1+lambda)x+(4-lambda)y+(2+lambda)=0 and (4-lambda)x-(1+lambda)y+(6-3lambda) =0 are concurrent at points A and B respectively and intersect at C then locus of centroid of DeltaABC " is " lambda is parameter
Answer» `(x+3/2)^2+(y+7/10)^2=17/50` `(x-3/2)^2+(y-7/10)^2=17/50` `(x-3/2)^2+(y+7/10)^2=17/450` `(x+3/2)^2+(y+7/10)^2=17/450` ANSWER :D

Discussion

11485.	Prove that sum_(r=0)^n 3^rn Cundersetr = 4^n.
Answer» ANSWER :` 4^(N)`

Discussion

11486.	If G(x)=-sqrt(25-x^2),t h e n("lim")_(xvec1)(G(x)-G(1))/(x-1)i s1/(24) (b) 1/5 (c) -sqrt(24) (d) none of these
Answer» `(1)/(4sqrt(6))` `(1)/(2sqrt(6))` `(1)/(SQRT(6))` `-(1)/(2sqrt(6))` ANSWER :B

Discussion

11487.	Three companies A,B,C get contracts form the Govt in the ratio 5:3:2. The probability that these companies finish the works in time,is 60%,80% and 70% respectively. A work given as a contract is finished in time. Find the probability that it is done by company B.
Answer» ANSWER :`=(6)/(17)`

Discussion

11488.	lim_(xto5^(+))[x]=……..
Answer» 0 5 -5 4 Answer :B

Discussion

11489.	Using the (r+1)^(th) term, find the 3rd,4th and 5th terms in the expansionof (3x+2y)^8
Answer» SOLUTION :81648x^6y^2,108864x^5y^3,90720x^4y^4`

Discussion

11490.	If tan theta = (1)/(2) and tan phi = (1)/(3), then the value of theta + phi is
Answer» `PI/6` `pi` 0 `pi/4` ANSWER :D

Discussion

11491.	The P.V.'s of A, B are bar(a), bar(b) respectively. The P.V. of 'C' is -3bar(a)+5bar(b) then 'C' lies
Answer» OUTSIDE `DELTAOAB` but inside `angleOAB` outside `DeltaOAB` but inside `ANGLEAOB` outside `DeltaOAB` but inside `angleOBA` out side the `Delta OAB` Answer :D

Discussion

11492.	The locus of the points equidistant from the pair of line x^2cos^2theta-2xysin^2theta-y^2sin^2theta=0 is
Answer» `x^2-y^2+xycosec^2theta=0` `x^2+y^2+xycosec^2theta=0` `x^2-y^2+2xycosec^2theta=0` `x^2+y^2+2xycosec^2theta=0` ANSWER :A

Discussion

11493.	Find Lt_(xto0)(1-cosx)/x^(2)
Answer» ANSWER :`1/2`

Discussion

11494.	Compute the following limits. Lt_(xtooo)(8\|x\|+3x)/(3\|x\|-2x)
Answer» ANSWER :11

Discussion

11495.	Express each of the complex number given in the form of a+ib i^(9) + i^(19)
Answer» ANSWER :0+i0

Discussion

11496.	The period of ( tan theta -(1)/(3) tan^(3) theta ) ((1)/(3) - tan^(2) theta )^(-1),where tan^(2) thetane (1)/(3) is :
Answer» `(PI)/(3)` `(2PI)/(3)` `pi` `2pi` ANSWER :A

Discussion

11497.	Find the ratio in which YZ-plane divides the line joining A(2,4,5) and B(3,5,-4). Also find the point of intersection.
Answer» " 5: 4 " " 2: 1 " " 1: 3 " " 3 : 2 " ANSWER :A

Discussion

11498.	Given that the side length of a rhombus is the geometric mean of the lengths of its diagonals. The degree measure of the acute angle of the rhombus is
Answer» `15^(@)` `30(@)` `45^(@)` `60^(@)` Answer :B

Discussion

11499.	Define Law of conservation of energy
Answer» SOLUTION :The law of conservation of ENERGY states that energy can neither be created nor destroyed. It MAY be transformed from one form to ANOTHER but the total energy of an isolated system remains constant.

Discussion

11500.	From a point (2, 0) the feet of perpendiculars to the lines of the pair x^2 -3xy + 2y^2 = 0 are L and M then find the distance LM.
Answer» ANSWER :`SQRT((14)/(5))`

Discussion

Explore topic-wise InterviewSolutions in .

Evaluate the following limits. Lt_(xto1)(sin(x-1))/(x^(2)-1)

If 0lexle 2pi and |cosx|le sin x, then

Common roots of the equations of cos2x+sin2x=cotx and 2cos^(2)x+ cos^(2)2x=1

If the image of (-7//5, -6//5) in a line is (1, 2), then the equation of the line is

From a committee of 8 persons, in how many ways can we choose a chairman and a vice chairman assuming one person can not hold more than one position ?

Let f(n)=2 cos nx AA n in N, then f(1)f(n+1)-f(n) is equal to

Three are 4 men and 6 women in a city council.If one council member is selected for a committee at random how likely is it that it is women ?

A box contains 1 red and 3 identical white balls. Two balls are drawn at random in succession without replacement. Write the sample space for this experiment.

List all the elements of the following sets : E= {x : x =(1)/(2n-1)n in N, 1 le n le 5}

If y= sin x +e^(x)then (d^2x)/(dy^2) =

A coin is tossed thrice. If all the three times, the result is tail, a die is thrown. Otherwise the experiment become end. Write the sample space for this experiment.

Match the following (##ANE_PMP_MAT_0XI_C14_E01_041_Q01.png" width="80%">

If A=[a_(ij)]_(nxxn) and a_(ij)="A.M." of {i,j} then A is

Find the radius of the circle in which a central angle of 60^(@) intercepts and arc of length 37.4cm use pi = (22)/(7).

ABCD is a rectangle in which AB=10 cmc , BC =8 cms. A point P is taken on AB such that PA =x. The the minimum value of PC^(2)+PD^(2) is obtained when x=

Match the following: Let A -(0, 1, 2, 3) then the relations R_(1), R_(2), R_(3), R_(4), R_(5) are given and their properties are given below..

If x in (45^(@),90^(@)), sin2x=1/2, then sin^(3)x-3/4 sinx=

If 'p then q' has its converse 'q then p'.

A= {0, 2, 4, 6, 8, 10}. Insert the appropriate symbol in" or "notin in the blank space. 12"………"A

Given the vertices A(2,-1,4), B(3,2,-6) and C(-5,0,2) of a triangle ABC Find the mid point of BC

If x=3cost-2cos^(3)t,y=3sint-2sin^(3)t then find dy/dx.

Three numbers are chosedn from 1 to 20 . Find the probability that they are not consecutive

If the d.c's of the two lines are (2)/(3),(2)/(3),(1)/(3),(5)/(13),(12)/(13),0 then the d.r.s of the line bisecting the angle between the lines are

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

If A= {-1, 2, 3} and B= {1, 3}, the determine B xx B

An event has odds in favour 4 : 5, then the probability that event occurs, is

Write the following as interval. {x : x in R, -2 lt x lt 5}

A and B stand in a ring with 10 other persons . If the arrangement of the twelve persons is at random , find the chance that there are exactly three persons between A and B.

If 1+sin x + sin^(2)x +….oo = 4 + 2sqrt(3), 0 lt x lt pi, x ne pi//2 then x =

The vertex of an equilateral triangle is (2, 3) and the equation of the opposite side is x + y = 2. Then the other two sides are y-3 =( 2 pm sqrt(3) ) ( x-2).

Median of nine observations is 20.45 . If 2 is added in last four observations, then new median is

Line (1+lambda)x+(4-lambda)y+(2+lambda)=0 and (4-lambda)x-(1+lambda)y+(6-3lambda) =0 are concurrent at points A and B respectively and intersect at C then locus of centroid of DeltaABC " is " lambda is parameter

Prove that sum_(r=0)^n 3^rn Cundersetr = 4^n.

If G(x)=-sqrt(25-x^2),t h e n("lim")_(xvec1)(G(x)-G(1))/(x-1)i s1/(24) (b) 1/5 (c) -sqrt(24) (d) none of these

Three companies A,B,C get contracts form the Govt in the ratio 5:3:2. The probability that these companies finish the works in time,is 60%,80% and 70% respectively. A work given as a contract is finished in time. Find the probability that it is done by company B.

lim_(xto5^(+))[x]=……..

Using the (r+1)^(th) term, find the 3rd,4th and 5th terms in the expansionof (3x+2y)^8

If tan theta = (1)/(2) and tan phi = (1)/(3), then the value of theta + phi is

The P.V.'s of A, B are bar(a), bar(b) respectively. The P.V. of 'C' is -3bar(a)+5bar(b) then 'C' lies

The locus of the points equidistant from the pair of line x^2cos^2theta-2xysin^2theta-y^2sin^2theta=0 is

Find Lt_(xto0)(1-cosx)/x^(2)

Compute the following limits. Lt_(xtooo)(8|x|+3x)/(3|x|-2x)

Express each of the complex number given in the form of a+ib i^(9) + i^(19)

The period of ( tan theta -(1)/(3) tan^(3) theta ) ((1)/(3) - tan^(2) theta )^(-1),where tan^(2) thetane (1)/(3) is :

Find the ratio in which YZ-plane divides the line joining A(2,4,5) and B(3,5,-4). Also find the point of intersection.

Given that the side length of a rhombus is the geometric mean of the lengths of its diagonals. The degree measure of the acute angle of the rhombus is

Define Law of conservation of energy

From a point (2, 0) the feet of perpendiculars to the lines of the pair x^2 -3xy + 2y^2 = 0 are L and M then find the distance LM.