14949 + Interview Questions in Maths in Class 11 Page 174 InterviewSolution

8651.	The value of 'theta' in the Lagrange's mean value theroem for f(x) = x^(3) , a= 1, h = 1//2 is
Answer» `(1)/( 3)` `SQRT(( 19)/( 56))` `sqrt(( 19)/( 3))+2` `sqrt(( 19)/( 3))-2` ANSWER :D

Discussion

8652.	Evaluate the following limits : Lim_(x to 1) (x-1)/(2x^(2)-7x + 5)
Answer» ANSWER :`-1/10 " " [ :' SQRT(X) - 1 != 0]`

Discussion

8653.	If A, B and C are three events, then which of the following is incorrect ?
Answer» P(Exatly two of A, B, C occur) `LEP(A cap B)+P(B cap C)+P(C cap A)` `P(A cup B cup C) le P(A)+P(B)+P(C )` P(Exactly one of A, B, C occur) `le P(A)+P(B)+P(C )-P(B cap C)-P(C cap A)-P(A cap B)` P(A and at LEAST one of B c, occurs)`ge P(A cap B)+P(A cap C)` Solution :We have, P(Exactly two of A, B, C occur) `=P(A cap B cap overline(C ))+P(A cap overline(B) cap C)+P(overline(A) cap B cap C)` `=P(A cap B)-P(A cap B cap C)+P(A cap C)-P(A cap B cap C)+P(B cap C-P(A cap B cap C))` `=P(A cap B)+P(B cap C)+P(A cap C)-3P(A cap B cap C) le P(A cap B)+P(B cap C)+P(A cap C)` Also, `P(A cup B cup C)` `=P(A cup B)+P(C )-P{(A cup B) cap C}` `le P(A cup B)+P(C )`. `le P(A)+P(B)+P(C ) "" [becauseP(A cup B) le P(A)+P(B)]` Now, P(Exactly one of A, B, C occurs) `=P(A cap overline(B) cap overline(C ))+P(overline(A) cap overline(B) cap C)+P(overline(A) cap B cap overline(C ))` `=P(A cap overline(B cup C))+P(overline(A cup B)cap C)+P(B cap overline(A cup C))` `=P(A)-P{A cap (B cap )}+P(C )-P{C cap (A cup B)}+P(B)-P{B cap (A cup C)}` `=P(A)-P{(A cap B) cup (A cap C)+P(C )-P{(C cap A) cup (C cap B)}+P(B)-P{(B cap A) cap (B cap C)}` `=P(A)+P(B)+P(C )=2P(A cap B)-2P(B cap C)-2P(A cap C)+3P(A cap B cap C)` `[P(A)+P(B)+P(C )-P(A cap B)-P(A cap cap)]` `-P[(A)+P(B)+P(C )-P(A cap C)-3P(A cap B cap C)]` `=P(A)+P(B)+P(C )-P(A cap B)-P(B cap C)-P(A cap C)-P("Exactly two of A, B, C occur")` `le P(A)+P(B)+P(C )-P(A cap B)-P(B cap C)-P(A cap C)` FINALLY, P(A and ATLEAST one of B, C occurs) `=P[A cap B cap C)]` `P[(A cap B) cup (A cap C)]` `=P(A cap B)+P(A cap C)-P(A cap B cap C)` `le P(A cap B)+P(A cap C)` So, OPTION (d) is incorrect.

Discussion

8654.	Write the inverse of the converse of p implies q.
Answer» <P> ANSWER :~Q =>~p

Discussion

8655.	Evaluate the following limits . Lim_(x to 0 ) ((1+x)^(n)-1)/x
Answer» ANSWER :N

Discussion

8656.	"sin"^(4)pi/8" +sin"^(4)(3pi)/8" +sin"^(4)(5pi)/8" +sin"^(4)(7pi)/8=
Answer» `1/2` `3/2` `3/4` `5/4` ANSWER :B

Discussion

8657.	If ' theta ' is inthe III quadrant then sqrt(4 sin^(4) theta + sin^(2) 2 theta )+ 4 cos^(2)""((pi)/4-(theta )/(2))=
Answer» 2 -2 0 1 Answer :A

Discussion

8658.	lim_(x to 0) {(log_(e)(1+x))/(x^(2))+(x-1)/(x)}=
Answer» `(1)/(2)` `(-1)/(2)` 1 `-1` ANSWER :A

Discussion

8659.	Find all the angles between 0^(@) and 720^(@) whose tangent is -(1)/(sqrt(3)).
Answer» ANSWER :`150^(@),330^(@),510^(@),690^(@)`

Discussion

8660.	If (sin alpha )/(a) = ( cos alpha )/(b) , thena sin 2alpha + b cos 2 alpha =
Answer» 1 B `1//a` `1//b` ANSWER :B

Discussion

8661.	If there is an error of 0.05 cm in the side of a cube 10 cm then the error in its surface area is
Answer» `6c.m^(2)` `12c.m^(2)` `5c.m^(2)` `3c.m^(2)` ANSWER :A

Discussion

8662.	Show that the statement p: If x is a real number such that x^(3)+4x=0, then x is 0 is true by (i) Direct method (ii) Method of contradiction (iii) Method of contrapositive
Answer» ANSWER :1

Discussion

8663.	If "tan"^(2)(pi-4)/(4)+"tan"^(2)(pi-B)/(4)+"tan"^(2)(pi-C)/(4)=1, then Delta ABC is
Answer» equilateral ISOCELES SCALENE OBTUSE ANGLE Answer :A

Discussion

8664.	Fourcards are drawn at random from a pack of 52 playing cards , Find the probability of getting one card from each suit ,
Answer» ANSWER :`(""^(13)C_(1))^(4)/(""^(52)C_(4))=(2197)/(20825)`

Discussion

8665.	Insert 6 numbers between 3 and 24 so that the resulting sequence is an A.P.
Answer» Answer :six , number between 3 and 24 are 6, 9, 12, 15, 18 and 21.

Discussion

8666.	If AD, BE , CF are internal bisectors of the angles of Delta ABC, " then " (cos A//2)/(AD) + (cos B//2)/(BE) + (cos C//2)/(CF) =
Answer» `(ABC)/(2s)` `(2s)/(abc)` `(AB + bc + CA)/(abc)` `(a + B + c)/(abc)` ANSWER :C

Discussion

8667.	InDelta ABCProve that sin ^(2) "" (A)/(2) + sin ^(2)""(B) /(2) + sin ^(2) ""( C) /(2) =1 -( r) / ( 2R)
Answer» ` 2 + ( R )/( R ) ` ` ( r )/( 2R ) ` ` 1 + ( r ) /( 2 R) ` ` 1- ( r ) /( 2 R) ` ANSWER :D

Discussion

8668.	Fill in the blanks of the following If \|z\|=4" and arg"(z)=(5pi)/(6), then z=.....
Answer» ANSWER :`-2sqrt(3)+2I`

Discussion

8669.	Rewrite each of the following statements in the form ''p if and only if q'' r: If a quadrilateral is equiangular, then it is a rectangle and if a quadrilateral is a rectangle, then it is equiangular.
Answer» ANSWER :A QUADRILATERAL is EQUIANGULAR if and only if it is a RECTANGLE.

Discussion

8670.	Solve 30 x lt 200 when (i) x is a natural number. (ii) x is an integer.
Answer» ANSWER :The solution SET of the INEQUALITY is `{…,-3,-2,-1,0,1,2,3,4,5,6)`

Discussion

8671.	Two unbiased dice are rolled . Findthe probability of (a) obtaining a total of at least 10. (b)getting a multiple of 2 on one die aanda multiple of 3 on the other die.(c )getting a multiple of 3 as the sum.
Answer» Answer :(a)`=(1)/(6)`. (b) `=(11)/(36)`. (C ) `=(1)/(3)`.

Discussion

8672.	If one angular bisector of a(x+1)^(2)+2h(x+1)(y-3)+b(y-3)^(2)=0 is 2x-3y+11=0 then equation of other angular bisector is
Answer» x+y=2 3x+2y+11=0 3x+2y=0 3x+2y-3=0 Answer :D

Discussion

8673.	Find the point of the -axis which is equidistant from the points A(1,5,7)n and B(5,1,-4)
Answer» ANSWER :` (0,0,(3)/(2))`

Discussion

8674.	If cotx=(-5)/(12),x lies in second quadrant, find the values of other five trigonometric functions.
Answer» Answer :`TANX=-(12)/(5),secx=pm(13)/(5),COSX=-(5)/(13),sinx=(12)/(13),COSECX=(13)/(12)`

Discussion

8675.	If f(x)=1/x , g(x)=1/x^(2) and h(x)=x^(2), then
Answer» `fog(x)=x^(2), x != 0 , h(G(x))= (1)/(x^(2))` `h(g(x))= (1)/(x^(2)), x != 0, fog(x)=x^(2)` `fog(x)=x^(2), x != 0, h(g(x))=(g(x))^(2), x != 0` `(fog)(x)=(1)/(x^(2)), x != 0, h(g(x))=g(x), x != 0` Answer :C

Discussion

8676.	For each n in N, 49^(n)+ 16n - 1 is divisible by :
Answer» 3 19 29 64 Answer :D

Discussion

8677.	Conisder P(x) to be a polynomial of degree 5 having extremum at x=-1,1andlim_(x to0)((P(x))/(x^(3)-2))=4.Then the value of [P(1) ] is (where[.] represents greatest integer function )__________
Answer» ANSWER :2

Discussion

8678.	Find the consumer price index number for the year 2010 as the base year 2000 by using method of weighted aggregates.
Answer» ANSWER :138.39.

Discussion

8679.	Sin^(-1)[xsqrt(1-x)-sqrt(x)sqrt(1-x^(2))]=
Answer» `SIN^(-1)X+sin^(-1)SQRT(x)` `sin^(-1)x-sin^(-1)sqrt(x)` `sin^(-1)sqrt(x)-sin^(-1)x` 0 Answer :B

Discussion

8680.	Find the ratio in which the line joining (-3, -2) & (-1, 4) is divided by the line joining (-4, 1) & (1, 2).
Answer» ANSWER :`4:3`

Discussion

8681.	Assertion (A) : The equation ax+by+s=0 represents a plane parallel to z-axis. Reason (R ) : If the plane ax+by+cz+d=0 perpendicular to the xy-plane then c=0.
Answer» Both (A) and (R) are TRUE R is correct REASON of A Both (A) and (R) are true R is not correctreason of A (A) is true but (R) is FALSE (A) is false but (R) is true Answer :A

Discussion

8682.	One corner of a long rectangular sheet of paper of whdth 1 units is folder over so as to reach the opposite edge of the sheet . The minimum length of the crease is
Answer» `(3sqrt(3))/(4)` `(3sqrt(3))/(2)` `4sqrt(3)` `3sqrt(3)` ANSWER :C

Discussion

8683.	In DeltaABC, a=6,b=4 and cos (A-B)=4//5 then its area is
Answer» 9 12 11 10 Answer :A

Discussion

8684.	Find the number of words which can be formed by taking two alike and two different letters from the work COMBINATION.
Answer» ANSWER :`756`

Discussion

8685.	If sec hx = (3)/(5) then tan h(2x) =
Answer» `(40)/(41)` `(41)/(40)` `(25)/(40)` `(16)/(41)` ANSWER :A

Discussion

8686.	Find the derivative of the w.r.t.x (sin (ax +b ))/( cos (cx +d ))
Answer» Answer :`(a COS (ax + B ) cos (CX +d )+ c SIN ( ax +b ) sin (cx +d ))/( cos ^(2) (cx + d ))`

Discussion

8687.	The numbers of terms in the expansion [(x+4y)^(4)]^(5) is .........
Answer» ANSWER :21

Discussion

8688.	One root of the equation 6x - 8x^3=sqrt3 is .........
Answer» ANSWER :`20^@`

Discussion

8689.	If (x+1, y-2)=(3,1), find the values of x and y.
Answer» ANSWER :x=2, y=3

Discussion

8690.	The transformed equation of 4x^(2) + 9y^(2) - 8x + 36 y + 4 = 0 when the axes are translated to the point (1,-2) is
Answer» `X^(2) + 2y^(2) = 1` `x^(2) + 3Y^(2) = 1` `X^(2) - Y^(2) + 3 = 0` `4X^(2) + 9y^(2) = 36` Answer :D

Discussion

8691.	Find the circumcentre of the triangle whose sides are given by x+y=0, 2x+y+5=0 and x-y=0
Answer» ANSWER :`(-1/3,2/3)`

Discussion

8692.	LetA = { 1, 2, { 3, 4 }, 5 }. Which of the following statements are incorrect and why? 1 ∈ A
Answer» ANSWER :1

Discussion

8693.	cos^(2)((pi)/(12))+cos^(2)((3pi)/(12))+cos^(2)((5pi)/(12))= …………
Answer» `-(1)/(2)` 0 `(1)/(2)` `(3)/(2)` ANSWER :D

Discussion

8694.	If tantheta+3cottheta=5sectheta then theta=(ninz)
Answer» `NPI+(-1)^(n)(pi)/(4)` `npi+(-1)^(n)(pi)/(6)` `npi+(-1)^(n)(pi)/(6)ornpi+(-1)^(n)(pi)/(3)` `npi+(-1)^(n)(pi)/(2)ornpi+(-1)^(n)(pi)/(6)` Answer :B

Discussion

8695.	If y = a^(a^x) then (dy)/(dx) =
Answer» `y.a^X(LOGA)^2` `y.a^(x).LOG a` `(y.a^x)^2` `(y.a^x)` ANSWER :A

Discussion

8696.	If the equation cot^(4) x - 2 cosec^(2) x + a^(2) = 0 has at least one solution, then the sum of all possible ntergral values of a is equal to
Answer» 4 3 2 0 Answer :D

Discussion

8697.	Find (a+b)^4 -(a-b)^4.Hence evaluate (sqrt(3)+sqrt(2))^4-(sqrt(3)-sqrt(2))^4.
Answer» ANSWER :8(`a^3`B + `ab^3`); 40 `SQRT6`

Discussion

8698.	PQR is an equitateral triangle such that the vertices Q and R lie on the line x+y=sqrt2 and x+y=7sqrt2 respectively. If P lie between the two lines at a distance 4 from one them then the length of side of equilateral triangle PQR is (in units)
Answer» 8 `(4sqrt7)/SQRT3` `sqrt85/3` `(4sqrt5)/sqrt3` ANSWER :B

Discussion

8699.	a cot A + b cos B + c cos C =
Answer» ` (DELTA)/( R) ` ` ( R)/(Delta ) ` ` (2DELTA)/ (R ) ` ` (4 Delta)/( R ) ` Answer :C

Discussion

8700.	A value of Tan^(-1){sin(Cos^(-1)sqrt(2/3))} is
Answer» `pi/4` `pi/2` `pi/3` `pi/6` ANSWER :D

Discussion

Explore topic-wise InterviewSolutions in .

The value of 'theta' in the Lagrange's mean value theroem for f(x) = x^(3) , a= 1, h = 1//2 is

Evaluate the following limits : Lim_(x to 1) (x-1)/(2x^(2)-7x + 5)

If A, B and C are three events, then which of the following is incorrect ?

Write the inverse of the converse of p implies q.

Evaluate the following limits . Lim_(x to 0 ) ((1+x)^(n)-1)/x

"sin"^(4)pi/8" +sin"^(4)(3pi)/8" +sin"^(4)(5pi)/8" +sin"^(4)(7pi)/8=

If ' theta ' is inthe III quadrant then sqrt(4 sin^(4) theta + sin^(2) 2 theta )+ 4 cos^(2)""((pi)/4-(theta )/(2))=

lim_(x to 0) {(log_(e)(1+x))/(x^(2))+(x-1)/(x)}=

Find all the angles between 0^(@) and 720^(@) whose tangent is -(1)/(sqrt(3)).

If (sin alpha )/(a) = ( cos alpha )/(b) , thena sin 2alpha + b cos 2 alpha =

If there is an error of 0.05 cm in the side of a cube 10 cm then the error in its surface area is

Show that the statement p: If x is a real number such that x^(3)+4x=0, then x is 0 is true by (i) Direct method (ii) Method of contradiction (iii) Method of contrapositive

If "tan"^(2)(pi-4)/(4)+"tan"^(2)(pi-B)/(4)+"tan"^(2)(pi-C)/(4)=1, then Delta ABC is

Fourcards are drawn at random from a pack of 52 playing cards , Find the probability of getting one card from each suit ,

Insert 6 numbers between 3 and 24 so that the resulting sequence is an A.P.

If AD, BE , CF are internal bisectors of the angles of Delta ABC, " then " (cos A//2)/(AD) + (cos B//2)/(BE) + (cos C//2)/(CF) =

InDelta ABCProve that sin ^(2) "" (A)/(2) + sin ^(2)""(B) /(2) + sin ^(2) ""( C) /(2) =1 -( r) / ( 2R)

Fill in the blanks of the following If |z|=4" and arg"(z)=(5pi)/(6), then z=.....

Rewrite each of the following statements in the form ''p if and only if q'' r: If a quadrilateral is equiangular, then it is a rectangle and if a quadrilateral is a rectangle, then it is equiangular.

Solve 30 x lt 200 when (i) x is a natural number. (ii) x is an integer.

Two unbiased dice are rolled . Findthe probability of (a) obtaining a total of at least 10. (b)getting a multiple of 2 on one die aanda multiple of 3 on the other die.(c )getting a multiple of 3 as the sum.

If one angular bisector of a(x+1)^(2)+2h(x+1)(y-3)+b(y-3)^(2)=0 is 2x-3y+11=0 then equation of other angular bisector is

Find the point of the -axis which is equidistant from the points A(1,5,7)n and B(5,1,-4)

If cotx=(-5)/(12),x lies in second quadrant, find the values of other five trigonometric functions.

If f(x)=1/x , g(x)=1/x^(2) and h(x)=x^(2), then

For each n in N, 49^(n)+ 16n - 1 is divisible by :

Conisder P(x) to be a polynomial of degree 5 having extremum at x=-1,1andlim_(x to0)((P(x))/(x^(3)-2))=4.Then the value of [P(1) ] is (where[.] represents greatest integer function )__________

Find the consumer price index number for the year 2010 as the base year 2000 by using method of weighted aggregates.

Sin^(-1)[xsqrt(1-x)-sqrt(x)sqrt(1-x^(2))]=

Find the ratio in which the line joining (-3, -2) & (-1, 4) is divided by the line joining (-4, 1) & (1, 2).

Assertion (A) : The equation ax+by+s=0 represents a plane parallel to z-axis. Reason (R ) : If the plane ax+by+cz+d=0 perpendicular to the xy-plane then c=0.

One corner of a long rectangular sheet of paper of whdth 1 units is folder over so as to reach the opposite edge of the sheet . The minimum length of the crease is

In DeltaABC, a=6,b=4 and cos (A-B)=4//5 then its area is

Find the number of words which can be formed by taking two alike and two different letters from the work COMBINATION.

If sec hx = (3)/(5) then tan h(2x) =

Find the derivative of the w.r.t.x (sin (ax +b ))/( cos (cx +d ))

The numbers of terms in the expansion [(x+4y)^(4)]^(5) is .........

One root of the equation 6x - 8x^3=sqrt3 is .........

If (x+1, y-2)=(3,1), find the values of x and y.

The transformed equation of 4x^(2) + 9y^(2) - 8x + 36 y + 4 = 0 when the axes are translated to the point (1,-2) is

Find the circumcentre of the triangle whose sides are given by x+y=0, 2x+y+5=0 and x-y=0

LetA = { 1, 2, { 3, 4 }, 5 }. Which of the following statements are incorrect and why? 1 ∈ A

cos^(2)((pi)/(12))+cos^(2)((3pi)/(12))+cos^(2)((5pi)/(12))= …………

If tantheta+3cottheta=5sectheta then theta=(ninz)

If y = a^(a^x) then (dy)/(dx) =

If the equation cot^(4) x - 2 cosec^(2) x + a^(2) = 0 has at least one solution, then the sum of all possible ntergral values of a is equal to

Find (a+b)^4 -(a-b)^4.Hence evaluate (sqrt(3)+sqrt(2))^4-(sqrt(3)-sqrt(2))^4.

PQR is an equitateral triangle such that the vertices Q and R lie on the line x+y=sqrt2 and x+y=7sqrt2 respectively. If P lie between the two lines at a distance 4 from one them then the length of side of equilateral triangle PQR is (in units)

a cot A + b cos B + c cos C =

A value of Tan^(-1){sin(Cos^(-1)sqrt(2/3))} is