14949 + Interview Questions in Maths in Class 11 Page 214 InterviewSolution

10651.	Is f defined by f(x)={{:((sin2x)/(x),"if "xne0),(1,"if "x=0):}"continuous"0 ?
Answer» ANSWER :`1/2`

Discussion

10652.	if second termsof a GP is 2 and the sun of itsinfinite terms is , then its first term is
Answer» `(1)/(4)` `(1)/(2)` 2 4 Answer :D

Discussion

10653.	The sinefunctionwhoseperiod 3 is
Answer» `SIN((2PI)/(3)X)` `sin(-(2pi)/(3)x )` `sin (+-(2pi)/(3)x)` `sin((x )/(3))` ANSWER :3

Discussion

10654.	Unit vector making angles pi/6, pi/6, pi/3 with bar(i), bar(j), bar(k) directions is
Answer» `1/sqrt(3)(BAR(i)+bar(J)+bar(K))` `1/sqrt(3)(bar(i)-bar(j)+bar(k))` `1/sqrt(3)(bar(i)-bar(j)-bar(k))` IMPOSSIBLE to get such a vector Answer :D

Discussion

10655.	cot 16^(@) cot 44^(@) + cot 44^(@) cot 76^(@) - cot 76^(@) cot 16^(@)=
Answer» 1 2 3 4 Answer :C

Discussion

10656.	For the given bases curve y = sinx, draw y = 1/2 sin 2x
Answer» ANSWER :`(##FM_MAT_XI_SP_MAR_19_E01_041_A01##)`

Discussion

10657.	(1)/(sec^(4) alpha ) +(1)/("cosec"^(4) alpha ) +(2)/(sec^(2) alpha+ "cosec"^(2) alpha )=
Answer» 0 1 `SIN^(2) ALPHA` `cos^(2)alpha` Answer :B

Discussion

10658.	Find, the equation of the circle which touches both the axes and whose centre lies on x-2y = 3
Answer» SOLUTION :`x^2+y^2+6x+6y+9 = 0`

Discussion

10659.	Let f: R rarr R be a continuous and differentiable function such that AA x in (0, oo) . Then the value of (f((16+y^(2))/(y^(2))))^((4)/(sqrt(y))) for y in (0, oo) is equal to
Answer» 5 25 125 625 Answer :B

Discussion

10660.	The ratio in which the line segment joining the points with P.V.'s bar(i)+2bar(j)+3bar(k), -3bar(i)+6bar(j)-8bar(k) is divided by xy-plane is
Answer» `3:8` `3:5` `5:3` `8:3` ANSWER :A

Discussion

10661.	If vec(a) xx vec(b) = vec(b) xx vec(c )= vec(c )xx vec(a), where vec(a), vec(b), vec(c ) are non zero vectors, then
Answer» `VEC(a) + vec(b) + vec(c )= vec(0)` `vec(a) + vec(b) + vec(c ) GT vec(0)` `vec(a) + vec(b) + vec(c ) LT vec(0)` `vec(a) + vec(b) + vec(c ) NE vec(0)` Answer :A

Discussion

10662.	Let h(x)=f(x)-(f(x))^(2)+(f(x))^(3)for every real number x . Then
Answer» h is INCREASING WHENEVER f is increasing h is increasing whenever f is DECREASING h is decreasing whenever f is decreasing nothing can be SAID in general Answer :A::C

Discussion

10663.	Find the values of k for which the line (k-3) x-(4-k^2) y+k^2 -7k+6=0 is (ii) Parallel to the y-axis.
Answer» ANSWER :`(a)3, (b) PM 2, (C ) 6 " or " 1`

Discussion

10664.	If (2,3 -1) is the foot of the perpendicular from (4,2,1) to a plane, the equation of plane is
Answer» `2X - y - 2Z - 3=0` `2x + y - 2z - 9=0` ` 2x + y + 2z -5=0` 2x-y+2z+1=02x + y + 2z + 1=0` ANSWER :D

Discussion

10665.	Determine the domain and range of the relation R defined by R={(x,x+5) : x in {0,1,2,3,4,5}}
Answer» ANSWER :DOMAIN of R={0,1,2,3,4,5} RANGE of R={5,6,7,8,9,10}

Discussion

10666.	If the angle between the vectors bari+bark and bari-barj+abark " is " pi/3, then a =
Answer» 0 4 3 -4 Answer :A

Discussion

10667.	If x_(1),x_(2),x_(3) are the roots of x^(3)-6x^(2)+11x-6=0 then cot^(-1)(x_(1))+cot^(-1)(x_(2))+cot^(-1)(x_(3)) is equal to
Answer» 0 `(PI)/(2)` `pi` `(3PI)/(2)` Answer :B

Discussion

10668.	sin 20^(@) (4 + sec 20^(@)) =
Answer» `1/2` `SQRT2` `SQRT3` `1` ANSWER :C

Discussion

10669.	The value of cot("cosec"^(-1)5/3+"tan"^(-1)2/3) is
Answer» `6/17` `3/17` `4/17` `5/17` ANSWER :A

Discussion

10670.	If x gt 0 , the maximum value of (log x) /x is
Answer» 1 `2//E` e `1//e` ANSWER :D

Discussion

10671.	A box contains 2 white balls, 3 black balls and 4 red balls. The number of ways three balls be drawn from the box, if atleast one black ball is to be included in the drawis ……
Answer» ANSWER :64

Discussion

10672.	Iftan A=(x sin B)/(1- x cos B) and tan B=(y sin A)/(1-y cos A) then (sin A )/(sin B)=
Answer» x/y y/x x+y x-y Answer :A

Discussion

10673.	S_(n) = (1+2+3+....+n)/( n) then S_(1)^(2) + S_(2)^(2) + S_(3)^(2) + ..... + S_(n)^(2) =
Answer» `(n)/( 24) (2n^(2) + 9N+13)` `(1)/( 24) ( 2n^(2) + 9n+13) ` `(n^2)/( 24) (2n^(2) + 9n+13)` `(n)/( 24) ( 2n^(2) - 9n +13)` ANSWER :A

Discussion

10674.	If alpha in (-(3pi)/2,-pi), then the value of tan^(-1)(cot alpha)-cot^(-1)(tan alpha)+sin^(-1)(sin alpha)+cos^(-1)(cos alpha) is equal to
Answer» `2pi+alpha` `pi+alpha` `0` `pi-alpha` ANSWER :C

Discussion

10675.	underset(x to oo) (Lt)( overset(n) underset(r=1) sum-overset(n) underset(r=1) sum2^(r))/(x-2)=
Answer» N `(n-i)2^(n)+l` `(n-1)2^(n)` `(n-1)2^(n)-1` ANSWER :B

Discussion

10676.	Find the condition for the lines joining the origin to the points of intersections of 5(x^(2)+y^(2)+bx+ay)=9 ab and (x)/(a)+(y)/(b)=1 are at right angles.
Answer» ANSWER :a = 2B or B = 2A

Discussion

10677.	The percentage error in measuring the side of a cube is 0.5. Then the percentage error in its volume is
Answer» `1//2` 1 `3//2` 2 Answer :C

Discussion

10678.	How many 3-digit even numbers can be made using the digits 1,2,3,4,6,7 if no digit is repeated?
Answer» ANSWER :60

Discussion

10679.	Let ABCDEFGHIJKL be a regular dodecagon. Then the value of(AB)/(AF)+(AF)/(AB) is equal to.......
Answer» 4 5 3 6 Answer :A

Discussion

10680.	State the converse and contrapositive of each of the following statements: p: A positive integer is prime only if it has no divisors other than 1 and itself.
Answer» ANSWER :it has DIVISOR 1 and other NUMBERS.

Discussion

10681.	If an even can occur in m ways and corresponding to each way another event can occur in p ways, then total number of occurrence of events is m.p.
Answer» ANSWER :TRUE STATEMENT

Discussion

10682.	Express ( a+b )/(a-b)tan ""( C)/(2)in terms of A and B
Answer» ANSWER :` COT ((A-B)/( 2))`

Discussion

10683.	If f(a)=log.(2+a)/(2-a)" for " 0lt a lt2 then (1)/(2)f((8a)/(4+a^(2)))=
Answer» `F(a)` `2F(a)` `1/2 f(a)` `-f(a)` ANSWER :A

Discussion

10684.	Find the range of k if the point (1, 1, k) lies on the origin side of the plane 3x-2y+6z-3=0.
Answer» ANSWER :`(-oo,1//3)`

Discussion

10685.	Prove thatr_1 +r_2+r_3-r = 4R
Answer» ` 4R ` ` 3 R ` ` 2 R` ` R ` ANSWER :A

Discussion

10686.	Prove that: tan(pi/4+theta)+tan(pi/4-theta)=2sec2theta.
Answer» ANSWER :`THETA=(3npi)/(2)+(PI)/(2), in in Z`

Discussion

10687.	sec h^(-1) ((1)/(3)) =
Answer» `log_(E) (3 + SQRT(8))` `log_(e) (3 - sqrt(8))` `log_(e) (sqrt(3 - sqrt(8)))` `log_(e) (sqrt(3 + sqrt(8)))` ANSWER :A

Discussion

10688.	Let tan x - tan^(2) x gt 0 and \|2 sin x\| lt 1 . Then the intersection of which of the following two sets satisfies both the inequalities ?
Answer» `X gt N PI, n in Z` `x gt n pi - pi //6, n in Z` `x lt n pi - pi//4, n pi Z` `x lt n pi + pi // 6 , n in Z` Answer :A::D

Discussion

10689.	Ifcos ^(2) A + cos ^(2) B = cos ^(2)C = 1then show thatDelta ABCis right angled
Answer» RIGHT ANGLED ISOSCELES EQUILATERAL Scalane ANSWER :A

Discussion

10690.	Area of quadrilateral formed by two pair of lines a^(2)x^(2)-b^(2)y^(2)-c(ax+by)=0 and a^(2)x^(2)-b^(2)y^(2)+c(ax-by)=0 is
Answer» `C^2/(ABS(AB))` `(2c^2)/(abs(ab))` `c^2/(2abs(ab))` `(4c^2)/(abs(ab))` ANSWER :C

Discussion

10691.	The point P is the foot of the perpendicular from A(0, t) to the line whose equation is y=tx. Determine the co-ordinates of P
Answer» <P> ANSWER : `P((t^(2))/(1+t^(2)),(t^(3))/(1+t^(2)))`

Discussion

10692.	a, b, c are three vectors such that \|a\| = 1, \|b\| = 2, \|c\| = 3 and b, c are perpendicular. If projection of b on a is the same as the projection of c on a, then \|a-b + c\| =
Answer» `SQRT2` `SQRT7` `SQRT14` `sqrt21` ANSWER :A

Discussion

10693.	The point P is the foot of the perpendicular from A(0, t) to the line whose equation is y=tx. Determine the equation of the line AP
Answer» ANSWER : `x+ty-t^(2)=0`

Discussion

10694.	From the top of a cliff x mts heigh, the angle of depression of the foot of a tower is found to be double the angle of elevation of the tower. If the height of the tower is h, the angle of elevation is
Answer» `TAN^(-1)sqrt(3-(2H)/(X))` `Tan^(-1)sqrt(3-(2h)/(x))` `Sin^(-1)sqrt((2h)/(x))` `COS^(-1)sqrt((2h)/(x))` ANSWER :B

Discussion

10695.	Find the centriod and hence find the area of the triangle formed by the following lines 2y^(2)-xy-6x^(2)=0 x+y+4=0
Answer» ANSWER :`((20)/(3),-(44)/(3)),(56)/(3)`

Discussion

10696.	State and prove Binomial theorem for a positive integer index.
Answer» <P> ANSWER :`P(m+1)` is TRUE.

Discussion

10697.	If A,B,C are three mutually exclusive and exhaustive events of an experiment such3P(A) = 2I = P(C ) , the P(A) is equal to .
Answer» `1/11` `2/11` `5/11` `6/11` ANSWER :B

Discussion

10698.	Letalpha , betabe such thatpi lt alpha - beta lt 3 pi. Ifsin alpha + sin beta =-(21)/(65) and cos alpha + cos beta =-(27)/(65) , then the value ofcos""(alpha - beta )/(2)is
Answer» `-(3)/(sqrt(130))` `(3)/(sqrt(130))` `(6)/(65)` `-(6)/(65)` Answer :A

Discussion

10699.	If the foot of the perpendicular from (0, 0, 0) to a plane is (1, 2, 3), then the equation of the plane is
Answer» `2X +y + 3z =14` `x + 2Y + 3z =14` `x +2y +3z + 14=0` `x + 2y - 3z = 14` Answer :B

Discussion

10700.	2x^(2) + x+1=0
Answer» ANSWER :`-(1)/(4)-(SQRT(7))/(4)`i

Discussion

Explore topic-wise InterviewSolutions in .

Is f defined by f(x)={{:((sin2x)/(x),"if "xne0),(1,"if "x=0):}"continuous"0 ?

if second termsof a GP is 2 and the sun of itsinfinite terms is , then its first term is

The sinefunctionwhoseperiod 3 is

Unit vector making angles pi/6, pi/6, pi/3 with bar(i), bar(j), bar(k) directions is

cot 16^(@) cot 44^(@) + cot 44^(@) cot 76^(@) - cot 76^(@) cot 16^(@)=

For the given bases curve y = sinx, draw y = 1/2 sin 2x

(1)/(sec^(4) alpha ) +(1)/("cosec"^(4) alpha ) +(2)/(sec^(2) alpha+ "cosec"^(2) alpha )=

Find, the equation of the circle which touches both the axes and whose centre lies on x-2y = 3

Let f: R rarr R be a continuous and differentiable function such that AA x in (0, oo) . Then the value of (f((16+y^(2))/(y^(2))))^((4)/(sqrt(y))) for y in (0, oo) is equal to

The ratio in which the line segment joining the points with P.V.'s bar(i)+2bar(j)+3bar(k), -3bar(i)+6bar(j)-8bar(k) is divided by xy-plane is

If vec(a) xx vec(b) = vec(b) xx vec(c )= vec(c )xx vec(a), where vec(a), vec(b), vec(c ) are non zero vectors, then

Let h(x)=f(x)-(f(x))^(2)+(f(x))^(3)for every real number x . Then

Find the values of k for which the line (k-3) x-(4-k^2) y+k^2 -7k+6=0 is (ii) Parallel to the y-axis.

If (2,3 -1) is the foot of the perpendicular from (4,2,1) to a plane, the equation of plane is

Determine the domain and range of the relation R defined by R={(x,x+5) : x in {0,1,2,3,4,5}}

If the angle between the vectors bari+bark and bari-barj+abark " is " pi/3, then a =

If x_(1),x_(2),x_(3) are the roots of x^(3)-6x^(2)+11x-6=0 then cot^(-1)(x_(1))+cot^(-1)(x_(2))+cot^(-1)(x_(3)) is equal to

sin 20^(@) (4 + sec 20^(@)) =

The value of cot("cosec"^(-1)5/3+"tan"^(-1)2/3) is

If x gt 0 , the maximum value of (log x) /x is

A box contains 2 white balls, 3 black balls and 4 red balls. The number of ways three balls be drawn from the box, if atleast one black ball is to be included in the drawis ……

Iftan A=(x sin B)/(1- x cos B) and tan B=(y sin A)/(1-y cos A) then (sin A )/(sin B)=

S_(n) = (1+2+3+....+n)/( n) then S_(1)^(2) + S_(2)^(2) + S_(3)^(2) + ..... + S_(n)^(2) =

If alpha in (-(3pi)/2,-pi), then the value of tan^(-1)(cot alpha)-cot^(-1)(tan alpha)+sin^(-1)(sin alpha)+cos^(-1)(cos alpha) is equal to

underset(x to oo) (Lt)( overset(n) underset(r=1) sum-overset(n) underset(r=1) sum2^(r))/(x-2)=

Find the condition for the lines joining the origin to the points of intersections of 5(x^(2)+y^(2)+bx+ay)=9 ab and (x)/(a)+(y)/(b)=1 are at right angles.

The percentage error in measuring the side of a cube is 0.5. Then the percentage error in its volume is

How many 3-digit even numbers can be made using the digits 1,2,3,4,6,7 if no digit is repeated?

Let ABCDEFGHIJKL be a regular dodecagon. Then the value of(AB)/(AF)+(AF)/(AB) is equal to.......

State the converse and contrapositive of each of the following statements: p: A positive integer is prime only if it has no divisors other than 1 and itself.

If an even can occur in m ways and corresponding to each way another event can occur in p ways, then total number of occurrence of events is m.p.

Express ( a+b )/(a-b)tan ""( C)/(2)in terms of A and B

If f(a)=log.(2+a)/(2-a)" for " 0lt a lt2 then (1)/(2)f((8a)/(4+a^(2)))=

Find the range of k if the point (1, 1, k) lies on the origin side of the plane 3x-2y+6z-3=0.

Prove thatr_1 +r_2+r_3-r = 4R

Prove that: tan(pi/4+theta)+tan(pi/4-theta)=2sec2theta.

sec h^(-1) ((1)/(3)) =

Let tan x - tan^(2) x gt 0 and |2 sin x| lt 1 . Then the intersection of which of the following two sets satisfies both the inequalities ?

Ifcos ^(2) A + cos ^(2) B = cos ^(2)C = 1then show thatDelta ABCis right angled

Area of quadrilateral formed by two pair of lines a^(2)x^(2)-b^(2)y^(2)-c(ax+by)=0 and a^(2)x^(2)-b^(2)y^(2)+c(ax-by)=0 is

The point P is the foot of the perpendicular from A(0, t) to the line whose equation is y=tx. Determine the co-ordinates of P

a, b, c are three vectors such that |a| = 1, |b| = 2, |c| = 3 and b, c are perpendicular. If projection of b on a is the same as the projection of c on a, then |a-b + c| =

The point P is the foot of the perpendicular from A(0, t) to the line whose equation is y=tx. Determine the equation of the line AP

From the top of a cliff x mts heigh, the angle of depression of the foot of a tower is found to be double the angle of elevation of the tower. If the height of the tower is h, the angle of elevation is

Find the centriod and hence find the area of the triangle formed by the following lines 2y^(2)-xy-6x^(2)=0 x+y+4=0

State and prove Binomial theorem for a positive integer index.

If A,B,C are three mutually exclusive and exhaustive events of an experiment such3P(A) = 2I = P(C ) , the P(A) is equal to .

Letalpha , betabe such thatpi lt alpha - beta lt 3 pi. Ifsin alpha + sin beta =-(21)/(65) and cos alpha + cos beta =-(27)/(65) , then the value ofcos""(alpha - beta )/(2)is

If the foot of the perpendicular from (0, 0, 0) to a plane is (1, 2, 3), then the equation of the plane is

2x^(2) + x+1=0