14949 + Interview Questions in Maths in Class 11 Page 77 InterviewSolution

3801.	If I is incentre of the triangle ABC, P_(1),P_(2),P_(3) are radii of circum circles of Delta^("le") IBC, ICA, IAB respectively
Answer» `2P_(1)=a secA//2` `2P_(2)=B secB//2` `2P_(3)=C secC//2` `P_(1)P_(2)P_(3)=2R^(2)r` ANSWER :abcd

Discussion

3802.	ax+b(sec(tan^(-1)x))=c and ay+b(sec(tan^(-1)y))=c The value of x+y is
Answer» `(2ac)/(a^(2)-B^(2))` `(c^(2)-b^(2))/(a^(2)-b^(2))` `(c^(2)-b^(2))/(a^(2)+b^(2))` None of these Answer :A

Discussion

3803.	Evaluate: int(xdx)/(x^(2)-5x+6)
Answer» ANSWER :`-2log\|x-2\|+log\|x-3\|+c`

Discussion

3804.	The negation of the statement 72 is divisible by 2 and 3 is…….
Answer» 72 is not DIVISIBLE by 2 or 72 is not divisible by 3. 72 is not divisible by 2 and 72 is not divisible by 3. 72 is divisible by 2 and 72 is not divisible by 3. 72 is not divisible by 2 and 72 is divisible by 3. Answer :B

Discussion

3805.	If cos^(2) x + cos^(4) x =1 then tan^(2) x + tan^(4) x=
Answer» 1 0 -1 2 Answer :A

Discussion

3806.	If the n^(th) terms of an A.P. 9, 7, 5,….. is equal to the n^(th) term of an A.P. 15, 12, 9……then find n
Answer» ANSWER :7

Discussion

3807.	f(x) - (1- cos (ax))/( x sin x) , x ne 0, f(0) = 1/2is continuous at x = 0 , a =
Answer» ` pm 2` `pm 3` `pm 1` `pm 4` ANSWER :C

Discussion

3808.	If f(x+y)=f(x)+f(y)-xy-1 AA x, y in R and f(1)=1 then the number of solution of f(n)=n, n in N is
Answer» 0 1 2 more than 2 Answer :B

Discussion

3809.	Find the valuesof other five trigonometric functions cosx=-(1)/(2),x lies in third quadrant.
Answer» ANSWER :`SIN X = - (sqrt3)/(2), cosec x =- (2)/( sqrt3), sec x =-2 , TAN x = sqrt3 ,COT x = (1)/(sqrt3)`

Discussion

3810.	If D, E are the midpoints of AB, AC of Delta ABC, then vec(B)E + vec(D)C=
Answer» `BAR(BC)` `1/2BAR(BC)` `2bar(BC)` `3/2bar(BC)` ANSWER :D

Discussion

3811.	If a straight line is given by vecr = (1+ t) hati + 3 t hatj +(1-t) hatk where l in R. If this line lies in the plane x + y + cz = d then the value of c +dis
Answer» `-1` 1 7 9 Answer :D

Discussion

3812.	A coin is tossed and then a die is rolled only in casehead is shown on the coin.
Answer» Answer :{H1, H2, H3, H4, H5, H6, T}

Discussion

3813.	If bara = (-4, 2,4) and barb = (sqrt2, - sqrt2, 0), " then " (2bara,(barb)/2)=
Answer» `45^(@)` `135^(@)` `90^(@)` `0^(@)` ANSWER :B

Discussion

3814.	Consider the expansion of (x+a)^n Find the (r+1)^(th)term in the expansion
Answer» SOLUTION :`"^nC_rx^(n-r)a^r`

Discussion

3815.	If in aDelta ABC , r_1 =2r_2=3r_3,then b: c=
Answer» ` 4: 3` ` 5: 4` ` 2: 1 ` ` 3: 2 ` Answer :A

Discussion

3816.	If bara, barb, barc is a right handed system, barb is perpendicular to both bara & barc , if (bara,barc)=cos^(-1)(4/5),abs(bara)=1,abs(barb)=2,abs(barc)=3 then abs(barabarbbarc)=
Answer» `-18` `18/7` `18/5` 18 Answer :C

Discussion

3817.	Where does z lie, if \|(z-5i)/(z+5i)\|=1?
Answer» ANSWER :So, Z LIES on REAL AXIS.

Discussion

3818.	If (x^(2)+1)/(2x)=cos theta then (x^(6)+1)/(2x^(3))=
Answer» `COS^(2) THETA` `Cos^(3) theta` `Cos 2 theta` `COS3 theta` ANSWER :D

Discussion

3819.	Any vector which is perpendicular to each of the vectors 2vec(i) + vec(j) -vec(k) and 3vec(i) -vec(j) + vec(k) is normal to
Answer» X-axis Y-axis Z-axis all the above Answer :A

Discussion

3820.	Find the domains of the following functionsf(x) = ( 1)/(x)
Answer» ANSWER :`R-{ 0}`

Discussion

3821.	The value of sum_(n=1)^(oo) (tan((theta)/(2^(n))))/(2^(n-1)"cos"(theta)/(2^(n-1))) is
Answer» `(2)/(SIN 2 THETA)-(1)/(theta)` `(2)/(sin 2 theta) + (1)/(theta)` `(1)/(sin 2 theta)-(1)/(theta)` `(1)/(sin theta) - (1)/(theta)` ANSWER :A

Discussion

3822.	If x, y, z are non-zero real numbers, bara=xbari+2barj,bara=ybarj+3barK and barc=xbari+ybarj+zbarj are such that baraxxbarb=zbari-3barj+bark then [barabarbbarc]=
Answer» 3 10 9 6 Answer :C

Discussion

3823.	Two sequences cannot be in both AP and GP together.
Answer» ANSWER :1

Discussion

3824.	Prove that: .^(47)C_(4) + .^(51)C_(3) +^(50)C_(3)+^(49) C_(3) +^(48)C_(3) +^(47)C_(3) =^(52)C_(4)
Answer» Solution :`L.H.S= .^(47)C_(4) +^(51)C_(3) +^(50)C_(3)+^(49)C_(3) +^(48)C_(3)+^(47)C_(3)` `= (.^(47)C_(4)+^(47)C_(3))+^(48)C_(3)+^(49)C_(3)+^(50)C_(3)+^(51)C_(3)` `= .^(48)C_(4) +^(48)C_(3)+^(49)C_(3)+^(50)C_(3)+^(51)C_(3) ( :' .^(n)C_(R) +^(n)C_(r-1)=^(n-1)C_(r))` `= .^(49)C_(4) +^(49)C_(3)+^(50)C_(3)+^(51)C_(3)` `= .^(50)C_(4)+^(50)C_(3)+^(51)C_(3)` `= .^(51)C_(4)+^(51)C_(3)` `= .^(51)C_(4) = R.H.S`. Hence Proved.

Discussion

3825.	Write down the euqation of the line which makes an intercepts of 2a on the x-axis and 3a on the y-axis. Given that the line passes through the point (14, -9), find the numerical value of a.
Answer» ANSWER : `3x+2y=6a, a=4`

Discussion

3826.	A die is thrown once . Find P(a number lt3),
Answer» ANSWER :`(2)/(6),i.e,(1)/(3)`

Discussion

3827.	The perimeter of the triangle formed by the points (1,0,0), (0,1,0), (0,0,1) is :
Answer» `SQRT(2)` `2sqrt(2)` `3sqrt(2)` `4sqrt(2)` ANSWER :C

Discussion

3828.	If the lines 3x - 4y + 4 = 0 and 6x - 8y - 7 = 0 are tangents to a circle, then find the radius of the circle.
Answer» ANSWER :`(3)/(4)` UNIT.

Discussion

3829.	Find the number of terms in the following expansions. (v) (3x+7)^(8) + (3x-7)^(8)
Answer» ANSWER :`=5`

Discussion

3830.	Is the given relation a function? Give reason for your answer. f = {(x, x)\|x is a real number}
Answer» ANSWER :It is a FUNCTION

Discussion

3831.	If y =a sin x + b cos x ,then y^2 + ((dy)/(dx))^2 is a
Answer» FUNCTION of X function of y function of x and y constant Answer :D

Discussion

3832.	If bara, barb are two unit perpendicular vectors then baraxx (baraxx barb) =
Answer» `-BARA` `bara` `BARB` `-barb` ANSWER :D

Discussion

3833.	In triangle ABC, angleA=60^(@), angle B=40^(@), and angle C=80^(@) If P is the center of the circumcircle of triangle ABC with radius unity, then the radius of the circumcircle of triangle BPC is
Answer» 1 `SQRT(3)` 2 `sqrt(3)//2` ANSWER :A

Discussion

3834.	If in a Delta^("le") ABC, a, b and angle A are given C_(1),C_(2) are possibel values of 3rd side then
Answer» `C_(1)+C_(2)=2B COSA` `C_(2)C_(2)=b^(2)-a^(2)` `C_(1)^(2)+C_(2)^(2)- angleC_(1)C_(2) Cos2A=4a^(2)cos^(2)A` `C_(1)+C_(2)=2A CosB` ANSWER :A::B::C

Discussion

3835.	Perimeter of a triangle is 10 cms and its base is 4 cms then maximum area of the triangle is
Answer» `SQRT(5)` `2sqrt(5)` `3sqrt(5)` `4sqrt(5)` ANSWER :B

Discussion

3836.	From a set of 17 cardsnumbered 1,2,3,4,…, 16,17 , one card is drawn at random : Show that the chance that its number is divisible by 3 or 7 is (7)/(17).
Answer» ANSWER :`=(7)/(17)`.

Discussion

3837.	Evaluate lim_(x rarr a) (sqrtx - sqrta)/(x -a)
Answer» SOLUTION :`1/2sqrta`

Discussion

3838.	Find the term independent of x in the expansion of (root3x + 1/(2root3x))^(18),x gt 0.
Answer» ANSWER :The REQUIRED TERM is `^18`Cunderset9 `1/2^9`.

Discussion

3839.	For G.P. 5, 10, 20,…..and 1280, 640, 320…., their n^(th) terms are equal then find n.
Answer» ANSWER :n=5

Discussion

3840.	The point (4,1) undergoesthe following successively (i) reflection about the line y = x (ii) translation through a distance 2 unit along the positive direction of y - axis. The final position of the point is
Answer» (3,4) (4,3) (-1,4) (1,6) ANSWER :D

Discussion

3841.	Statement P (n): n^(3) +3n^2 + 5n +3 is multiple of .......smellest odd number.
Answer» ANSWER :N = 3

Discussion

3842.	If A and B are acute positive angles satisfying the equations 3sin^(2)A+2sin^(2)B=1 and 3sin2A-2sin 2B=0, then A+2B is equal to
Answer» `PI` `(pi)/(2)` `(pi)/(4)` `(pi)/(6)` ANSWER :B

Discussion

3843.	We know that any real number x can be expressed as followigx=[x]+{x}, where [x] is an integer and 0 le {x} lt 1. We define [x]as the greatest integer less than or equal to x or integer part of x and [x] as the fractional part of x. Suppose for any real number x, we write x=(x)-(x), where (x) is integer and 0 le (x) lt 1. We define (x) as theleast integer greater than (or) equal to x. For example (3.26) =4(-14.4)= - 14(5)=5 elearly, if x in I then (x)=[x]. If x !in I, then (x)=[x]+1 we can also define that x in ( n , in +1) rArr (x)=n+1, where n in I The domain of defination of the function f(x)=(1)/(sqrt(x-(x))) is
Answer» I `R-I` `(0, OO)` `PHI` ANSWER :D

Discussion

3844.	Find D_(8) and P_(40) from the following distribution:
Answer» ANSWER :31.5, 22.88

Discussion

3845.	We know that any real number x can be expressed as followigx=[x]+{x}, where [x] is an integer and 0 le {x} lt 1. We define [x]as the greatest integer less than or equal to x or integer part of x and [x] as the fractional part of x. Suppose for any real number x, we write x=(x)-(x), where (x) is integer and 0 le (x) lt 1. We define (x) as theleast integer greater than (or) equal to x. For example (3.26) =4(-14.4)= - 14(5)=5 elearly, if x in I then (x)=[x]. If x !in I, then (x)=[x]+1 we can also define that x in ( n , in +1) rArr (x)=n+1, where n in I The range of the function f(x)=(1)/(sqrt((x)-[x])) is
Answer» `phi` {1} `{ 1/sqrt(N) , n in N}` `(1, OO)` Answer :B

Discussion

3846.	If vec(i), vec(j), vec(k) are unit orthonormal vectors and vec(a) is a vector of magnitude 2 units satisfying vec(a) xx vec(i)= vec(j), then vec(a).vec(i)=
Answer» `+- SQRT3` `+-SQRT2` 0 1 Answer :A

Discussion

3847.	Obtain equation of circle in Centre (sqrt(2), - sqrt(5)) and radius sqrt(5).
Answer» ANSWER :`X^(2) + y^(2)-2sqrt(2X)+2sqrt(5Y)+2=0`

Discussion

3848.	A line L is such that its segmentbetween the straightlines 5x - y - 4 = 0 and 3 x + 4y - 4 = 0 is bisected at the point (1,5) . Obtain the equation.
Answer» Answer :`83 X - 35 y + 92 = 0 `

Discussion

3849.	A line with d.r.s (2,7,-5) is drawn to intersect the lines (x-5)/(3) = (y-7)/(-1) = (z +2)/(1) and ( x +3)/(-3) = (y-3)/(2) = (z-6)/(4) at P and Q respectively. Length of PQ is
Answer» `sqrt78` `sqrt77` `sqrt54` `sqrt74` ANSWER :A

Discussion

3850.	The slopes of sides of a triangle are 1,-2,3. If the orhtocentre of the triangle is the origin O, then the locus of its centroid is y/x=
Answer» `2/3` `2/5` `2/7` `2/9` ANSWER :B

Discussion

Explore topic-wise InterviewSolutions in .

If I is incentre of the triangle ABC, P_(1),P_(2),P_(3) are radii of circum circles of Delta^("le") IBC, ICA, IAB respectively

ax+b(sec(tan^(-1)x))=c and ay+b(sec(tan^(-1)y))=c The value of x+y is

Evaluate: int(xdx)/(x^(2)-5x+6)

The negation of the statement 72 is divisible by 2 and 3 is…….

If cos^(2) x + cos^(4) x =1 then tan^(2) x + tan^(4) x=

If the n^(th) terms of an A.P. 9, 7, 5,….. is equal to the n^(th) term of an A.P. 15, 12, 9……then find n

f(x) - (1- cos (ax))/( x sin x) , x ne 0, f(0) = 1/2is continuous at x = 0 , a =

If f(x+y)=f(x)+f(y)-xy-1 AA x, y in R and f(1)=1 then the number of solution of f(n)=n, n in N is

Find the valuesof other five trigonometric functions cosx=-(1)/(2),x lies in third quadrant.

If D, E are the midpoints of AB, AC of Delta ABC, then vec(B)E + vec(D)C=

If a straight line is given by vecr = (1+ t) hati + 3 t hatj +(1-t) hatk where l in R. If this line lies in the plane x + y + cz = d then the value of c +dis

A coin is tossed and then a die is rolled only in casehead is shown on the coin.

If bara = (-4, 2,4) and barb = (sqrt2, - sqrt2, 0), " then " (2bara,(barb)/2)=

Consider the expansion of (x+a)^n Find the (r+1)^(th)term in the expansion

If in aDelta ABC , r_1 =2r_2=3r_3,then b: c=

If bara, barb, barc is a right handed system, barb is perpendicular to both bara & barc , if (bara,barc)=cos^(-1)(4/5),abs(bara)=1,abs(barb)=2,abs(barc)=3 then abs(barabarbbarc)=

Where does z lie, if |(z-5i)/(z+5i)|=1?

If (x^(2)+1)/(2x)=cos theta then (x^(6)+1)/(2x^(3))=

Any vector which is perpendicular to each of the vectors 2vec(i) + vec(j) -vec(k) and 3vec(i) -vec(j) + vec(k) is normal to

Find the domains of the following functionsf(x) = ( 1)/(x)

The value of sum_(n=1)^(oo) (tan((theta)/(2^(n))))/(2^(n-1)"cos"(theta)/(2^(n-1))) is

If x, y, z are non-zero real numbers, bara=xbari+2barj,bara=ybarj+3barK and barc=xbari+ybarj+zbarj are such that baraxxbarb=zbari-3barj+bark then [barabarbbarc]=

Two sequences cannot be in both AP and GP together.

Prove that: .^(47)C_(4) + .^(51)C_(3) +^(50)C_(3)+^(49) C_(3) +^(48)C_(3) +^(47)C_(3) =^(52)C_(4)

Write down the euqation of the line which makes an intercepts of 2a on the x-axis and 3a on the y-axis. Given that the line passes through the point (14, -9), find the numerical value of a.

A die is thrown once . Find P(a number lt3),

The perimeter of the triangle formed by the points (1,0,0), (0,1,0), (0,0,1) is :

If the lines 3x - 4y + 4 = 0 and 6x - 8y - 7 = 0 are tangents to a circle, then find the radius of the circle.

Find the number of terms in the following expansions. (v) (3x+7)^(8) + (3x-7)^(8)

Is the given relation a function? Give reason for your answer. f = {(x, x)|x is a real number}

If y =a sin x + b cos x ,then y^2 + ((dy)/(dx))^2 is a

If bara, barb are two unit perpendicular vectors then baraxx (baraxx barb) =

In triangle ABC, angleA=60^(@), angle B=40^(@), and angle C=80^(@) If P is the center of the circumcircle of triangle ABC with radius unity, then the radius of the circumcircle of triangle BPC is

If in a Delta^("le") ABC, a, b and angle A are given C_(1),C_(2) are possibel values of 3rd side then

Perimeter of a triangle is 10 cms and its base is 4 cms then maximum area of the triangle is

From a set of 17 cardsnumbered 1,2,3,4,…, 16,17 , one card is drawn at random : Show that the chance that its number is divisible by 3 or 7 is (7)/(17).

Evaluate lim_(x rarr a) (sqrtx - sqrta)/(x -a)

Find the term independent of x in the expansion of (root3x + 1/(2root3x))^(18),x gt 0.

For G.P. 5, 10, 20,…..and 1280, 640, 320…., their n^(th) terms are equal then find n.

The point (4,1) undergoesthe following successively (i) reflection about the line y = x (ii) translation through a distance 2 unit along the positive direction of y - axis. The final position of the point is

Statement P (n): n^(3) +3n^2 + 5n +3 is multiple of .......smellest odd number.

If A and B are acute positive angles satisfying the equations 3sin^(2)A+2sin^(2)B=1 and 3sin2A-2sin 2B=0, then A+2B is equal to

Find D_(8) and P_(40) from the following distribution:

If vec(i), vec(j), vec(k) are unit orthonormal vectors and vec(a) is a vector of magnitude 2 units satisfying vec(a) xx vec(i)= vec(j), then vec(a).vec(i)=

Obtain equation of circle in Centre (sqrt(2), - sqrt(5)) and radius sqrt(5).

A line L is such that its segmentbetween the straightlines 5x - y - 4 = 0 and 3 x + 4y - 4 = 0 is bisected at the point (1,5) . Obtain the equation.

A line with d.r.s (2,7,-5) is drawn to intersect the lines (x-5)/(3) = (y-7)/(-1) = (z +2)/(1) and ( x +3)/(-3) = (y-3)/(2) = (z-6)/(4) at P and Q respectively. Length of PQ is

The slopes of sides of a triangle are 1,-2,3. If the orhtocentre of the triangle is the origin O, then the locus of its centroid is y/x=