14949 + Interview Questions in Maths in Class 11 Page 89 InterviewSolution

4401.	Find the ratio in which the line joining the points (6, 12) and (4, 9) is divided by the curve x^(2)+y^(2)=4.
Answer» Answer :EXTERNALLY in the RATIO `4 : 3 and 44 : 31`

Discussion

4402.	Match the following from List - I to List - II {:("List-I","List-II"),((I)\|{:(1,1,1),(a,b,c),(bc,ca,ab):}\|=,(a)(a-b)(b-c)(c-a)),((II)\|{:(a,b,c),(a^(2),b^(2),c^(2)),(a^(3),b^(3),c^(3)):}\|=,(b)(a-b)(b-c)(c-a)abc),((III)\|{:(1,1,1),(a,b,c),(a^(3),b^(3),c^(3)):}\|=,(c)(a-b)(b-c)(c-a)(a+b+c)):}
Answer» B,C,a b,a,c a,b,c a,c,a Answer :C

Discussion

4403.	If A and B are two events such that P(barA)=(3)/(4),P((A)/(B))=(1)/(2)andP((B)/(A))=(2)/(3)then P(B)is:
Answer» `(1)/(3)` `(2)/(3)` `(1)/(6)` `(1)/(2)` ANSWER :A

Discussion

4404.	State true of false for the following: the inequality \|z-4\| lt \|z-2\| represents the region given by x gt 3
Answer» ANSWER :1

Discussion

4405.	Centroid of triangle formed by feet of perpendicular from (-3,-6,-9) on coordinate axesis
Answer» (-1,-2,-3) (1,2,3) (1,-2,-3) (1,-2,3) ANSWER :A

Discussion

4406.	Sides of Delta ABC " are in A.P. if " a ltmin {b, c},then cosA may be equal to
Answer» `(4B - 3c)/(2B)` `(3c- 4b)/(2c)` `(4C - 3B)/(2b)` `(4c - 3b)/(2c)` Answer :A::C

Discussion

4407.	Using definition , find the derivative of f(x)=sinsqrt(x).
Answer» ANSWER :`(cossqrt(X))/(2sqrt(x))`

Discussion

4408.	If bara=4bari+5barj-bark, barb=bari-4barj+5bark, barc=3bari+barj-bark such thatbarpbotbara,barpbotbarb and barp.barc=21 , thenbarp=
Answer» `6(bari+barj+bark)` `7(bari+barj+bark)` `6(bari-barj-bark)` `7(bari-barj-bark)` ANSWER :D

Discussion

4409.	A card is drawn at random froma well-shuffled pack of 52 cards. Find the probability that it is neither aking nor a heart.
Answer» ANSWER :`(9)/(13)`

Discussion

4410.	Find the slope of the line joining the points (a cos theta , b sin theta) and (a cos phi, b sin phi)
Answer» SOLUTION :`(B(SIN THETA - sin phi))/(a (cos theta - cos phi))`

Discussion

4411.	If the lines x+2ay+a=0, x+3by+b=0, x+4cy+c=0 are concurrent, then a, b, c are in
Answer» A.P G.P H.P A.G.P Answer :C

Discussion

4412.	A line passes thorough (x_(1) , y_(1) ) and (h, k). If slope of the line is m, show that, k-y_1 = m(h-x_1).
Answer» ANSWER :`k-y_1 = m(H- x_1)`

Discussion

4413.	Derive function of 120^(@)from functions of 60^(@) andcheck by using relations between functions of supplementary angles.
Answer» ANSWER :`SIN 120^(@) = (sqrt3)/(2), COS 120^(@) =- (1)/(2) , tan 120^(@) =- sqrt3`

Discussion

4414.	Point (-4,2,-5) lies in third octant.
Answer» ANSWER :FALSE STATEMENT

Discussion

4415.	Consider a triangle PQR with coordinates of its vertices as P(-8,5), Q(-15,-19), and R(1,-7). The bisector of the interior angle of P has the equation which can be written in the form ax+2y+c=0 The radius of the incircle of triangle PQR is
Answer» 4 5 6 8 Answer :A

Discussion

4416.	Consider a triangle PQR with coordinates of its vertices as P(-8,5), Q(-15,-19), and R(1,-7). The bisector of the interior angle of P has the equation which can be written in the form ax+2y+c=0 The sum a+c is
Answer» 129 78 89 none of these ANSWER :C

Discussion

4417.	Consider a triangle PQR with coordinates of its vertices as P(-8,5), Q(-15,-19), and R(1,-7). The bisector of the interior angle of P has the equation which can be written in the form ax+2y+c=0 The distance between the orthocenter and the circumcenter of triangle PQR is
Answer» `25//2` `29//2` `37/82` `51/2` ANSWER :A

Discussion

4418.	Complete the following table (##ANE_PMP_MAT_0XI_C11_E03_028_Q01##)
Answer» Solution :[SUM of local DISTANCES of any POINT : `12,4,1/2 e:sqrt11/6,1/2,3/5` latus RECTUM `25/3,3,8/25`

Discussion

4419.	The position vectors of the three non-collinear points A, B, C, are bara, barb, barc respectively. The distance of the origin from the plane through A, B, C is
Answer» `[bara BARB barc]` `(abs([bara barb barc]))/([baraxxbarb+barbxxbarc+barcxxbara])` `abs(([bara barb barc])/(baraxxbarb+barbxxbarc+barcxxbara))` `2[bara barb barc]` Answer :C

Discussion

4420.	Refer to question 6 above, state true or false : (give reason for your answer) A and B are mutually exclusive.
Answer» ANSWER :`:.` GIVEN STATEMENT is TRUE.

Discussion

4421.	Refer to question 6 above, state true or false : (give reason for your answer) A and B are mutually exclusive and exhaustive
Answer» ANSWER :`:.` GIVEN STATEMENT is TRUE.

Discussion

4422.	If the range of the function f(x)=((1+x+x^(2))(1+x^(4)))/(x^(3)) when x gt 0 is [K, oo) then K is
Answer» ANSWER :6

Discussion

4423.	If 4 cos theta - 3 sec theta = tantheta, " then " theta=
Answer» `THETA = n PI + (-1)^(n) BETA , n in Z " where SIN " beta = (1 + sqrt(17))/(8)` `theta = n pi + (-1)^(n) beta , n in Z " where sin " beta = (-1 - sqrt(17))/(8)` `theta = n pi + (-1)^(n) beta , n in Z " where sin " beta = (-1 + sqrt(17))/(4)` `theta = n pi + (-1)^(n) beta , n in Z " where sin " beta = (-1sqrt(17))/(4)` ANSWER :B

Discussion

4424.	Express (5pi^(c))/(3)in degree measure ?
Answer» ANSWER :`300^(@)`

Discussion

4425.	Examine the nature of the roots of the equations (i) 2x^(2)+2x+3=0 (ii) 2x^(2)-7x+3=0 (iii) x^(2)_5x-2=0 (iv) 4x^(2)-4x+1=0
Answer» ANSWER :(i) -20, is NEGATIVE

Discussion

4426.	If the position vectors of A,Band C are respectively 2bari-barj+bark, bari -3barj-5bark and 3bari - 4barj - 4bark, " then " cos^(2)A =
Answer» 0 `6/41` `35/41` 1 Answer :C

Discussion

4427.	x + 2y le 10,x + y ge 1,x-y le 0,x ge 0, yge 0
Answer» SOLUTION :

Discussion

4428.	If y^2 = p(x) , a polyomial of degree 3 , then 2(d)/(dx)(y^3(d^2y)/(dx^2)) is equal to
Answer» `p^(111)(X)+p^(1)(x)` `p^(11)(x)+p^(111)(x)` `p(x)p^(111)(x)` CONSTANT Answer :C

Discussion

4429.	Consider the system of equations sin x cos 2 y = (a ^(2) - 1)^(2) + 1, cos x sin 2 y = a = 1The number of values of y in [0, 2 pi] , when the systemhas solution for permissiblevalues of a is/ are
Answer» 2 3 4 5 Answer :D

Discussion

4430.	IfA(n, n^2) (where n in N) is any point in the interior of the quadrilateralformed by x=0, y=0, 3x+y-4=0 and 4x+y-20=0 then the possible number of position of A is
Answer» ANSWER :1

Discussion

4431.	The lines 2x+3y=6, 2x+3y=8 cut the X-axis at A, B respectively. A line l drawn through the point (2, 2) meets the X-axis at C in such a way that abscissae of A, B and C are in arithmetic progression. Then the equation of the line l is
Answer» `2x+3y=10` `3x+2y=10` `2x-3y=10` `3x-2y=10` ANSWER :A

Discussion

4432.	The product of the perpendiculars drawn from the points pm sqrt(a^(2) -b^(2),0) on the line x/a cos theta+ y/b sin theta =1, is
Answer» `a^(2)` `B^(2)` `a^(2) +b^(2)` `a^(2) -b^(2)` ANSWER :B

Discussion

4433.	If alpha,beta are the roots of the equation 3x^(2)-6x+4=0, find the value of ((alpha)/(beta)+(beta)/(alpha))+2((1)/(alpha)+(1)/(beta))+3alphabeta.
Answer» ANSWER :8

Discussion

4434.	((33),(10))....((33),(8)).
Answer» gt lt = `GE` ANSWER :A

Discussion

4435.	If x = a (t + sin t), y= a (1- cost) and (dx)/(dy) =cotp then p =
Answer» t `2T` `t/2` `-t^2` ANSWER :C

Discussion

4436.	If sin A = (1)/(sqrt3) and sin B = (1)/(sqrt5)find the value oftan ""(1)/(2) (A + B) . Cot "" (1)/(2) (A-B).
Answer» ANSWER :`4 + sqrt15`

Discussion

4437.	Cot^(-1)3+Cot^(-1)7+Cot^(-1)13+……n terms =
Answer» `TAN^(-1)(N/(n+2))` `Tan^(-1)((n+2)/n)` `"Tan"^(-1)(3N)/(4n+1)` `Tan^(-1)((4n+1)/(3n))` ANSWER :A

Discussion

4438.	Which of the following is true for z=(3+2i sin theta)//(1-2 i sin theta), where i=sqrt(-1)?
Answer» Z is purely imaginary for `theta=N PI+-pi//3,n in Z` z is purely imaginalry for `theta =npi +-pi//2, n in Z` z is purely imaginary for `theta=n pi , n in Z` z is purely imaginary for `theta=2 n pi, n inZ` ANSWER :A

Discussion

4439.	Find the eccentricity of the ellipse whose latus rectum is 4 and distance of the vertex from the nearest focus is 1.5 cm.
Answer» ANSWER :`1/3`

Discussion

4440.	Let f(x) = 2^(2x - 1) and phi(x) = -2^(x) + 2x "log" 2. If f'(x) gt phi'(x), then
Answer» `0 lt X lt 1` `0 LE x lt 1` `x gt 0` `x ge 0` Answer :C

Discussion

4441.	The most general value of x for which sinx+cosx= "min"_(a in R) {1, a^(2)-4a+6} are given by
Answer» `2n pi+(pi)/(6)` `2n pi+(pi)/(3)` `N pi+(-1)^(n)(pi)/(4)-(pi)/(4)` `NPI` Answer :C

Discussion

4442.	If f(x+y)=f(x)f(y) for all x and y if f(1)=2, then area enclosed by 3absx+2absyle8 is
Answer» `f(5)sq.units` `1//3 f(6)sq.units` `f(6)sq.units` `f(4)sq.units` Answer :B

Discussion

4443.	If thetainQ_(3) , then sqrt(4sin^4theta+sin^(2)2theta)+4cos^2(pi/4-theta/2)=
Answer» 2 `-2` 0 1 Answer :A

Discussion

4444.	Power set of the set A= {1, 2}" is ""………."
Answer» <P> ANSWER :`P(A)= {PHI, {1}, {2}, {1, 2}}`

Discussion

4445.	Let the lines represented by equation x^2y^2-y^2+1=0 form a square ABCD. A point 'P' is taken on the same plane of square such that atleast two sides of all the triangles PAB, PBC,PCD and PDA are equal. The number of possible position of th point 'P'
Answer» 1 5 17 9 Answer :D

Discussion

4446.	Let the lines represented by equation x^2y^2-y^2+1=0 form a square ABCD. A point 'P' is taken on the same plane of square such that atleast two sides of all the triangles PAB, PBC,PCD and PDA are equal. For all the possible position of the 'P' . The number of the given triangles have all the three side equal
Answer» 0 4 8 5 Answer :C

Discussion

4447.	Let the lines represented by equation x^2y^2-y^2+1=0 form a square ABCD. A point 'P' is taken on the same plane of square such that atleast two sides of all the triangles PAB, PBC,PCD and PDA are equal. One of the possible position of the 'P' such that atleast one of the given triangle is equilateral given by
Answer» (0,0) `(sqrt3+1,0)` `(0,sqrt3-2)` `(sqrt3+1,sqrt3-1)` ANSWER :B

Discussion

4448.	For specifying a straight line, how many geometrical parameters should be known ?
Answer» `1` `2` `4` `3` ANSWER :B

Discussion

4449.	f(x) = (tan^(-1) (x +2))/(\|x =2\|) , x ne -2 " and " f(-2) =-1 then at x = -2 , f is
Answer» LEFT CONTINUOUS RIGHT continuous continuous none ANSWER :A

Discussion

4450.	Let f(x)=(x-3)^(5)(x+1)^(4) then
Answer» `x=7//9`is a POINT of maxima x=3 is a point of minimum x=-1 is a POINTOF maxima f has no point of MAXIMUM or minimum Answer :D

Discussion

Explore topic-wise InterviewSolutions in .

Find the ratio in which the line joining the points (6, 12) and (4, 9) is divided by the curve x^(2)+y^(2)=4.

Match the following from List - I to List - II {:("List-I","List-II"),((I)|{:(1,1,1),(a,b,c),(bc,ca,ab):}|=,(a)(a-b)(b-c)(c-a)),((II)|{:(a,b,c),(a^(2),b^(2),c^(2)),(a^(3),b^(3),c^(3)):}|=,(b)(a-b)(b-c)(c-a)abc),((III)|{:(1,1,1),(a,b,c),(a^(3),b^(3),c^(3)):}|=,(c)(a-b)(b-c)(c-a)(a+b+c)):}

If A and B are two events such that P(barA)=(3)/(4),P((A)/(B))=(1)/(2)andP((B)/(A))=(2)/(3)then P(B)is:

State true of false for the following: the inequality |z-4| lt |z-2| represents the region given by x gt 3

Centroid of triangle formed by feet of perpendicular from (-3,-6,-9) on coordinate axesis

Sides of Delta ABC " are in A.P. if " a ltmin {b, c},then cosA may be equal to

Using definition , find the derivative of f(x)=sinsqrt(x).

If bara=4bari+5barj-bark, barb=bari-4barj+5bark, barc=3bari+barj-bark such thatbarpbotbara,barpbotbarb and barp.barc=21 , thenbarp=

A card is drawn at random froma well-shuffled pack of 52 cards. Find the probability that it is neither aking nor a heart.

Find the slope of the line joining the points (a cos theta , b sin theta) and (a cos phi, b sin phi)

If the lines x+2ay+a=0, x+3by+b=0, x+4cy+c=0 are concurrent, then a, b, c are in

A line passes thorough (x_(1) , y_(1) ) and (h, k). If slope of the line is m, show that, k-y_1 = m(h-x_1).

Derive function of 120^(@)from functions of 60^(@) andcheck by using relations between functions of supplementary angles.

Point (-4,2,-5) lies in third octant.

Consider a triangle PQR with coordinates of its vertices as P(-8,5), Q(-15,-19), and R(1,-7). The bisector of the interior angle of P has the equation which can be written in the form ax+2y+c=0 The radius of the incircle of triangle PQR is

Consider a triangle PQR with coordinates of its vertices as P(-8,5), Q(-15,-19), and R(1,-7). The bisector of the interior angle of P has the equation which can be written in the form ax+2y+c=0 The sum a+c is

Consider a triangle PQR with coordinates of its vertices as P(-8,5), Q(-15,-19), and R(1,-7). The bisector of the interior angle of P has the equation which can be written in the form ax+2y+c=0 The distance between the orthocenter and the circumcenter of triangle PQR is

Complete the following table (##ANE_PMP_MAT_0XI_C11_E03_028_Q01##)

The position vectors of the three non-collinear points A, B, C, are bara, barb, barc respectively. The distance of the origin from the plane through A, B, C is

Refer to question 6 above, state true or false : (give reason for your answer) A and B are mutually exclusive.

Refer to question 6 above, state true or false : (give reason for your answer) A and B are mutually exclusive and exhaustive

If the range of the function f(x)=((1+x+x^(2))(1+x^(4)))/(x^(3)) when x gt 0 is [K, oo) then K is

If 4 cos theta - 3 sec theta = tantheta, " then " theta=

Express (5pi^(c))/(3)in degree measure ?

Examine the nature of the roots of the equations (i) 2x^(2)+2x+3=0 (ii) 2x^(2)-7x+3=0 (iii) x^(2)_5x-2=0 (iv) 4x^(2)-4x+1=0

If the position vectors of A,Band C are respectively 2bari-barj+bark, bari -3barj-5bark and 3bari - 4barj - 4bark, " then " cos^(2)A =

x + 2y le 10,x + y ge 1,x-y le 0,x ge 0, yge 0

If y^2 = p(x) , a polyomial of degree 3 , then 2(d)/(dx)(y^3(d^2y)/(dx^2)) is equal to

Consider the system of equations sin x cos 2 y = (a ^(2) - 1)^(2) + 1, cos x sin 2 y = a = 1The number of values of y in [0, 2 pi] , when the systemhas solution for permissiblevalues of a is/ are

IfA(n, n^2) (where n in N) is any point in the interior of the quadrilateralformed by x=0, y=0, 3x+y-4=0 and 4x+y-20=0 then the possible number of position of A is

The lines 2x+3y=6, 2x+3y=8 cut the X-axis at A, B respectively. A line l drawn through the point (2, 2) meets the X-axis at C in such a way that abscissae of A, B and C are in arithmetic progression. Then the equation of the line l is

The product of the perpendiculars drawn from the points pm sqrt(a^(2) -b^(2),0) on the line x/a cos theta+ y/b sin theta =1, is

If alpha,beta are the roots of the equation 3x^(2)-6x+4=0, find the value of ((alpha)/(beta)+(beta)/(alpha))+2((1)/(alpha)+(1)/(beta))+3alphabeta.

((33),(10))....((33),(8)).

If x = a (t + sin t), y= a (1- cost) and (dx)/(dy) =cotp then p =

If sin A = (1)/(sqrt3) and sin B = (1)/(sqrt5)find the value oftan ""(1)/(2) (A + B) . Cot "" (1)/(2) (A-B).

Cot^(-1)3+Cot^(-1)7+Cot^(-1)13+……n terms =

Which of the following is true for z=(3+2i sin theta)//(1-2 i sin theta), where i=sqrt(-1)?

Find the eccentricity of the ellipse whose latus rectum is 4 and distance of the vertex from the nearest focus is 1.5 cm.

Let f(x) = 2^(2x - 1) and phi(x) = -2^(x) + 2x "log" 2. If f'(x) gt phi'(x), then

The most general value of x for which sinx+cosx= "min"_(a in R) {1, a^(2)-4a+6} are given by

If f(x+y)=f(x)f(y) for all x and y if f(1)=2, then area enclosed by 3absx+2absyle8 is

If thetainQ_(3) , then sqrt(4sin^4theta+sin^(2)2theta)+4cos^2(pi/4-theta/2)=

Power set of the set A= {1, 2}" is ""………."

Let the lines represented by equation x^2y^2-y^2+1=0 form a square ABCD. A point 'P' is taken on the same plane of square such that atleast two sides of all the triangles PAB, PBC,PCD and PDA are equal. The number of possible position of th point 'P'

For specifying a straight line, how many geometrical parameters should be known ?

f(x) = (tan^(-1) (x +2))/(|x =2|) , x ne -2 " and " f(-2) =-1 then at x = -2 , f is

Let f(x)=(x-3)^(5)(x+1)^(4) then