14949 + Interview Questions in Maths in Class 11 Page 112 InterviewSolution

5551.	Find the equation of the bisector of the acute angle between the lines 3x-4y+7=0 and 12x+5y-2=0.
Answer» ANSWER : `11x-3y+9=0`

Discussion

5552.	The maximum value of sin^3x.cos^3x is … and is obtained at x=......
Answer» `1/8,pi/4` `(-2)/3,pi/4` `1/3,pi/8` `(-1)/8,pi/4` ANSWER :A

Discussion

5553.	If 3 sec alpha- 5 tanalpha= k and 6 sec alpha+k tan alpha=5 then k^(2)=
Answer» 20 25 34 37 Answer :A

Discussion

5554.	D(2,1,0) ,E(2,0,0),F(0,1,0)are midpoints of the sides BC,CA,AB of DeltaABC respectively . The , the centroid of DeltaABc is
Answer» `((1)/(3), (1)/(3), (1)/(3))` `((4)/(3), (2)/(3), 0)` `(-(1)/(3), (1)/(3), (1)/(3))` `((2)/(3), (1)/(3), (1)/(3))` ANSWER :b

Discussion

5555.	If (4.2)^(x) = (0.42)^(y) = 100, " then "(1)/(x) -(1)/(y)=
Answer» 1 2 `(1)/(2)` `-1` ANSWER :C

Discussion

5556.	State which of the following sets are finite or infinite : {x : x in N and x is odd}
Answer» ANSWER :INFINITE

Discussion

5557.	If cosh (alpha-beta)=a cosh(alpha+beta) then cot h alpha cot h beta=
Answer» `(a+1)/(a-1)` `(1+a)/(1-a)` `(a-1)/(a+B)` `(1-a)/(1+a)` ANSWER :B

Discussion

5558.	Evaluate the following limits : lim_(x to oo) (2x^(2)+7x+5)/(4x^(2)+3x-1)
Answer» ANSWER :`1/2`

Discussion

5559.	(a) The probabilitythat a car beingfilled with petrol will also need an oil change is 0.30 , the probabilitythat It needs a new , oilfilteris 0.40 . And the probabilitythat both the oilfiliter needchangingis 0.15. (OR) (b) An advertisitingexecutive is studyingtelevision viewinghabits of married men and womanduringprimetime hours.Based ont he pastviewingrecords he hasdeterminedthat duringprime time wives are watchingtelevision 60%of the time. It has also been determinedthatwhenthe wife is watching.When the wifeis not watchingthe television 30 %of the time the husbandis watchingthe televison . findthe probabilitythat (i) The husband is watchingthe televisionduringthe prime time of television (ii) if the husbandis watching the television , the wifeis alsowatchingthe television .
Answer» ANSWER :(a) 0.375 (B)`2/3 `

Discussion

5560.	The X-axis and Y-axis taken together determine a plane known as ____
Answer» ANSWER :XY - PLANE

Discussion

5561.	Find the centroid and the area of the triangle formed by the lines 12x^2-20xy+7y^2=0,2x-3y+4=0
Answer» `((2)/(3),(2)/(3))` `((8)/(3),(8)/(3))` `((3)/(8),(3)/(8))` `((4)/(3),(4)/(3))` Answer :B

Discussion

5562.	Find the approximate value of sqrt(25.2)
Answer» ANSWER :5.02

Discussion

5563.	If Deltais the area of a triangle with side lengths a , b , and c , then
Answer» `4 DELTA ge sqrt(abc(a + b + c))` `Delta ge sqrt(abc(a + b+ c))` `4 Delta lesqrt(abc(a+b+c))` `Delta lesqrt((a+b+c)abc)` ANSWER :C

Discussion

5564.	Express the following as functions of angles less than 45^(@) : "cosec"(-7498^(@)).
Answer» ANSWER :`sec28^(@)`

Discussion

5565.	Prove that (dy)/(dx)= -1
Answer» SOLUTION :- SIN X

Discussion

5566.	Consider the equation tan^(2)(cos sqrt(4pi^(2)-x^(2)))-4a tan (cos sqrt(4pi^(2)-x^(2)))+2+2a=0,a being a parameter. (Given tan1=1.56) If a=1/2 then the number of distinct real roots of the equation is
Answer» 0 1 2 infinite Answer :C

Discussion

5567.	Find the derivativ of the function w.r.to x sin ^-1 (e ^(x) )
Answer» ANSWER :`(e ^(X))/( SQRT (1- e ^(2X)))`

Discussion

5568.	Write the negation of the statement: "sqrt7 is rational.
Answer» SOLUTION :`SQRT7` is not RATIONAL

Discussion

5569.	Prove that : cos((pi)/4+x)+cos((pi)/4-x)=sqrt(2)cosx
Answer» ANSWER :`SQRT2 COS X = R.H.S.`

Discussion

5570.	If the sines of the angle A and B of a triangle ABC satisfy the equation c^(2)x^(2) - c(a + b) x + ab = 0. Then the triangle
Answer» is acute angled is right angled is OBTUSE angled satisfy `SIN A + cos A = ((a + b))/C` ANSWER :B::D

Discussion

5571.	If tantheta+tan2theta+sqrt(3)tanthetatan2theta=sqrt(3), then the general solution is theta
Answer» `(3n+1)(pi)/(3)` `(3n+1)(pi)/(9)` `(3n+1)(pi)/(6)` `(2n+1)(pi)/(9)` ANSWER :B

Discussion

5572.	A circle of radius 4 cm is inscribed in AABC, which touches the side BC at D. If BD = 6 cm, DC = 8 cm, then
Answer» the TRIANGLE is necessarily acute angled `"tan"(A)/(2)=(4)/(7)` perimeter of the triangle ABC is 42 cm area of `DELTABC is 84 cm^(2)` Answer :A::B::C::D

Discussion

5573.	Find the equation of set of points P such that PA^(2)+PB^(2)=2k^(2) whereA and Bare the points(3,4,5) and(-1,3,-7) respectively
Answer» ANSWER :`X^(2)+y^(2)+Z^(2)-2x-7y+2z=(K^(2)-109)/(2)`

Discussion

5574.	Letf(x+y)=f(x).f(y) AA x,y in R. f(1)=2. " Area enclosed by " 3absx+2absyle8 " is " (f(k))/m. The point P (2,6) is transtated parallel to y=kx in the first quadrant through a 'k' unit distance. The coordinates of the new position of P is//are
Answer» `(2pm2/sqrt10,6pm1/sqrt10)` `(2pm2/sqrt10,6pm18/sqrt10)` `(2pm6/sqrt10,6pm18/sqrt10)` `(2pm6/sqrt10,6pm18/sqrt10)` ANSWER :B

Discussion

5575.	Find the values of a and b so that the function defined by f(x) = f(x)={{:(ax^(2)+9x-5,ifxlt1),(b,ifx=1),((x+3)(6x-b),ifxlt 1):} continuous on R.
Answer» ANSWER :2

Discussion

5576.	If 2tan^(2)x-5secx=1 for exactly 7 distinct values of x in [0,(npi)/2], n in N then greatest value of n is
Answer» 6 12 13 15 Answer :D

Discussion

5577.	Three numbers are chosen from 1 to 30 . Theprobability that they are not consecutive , is
Answer» `(142)/(145)` `(144)/(145)` `(143)/(145)` `(1)/(145)` ANSWER :B

Discussion

5578.	Two lines passing through the point (2, 3) intersects each other at an angle of 60^(@). If slope of one line is 2, find equation of the other line.
Answer» ANSWER :`(sqrt3 + 2) X + (2 sqrt3 - 1) y = 8 sqrt3 + 1 " or " ( sqrt3 - 2) x + (1 + 2 sqrt3) y = - 1 + 8 sqrt3`

Discussion

5579.	Find the positive integers x and y such that x+y=60 " and" xy^(3) is maximum.
Answer» ANSWER :15, 45

Discussion

5580.	The number of triangles that are formed by choosing the vertices from a set of 12 points, saven of which lie on the same line is
Answer» 105 15 175 185 Answer :A

Discussion

5581.	Solve the general vlaue. 2 sin 2 x - sin x =0
Answer» Answer :`n PI, 2 npipm alpha` when ` COS alpha = (1)/(4)`

Discussion

5582.	A+B = 90^(@) rArr sin A + sin Bin
Answer» [-1, 1] `[-sqrt(2), sqrt(2)]` `[-sqrt(3), sqrt(3)]` [-2, 2] ANSWER :B

Discussion

5583.	Find the sum to infinity in each of the following G.P 6, 1.2, 0.24……
Answer» ANSWER :`(15)/(2)`

Discussion

5584.	In how many ways can 5 letters be posted in 4 letter boxes?
Answer» ANSWER :` 1024`

Discussion

5585.	i^(9)+i^(10)-3i^(12)=-4
Answer» ANSWER :TRUE STATEMENT

Discussion

5586.	Which of the following statements are true and whihc are false? In each case give a valid reason for saying so. (i) p: each radius of a circle is a chord of the circle. (ii) q: the centre of a circle bisects each chord of the circle. (iii) r: circles is a particular case of an ellipse. (iv) s : if x and y are integeres such that xgty , then -xlarry. (v) t: sqrt(11) is a rational number.
Answer» Solution :(i) Given statement : each radius of a circle is a chord of the circle. `because` A chord MEETS the circle at two different POINTS but the radius meets the circle at one point only . `therefore` Any radius of the circle cannot be the chord of the circle . Therefore, given statement is false. (ii) Given statement : the centre of a circle BISECTS each chord of the circle. `because` only the diameter of a circle is a circle is a chord at which the centre of the circle lie. centre does not lie on the other chords. `therefore` centre does not bisect all chords. therefore, given statement is false. (iii) Given statement: circle is a particular case of an ellipse. Equation of ellipse `: (x^2)/(a^2)+(y^2)/(b^2)=1` If `a=b` then `(x^2)/(a^2)+(y^2)/(a^2)=1rArrx^2+y^2=a^2` which is the equation of a circle. `rArr` circle is a particular case of ellipse. (iv) Given statement : if x and y are INTEGERS such that `xgty` then `-xlarry`. from the law of inequations `xgtyrArr-xlarry` therefore , given statement is true. (V) Given statement : `sqrt(11)` is a rational number. every rational number can be expressed in the form `(P)/(q)` where p and q are integers and `q ne 0`. But `sqrt(11)` cannot be expressed in the form `(p)/(q)`. `therefore` Given statement is false.

Discussion

5587.	If A(cos alpha,sin alpha,0), B(cos beta,sin beta,0),C(cos gamma,sin gamma,0) are vertices of DeltaABC and let cos alpha+cos beta+cos gamma=3a,sin alpha+sin beta+sin gamma=3b, then find i) Circumcentreii) Centroidiii) Orthocentre
Answer» ANSWER :(i) (0, 0, 0) (II) (a,b,0) (III) (3a,3b,0)

Discussion

5588.	Ifa= 5 , b-=12 , c=13 thentan ""(A)/(2) =
Answer» ` (1)/(5) ` ` (2)/(5) ` ` ( 3)/(5) ` `( 4)/(5)` ANSWER :A

Discussion

5589.	A right triangle is drawn in a semicircleof radius (1)/(2) with one of itslegs along the diameter . If the maximum area of the triangle is M , thenthe valueof 32sqrt(3)Mc is _______
Answer» ANSWER :192

Discussion

5590.	Find the square roots of the following : 8-15i
Answer» ANSWER :`+-((5)/(SQRT(2))-(3I)/(sqrt(2)))`

Discussion

5591.	If the line y = mx + 1 is tangent to the parabola y^(2) = 4x then find the value of m.
Answer» ANSWER :1

Discussion

5592.	From the following data, compute price index by using simple average of pricerelatives:
Answer» ANSWER :`=105.94`

Discussion

5593.	If f(x)=\|(Sinx , 1, 0),(x - pi/2,Sinx,1),(0,1,Sinx)\| then (df)/(dx) atx = pi/2 is
Answer» 2 `pi/2` `-1` 8 Answer :C

Discussion

5594.	Write each of the statements in the form ''if p, then q'' q: There is traffic jam whenever it rains.
Answer» ANSWER :If it RAINS, then there is TRAFFIC JAM.

Discussion

5595.	Obtain Equation of line which satisfy given condition : Passing through (2, 2sqrt3) and inclined with the X-axis at an angle of 75°.
Answer» ANSWER :`(SQRT3 + 1) X - ( sqrt3 - 1) y = 4 (sqrt3- 1)`

Discussion

5596.	A circular wire of radius 3 cm is out bent so as to lie along the circumference of a sector whose radius is 48cm. Find in degress the angle which is substended at the centre of the sector.
Answer» ANSWER :`22^(@)30'`

Discussion

5597.	Find the mean deviation using arithmetic mean for the following
Answer» SOLUTION :NA

Discussion

5598.	If'n_1 ' is the number of points on the line 3x+4y=5 which is at a distance of1+sin^2 theta ' units form (2,3) and 'n_2 ' denotes number of point on 3x+4y=5which is at a distance of ' sec^2 theta + 2 cosec^2 theta ' unit from (1,3) then sum of the root of n_2x^2-6x+n_1=0 is
Answer» ANSWER :3

Discussion

5599.	………of the following is not statement.
Answer» SMOKING in INJURIOUS to HEALTH. `2+2=4` 2 is the only EVEN primenumber Come here Answer :D

Discussion

5600.	Let f(x)=ax^(2)+bx+c,a,b,c in Randa ne0 suppose f(x)gt0for all x in R Let g(x)=f(x)+f(x)+f'(x)then
Answer» `g(x)gt0AA x in R` `g(x)lt0AA x in R` `g(x)=0`has no REAL complex roots sum of the roots of g(x)=0 is -3 if `OMEGA,omega^(2)`are roots of f(x)=0 where `omega` is the CUBE roots of unity Answer :A::C::D

Discussion

Explore topic-wise InterviewSolutions in .

Find the equation of the bisector of the acute angle between the lines 3x-4y+7=0 and 12x+5y-2=0.

The maximum value of sin^3x.cos^3x is … and is obtained at x=......

If 3 sec alpha- 5 tanalpha= k and 6 sec alpha+k tan alpha=5 then k^(2)=

D(2,1,0) ,E(2,0,0),F(0,1,0)are midpoints of the sides BC,CA,AB of DeltaABC respectively . The , the centroid of DeltaABc is

If (4.2)^(x) = (0.42)^(y) = 100, " then "(1)/(x) -(1)/(y)=

State which of the following sets are finite or infinite : {x : x in N and x is odd}

If cosh (alpha-beta)=a cosh(alpha+beta) then cot h alpha cot h beta=

Evaluate the following limits : lim_(x to oo) (2x^(2)+7x+5)/(4x^(2)+3x-1)

The X-axis and Y-axis taken together determine a plane known as ____

Find the centroid and the area of the triangle formed by the lines 12x^2-20xy+7y^2=0,2x-3y+4=0

Find the approximate value of sqrt(25.2)

If Deltais the area of a triangle with side lengths a , b , and c , then

Express the following as functions of angles less than 45^(@) : "cosec"(-7498^(@)).

Prove that (dy)/(dx)= -1

Consider the equation tan^(2)(cos sqrt(4pi^(2)-x^(2)))-4a tan (cos sqrt(4pi^(2)-x^(2)))+2+2a=0,a being a parameter. (Given tan1=1.56) If a=1/2 then the number of distinct real roots of the equation is

Find the derivativ of the function w.r.to x sin ^-1 (e ^(x) )

Write the negation of the statement: "sqrt7 is rational.

Prove that : cos((pi)/4+x)+cos((pi)/4-x)=sqrt(2)cosx

If the sines of the angle A and B of a triangle ABC satisfy the equation c^(2)x^(2) - c(a + b) x + ab = 0. Then the triangle

If tantheta+tan2theta+sqrt(3)tanthetatan2theta=sqrt(3), then the general solution is theta

A circle of radius 4 cm is inscribed in AABC, which touches the side BC at D. If BD = 6 cm, DC = 8 cm, then

Find the equation of set of points P such that PA^(2)+PB^(2)=2k^(2) whereA and Bare the points(3,4,5) and(-1,3,-7) respectively

Letf(x+y)=f(x).f(y) AA x,y in R. f(1)=2. " Area enclosed by " 3absx+2absyle8 " is " (f(k))/m. The point P (2,6) is transtated parallel to y=kx in the first quadrant through a 'k' unit distance. The coordinates of the new position of P is//are

Find the values of a and b so that the function defined by f(x) = f(x)={{:(ax^(2)+9x-5,ifxlt1),(b,ifx=1),((x+3)(6x-b),ifxlt 1):} continuous on R.

If 2tan^(2)x-5secx=1 for exactly 7 distinct values of x in [0,(npi)/2], n in N then greatest value of n is

Three numbers are chosen from 1 to 30 . Theprobability that they are not consecutive , is

Two lines passing through the point (2, 3) intersects each other at an angle of 60^(@). If slope of one line is 2, find equation of the other line.

Find the positive integers x and y such that x+y=60 " and" xy^(3) is maximum.

The number of triangles that are formed by choosing the vertices from a set of 12 points, saven of which lie on the same line is

Solve the general vlaue. 2 sin 2 x - sin x =0

A+B = 90^(@) rArr sin A + sin Bin

Find the sum to infinity in each of the following G.P 6, 1.2, 0.24……

In how many ways can 5 letters be posted in 4 letter boxes?

i^(9)+i^(10)-3i^(12)=-4

If A(cos alpha,sin alpha,0), B(cos beta,sin beta,0),C(cos gamma,sin gamma,0) are vertices of DeltaABC and let cos alpha+cos beta+cos gamma=3a,sin alpha+sin beta+sin gamma=3b, then find i) Circumcentreii) Centroidiii) Orthocentre

Ifa= 5 , b-=12 , c=13 thentan ""(A)/(2) =

A right triangle is drawn in a semicircleof radius (1)/(2) with one of itslegs along the diameter . If the maximum area of the triangle is M , thenthe valueof 32sqrt(3)Mc is _______

Find the square roots of the following : 8-15i

If the line y = mx + 1 is tangent to the parabola y^(2) = 4x then find the value of m.

From the following data, compute price index by using simple average of pricerelatives:

If f(x)=|(Sinx , 1, 0),(x - pi/2,Sinx,1),(0,1,Sinx)| then (df)/(dx) atx = pi/2 is

Write each of the statements in the form ''if p, then q'' q: There is traffic jam whenever it rains.

Obtain Equation of line which satisfy given condition : Passing through (2, 2sqrt3) and inclined with the X-axis at an angle of 75°.

A circular wire of radius 3 cm is out bent so as to lie along the circumference of a sector whose radius is 48cm. Find in degress the angle which is substended at the centre of the sector.

Find the mean deviation using arithmetic mean for the following

If'n_1 ' is the number of points on the line 3x+4y=5 which is at a distance of1+sin^2 theta ' units form (2,3) and 'n_2 ' denotes number of point on 3x+4y=5which is at a distance of ' sec^2 theta + 2 cosec^2 theta ' unit from (1,3) then sum of the root of n_2x^2-6x+n_1=0 is

………of the following is not statement.

Let f(x)=ax^(2)+bx+c,a,b,c in Randa ne0 suppose f(x)gt0for all x in R Let g(x)=f(x)+f(x)+f'(x)then