14949 + Interview Questions in Maths in Class 11 Page 29 InterviewSolution

1401.	The value of cos(480^(@))sin(150^(@))+sin(600^(@))cos(390^(@)) is ………….
Answer» `-(1)/(2)` 0 `-1` `(1)/(2)` ANSWER :C

Discussion

1402.	If y=(sin^4x-cos^4x+sin^2xcos^2x)/(sin^4x+cos^4x+sin^2xcos^2x), x in(0,pi/2) , then
Answer» `-3/2leyle1/2` `1leyle1/2` `-5/3leyle1` NONE of these Answer :C

Discussion

1403.	Expand (1+4x)^(5).
Answer» ANSWER :`=1+ 20x + 160x^(2) + 640x^(3) + 1280x^(4) + 1024x^(5)`

Discussion

1404.	Solve the following equations by Sridharacharya's formula : (i) x^(2)+x+4=0 (ii) 2x^(2)-2x+3=0 (iii) sqrt(2)x^(2)+x+sqrt(2)=0 (iv) x^(2)-x+2=0 (v) 25x^(2)-30x+11=0 (vi) x^(2)+3x+5=0 (vii) x^(2)-14x+58=0 (viii)x^(2)+13ix -42=0 (ix) x^(2)-11ix-30=0
Answer» Solution :(i) `(-1pmisqrt(5))/(2)` (II) `(1pmisqrt(5))/(2)` (iii) `(-1pmisqrt(7))/(2sqrt(2))` (IV) ` (1pmisqrt(7))/(2)` (V) ` (3pmisqrt(2))/(5)` (vi) `(-3pmisqrt(11))/(2)` (vii) `7pm 3i` (viii) `-6i, -7i` (ix) `5i,6i`

Discussion

1405.	Let f(x)be a periodic function with period 3 and f((-2)/( 3)) = 7and g(x)= int _0^(2) f (t+n ) dtwhere n=3 K , K inN " then "g^(-1)((7)/(3)) =
Answer» `(-2)/(3)` 7 -7 `7/3` ANSWER :B

Discussion

1406.	If O is origin, and P= (1, -2, 1) and OP _\|_ OQ then Q =
Answer» (4, 3, 2) (3, 2, 4) (2, -3, 4) (1, -2, 3) ANSWER :A

Discussion

1407.	If x, y, z, t are real numbers such that x^(2)+y^(2)=9, z^(2)+t^(2)=4 and xt-yz=6 then the greatest value of xz is
Answer» 1 2 3 4 Answer :C

Discussion

1408.	y = log(tan^(-1)(sinx))find dy/dx.
Answer» Answer :`dy/dx= e^(sin^(X^(2))) COS(x^(2)) 2x`

Discussion

1409.	Find Karl Pearson's correlaction coefficient from the given data
Answer» ANSWER :`1`

Discussion

1410.	Find the equation of a circle of radius 5 whose centre lies on x-axis and which passes through the point (2,3) .
Answer» ANSWER :`X^(2)+y^(2)+4x-21=0&x^(2)+y^(2)-12x+11=0`

Discussion

1411.	Let a^(2) + b^(2) = alpha^(2) + beta^(2) = 2 then show that the maximum value of S= ( 1-a) ( 1-b) + (1-alpha) (1- beta)is
Answer» ANSWER :8

Discussion

1412.	If f(3x+2)+f(3x+29)=0 AA x in R, then the period of f(x) is
Answer» 7 8 10 54 Answer :D

Discussion

1413.	If cos A = 3/4then (2cos A+ 3 sin A)/(4 cos A - sin A) =
Answer» `13//4` `9//4` `15//4` `-9//4` ANSWER :B

Discussion

1414.	(ax^(2)+sinx)(p+q cos x)
Answer» ANSWER :`(-qsinx)(AX^(2)+SINX)+(p+q COSX)(2ax+cosx)`

Discussion

1415.	The ratio in which the plane 2x+3y-2z+7=0 divides the line segment joining the points (-1,2,3),(2,3,5) is
Answer» `3:5` `7:5` `9:11` `1:2` EXTERNALLY ANSWER :D

Discussion

1416.	Shift the origin to a suitable point so that the equation y^(2) + 4y + 8x - 2 = 0 will not contain y, constant terms is
Answer» (3/4, -2) (3/4, 2) (2,3/4) (2, -3/4) ANSWER :A

Discussion

1417.	State which of the following statement is true ?
Answer» If a mathematical relation involving the natural NUMBER N is true for all `ninNN`. A mathematical statement may be true or false. `(n^(2)+n+41)` is a prime number for all natural number n. If `ninNN` and `nge2`. Then n n(n+1) is ALWAYS divisible by 3. Answer :B

Discussion

1418.	Let AD be a median of the DeltaABC. If AE and AF are medians of the triangle ABD and ADC respectively, and AD=m_(1), AE=m_(2), AF=m_(3), then a^(2)//8 is equal to
Answer» `m_(2)^(2)+m_(3)^(2)-2m_(1)^(2)` `m_(1)^(2)+m_(2)^(2)-2m_(3)^(2)` `m_(1)^(2)+m_(3)^(2)-2m_(2)^(3)` None of these Answer :A

Discussion

1419.	If af(Tanx)+bf (cot x)= xthen f^(1)(cotx)=
Answer» `1/(a-b)` `(sin^2x)/(a+b)` `(sin^2x)/(a-b)` `(sin^2x)/(b-a)` ANSWER :C

Discussion

1420.	If y is an implicit funtiion of x given by the relation, find (dy)/(dx). 2x ^(2) - 3 xy + y ^(2) + x + 2y - 8=-0.
Answer» ANSWER :`(3Y - 4x -1)/(2Y - 3X +2)`

Discussion

1421.	Find the algebraic sum of the deviations of all the observations from theirmean.
Answer» ANSWER :`m/2 = n/4`

Discussion

1422.	Find the slope of a line perpendicular to the line whose slope is -5(1)/(7)
Answer» ANSWER : `7/(36)`

Discussion

1423.	Write the slopes of the lines 2x+3y-9=0 and 4x+6y+19=0. What do you observe?
Answer» SOLUTION :(-2/3, -2/3) the LINES are PARALLEL

Discussion

1424.	If [sinx]+[sqrt(2)cosx]=-3,x I [0,2pi] ([.] denotes the greatest integer function), then x belongs to
Answer» `(PI,(5PI)/4)` `[pi,(5pi)/4]` `((5pi)/4, 2PI)` `[(5pi),4, 2pi]` ANSWER :A

Discussion

1425.	6 boys and 6 grils sit in a row at random. The probability that all the girls sit together is
Answer» `(1)/(432)` `(12)/(431)` `(1)/(132)` none of these ANSWER :C

Discussion

1426.	A die has two faces each with number '1', three faces each with number '2' and one face with number '3'. If die is rolled once, determine (i) P(2)(ii) P(1 or 3)(iii) P(not 3)
Answer» ANSWER :(i) `1/2`, (II) `1/2`, (III) `5/6`

Discussion

1427.	If A+B+C=180^(@) " then " sum(cot A + cot B)/(tan A + tan B)=
Answer» -1 0 1 2 Answer :C

Discussion

1428.	If f: R rarr R, f(x)=x^(3)+3x^(2)+10x+2sin x then the range of the function is given by
Answer» `(-OO, oo)` `[0, oo)` `(-oo, 0]` `PHI` ANSWER :A

Discussion

1429.	If the bisector of the angle lfloor Cof a triangle ABC cuts AB in D and circum circle in E then (CE)/(DE) =
Answer» `((a + B)^(2))/C^(2)` `SQRT(((a + b))/c)` `sqrt(((a- b)^(2))/c^(2))` `sqrt(((a - b))/c) ` ANSWER :A

Discussion

1430.	Find the derivative of the function e ^(x) + sin x.cos x
Answer» ANSWER :`E ^(X) + COS 2X `

Discussion

1431.	Observe the following lists : {:(,ul"List-I"" (Equation of a plane)",,"List-II"),("A)","through (0,0,0) and (1,1,1)","1)",2x+3y-4z=5),("B)","perpendicular to the plane x + 6y + 5z = 0","2)",3x-2y+4z=7),("C)","parallel to the plane 3x - 2y + 4z = 5","3)",4x+4y-5z=0),(,,"4)",x-4y+3z=0):} Match List-I to List-II :
Answer» `{:(UL"A",ul"B",ul"C"),(3,1,2):}` `{:(ul"A",ul"B",ul"C"),(2,1,3):}` `{:(ul"A",ul"B",ul"C"),(4,3,1):}` `{:(ul"A",ul"B",ul"C"),(4,1,2):}` ANSWER :D

Discussion

1432.	Let f''(x) gt 0 AA x in R and g(x) = g(x) = 2f((x^(2))/(2)) + f(6-x^(2)). Then show that g(x) possesses one maximum and two minima.
Answer» ANSWER :MINIMUM for `X = PM 2` and maximum for `x = 0`

Discussion

1433.	The total revenue in rupees received from the sale os x units of a produce is given by R(x)= 13x^2+ 26x +15. Find the marginal revenue when x =7.
Answer» ANSWER :208

Discussion

1434.	Find the middle term (terms ) in the expansion of (x/a =a/x)^(10)
Answer» ANSWER :` :. "MIDDLE TERM " = - 252 `

Discussion

1435.	(i) Find the eccentricity of hyperbola whose latus rectum is half of its transverse axis. (ii) Prove that the straight lines (x)/(a)-(y)/(b)=mand(x)/(a)-(y)/(b)=(1)/(m) always meet at a hyperbola, where 'm' is a constant.
Answer» ANSWER :`SQRT((3)/(2))`

Discussion

1436.	At x=0, f(x)=sinx-x+(x^(3))/(6)-(x^(4))/(24)
Answer» Has a minimum Has a maximum Does not have an extremum Is not defined Answer :B

Discussion

1437.	The minimum vertical distance between the graphs of y = 2 + sin x and y = cos x is
Answer» 2 1 `SQRT(2)` `2-sqrt(2)` ANSWER :D

Discussion

1438.	Compute the following limits. Lt_(xtooo)(x^(2)+2x-1)/(x^(2)-4x+4)
Answer» ANSWER :1

Discussion

1439.	Given P(A) = 3/5 and P(B) = 1/5. Find P(A or B), if A and B are mutually excluive events.
Answer» ANSWER :`4/5`

Discussion

1440.	If the roots of the equation (q-r)x^(2)+(r-p)x+p-q=0 are equal, then show that p, q and r are in AP.
Answer» ANSWER :`p+r = 2Q`

Discussion

1441.	Let f(x) =\|{:(1,1,1),(3-x,5-3x^(2),3x^(3)-1),(2x^(2)-1,3x^(5)-1,7x^(8)-1):}\| then the equation f(x) =0has
Answer» no REAL ROOT atmost ONE real root atleast 2 real root exactly one real root in (0,1) an no other real root Answer :C

Discussion

1442.	If cosx^(@)=sin 200^(@), find the possible values of x between -180^(@) and 360^(@).
Answer» ANSWER :`pm110^(@),250^(@)`

Discussion

1443.	d/(dx){Tan^(-1)""(x)/(1+x^2)+Tan^(-1)""(1+x^2)/x} =
Answer» 0 1 `1/2` 2 Answer :A

Discussion

1444.	sec^(2)2x=1-tan2x
Answer» Answer :`x = (NPI)/( 2), or (npi)/(2) + ( npi)/(2) + (3pi)/(8), n in Z`

Discussion

1445.	If (1)/(a),(1)/(b),(1)/(c) are also in A.P. then prove that :(i) ((b+c))/(a),((c+a))/(b),((a+b))/(c)are also in A.P.(ii) ((b+c-a))/(a),((c+a-b))/(b),((a+b-c))/(c) are also in A.P.
Answer» SOLUTION :N/a

Discussion

1446.	Circumcentre of the trianlge formed by the points (2,3),(0,1),(4,1) is
Answer» `(1,-2)` `(1,2)` `(2,-2)` `(2,1)` ANSWER :D

Discussion

1447.	If a metallic circular plate of radius 50 cm is heated s that its radius increases at the rate of 1 mm per hour, then the rate at which, the area of the plate increases ("in" cm^(2)// "hour") is
Answer» `5PI` `10PI` `100pi` `50PI` ANSWER :C

Discussion

1448.	If cosalpha=-(4)/(5),(pi)/(2)ltalphaltpi then tan((alpha)/(2))= ……….
Answer» `-3` 3 `(1)/(3)` `-(1)/(3)` ANSWER :B

Discussion

1449.	If the point P(a^2,a) lies in the region corresponding to the acute angle between the line 2y=x and 4y=x, then
Answer» `a in [2,4]` `a in [2,4]` `a in [2,5]` `a in [2,4]` ANSWER :A

Discussion

1450.	Three circles touch one another externally , The tangents at their points of contact meet at a point whose distance from the point of contact is 4. The ratio of product of their radii to the sum of radii of the circles is
Answer» `16:1` `1:16` `15:2` None Answer :A

Discussion

Explore topic-wise InterviewSolutions in .

The value of cos(480^(@))sin(150^(@))+sin(600^(@))cos(390^(@)) is ………….

If y=(sin^4x-cos^4x+sin^2xcos^2x)/(sin^4x+cos^4x+sin^2xcos^2x), x in(0,pi/2) , then

Expand (1+4x)^(5).

Solve the following equations by Sridharacharya's formula : (i) x^(2)+x+4=0 (ii) 2x^(2)-2x+3=0 (iii) sqrt(2)x^(2)+x+sqrt(2)=0 (iv) x^(2)-x+2=0 (v) 25x^(2)-30x+11=0 (vi) x^(2)+3x+5=0 (vii) x^(2)-14x+58=0 (viii)x^(2)+13ix -42=0 (ix) x^(2)-11ix-30=0

Let f(x)be a periodic function with period 3 and f((-2)/( 3)) = 7and g(x)= int _0^(2) f (t+n ) dtwhere n=3 K , K inN " then "g^(-1)((7)/(3)) =

If O is origin, and P= (1, -2, 1) and OP _|_ OQ then Q =

If x, y, z, t are real numbers such that x^(2)+y^(2)=9, z^(2)+t^(2)=4 and xt-yz=6 then the greatest value of xz is

y = log(tan^(-1)(sinx))find dy/dx.

Find Karl Pearson's correlaction coefficient from the given data

Find the equation of a circle of radius 5 whose centre lies on x-axis and which passes through the point (2,3) .

Let a^(2) + b^(2) = alpha^(2) + beta^(2) = 2 then show that the maximum value of S= ( 1-a) ( 1-b) + (1-alpha) (1- beta)is

If f(3x+2)+f(3x+29)=0 AA x in R, then the period of f(x) is

If cos A = 3/4then (2cos A+ 3 sin A)/(4 cos A - sin A) =

(ax^(2)+sinx)(p+q cos x)

The ratio in which the plane 2x+3y-2z+7=0 divides the line segment joining the points (-1,2,3),(2,3,5) is

Shift the origin to a suitable point so that the equation y^(2) + 4y + 8x - 2 = 0 will not contain y, constant terms is

State which of the following statement is true ?

Let AD be a median of the DeltaABC. If AE and AF are medians of the triangle ABD and ADC respectively, and AD=m_(1), AE=m_(2), AF=m_(3), then a^(2)//8 is equal to

If af(Tanx)+bf (cot x)= xthen f^(1)(cotx)=

If y is an implicit funtiion of x given by the relation, find (dy)/(dx). 2x ^(2) - 3 xy + y ^(2) + x + 2y - 8=-0.

Find the algebraic sum of the deviations of all the observations from theirmean.

Find the slope of a line perpendicular to the line whose slope is -5(1)/(7)

Write the slopes of the lines 2x+3y-9=0 and 4x+6y+19=0. What do you observe?

If [sinx]+[sqrt(2)cosx]=-3,x I [0,2pi] ([.] denotes the greatest integer function), then x belongs to

6 boys and 6 grils sit in a row at random. The probability that all the girls sit together is

A die has two faces each with number '1', three faces each with number '2' and one face with number '3'. If die is rolled once, determine (i) P(2)(ii) P(1 or 3)(iii) P(not 3)

If A+B+C=180^(@) " then " sum(cot A + cot B)/(tan A + tan B)=

If f: R rarr R, f(x)=x^(3)+3x^(2)+10x+2sin x then the range of the function is given by

If the bisector of the angle lfloor Cof a triangle ABC cuts AB in D and circum circle in E then (CE)/(DE) =

Find the derivative of the function e ^(x) + sin x.cos x

Let f''(x) gt 0 AA x in R and g(x) = g(x) = 2f((x^(2))/(2)) + f(6-x^(2)). Then show that g(x) possesses one maximum and two minima.

The total revenue in rupees received from the sale os x units of a produce is given by R(x)= 13x^2+ 26x +15. Find the marginal revenue when x =7.

Find the middle term (terms ) in the expansion of (x/a =a/x)^(10)

(i) Find the eccentricity of hyperbola whose latus rectum is half of its transverse axis. (ii) Prove that the straight lines (x)/(a)-(y)/(b)=mand(x)/(a)-(y)/(b)=(1)/(m) always meet at a hyperbola, where 'm' is a constant.

At x=0, f(x)=sinx-x+(x^(3))/(6)-(x^(4))/(24)

The minimum vertical distance between the graphs of y = 2 + sin x and y = cos x is

Compute the following limits. Lt_(xtooo)(x^(2)+2x-1)/(x^(2)-4x+4)

Given P(A) = 3/5 and P(B) = 1/5. Find P(A or B), if A and B are mutually excluive events.

If the roots of the equation (q-r)x^(2)+(r-p)x+p-q=0 are equal, then show that p, q and r are in AP.

Let f(x) =|{:(1,1,1),(3-x,5-3x^(2),3x^(3)-1),(2x^(2)-1,3x^(5)-1,7x^(8)-1):}| then the equation f(x) =0has

If cosx^(@)=sin 200^(@), find the possible values of x between -180^(@) and 360^(@).

d/(dx){Tan^(-1)""(x)/(1+x^2)+Tan^(-1)""(1+x^2)/x} =

sec^(2)2x=1-tan2x

If (1)/(a),(1)/(b),(1)/(c) are also in A.P. then prove that :(i) ((b+c))/(a),((c+a))/(b),((a+b))/(c)are also in A.P.(ii) ((b+c-a))/(a),((c+a-b))/(b),((a+b-c))/(c) are also in A.P.

Circumcentre of the trianlge formed by the points (2,3),(0,1),(4,1) is

If a metallic circular plate of radius 50 cm is heated s that its radius increases at the rate of 1 mm per hour, then the rate at which, the area of the plate increases ("in" cm^(2)// "hour") is

If cosalpha=-(4)/(5),(pi)/(2)ltalphaltpi then tan((alpha)/(2))= ……….

If the point P(a^2,a) lies in the region corresponding to the acute angle between the line 2y=x and 4y=x, then

Three circles touch one another externally , The tangents at their points of contact meet at a point whose distance from the point of contact is 4. The ratio of product of their radii to the sum of radii of the circles is