14949 + Interview Questions in Maths in Class 11 Page 67 InterviewSolution

3301.	Which of the followingstatementis true : Statement -I : InDelta ABC if r_1 = s" then "DeltaABCis Equilateral. Statement -II : InDelta ABCr= ( s-b) cot ((C )/(2))
Answer» Only I Only II Both I & II neither I nor II Answer :D

Discussion

3302.	If tan(theta/2)=cosec theta-sintheta then the numerical balue of "cos"^(2)theta/2=
Answer» `(sqrt5-1)/4` `(sqrt5+1)/4` `(sqrt3-1)/(2SQRT2)` `(sqrt3+1)/(2sqrt2)` ANSWER :B

Discussion

3303.	If siny=xsin(a+y), then prove that (dy)/(dx)=(sin^(2)(a+y))/sina, a ne npi.
Answer» ANSWER :`(SIN^(2)(a + y))/(sin a) = (DY)/(DX)`

Discussion

3304.	A sector OABO of central angle theta is constructed in a circle with centre O and of radius 6. The radius of the circle that is circumscribed about the triangle OAB, is
Answer» `6 "COS" (THETA)/(2)` `6 "sec" (theta)/(2)` `3 "sec" (theta)/(2)` `3("cos"(theta)/(2)+2)` ANSWER :C

Discussion

3305.	There are 50 apple trees in an orchard Each tree produces 800 apples . Foreach additional tree planted in the orchard , the output per additional tree drops by 10 apples . Number of trees that should be be added to the existing orchard for maximising the output of the trees , is
Answer» 5 10 15 20 Answer :C

Discussion

3306.	Following are the marks obtained ,out of 100, by two student Ravi and Hashina in 10 tests Who is more intellogent and who is more consistent ?
Answer» Solution : `sigma=sqrt((Sigmad^(2)i)/N-((Sigmad_(i))/n)^(2))` ltbr gt `=sqrt((1699)/10-((-14)/10)^(2))=sqrt(169.9-0.0196)` `=sqrt(169.88)=13.03` Now`barx=A+(Sigmad_(i))/(Sigmaf_(i))=45-14/10=43.6` `thereforeMean = 55` `becausesigma =sqrt(6368)/(10)=sqrt(636.8)=25.2` For Ravi`CV=(sigma)/(x)xx100=(13.03)/(43.6)xx100=29.88` For HASHINA`CV=(sigma )/(x)xx100=(25.5)/(55)xx100=45.89` Hence ,HASINA is more consistent and inlligent .

Discussion

3307.	If 1 + cos alpha + cos^(2) alpha + ….oo= 2- sqrt2 then find the value of alpha. (0 lt alpha lt pi)
Answer» ANSWER :`(3PI)/(4)`

Discussion

3308.	Find the term independent of 'x', x ne 0 in the expansion of(3 - (x^3)/(6) )^7
Answer» ANSWER :`3^7`

Discussion

3309.	Compute the following limits : Lt_(xto1)((2x-1)(sqrtx-1))/(2x^(2)+x-3)
Answer» ANSWER :`1/10`

Discussion

3310.	Let bar(a),bar(b) be two non-collinear unit vectors, if bar(alpha) = bar(a) -(bar(a).bar(b))bar(b) and bar(beta) = bar(a) xx bar(b), then show that \|bar(beta)\| = \|bar(alpha)\|.
Answer» ANSWER :`\|BAR(BETA)\|= \|bar(ALPHA\|)`

Discussion

3311.	Let f be a function defined by f:xto5x^(2)+2,x in R (i) Express f as a set of ordered pairs using set builder notation. (ii) Is f a one-one function (iii) Find the image of 3 under f (iv) Find x such that f(x)=2
Answer» Answer :`f={(x,y);y=5x^(2)+2,x inR}` (II) Not one one FUNCTION (iii) 47 (iv) 0

Discussion

3312.	The mean of 200 items is 48 and their standard deviation is 3. Find the sum of squares of all items.
Answer» ANSWER : 4,62,600

Discussion

3313.	For the given relation R on a set S, determine which are equivalence relations: (a) (i) S is the set of all rational number a R b iff a= b (ii) S is the set of all real numbers iff: (I) \|a\| = \|b\| (II) a ge b (b) (i) S is the set of all traingles in a plane a R b iff a is congrunet to b. (ii) S is the set of all triangles in a place a R b iff a and b have equal perimeters. (iii) S is the set of all people in India today, a R b iff a and b have same mother-tongue. (iv) S is the of all people in the world today aRb iff a and b have same mother-tongue. (v) S is the set of all people in the world today a R b iff a lives within 75 kilometres of b.
Answer» ANSWER :(a) (i), (II) (B) (ii)

Discussion

3314.	The locus of a point which is collinear with the points (3, 4) and (-4, 3) is
Answer» ANSWER :`x-7y+25=0`

Discussion

3315.	An equation of a line whose segment between the coordinates axes is divided by the point ((1)/(2),(1)/(3)) in the ratio 2:3 is
Answer» `6x+9y=5` `9x+6y=5` `4x+9y=5` `9x+4y=5` ANSWER :C

Discussion

3316.	Write and simplify the coefficient of the term independent of 'x' in theexpansion of (x^3 - 1/x)^12 , x ne 0
Answer» ANSWER :`-220`

Discussion

3317.	Find root(3)(65)
Answer» ANSWER :`=4.02`

Discussion

3318.	Let the curve C be the mirror image of the variable point (t^2,2t) with respect to the line x+y+4 =0. If A and B are the point of intersection of C with the line y=-5, then the distance between A and B is
Answer» 8 6 4 2 Answer :C

Discussion

3319.	If "Tan"^(-1)1/(1+2x)+"Tan"^(-1)1/(4x+1)" = Tan"^(-1)2/(x^(2)) then x(x!=0)=
Answer» `1` 3 0 `2//3` ANSWER :B

Discussion

3320.	Choose the most appropriate answer from those given in bracket lim_(xrarr0)(sin ax)/(x cos bx) = ………
Answer» 0 a B not defined Answer :B

Discussion

3321.	The side of a square increases at the rate of lem per second. Find the rate at which the area of the square increases wen the sideris 15 cm. Also find the rite at which the perimeter increases
Answer» ANSWER :(a) 30 `cm^(2)` (ii) 4CM

Discussion

3322.	Ifcos alpha + cos beta =0 = sin alpha + sin beta " then " cos (alpha - beta )=
Answer» 0 1 -1 2 Answer :C

Discussion

3323.	Find the coefficient of 1/(x^(17)) in the expansion (x^(4)-1/(x^(3)))^(15)
Answer» ANSWER :` = - 1365`

Discussion

3324.	Differentiate the following functions w.r.t. x. (2x +3) (x^3 - x+ 2)
Answer» ANSWER :`6X^(2) + 2X +1`

Discussion

3325.	Find the mean deviation from the mean for following marks: 37, 48, 50, 23, 47, 58, 29, 31, 40.
Answer» ANSWER :9.6

Discussion

3326.	Write the following interval in set builder form. (0, 10)
Answer» ANSWER :`{X : x in R, 0 le x le 10}`

Discussion

3327.	If costheta = cosalpha .cosbetathen tan""(theta+alpha)/2tan""(theta-alpha)/2is equal to
Answer» `TAN^(2)(alpha//2)` `tan^2(beta//2)` `tan^2(theta//2)` `cot^2(beta//2)` ANSWER :B

Discussion

3328.	Expand (x+(1)/(x) )^(6). ( x ne 0)
Answer» Answer :`=x^(6) + 6x^(4) + 15X^(2)+ 20+ (15)/(x^(2) ) + (6)/(x^(4) ) + (1)/( x^6)`.

Discussion

3329.	If x= sin alpha + sin betga , y = cos alpha + cos beta tan alpha + tan beta =
Answer» `(8 XY)/( 2 (y ^(2) - X ^(2)) + ( x ^(2) + y ^(2)) (x ^(2) + y ^(2) - 2))` `(4 xy)/((y ^(2) - x ^(2)) + ( x ^(2) + y ^(2)) (x ^(2) + y ^(2) - 2))` `(8XY )/( (x ^(2) +y ^(2)) (x ^(2) +y ^(2) -2))` `4xy` ANSWER :A

Discussion

3330.	Differentiate the following functions: sqrt( x ) - (1)/( sqrt x) , x ne 0
Answer» Answer :`(1)/( 2 SQRTX) + (1)/( 2x^((2)/(3)) )`

Discussion

3331.	There are five routes for a journey from stations . A to B . In how many different ways can a man go from A to B and return , if for returning. the same route is taken
Answer» ANSWER :` 5 XX 1 =5`

Discussion

3332.	There are five routes for a journey from stations . A to B . In how many different ways can a man go from A to B and return , if for returning. the same route is not taken?
Answer» ANSWER :` 5 XX 4= 20 `

Discussion

3333.	There are five routes for a journey from stations . A to B . In how many different ways can a man go from A to B and return , if for returning. any of the routes is taken
Answer» ANSWER :` 5 XX 5 = 25`

Discussion

3334.	If two sides of the quadrilateral are along the lines x+2y+3=0 and x+2y=5. Find its area.
Answer» ANSWER :`(64)/(5) SQ. UNIT

Discussion

3335.	Find the equation of the line passing through (0, 0) with slope m.
Answer» ANSWER :`y = MX`

Discussion

3336.	Show that \|(a,b,c),(b,c,a),(c,a,b)\|^(2)=\|(c^(2)-a^(2)-b^(2),(ac-ab-bc),(bc-ab-ca),(ac-ab-bc,a^(2)-b^(2)-c^(2),ab-bc-ca),(bc-ab-ac,ab-bc-ca,b^(2)-a^(2)-c^(2))\|
Answer» ANSWER :#NAME?

Discussion

3337.	A ray of light along x + sqrt(3)y = sqrt(3) gets reflected upon reaching x-axis, the equation of the reflected ray is
Answer» `y=x+SQRT(3)` `sqrt(3)y=x-sqrt(3)` `y=sqrt(3)x-sqrt(3)` `sqrt(3)y=x-1` ANSWER :B

Discussion

3338.	baralpha=a_(1)bari+a_(2)barj+a_(3)bark where a_(1), a_(2), a_(3) are rational numbers. If baralpha makes an angle 45^(0) with the vector bar beta=sqrt(2)i+3sqrt(2)j+4bark and \|baralpha\| is rational, then \|baralpha\| lies in
Answer» ZX plane YZ plane XY plane in the ANGLE between `-barbeta` and `baralpha` ANSWER :C

Discussion

3339.	Write the first five terms of each of the sequences whose n^(th) terms are as following a_(n)= (3-n)/(2)
Answer» ANSWER :`1,(1)/(2), 2, (3)/(2), 3`

Discussion

3340.	If(CosA)/(CosB)=nand(SinA)/(SinB)=m then (m^(2) - n^(2)) Sin^(2) B =
Answer» `1 - N^(2)` `1 + n^(2)` 1 -n 1 + n Answer :A

Discussion

3341.	Some statements are given in (a) and (b) identify the statements given below as contrapositive or converse of each other. (a) if you live in Delhi,then you have winter clothes.(i) if you do not have winter clothes, then you do not live in Delhi. (ii) if you do not have winter clothes, then you do not live in delhi. (b) if a quadrilateral is a parallelogram, then its diagonals biset each other. (i) if the diagonals of a quadrilateral do not biset each other, then the quadrilateral is not a parallelogram. (ii) if the diagonals of a quadrilateral bisect each other, then it is a parallelogram.
Answer» SOLUTION :(4) (a) (i)CONTRAPOSITIVE (ii) CONVERSE (b)(i) contropositive (ii) converse

Discussion

3342.	Areal value of x satsifies the equation ((3-4ix)/(3+4ix)) =alpha- ibeta(alpha, beta in R), if alpha^(2)+beta^(2) is equal to
Answer» 1 `-1` 2 `-2` ANSWER :A

Discussion

3343.	If (-1,-2) and (5,2) are the end points of a diameter of a circle, find its centre and radius
Answer» SOLUTION :(2,0), `SQRT13`

Discussion

3344.	If f(x) = {{:(2a-x, "for",-a lt x lt a),(3x-2a ,"for", x ge a):}, then which one of the following is true?
Answer» f(X) is not DIFFERENTIABLE at x=a f(x) is DISCONTINUOUS at x=a f(x) is continuous for all x in R f(x) is differentiable for all `x GE a` ANSWER :A

Discussion

3345.	IfP_1 , P_2 , P_3are lengths ofaltitudesof a triangle from itsverticesto the oppositesidesthen(1)/(p_1) + ( 1)/(P_2) +(1)/(p_3)=
Answer» `(1)/( r_1) ` ` ( 1)/(r_2)` `( 1)/ ( r_3) ` ` (1)/ ( R ) ` ANSWER :D

Discussion

3346.	Find the coefficent of x^(32) and 1/x^(17) " in the expansion of "(x^(4)-1/x^(3))^(15)
Answer» Solution :The general term in the GIVEN expansion is given by `T_(r+1) = (-1)^(r) xx .^(15) C _(r) xx (x^(4))^((15-r)) xx (1/(x^(3)))^(r)` `rArr T _(r+1) = (-1)^(r) xx .^(15) C _(r) xx x ^((60-7r)).""` … (i) Putting `60- 7r = 32, " we get " 7r = 28 rArr r = 4 rArr r+1 = 5.` Now, `T_(5)= T_(4+1) = (-1)^(4) xx .^(15) C _ (4) xx x^((60-28)) = .^(15 ) C _(4) xx x^(32)`. `:. " coefficent of" x^(32) = .^(15) C _(4) ((15 xx 14 xx 13 xx 12)/(4 xx 3 xx 2 xx 1 ))= 1365.` Let `T_ (s+1) " be the term containing "x^(-17) ""[:' 1/(x^(17)) = x^(-17)].` Then,` T_(s+1) = (-1) ^(s) xx .^(15) C _(s) xx x^((60-7s))""` ...(ii) [putting r = s in(i)] Putting `60-7s = -17, " we get " s = 11 and " therefore " , s+ 1 = 12.` Thus, the 12th term contains `x^(-17)`. Now, `T_(12) = T _((11+1))` ` = (-1)^(11) xx .^15 C _(11) xx x^((60-77)""` [putting s = 11 in (ii)] `=.-^15C_(4) xx x^(-17).` `:. " coefficent of " x^(-17) =-.^(15)C_(4)= - ((15 xx 14 xx 13 xx 12)/(4 xx 3 xx 2 xx 1 ))=-1365.` So,the coefficent of `x^(-17)`in the given expansion is-1365. HENCE, the coefficent of `x^(32)" is 1365 and that of " x^(-17) is -1365.`

Discussion

3347.	For non - coplanar vectors bara,barb and barc determine p for which the vectors bara+barb+barc,bara+pbarb+2barc and -bara+barb+barc are coplaner.
Answer» 6 4 2 0 Answer :C

Discussion

3348.	If a Delta ABC
Answer» `sin A sin B sin C LE (3sqrt(3))/(8)` `sin^(2) A + sin^(2) B + sin^(2) Cle (9)/(4)` sin A sin B sin C is ALWAYS positive `sin^(1)A + sin^(2) B le 1 + cos C` Answer :A::B::C::D

Discussion

3349.	Find the distance between following pair of parallel lines : (i) 15x + 8y - 34=0 and 15 x + 8y +31=0
Answer» ANSWER :`= (65)/( 17)` UNIT

Discussion

3350.	Calculate the index number for the year 2006 with 1996 as the base year by the weighted average of price relatives method from the following data.
Answer» ANSWER :`130`

Discussion

Explore topic-wise InterviewSolutions in .

Which of the followingstatementis true : Statement -I : InDelta ABC if r_1 = s" then "DeltaABCis Equilateral. Statement -II : InDelta ABCr= ( s-b) cot ((C )/(2))

If tan(theta/2)=cosec theta-sintheta then the numerical balue of "cos"^(2)theta/2=

If siny=xsin(a+y), then prove that (dy)/(dx)=(sin^(2)(a+y))/sina, a ne npi.

A sector OABO of central angle theta is constructed in a circle with centre O and of radius 6. The radius of the circle that is circumscribed about the triangle OAB, is

There are 50 apple trees in an orchard Each tree produces 800 apples . Foreach additional tree planted in the orchard , the output per additional tree drops by 10 apples . Number of trees that should be be added to the existing orchard for maximising the output of the trees , is

Following are the marks obtained ,out of 100, by two student Ravi and Hashina in 10 tests Who is more intellogent and who is more consistent ?

If 1 + cos alpha + cos^(2) alpha + ….oo= 2- sqrt2 then find the value of alpha. (0 lt alpha lt pi)

Find the term independent of 'x', x ne 0 in the expansion of(3 - (x^3)/(6) )^7

Compute the following limits : Lt_(xto1)((2x-1)(sqrtx-1))/(2x^(2)+x-3)

Let bar(a),bar(b) be two non-collinear unit vectors, if bar(alpha) = bar(a) -(bar(a).bar(b))bar(b) and bar(beta) = bar(a) xx bar(b), then show that |bar(beta)| = |bar(alpha)|.

Let f be a function defined by f:xto5x^(2)+2,x in R (i) Express f as a set of ordered pairs using set builder notation. (ii) Is f a one-one function (iii) Find the image of 3 under f (iv) Find x such that f(x)=2

The mean of 200 items is 48 and their standard deviation is 3. Find the sum of squares of all items.

The locus of a point which is collinear with the points (3, 4) and (-4, 3) is

An equation of a line whose segment between the coordinates axes is divided by the point ((1)/(2),(1)/(3)) in the ratio 2:3 is

Write and simplify the coefficient of the term independent of 'x' in theexpansion of (x^3 - 1/x)^12 , x ne 0

Find root(3)(65)

Let the curve C be the mirror image of the variable point (t^2,2t) with respect to the line x+y+4 =0. If A and B are the point of intersection of C with the line y=-5, then the distance between A and B is

If "Tan"^(-1)1/(1+2x)+"Tan"^(-1)1/(4x+1)" = Tan"^(-1)2/(x^(2)) then x(x!=0)=

Choose the most appropriate answer from those given in bracket lim_(xrarr0)(sin ax)/(x cos bx) = ………

The side of a square increases at the rate of lem per second. Find the rate at which the area of the square increases wen the sideris 15 cm. Also find the rite at which the perimeter increases

Ifcos alpha + cos beta =0 = sin alpha + sin beta " then " cos (alpha - beta )=

Find the coefficient of 1/(x^(17)) in the expansion (x^(4)-1/(x^(3)))^(15)

Differentiate the following functions w.r.t. x. (2x +3) (x^3 - x+ 2)

Find the mean deviation from the mean for following marks: 37, 48, 50, 23, 47, 58, 29, 31, 40.

Write the following interval in set builder form. (0, 10)

If costheta = cosalpha .cosbetathen tan""(theta+alpha)/2tan""(theta-alpha)/2is equal to

Expand (x+(1)/(x) )^(6). ( x ne 0)

If x= sin alpha + sin betga , y = cos alpha + cos beta tan alpha + tan beta =

Differentiate the following functions: sqrt( x ) - (1)/( sqrt x) , x ne 0

There are five routes for a journey from stations . A to B . In how many different ways can a man go from A to B and return , if for returning. the same route is taken

There are five routes for a journey from stations . A to B . In how many different ways can a man go from A to B and return , if for returning. the same route is not taken?

There are five routes for a journey from stations . A to B . In how many different ways can a man go from A to B and return , if for returning. any of the routes is taken

If two sides of the quadrilateral are along the lines x+2y+3=0 and x+2y=5. Find its area.

Find the equation of the line passing through (0, 0) with slope m.

Show that |(a,b,c),(b,c,a),(c,a,b)|^(2)=|(c^(2)-a^(2)-b^(2),(ac-ab-bc),(bc-ab-ca),(ac-ab-bc,a^(2)-b^(2)-c^(2),ab-bc-ca),(bc-ab-ac,ab-bc-ca,b^(2)-a^(2)-c^(2))|

A ray of light along x + sqrt(3)y = sqrt(3) gets reflected upon reaching x-axis, the equation of the reflected ray is

baralpha=a_(1)bari+a_(2)barj+a_(3)bark where a_(1), a_(2), a_(3) are rational numbers. If baralpha makes an angle 45^(0) with the vector bar beta=sqrt(2)i+3sqrt(2)j+4bark and |baralpha| is rational, then |baralpha| lies in

Write the first five terms of each of the sequences whose n^(th) terms are as following a_(n)= (3-n)/(2)

If(CosA)/(CosB)=nand(SinA)/(SinB)=m then (m^(2) - n^(2)) Sin^(2) B =

Areal value of x satsifies the equation ((3-4ix)/(3+4ix)) =alpha- ibeta(alpha, beta in R), if alpha^(2)+beta^(2) is equal to

If (-1,-2) and (5,2) are the end points of a diameter of a circle, find its centre and radius

If f(x) = {{:(2a-x, "for",-a lt x lt a),(3x-2a ,"for", x ge a):}, then which one of the following is true?

IfP_1 , P_2 , P_3are lengths ofaltitudesof a triangle from itsverticesto the oppositesidesthen(1)/(p_1) + ( 1)/(P_2) +(1)/(p_3)=

Find the coefficent of x^(32) and 1/x^(17) " in the expansion of "(x^(4)-1/x^(3))^(15)

For non - coplanar vectors bara,barb and barc determine p for which the vectors bara+barb+barc,bara+pbarb+2barc and -bara+barb+barc are coplaner.

If a Delta ABC

Find the distance between following pair of parallel lines : (i) 15x + 8y - 34=0 and 15 x + 8y +31=0

Calculate the index number for the year 2006 with 1996 as the base year by the weighted average of price relatives method from the following data.