14949 + Interview Questions in Maths in Class 11 Page 98 InterviewSolution

4851.	Express cos 6 alphain terms ofcos 3 alpha .
Answer» ANSWER :`2 COS ^(2) 3 alpha -1`

Discussion

4852.	Find the value of h if the slopes of the lines represented by 6x^(2)+2hxy+y^(2)=0 are in the ratio 1:2.
Answer» ANSWER :`+-(3sqrt(3))/(2)`

Discussion

4853.	CalculateKarl Pearson's coefficient of correlation between the heights of husbands and wivesbased on the followingdata ( givenin inches ) and interpretthe result. Takeassumed means of husbands and wivesare 70 and 66 respectively .
Answer» ANSWER :KARL PEARSON's COEFFICIENT of correlation (r ) = `0.9`

Discussion

4854.	sin20^@(4+sec20^@)
Answer» `1/2` `SQRT2` `SQRT3` 1 Answer :C

Discussion

4855.	Write two examplesfor inertia of direction.
Answer» Solution :(i) A STONE MOVES tangential to Circle. (ii) When a CAR moves TOWARDS left, we turn to the RIGHT.

Discussion

4856.	A die is thrown two times. what will be the sample space
Answer» ANSWER :`{(X, Y) : X, Y = 1, 2, 3, 4, 5, 6}` or `{(1,1), (1,2), (1,3), … , (1,6), (2, 1), (2, 2), … , (2,6), …. (6, 1), (6, 2), … , (6, 6)}`

Discussion

4857.	If (-4,5) is one verted and 7x-y+8=0 is one diagonal of a square, then the equation of the second diagonal is
Answer» `x+7y-13=0` `x+7y-15=0` `x+7y+8=0` `7x-y-31=0` ANSWER :A

Discussion

4858.	If r_(1),r_(3),r_(1) are the radii of the escribed circles of a DeltaABC and if r is the radius of its incircle then r_(1)r_(2)r_(3)-r(r_(1)r_(2)+r_(2)r_(3)+r_(3)r_(1))=
Answer» 0 1 2 3 Answer :A

Discussion

4859.	If (cos x )/(a)= (cos (x + theta))/( b ) = ( cos (x + 2 theta ))/( c) = (cos (x + 3 theta ))/( d)then (a+c)/(b+d) is equal to
Answer» `a//d` `C//d` `b//c` `d//a` ANSWER :C

Discussion

4860.	Consider the points A(0,1) and B (2,0) and P be a point on the line 4x+3y+9=0. Coordinates of P such that abs(PA-PB) is maximum are
Answer» `((-24)/5,17/5)` `((-84)/5,13/5)` `((-6)/5,17/5)` (0,-3) Answer :A

Discussion

4861.	In Delta ABC, r_1^2+r_2^2+r_3^2+r^2=
Answer» ANSWER :` ( a^(2) + B^( 2) +C^(2) ) `

Discussion

4862.	If y = mx - 1 istangent to the hyberbola (x^(2))/(16) - (y^(2))/(9) = 1 then value of m = ……..
Answer» `-SQRT((5)/(2))` `sqrt((5)/(2))` `sqrt((5)/(2))` `(1)/(2) sqrt((5)/(2))` ANSWER :C

Discussion

4863.	Assertion (A): The radius of the circleinscribedin the triangle obtained by joining the middle pointsof the sidesofDelta ABCis equalto half the radiusof incircleof Delta ABCReason (R ) :In Delta ABC, D,E,Fbe midpointsof the sidesof Delta ABC , Delta ' , 2s'denotesarea andperimeter of Delta DEF" then "Delta ' = Delta//4and s' =s//2
Answer» A is TRUE , R is true and R is correct explanationof A A is true , R is true and R is not correct EXPLANATION of A A is true R is FALSE A is false , R is true Answer :A

Discussion

4864.	If the relative error in the radius of a circle is 0.2 then the relative error in its area is
Answer» 0.2 0.1 0.4 0.3 Answer :C

Discussion

4865.	If""^(43)C_(r-6)= ""^(43)C_(3r+1) , then the value of r is
Answer» 12 8 6 4 Answer :A

Discussion

4866.	Solve the equation sqrt3 cos x + sin x =1for - 2pi lt x le 2pi.
Answer» ANSWER :`X = 2 n PI + (pi)/(2) , 2 n pi - (pi)/(6)`

Discussion

4867.	f (x) = x cos ((1)/(x^(2))),x in 0 , f (0) = 1atx = 0 f is
Answer» LEFT CONTINUOUS DISCONTINUOUS rightdetermined continuous ANSWER :B

Discussion

4868.	There are three planes prod_(1),prod_(2),prod_(3) such that prod_(1) is perpendicular to prod_(2) and prod_(1) is parallel to prod_(3). If n_(1),n_(2),n_(3) are the nomals to the planes prod_(1),prod_(2),prod_(3) respectively then
Answer» `n_(1),n_(2), and n_(3)` are PARALLEL `n_(1)` is parallel to `n_(3)andn_(1)` is PERPENDICULAR to `n_(2)` `n_(1),n_(2),n_(3)` are mutually perpendicular `n_(1),n_(2)` are parallel to X -axis and `n_(3)` is parallel to Z-axis ANSWER :B

Discussion

4869.	\|Cosecx\| gek then k=
Answer» 1 2 3 4 Answer :4

Discussion

4870.	Using binomial theorem, the value of (0.999)^3 correct to 3 decimal places is
Answer» (a) `0.999` (B) `0.998` (C) `0.997` (d) `0.995` ANSWER :C

Discussion

4871.	What is the value of (cos 10 ^(@) + sin 20^(@))/( cos 20^(@) - sin 10 ^(@))?
Answer» ANSWER :`SQRT3`

Discussion

4872.	If veca =veci-2vecj+veck,vecb=2veci-vecj+2veck, vecc=3veci+vecj-veck be such that ((veca)/(lambdavecb)) is perpendicular to c, the the value of lambda is:
Answer» `(1)/(2)` -1 1 0 Answer :D

Discussion

4873.	If sin^(-1)x+sin^(-1)y=(pi)/2 and sin2x=cos3y, then
Answer» `X=(PI)/8=sqrt(1/2-(pi^(2))/64)` `y=sqrt(1/2-(pi^(2))/64)-(pi)/12` `x=(pi)/12+sqrt(1/2=(pi^(2))/64)` `y=sqrt(1/2-(pi^(2))/64)-(pi)/8` ANSWER :A::D

Discussion

4874.	Theperiodof ((1)/(2))^(cosx)
Answer» `(PI)/(2)` `pi` `2PI` `(pi)/(3)` ANSWER :3

Discussion

4875.	The value of "cot"(7pi)/(16)+"2 cot"(3pi)/(8)+"cot"(15pi)/(16) is
Answer» 4 2 `-2` `-4` ANSWER :B

Discussion

4876.	Find how many arrangements can be made with the lettersof the word ' MATHEMATICS'?
Answer» ANSWER :` (11!)/( 2!2!2!) = 4989600`

Discussion

4877.	A particle is moving in a straight line so that after 't' seconds its distance is 'S' (in cms) from a fixed point of the line is given be S=f(t)=8t+t^3. Find (i) the velocity at time t=2 (ii) the initial velocity (iii) acceleration at t=2 sec
Answer» ANSWER :(i) 20 cm/sec (ii) 8 cm/sec (iii) 12 cm/sec`""^(2)`

Discussion

4878.	Evaluate the following limits : Lim_(x to 9 ) (x^(3//2)-27)/(x-9)
Answer» ANSWER :`9/2`

Discussion

4879.	Evaluate the following limits in Exercises lim_(zto1)(z^((1)/(3))-1)/(z^((1)/(6))-1)
Answer» ANSWER :2

Discussion

4880.	A vertical pole more than 100ft high consists of two portions the lower being 1//3 of the whole. If the upper portion subtends an angle tan^(-1)((1)/(2)) at a point distant 40 ft From the foot of the pole. The height of the pole is
Answer» `105` `120` `135` `150` ANSWER :B

Discussion

4881.	The second, third and fourth terms in the binomial expansion (x + a)^n are 240, 720 and 1080, respectively. Find x,a and n.
Answer» ANSWER :x=2 , a = 3 and N = 5

Discussion

4882.	If tan theta=(4)/(3), in which quadrant does theta lie ?
Answer» ANSWER :As `tan theta` is POSITIVE, `theta` can be either in first or third QUADRANT.

Discussion

4883.	Which of the following sentences are statement? Give reason for your answer: x+3=17
Answer» ANSWER :Not a STATEMENT

Discussion

4884.	If p_(1),p_(2) are the perpendicular distance from the origin to the two straight lines which are perpendicular to each other, then the locus of the point of intersection of the perpendicular lines is
Answer» <P>`X^(2)+y^(2)=p_(1)+p_(2)` `x^(2)+y^(2)=P_(1)^(2)+P_(2)^(2)` `(x_(1)^(2))/(p_(1)^(2))+(y_(1)^(2))/(p_(2)^(2))=1` `xy=p_(1)p_(2)` ANSWER :B

Discussion

4885.	Show that the function f(x)=(x)/(1+e^(1//x),x ne 0, f(0)= 0 is continuous at x = 0
Answer» ANSWER :x=0

Discussion

4886.	If non-zer real numbers b and c are such that min f(x) gt max (g)x, where f(x)=x^(2)+2bx+2c^(2) and g(x)=-x^(2)-2cx+b^(2)(x in R), Then \|(c)/(b)\| lies in the interval
Answer» `(0,(1)/(2))` `[(1)/(2),(1)/(sqrt(2)))` `[(1)/(sqrt(2)),sqrt(2)]` `(sqrt(2),oo)` ANSWER :D

Discussion

4887.	sin 315^@=……….a)-1/2 b)-1/sqrt2c)-sqrt3/2 d)1
Answer» `-1/2` `-1/sqrt2` `-sqrt3/2` 1 Answer :B

Discussion

4888.	Find equation of line passes from point P(1,-7) which intersects axis is at points A and B such that 4AP- 3BP=0.
Answer» ANSWER :`28X - 3Y = 49`

Discussion

4889.	d/dx(tan x)=………
Answer» SOLUTION :`sec^2 X`

Discussion

4890.	Coefficient of variation of two distributions are 50 and 60, and their arithmetic means are 30 and 25 respectively. Difference of their standard deviation is ……
Answer» 0 1 1.5 2.5 Answer :A

Discussion

4891.	Let x=sin1^(@), then the value of the expression (1)/(cos 0^(@).cos 1^(@))+(1)/(cos 1^(@).cos 2^(@))+(1)/(cos 2^(@),cos3^(@))+……..+(1)/(cos 44^(@).cos45^(@)) is equal to
Answer» X 1/x `SQRT(2)//x` `x//sqrt(2)` ANSWER :B

Discussion

4892.	Evaluate the following limits : Lim_(x to 2) (x^(2)(x^(2)-4))/(x-2)
Answer» ANSWER :16

Discussion

4893.	Prove that · (cos 135^@ - cos 120^@)/(cos 135^@ +cos 120^@) = 3-2sqrt2
Answer» ANSWER :`3-2sqrt2`

Discussion

4894.	If A =(1,2,3) and B=(3,5,7) and P, Q are the points on AB such that AP= PQ =QB,then the mid point of PQ is
Answer» (2,3,5) (2,3.5,5) (2,4,5) (4,7,10) ANSWER :B

Discussion

4895.	If sin x + cos x + tan x + cot x + sec x + cosec x = 7, 0 lt x lt pi//2 and sin = 2x=a-b sqrt(7) then (a, b in Z^(+))
Answer» a = 8 B = 22 a = 22 b = 8 Answer :C::D

Discussion

4896.	The statement (3sin^(4)x-2cos^(6)x+y-2sin^(6)x+3cos^(4)x)^(2)=9 is true of
Answer» `x=(5pi)/13` and `y=2` `x=(7pi)/16` and `y=-4` `x=(pi)/7` and `y=1` `x=(pi)/5` and `y=-1` ANSWER :A::B

Discussion

4897.	A manufacturer reckons that the value of a machine, which costs him Rs. 15625,will depreciate each year by 20%. Find the estimated value at the end of 5 years.
Answer» ANSWER :RS 5120

Discussion

4898.	Find the n^(th) term of the series 1+(1+2)+(1+2+3)+..
Answer» SOLUTION :`(N(n+1))/2`

Discussion

4899.	The value of cos1^(@)cos2^(@)cos3^(@)…..cos179^(@) is
Answer» `(1)/(sqrt(2))` 0 1 `-1` ANSWER :B

Discussion

4900.	Find the point of intersection of the lines 4x+8y-1=0, 2x-8y+1=0
Answer» ANSWER :`(0,1/8)`

Discussion

Explore topic-wise InterviewSolutions in .

Express cos 6 alphain terms ofcos 3 alpha .

Find the value of h if the slopes of the lines represented by 6x^(2)+2hxy+y^(2)=0 are in the ratio 1:2.

CalculateKarl Pearson's coefficient of correlation between the heights of husbands and wivesbased on the followingdata ( givenin inches ) and interpretthe result. Takeassumed means of husbands and wivesare 70 and 66 respectively .

sin20^@(4+sec20^@)

Write two examplesfor inertia of direction.

A die is thrown two times. what will be the sample space

If (-4,5) is one verted and 7x-y+8=0 is one diagonal of a square, then the equation of the second diagonal is

If r_(1),r_(3),r_(1) are the radii of the escribed circles of a DeltaABC and if r is the radius of its incircle then r_(1)r_(2)r_(3)-r(r_(1)r_(2)+r_(2)r_(3)+r_(3)r_(1))=

If (cos x )/(a)= (cos (x + theta))/( b ) = ( cos (x + 2 theta ))/( c) = (cos (x + 3 theta ))/( d)then (a+c)/(b+d) is equal to

Consider the points A(0,1) and B (2,0) and P be a point on the line 4x+3y+9=0. Coordinates of P such that abs(PA-PB) is maximum are

In Delta ABC, r_1^2+r_2^2+r_3^2+r^2=

If y = mx - 1 istangent to the hyberbola (x^(2))/(16) - (y^(2))/(9) = 1 then value of m = ……..

If the relative error in the radius of a circle is 0.2 then the relative error in its area is

If""^(43)C_(r-6)= ""^(43)C_(3r+1) , then the value of r is

Solve the equation sqrt3 cos x + sin x =1for - 2pi lt x le 2pi.

f (x) = x cos ((1)/(x^(2))),x in 0 , f (0) = 1atx = 0 f is

There are three planes prod_(1),prod_(2),prod_(3) such that prod_(1) is perpendicular to prod_(2) and prod_(1) is parallel to prod_(3). If n_(1),n_(2),n_(3) are the nomals to the planes prod_(1),prod_(2),prod_(3) respectively then

|Cosecx| gek then k=

Using binomial theorem, the value of (0.999)^3 correct to 3 decimal places is

What is the value of (cos 10 ^(@) + sin 20^(@))/( cos 20^(@) - sin 10 ^(@))?

If veca =veci-2vecj+veck,vecb=2veci-vecj+2veck, vecc=3veci+vecj-veck be such that ((veca)/(lambdavecb)) is perpendicular to c, the the value of lambda is:

If sin^(-1)x+sin^(-1)y=(pi)/2 and sin2x=cos3y, then

Theperiodof ((1)/(2))^(cosx)

The value of "cot"(7pi)/(16)+"2 cot"(3pi)/(8)+"cot"(15pi)/(16) is

Find how many arrangements can be made with the lettersof the word ' MATHEMATICS'?

A particle is moving in a straight line so that after 't' seconds its distance is 'S' (in cms) from a fixed point of the line is given be S=f(t)=8t+t^3. Find (i) the velocity at time t=2 (ii) the initial velocity (iii) acceleration at t=2 sec

Evaluate the following limits : Lim_(x to 9 ) (x^(3//2)-27)/(x-9)

Evaluate the following limits in Exercises lim_(zto1)(z^((1)/(3))-1)/(z^((1)/(6))-1)

A vertical pole more than 100ft high consists of two portions the lower being 1//3 of the whole. If the upper portion subtends an angle tan^(-1)((1)/(2)) at a point distant 40 ft From the foot of the pole. The height of the pole is

The second, third and fourth terms in the binomial expansion (x + a)^n are 240, 720 and 1080, respectively. Find x,a and n.

If tan theta=(4)/(3), in which quadrant does theta lie ?

Which of the following sentences are statement? Give reason for your answer: x+3=17

If p_(1),p_(2) are the perpendicular distance from the origin to the two straight lines which are perpendicular to each other, then the locus of the point of intersection of the perpendicular lines is

Show that the function f(x)=(x)/(1+e^(1//x),x ne 0, f(0)= 0 is continuous at x = 0

If non-zer real numbers b and c are such that min f(x) gt max (g)x, where f(x)=x^(2)+2bx+2c^(2) and g(x)=-x^(2)-2cx+b^(2)(x in R), Then |(c)/(b)| lies in the interval

sin 315^@=……….a)-1/2 b)-1/sqrt2c)-sqrt3/2 d)1

Find equation of line passes from point P(1,-7) which intersects axis is at points A and B such that 4AP- 3BP=0.

d/dx(tan x)=………

Coefficient of variation of two distributions are 50 and 60, and their arithmetic means are 30 and 25 respectively. Difference of their standard deviation is ……

Let x=sin1^(@), then the value of the expression (1)/(cos 0^(@).cos 1^(@))+(1)/(cos 1^(@).cos 2^(@))+(1)/(cos 2^(@),cos3^(@))+……..+(1)/(cos 44^(@).cos45^(@)) is equal to

Evaluate the following limits : Lim_(x to 2) (x^(2)(x^(2)-4))/(x-2)

Prove that · (cos 135^@ - cos 120^@)/(cos 135^@ +cos 120^@) = 3-2sqrt2

If A =(1,2,3) and B=(3,5,7) and P, Q are the points on AB such that AP= PQ =QB,then the mid point of PQ is

If sin x + cos x + tan x + cot x + sec x + cosec x = 7, 0 lt x lt pi//2 and sin = 2x=a-b sqrt(7) then (a, b in Z^(+))

The statement (3sin^(4)x-2cos^(6)x+y-2sin^(6)x+3cos^(4)x)^(2)=9 is true of

A manufacturer reckons that the value of a machine, which costs him Rs. 15625,will depreciate each year by 20%. Find the estimated value at the end of 5 years.

Find the n^(th) term of the series 1+(1+2)+(1+2+3)+..

The value of cos1^(@)cos2^(@)cos3^(@)…..cos179^(@) is

Find the point of intersection of the lines 4x+8y-1=0, 2x-8y+1=0