14949 + Interview Questions in Maths in Class 11 Page 288 InterviewSolution

14351.	An angle theta through which a pulley turns with time 't' is completed by theta = t^(2) + 3t - 5 sq. cms / min Then the angular velocity for t = 5 sec.
Answer» `5^(E )//SEC` `13^(e ) //sec` `23^(e )//sec` `35^(e )//sec` ANSWER :B

Discussion

14352.	Evaluate the following limits : Lim_(x to 0 ) ((sin ax)/(sin bx))^(k)
Answer» ANSWER :`(a/b)^(K)`

Discussion

14353.	Prove that in Delta ABCS (( r_1- r_2) /( a) + ( r_2- r)/( b) + ( r_3- r)/( c ) ) = r_1+ r_2+ r_3 Prove that in Delta ABC
Answer» ` r_1 + r_2+r_3` ` r_1+ r_2- r_3` ` r_1- r_2+r_3` ` -r_1+r_2+r_3` ANSWER :A

Discussion

14354.	Evaluate : 2 cos ^(2) 157.5^(@) -1
Answer» ANSWER :`(SQRT3)/(2)`

Discussion

14355.	Given P(A)=(3)/(5) and P(B)=(1)/(5) Find P(A or B), if A and B are mutually exclusive events.
Answer» ANSWER :`4/5`

Discussion

14356.	Find (a +b)^4 - (a - b)^4. Hence, evaluate (sqrt3 + sqrt2)^4 - (sqrt3 - sqrt2)^4.
Answer» ANSWER :`= 40sqrt(6)`

Discussion

14357.	Prove that orthocentre of triangle formed by pair of lines ax^(2)+2hxy+by^(2)=0 an the line lx+my+n=0 is (kl, km) where k=(-n(a+b))/(am^(2)-2hlm+bl^(2))
Answer» ANSWER :`K=(-N(a+b))/(am^(2)-2hlm+bl^(2))`

Discussion

14358.	If sin^(-1)x+sin^(-1)y+sin^(-1)z=(3pi)/z then the value of sum((x^(201)+y^(201))/(x^(603)+y^(603))).((x^(402)+y^(402))/(x^(804)+y^(804)))=
Answer» 0 1 2 3 Answer :D

Discussion

14359.	If A+B=225^(@) than prove that (cot A)/(1+cotA). (cot B)/(1+cotB)=(1)/(2)
Answer» 0 `(1)/(2)` `(1)/(4)` `(3)/(4)` Answer :B

Discussion

14360.	Find the roots of the equations. Q. 3x^(2)-17x+25=0.
Answer» ANSWER :`(17pmsqrt(-11))/(6)`.

Discussion

14361.	Represent on complex plane the complex numbers w=3 + 4i and z= 6-3i together with w +z and w-z. Obtain the modulus and argument of w and z.
Answer» ANSWER :`79^(@)42'`

Discussion

14362.	Verify by the method of contradiction thatsqrt(7) is irrational.
Answer» ANSWER :TYPE solvedEx.30.

Discussion

14363.	Find the axes, vertices , foci , exentricity, equations of the directrices and length of the latus rectum of the hyperbola 5y ^(2) - 9x ^(2) = 36.
Answer» ANSWER :`(4 SQRT5)/(3)`

Discussion

14364.	If Cos theta - Sin theta = sqrt(2) Cos theta then Cos theta + Sin theta =
Answer» `sqrt(2) SIN theta` `-sqrt(2) Sin theta` `-sqrt(2) Cos theta` `2 Sin theta` ANSWER :B

Discussion

14365.	The periodof sin^3x + cos^3 xis
Answer» `(PI)/(2)` `pi` `2pi` `(3pi)/(2)` Answer :3

Discussion

14366.	Approximate value of tan46^(@) is ( 1^(@)=0.01745 radians )
Answer» 1.0349 1.03 1.349 1.0394 Answer :A

Discussion

14367.	A person writes a letter to four of his friends. He asks each one of them to copy the letter and mail to four different persons with instruction that they move the chain similarly. Assuming that the chain is not broken and that it costs 50 paise to mail one letter. Find the amount spent on the postage when 8th set of letter is mailed.
Answer» ANSWER :RS. 43690

Discussion

14368.	Let the sequence a_nbe defined as follows: a_1 = 1, a_n = a_(n - 1) + 2for n ge2 . Find first five terms and write corresponding series
Answer» ANSWER :9

Discussion

14369.	Show that the line lx + my = 1 will touch the ellipse (x ^(2))/( a ^(2)) + (y ^(2))/(b ^(2)) =1ifa ^(2) l ^(2) + b ^(2)m ^(2) = 1.
Answer» ANSWER :`(-1, 0)`

Discussion

14370.	Show that the coefficient of the middle term in the expansion of (1+x)^(2n) is equal to the sum of the coefficients of two middle terms in the expansion of (1 + x)^(2n-1)
Answer» ANSWER :`^2N`Cundersetn

Discussion

14371.	x = cos theta, y = sin 5 theta implies (1- x ^(2)) (d^(2)y)/(dx ^(2)) -x (dy)/(dx) =
Answer» `-5Y` `5y` `25Y` `-25y` ANSWER :D

Discussion

14372.	Find the equation of the locus of a point whose distance from the y-axis is equal to its distance from (2,1,-1).
Answer» `SQRT(2)` `sqrt(3/2)` `(sqrt(3))/2` `2/(sqrt(3))` ANSWER :B

Discussion

14373.	The value of p so that the lines (1-x)/(3) = (7y - 14)/(2p) = (z -3)/(2) and (7-7 x)/(3p) = (y-5)/(1) = (6 -z)/(5) are at right angles are
Answer» `70//11` `7//11` `10//7` `17//11` ANSWER :A

Discussion

14374.	If vec(a) xx vec(b)= vec(c ) xx vec(d), vec(a) xx vec(c )= vec(b) xx vec(d), then
Answer» `(VEC(a)-vec(d))//(vec(B)-vec(C ))` `(vec(a)-vec(b))//(vec(c )-vec(d))` `(vec(a)-vec(c ))//(vec(b)- vec(d))` `(vec(a) + vec(b))//(vec(c ) + vec(d))` ANSWER :A

Discussion

14375.	Evaluate (cos3 theta-2cos 4theta)/(sin 3 theta+2sin 4theta), when theta=150^(@).
Answer» ANSWER :`-1/2(1+sqrt(3))`

Discussion

14376.	How many four -digits even integerscan be formed using the digits 0,1,2,3,4,5?
Answer» ANSWER :` 540 `

Discussion

14377.	Find the sum of all 3 digit numbers that canbe formed using the digits 1,2, 3, 5, 6.
Answer» ANSWER :170908

Discussion

14378.	Let S = (1)/( 1.4) + (1)/( 4.7) + (1)/(7.10) + .....n terms, Observe the following lists. {:("List-I","List-II"),("A)" underset(n to prop) (Lt) S=, "1)"0 ),("B)" underset(n to 0 ) (Lt) S=,"2)" 3//10),("C)" underset(n to 3) (Lt) S=,"3)"1//3),("D)" underset(n to 4) (Lt) S=,"4)"1),(,"5)"4//13):}
Answer» A-3, B-4, C-5, D-1 A-2, B-4, C-1, D-2 A-2, B-5, C-1, D-3 A-3, B-1 , C-2, D-5 Answer :D

Discussion

14379.	An equation of the plane passing through the origin and containing the lines whose direction consines are proportional to 1, -2, 2 and 2,3,-1is
Answer» `(1, -2, 2)` `(2,3,-1)` `(3,1,1)` `(-4,5,7)` ANSWER :D

Discussion

14380.	An arch is in the from of a semi - ellipse. It is 8 m wide and 2 m high at the centre. Find the height of the arch at a point 1.5 m from one end.
Answer» ANSWER :`1.56` m (APPROX.)

Discussion

14381.	Find the coefficient of x^(2) in the expansion of e^(2x+3) as a series in powers of x.
Answer» ANSWER :`2E^(3)`

Discussion

14382.	IfC (n,10) =C(n,12) ,dertermine C(n,5)
Answer» ANSWER :` 26334`

Discussion

14383.	.........is the standard equation of circle with centre (1,0) and its circumterence is 10pi.
Answer» ANSWER :25

Discussion

14384.	The value of sin^(-1)(cos2)-cos^(-1)(sin2)+tan^(-1)(cot4)-cot^(-1)(tan4)+sec^(-1)(cosec6)-cosec^(-1)(sec6) is
Answer» 0 `3PI` `8-3pi` `5pi-16` ANSWER :D

Discussion

14385.	A bag contains 5 black and 6 red balls. Determine the number of ways in which 2 black and 3 red balls can be selected from lot.
Answer» ANSWER :200

Discussion

14386.	If 'n' is a positive integer, then n.1+ (n-1) . 2+ (n-2). 3+….. + 1.n=
Answer» `(N (n+1) )/(2)` `(n (n+1) (n+2) )/( 6)` `( (n+1)(n+2))/( 2)` `(n(n+1) (2n+1))/(6)` ANSWER :B

Discussion

14387.	Check whether the following pair of statements are negation of each other. Give reasons for your answer x + y = y + x is true for every real numbers x and y. There exists real numbers x and y for which x + y = y + x.
Answer» Answer :No. The NEGATION of the STATEMENT in (i) is ''There exists real number X and y for which `x + y ney + x`'', instead of the statement given in (II).

Discussion

14388.	x^(2) + x + 1/sqrt(2)=0
Answer» ANSWER :`(-1 +-SQRT((2sqrt(2)-1)i))/2`

Discussion

14389.	Find the derivative of the w.r.to x. (x ^(x)) x
Answer» ANSWER :`(X ^(x)) ^(x) x [1+ 2 LOG x]`

Discussion

14390.	Find the derivative of the w.r.to x. x ^(x ^(x))
Answer» ANSWER :`X ^(x ^(x)) x ^(x-1) [1 + x LOG x) (1+ log x) ]`

Discussion

14391.	The value of sin(45^(@)+theta)-cos(45^(@)-theta)is
Answer» `2costheta` `2sintheta` 1 0 Answer :D

Discussion

14392.	If Sin theta_(1) + Sin theta_(2) + Sin theta_(3) = 3 then Cos theta_(1) + Cos theta_(2) + Cos theta_(3) =
Answer» 0 1 2 3 Answer :A

Discussion

14393.	Mark the correct statement of the following
Answer» For FIXED perimeter , right TRIANGLE have MAXIMUM area for fixed perimeter, EQUILATERAL triangle have maximum area for fixed perimeter, isosceles triangle have maximum area for fixed perimeter, SCALENE triangle have maximum area Answer :A::D

Discussion

14394.	If sin^(-1)x-cos^(-1)x=(pi)/6 then x=
Answer» `1//2` `SQRT(3)/2` `pi/4` `(3pi)/4` Answer :B

Discussion

14395.	The areaof the region bounded by the parabolay^2 =4axanditslatusrectumis …Sq. units.
Answer» 8 4 2 5 Answer :B

Discussion

14396.	Identify the Quantifiers in the following statements: There exists a even prime number other than 2.
Answer» ANSWER :EXISTENTIAL quanifier is USED

Discussion

14397.	Complete the table using calculator and use the result to estimate the limit. lim_(xrarr-3)[sqrt(1-x) -2]/(x+3)
Answer» ANSWER :-0.25

Discussion

14398.	Assertion (A) : The angle between equal sides of an isosceles triangles is60 ^(@)then r: R= 1: 2 Reason (R ) : Every isosceles triangles is equilateral triangle
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 :C

Discussion

14399.	Fill in the blanks to make each of the following a true statement : A ∩ A′ = . . .
Answer» ANSWER :`PHI`

Discussion

14400.	If the slopes of the lines represented by 6x^(2)+2hxy+y^(2)=0 are in the ratio 1:2 then h=
Answer» `(SQRT(3))/(2)` `(1)/(2)` `-(1)/(2)` `-(3 sqrt(3))/(2)` ANSWER :D

Discussion

Explore topic-wise InterviewSolutions in .

An angle theta through which a pulley turns with time 't' is completed by theta = t^(2) + 3t - 5 sq. cms / min Then the angular velocity for t = 5 sec.

Evaluate the following limits : Lim_(x to 0 ) ((sin ax)/(sin bx))^(k)

Prove that in Delta ABCS (( r_1- r_2) /( a) + ( r_2- r)/( b) + ( r_3- r)/( c ) ) = r_1+ r_2+ r_3 Prove that in Delta ABC

Evaluate : 2 cos ^(2) 157.5^(@) -1

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

Find (a +b)^4 - (a - b)^4. Hence, evaluate (sqrt3 + sqrt2)^4 - (sqrt3 - sqrt2)^4.

Prove that orthocentre of triangle formed by pair of lines ax^(2)+2hxy+by^(2)=0 an the line lx+my+n=0 is (kl, km) where k=(-n(a+b))/(am^(2)-2hlm+bl^(2))

If sin^(-1)x+sin^(-1)y+sin^(-1)z=(3pi)/z then the value of sum((x^(201)+y^(201))/(x^(603)+y^(603))).((x^(402)+y^(402))/(x^(804)+y^(804)))=

If A+B=225^(@) than prove that (cot A)/(1+cotA). (cot B)/(1+cotB)=(1)/(2)

Find the roots of the equations. Q. 3x^(2)-17x+25=0.

Represent on complex plane the complex numbers w=3 + 4i and z= 6-3i together with w +z and w-z. Obtain the modulus and argument of w and z.

Verify by the method of contradiction thatsqrt(7) is irrational.

Find the axes, vertices , foci , exentricity, equations of the directrices and length of the latus rectum of the hyperbola 5y ^(2) - 9x ^(2) = 36.

If Cos theta - Sin theta = sqrt(2) Cos theta then Cos theta + Sin theta =

The periodof sin^3x + cos^3 xis

Approximate value of tan46^(@) is ( 1^(@)=0.01745 radians )

Let the sequence a_nbe defined as follows: a_1 = 1, a_n = a_(n - 1) + 2for n ge2 . Find first five terms and write corresponding series

Show that the line lx + my = 1 will touch the ellipse (x ^(2))/( a ^(2)) + (y ^(2))/(b ^(2)) =1ifa ^(2) l ^(2) + b ^(2)m ^(2) = 1.

Show that the coefficient of the middle term in the expansion of (1+x)^(2n) is equal to the sum of the coefficients of two middle terms in the expansion of (1 + x)^(2n-1)

x = cos theta, y = sin 5 theta implies (1- x ^(2)) (d^(2)y)/(dx ^(2)) -x (dy)/(dx) =

Find the equation of the locus of a point whose distance from the y-axis is equal to its distance from (2,1,-1).

The value of p so that the lines (1-x)/(3) = (7y - 14)/(2p) = (z -3)/(2) and (7-7 x)/(3p) = (y-5)/(1) = (6 -z)/(5) are at right angles are

If vec(a) xx vec(b)= vec(c ) xx vec(d), vec(a) xx vec(c )= vec(b) xx vec(d), then

Evaluate (cos3 theta-2cos 4theta)/(sin 3 theta+2sin 4theta), when theta=150^(@).

How many four -digits even integerscan be formed using the digits 0,1,2,3,4,5?

Find the sum of all 3 digit numbers that canbe formed using the digits 1,2, 3, 5, 6.

Let S = (1)/( 1.4) + (1)/( 4.7) + (1)/(7.10) + .....n terms, Observe the following lists. {:("List-I","List-II"),("A)" underset(n to prop) (Lt) S=, "1)"0 ),("B)" underset(n to 0 ) (Lt) S=,"2)" 3//10),("C)" underset(n to 3) (Lt) S=,"3)"1//3),("D)" underset(n to 4) (Lt) S=,"4)"1),(,"5)"4//13):}

An equation of the plane passing through the origin and containing the lines whose direction consines are proportional to 1, -2, 2 and 2,3,-1is

An arch is in the from of a semi - ellipse. It is 8 m wide and 2 m high at the centre. Find the height of the arch at a point 1.5 m from one end.

Find the coefficient of x^(2) in the expansion of e^(2x+3) as a series in powers of x.

IfC (n,10) =C(n,12) ,dertermine C(n,5)

.........is the standard equation of circle with centre (1,0) and its circumterence is 10pi.

The value of sin^(-1)(cos2)-cos^(-1)(sin2)+tan^(-1)(cot4)-cot^(-1)(tan4)+sec^(-1)(cosec6)-cosec^(-1)(sec6) is

A bag contains 5 black and 6 red balls. Determine the number of ways in which 2 black and 3 red balls can be selected from lot.

If 'n' is a positive integer, then n.1+ (n-1) . 2+ (n-2). 3+….. + 1.n=

Check whether the following pair of statements are negation of each other. Give reasons for your answer x + y = y + x is true for every real numbers x and y. There exists real numbers x and y for which x + y = y + x.

x^(2) + x + 1/sqrt(2)=0

Find the derivative of the w.r.to x. (x ^(x)) x

Find the derivative of the w.r.to x. x ^(x ^(x))

The value of sin(45^(@)+theta)-cos(45^(@)-theta)is

If Sin theta_(1) + Sin theta_(2) + Sin theta_(3) = 3 then Cos theta_(1) + Cos theta_(2) + Cos theta_(3) =

Mark the correct statement of the following

If sin^(-1)x-cos^(-1)x=(pi)/6 then x=

The areaof the region bounded by the parabolay^2 =4axanditslatusrectumis …Sq. units.

Identify the Quantifiers in the following statements: There exists a even prime number other than 2.

Complete the table using calculator and use the result to estimate the limit. lim_(xrarr-3)[sqrt(1-x) -2]/(x+3)

Assertion (A) : The angle between equal sides of an isosceles triangles is60 ^(@)then r: R= 1: 2 Reason (R ) : Every isosceles triangles is equilateral triangle

Fill in the blanks to make each of the following a true statement : A ∩ A′ = . . .

If the slopes of the lines represented by 6x^(2)+2hxy+y^(2)=0 are in the ratio 1:2 then h=