14949 + Interview Questions in Maths in Class 11 Page 265 InterviewSolution

13201.	Which of the following sentences are statements? Give reasons for your answer Answer this question.
Answer» ANSWER :It is an ORDER and THEREFORE, is not a STATEMENT.

Discussion

13202.	Let f(x)=x^(2)- x+1, x ge 1//2, then the solution of the equation f^(-1)(x)=f(x) is
Answer» `X=1` `x=2` `x = 1/2` `x=0` ANSWER :A

Discussion

13203.	If x+y = 6543298 and x^(11)y^5 is maximum then the ratio of the numbers is
Answer» `12:4` `3:13` `14:2` `11:5` ANSWER :D

Discussion

13204.	Usingthe mathematical induction , showthat for anynatural number n, 1/( 1.2.3) + 1/( 2.3.4) + 1/( 3.4.5)+ ..+ 1/( n (n +1) (n+2)) = ( n(n+3))/( 4 (n+1) (n+2))
Answer» ANSWER :N

Discussion

13205.	If the equation cos^(2)((pi)/4(sinx+sqrt(2)cos^(2)x))-tan^(2)(x+(pi)/4tan^(2)x)=1 then x=
Answer» `2kpi-(pi)/4, k in Z` `2kpi+(pi)/3, k in Z` `2kpi +(pi)/4, k in Z` `2K pi +(pi)/4, k INZ` ANSWER :A

Discussion

13206.	Transform the following equations into a. Slope intercpetform b. Intercept form c. Normal form 4x-3y+12=0
Answer» ANSWER :a. `y=4/3x+4;`B. `X/(-3)+y/4=1` c. `x((-4)/5)+y(3/5)=12/5`

Discussion

13207.	Obtain equation of circle inx^(2) + y^(2) - 2x - 2y + 1 = 0
Answer» ANSWER :CENTRE (1,1), RADIUS 1

Discussion

13208.	(3costheta+cos3theta)/(3sintheta-sin3theta)=
Answer» `cot^(2)THETA` `cot^(4)theta` `cot^(3)theta` `3cot theta` Answer :C

Discussion

13209.	If y = x -\|x\| then (dy)/(dx) .............., x lt 0
Answer» ANSWER :2

Discussion

13210.	Examine whether the following statements are true or false : {pi} sub R. Where R is the set of real number.
Answer» ANSWER :1

Discussion

13211.	Evaluate : sin^(2) (pi/8 +x/2) - sin^(2) (pi/8 - x/2)
Answer» ANSWER :`1/(SQRT(2)) sin X `

Discussion

13212.	For non null sets A and B if n(A) =16,n(B) = 14 , n(A cup B) = 25 then n(A capB)= .........
Answer» ANSWER :5

Discussion

13213.	Find the sum up to the 17^(th) term of the series (1^(3))/(1)+(1^(3)+2^(3))/(1+3)+(1^(3)+2^(3)+3^(3))/(1+3+5)+….
Answer» ANSWER :`= 527`

Discussion

13214.	Let bara=bari-barj,barb=barj-bark,barc=bark-bari. lf dis a unit vector such that bara.bard =0=[barb barc bard] then bard is equals to
Answer» ANSWER :`bot1/(SQRT6)(bari+barj-bar2k)`

Discussion

13215.	Find the circumcentre of the triangle formed by the lines x+y=0, 2x+y+5=0 and x-y=2
Answer» ANSWER :`alpha-2beta+5=0`

Discussion

13216.	3 sin x+ 4 cos x= 5implies 6 tan""(x)/(2)-9 tan^(2)""(x)/(2)=
Answer» 0 1 3 4 Answer :B

Discussion

13217.	{x in RR:(2x-1)/(x^(3)+4x^(2)+3x) in RR}=
Answer» `R-{0}` `R-{0,1,3}` `R-{0, -1, -3}` `R-{0,-1,-3,+1//2}` ANSWER :C

Discussion

13218.	Number of integral solutions of the equation sin^(-1)(sinx)=cos^(-1)(cosx)" in "[0, 5pi] is
Answer» 2 3 4 infinite Answer :C

Discussion

13219.	A man standing on a level plane observes the anlge of elevation of top of pole to be 'alpha'. He walks a distance equal to double the height of pole towards it and finds that the elevation in 2 alpha " then " alpha =
Answer» `pi/12` `pi/4` `pi/6` `pi/3` ANSWER :A

Discussion

13220.	If tantheta.tan(120^(@)-theta)tan(120^(@)+theta)=(1)/(sqrt(3)) then theta =
Answer» `(NPI)/(3)-(pi)/(12)` `(npi)/(3)-(pi)/(18)` `(npi)/(3)+(pi)/(18)` `(npi)/(3)+(pi)/(12)` ANSWER :C

Discussion

13221.	Write the negation of the following statements: p: For every positive real number x, the number x - 1 is also positive.
Answer» ANSWER :There EXISTS a POSITIVE real number X such that `x–1` is not positive.

Discussion

13222.	Let f(x) and g(x) be differentiable functions in (a,b) continuous in [a,b] and g(x) cancel(=) 0 in [a,b] for atleast one c in (a,b) such that (g(a) f(b)- f(a) g(b))/(g(c ) f'(c ) -f(c ) g'(c ) ) = k (g (a) g(b))/(g(c )^(2))then k =
Answer» (b-a) (b+a) (2b+a) (b-2a) ANSWER :A

Discussion

13223.	Can you write the equation of circle by using two different methods?
Answer» SOLUTION :(x+1)(x-5)+(y+2)(y-2)=0, `(x-2)^2+(y-0)^2=13`

Discussion

13224.	In the matrix [(1,0,-2),(3,-1,2),(4,5,6)] find the minor and cofactor of the element '5'.
Answer» ANSWER :`-8`

Discussion

13225.	Find the coordinates of the foot of perpendicular from the point (-1, 3) to the line 3x - 4y - 16 = 0 .
Answer» ANSWER :`(68/25, - 49/25)`

Discussion

13226.	If the sample space has ninN different elements then it has exactly ninN primary events .
Answer» ANSWER :TRUE STATEMENT

Discussion

13227.	Number of solution of equation cos^(4)x - 2cos^2x+1=0 in interval [0,2pi] are only two .
Answer» ANSWER :FALSE STATEMENT

Discussion

13228.	Let p(x) be a real polynomial of least degree which has a local maximum at x=1 and a local minimum at x=3 . If p(1) =6andp(3)=2,then p(0) is
Answer» ANSWER :9

Discussion

13229.	Evaluate \|(45,71,26),(35,-21,14),(77,50,40)\|:
Answer» 0 275 572 635 Answer :A

Discussion

13230.	Using binomial theorem, evaluate:(96)^3
Answer» ANSWER :884736

Discussion

13231.	Using binomial theorem, evaluate(102)^5
Answer» ANSWER :11040808032

Discussion

13232.	A sphere of radius 'a' substends an angle 60^(@) at a point P. Then the distance of P from the centre of the sphere is
Answer» `(a)/(sqrt(3))` `2A` `(asqrt(3))/(2)` `(2a)/(sqrt(3))` Answer :B

Discussion

13233.	Find the dimensions of the right circular cylinder with the greatest volume that can be inscribed in a sphere of radius a.
Answer» ANSWER :`"HEIGHT"=(2A)/SQRT3," RADIUS"=(asqrt2)/sqrt3`

Discussion

13234.	Let A = {x, y, z) and B = {1, 2}. Find the number of relations from A to B.
Answer» ANSWER :No. of RELATIONS from A into `B=2^(6)`

Discussion

13235.	Statement I :Minimum value of (3 sn theta -4 cos theta ) ( 3 cos theta + 4 sin theta )is -(25)/(2) StatementII :Minimum valueof9 tan^(2) x+16 cot^(2) x is 24 Whichof the abovestatementis correct ?
Answer» ONLYI ONLYII BothI & II NeitherI norII Answer :3

Discussion

13236.	Find (x + 1)^6 + (x-1)^6. Hence or otherwise evaluate (sqrt2 + 1)^6 + (sqrt2 - 1)^6.
Answer» ANSWER :2(`x^6` + `15x^4` + 1), 198

Discussion

13237.	Points (5,-4, 2),(4,-3, 1),(7,6,4)and(8,7,5) represents ______ in plane.
Answer» Rectangle Square Parallelogram None of these Answer :A

Discussion

13238.	The point of intersection of the lines bar(r)=bar(a)+t(bar(b)+bar(c)), bar(r)=bar(b)+s(bar(c)+bar(a)) is
Answer» `BAR(C)` `bar(a)` `bar(B)` `bar(a)+bar(b)+bar(c)` ANSWER :D

Discussion

13239.	Find the distance between the parallel lines 3x – 4y + 5 = 0 and 3x – 4y + 7 = 0
Answer» ANSWER :`= 2/5`

Discussion

13240.	If u=log_(e )"Tan"((3pi)/(4)+(theta)/(2)) then coshu=
Answer» `SEC THETA` `TAN theta` `-sec theta` `-tan theta` ANSWER :C

Discussion

13241.	ABC is a triangle and 'O', any point in the palne of the triangle. The lines AO, BO and CO meet the sides BC, CA and AB is D,E,F respectively. Then (OD)/(AD)+(OE)/(BE)+(OF)/(CF) equal to
Answer» 1 2 `-1` `-2` ANSWER :a

Discussion

13242.	If r is in radius of Delta^("le")ABC and R is its circum radius then Delta^("le")ABC is Equilateral if (R)/(r)=
Answer» 1 2 3 4 Answer :B

Discussion

13243.	Solve sqrt(5)x^(2) + x + sqrt(5)=0
Answer» ANSWER :`(-1 + SQRT(19)i)/(2sqrt(5))`

Discussion

13244.	If k=( sec A + tan A) ( sec B+ tan B) sec C + tan C)=(sec A - tan A)(sec B- tan B)(sec C - tan C) " then " k=
Answer» 0 `pm1` `PM3` `PM4` ANSWER :B

Discussion

13245.	Find the mean deviation about the median for the following data:3,9,5,3,12,10,18,4,7,19,21.
Answer» ANSWER :5.27

Discussion

13246.	Difference of (r+1) term from beginning and (r+1) term from last in expansion (a+b)^n is 2 ((n),(r)) .
Answer» ANSWER :FALSE STATEMENT

Discussion

13247.	the orthocentre of the triangle formed by the lines x+y = 1 and 2y^(2)-xy-6x^(2)=0 is
Answer» `((4)/(3),(4)/(3))` `((2)/(3),(2)/(3))` `((2)/(3),(-2)/(3))` `((4)/(3),(-4)/(3))` ANSWER :A

Discussion

13248.	A line through P(3,4) cute the lines x =6 and y=8 at L and M respectively. Q is a variable point on the line such that 1/PQ=1/PL+1/PM then the locus of Q is
Answer» `4x+3y-36 = 0` `x^2+y^2 = 36` `3x-4y-36 = 0` `4x^2+9y^2 = 36` ANSWER :A

Discussion

13249.	A circular plate expands when heated from a radius of 5 cm to 5.06 cm. The approximate increase in area is
Answer» 0.6 1.2 2.4 0.12 Answer :C

Discussion

13250.	If the tangentat the point (at^(2),at^(3)) on the curve ay^(2)=x^(3) meets the curve again at
Answer» `((at^(2))/(4),-(at^(3))/(8))` `((at^(3))/(4),8at)` `(at^(2)/(2),2at^(2)` `(at^(2),2at)` Answer :A

Discussion

Explore topic-wise InterviewSolutions in .

Which of the following sentences are statements? Give reasons for your answer Answer this question.

Let f(x)=x^(2)- x+1, x ge 1//2, then the solution of the equation f^(-1)(x)=f(x) is

If x+y = 6543298 and x^(11)y^5 is maximum then the ratio of the numbers is

Usingthe mathematical induction , showthat for anynatural number n, 1/( 1.2.3) + 1/( 2.3.4) + 1/( 3.4.5)+ ..+ 1/( n (n +1) (n+2)) = ( n(n+3))/( 4 (n+1) (n+2))

If the equation cos^(2)((pi)/4(sinx+sqrt(2)cos^(2)x))-tan^(2)(x+(pi)/4tan^(2)x)=1 then x=

Transform the following equations into a. Slope intercpetform b. Intercept form c. Normal form 4x-3y+12=0

Obtain equation of circle inx^(2) + y^(2) - 2x - 2y + 1 = 0

(3costheta+cos3theta)/(3sintheta-sin3theta)=

If y = x -|x| then (dy)/(dx) .............., x lt 0

Examine whether the following statements are true or false : {pi} sub R. Where R is the set of real number.

Evaluate : sin^(2) (pi/8 +x/2) - sin^(2) (pi/8 - x/2)

For non null sets A and B if n(A) =16,n(B) = 14 , n(A cup B) = 25 then n(A capB)= .........

Find the sum up to the 17^(th) term of the series (1^(3))/(1)+(1^(3)+2^(3))/(1+3)+(1^(3)+2^(3)+3^(3))/(1+3+5)+….

Let bara=bari-barj,barb=barj-bark,barc=bark-bari. lf dis a unit vector such that bara.bard =0=[barb barc bard] then bard is equals to

Find the circumcentre of the triangle formed by the lines x+y=0, 2x+y+5=0 and x-y=2

3 sin x+ 4 cos x= 5implies 6 tan""(x)/(2)-9 tan^(2)""(x)/(2)=

{x in RR:(2x-1)/(x^(3)+4x^(2)+3x) in RR}=

Number of integral solutions of the equation sin^(-1)(sinx)=cos^(-1)(cosx)" in "[0, 5pi] is

A man standing on a level plane observes the anlge of elevation of top of pole to be 'alpha'. He walks a distance equal to double the height of pole towards it and finds that the elevation in 2 alpha " then " alpha =

If tantheta.tan(120^(@)-theta)tan(120^(@)+theta)=(1)/(sqrt(3)) then theta =

Write the negation of the following statements: p: For every positive real number x, the number x - 1 is also positive.

Let f(x) and g(x) be differentiable functions in (a,b) continuous in [a,b] and g(x) cancel(=) 0 in [a,b] for atleast one c in (a,b) such that (g(a) f(b)- f(a) g(b))/(g(c ) f'(c ) -f(c ) g'(c ) ) = k (g (a) g(b))/(g(c )^(2))then k =

Can you write the equation of circle by using two different methods?

In the matrix [(1,0,-2),(3,-1,2),(4,5,6)] find the minor and cofactor of the element '5'.

Find the coordinates of the foot of perpendicular from the point (-1, 3) to the line 3x - 4y - 16 = 0 .

If the sample space has ninN different elements then it has exactly ninN primary events .

Number of solution of equation cos^(4)x - 2cos^2x+1=0 in interval [0,2pi] are only two .

Let p(x) be a real polynomial of least degree which has a local maximum at x=1 and a local minimum at x=3 . If p(1) =6andp(3)=2,then p(0) is

Evaluate |(45,71,26),(35,-21,14),(77,50,40)|:

Using binomial theorem, evaluate:(96)^3

Using binomial theorem, evaluate(102)^5

A sphere of radius 'a' substends an angle 60^(@) at a point P. Then the distance of P from the centre of the sphere is

Find the dimensions of the right circular cylinder with the greatest volume that can be inscribed in a sphere of radius a.

Let A = {x, y, z) and B = {1, 2}. Find the number of relations from A to B.

Statement I :Minimum value of (3 sn theta -4 cos theta ) ( 3 cos theta + 4 sin theta )is -(25)/(2) StatementII :Minimum valueof9 tan^(2) x+16 cot^(2) x is 24 Whichof the abovestatementis correct ?

Find (x + 1)^6 + (x-1)^6. Hence or otherwise evaluate (sqrt2 + 1)^6 + (sqrt2 - 1)^6.

Points (5,-4, 2),(4,-3, 1),(7,6,4)and(8,7,5) represents ______ in plane.

The point of intersection of the lines bar(r)=bar(a)+t(bar(b)+bar(c)), bar(r)=bar(b)+s(bar(c)+bar(a)) is

Find the distance between the parallel lines 3x – 4y + 5 = 0 and 3x – 4y + 7 = 0

If u=log_(e )"Tan"((3pi)/(4)+(theta)/(2)) then coshu=

ABC is a triangle and 'O', any point in the palne of the triangle. The lines AO, BO and CO meet the sides BC, CA and AB is D,E,F respectively. Then (OD)/(AD)+(OE)/(BE)+(OF)/(CF) equal to

If r is in radius of Delta^("le")ABC and R is its circum radius then Delta^("le")ABC is Equilateral if (R)/(r)=

Solve sqrt(5)x^(2) + x + sqrt(5)=0

If k=( sec A + tan A) ( sec B+ tan B) sec C + tan C)=(sec A - tan A)(sec B- tan B)(sec C - tan C) " then " k=

Find the mean deviation about the median for the following data:3,9,5,3,12,10,18,4,7,19,21.

Difference of (r+1) term from beginning and (r+1) term from last in expansion (a+b)^n is 2 ((n),(r)) .

the orthocentre of the triangle formed by the lines x+y = 1 and 2y^(2)-xy-6x^(2)=0 is

A line through P(3,4) cute the lines x =6 and y=8 at L and M respectively. Q is a variable point on the line such that 1/PQ=1/PL+1/PM then the locus of Q is

A circular plate expands when heated from a radius of 5 cm to 5.06 cm. The approximate increase in area is

If the tangentat the point (at^(2),at^(3)) on the curve ay^(2)=x^(3) meets the curve again at