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Maths-

General

Easy

Question

In the adjoining figure, the circle meets the sides of an equilateral triangle at six points. If Ag = 2, GF = 13, FC = 1 and HJ = 7, then DE equals

$2 \sqrt{22}$
$7 \sqrt{3}$
9
10

The correct answer is: $2 square root of 22$

Related Questions to study

If a line segment AM = a moves in the plane XOY remaining parallel to OX so that the left end point A slides along the circle $x to the power of 2 end exponent plus y to the power of 2 end exponent equals a to the power of 2 end exponent comma text the locus of end text M text is end text$

If a line segment AM = a moves in the plane XOY remaining parallel to OX so that the left end point A slides along the circle $x to the power of 2 end exponent plus y to the power of 2 end exponent equals a to the power of 2 end exponent comma text the locus of end text M text is end text$

The triangle PQR is inscribed in the circle $x to the power of 2 end exponent plus y to the power of 2 end exponent equals 25 text . end text$ If Q and R have coordinates (3, 4) and (-4, 3) respectively, then $angle Q P R$ is

The triangle PQR is inscribed in the circle $x to the power of 2 end exponent plus y to the power of 2 end exponent equals 25 text . end text$ If Q and R have coordinates (3, 4) and (-4, 3) respectively, then $angle Q P R$ is

For all values of m ÎR the line y-mx + m-1 = 0 cuts the circle $x to the power of 2 end exponent plus y to the power of 2 end exponent minus 2 x minus 2 y plus 1 equals 0 text end text$ at an angle

For all values of m ÎR the line y-mx + m-1 = 0 cuts the circle $x to the power of 2 end exponent plus y to the power of 2 end exponent minus 2 x minus 2 y plus 1 equals 0 text end text$ at an angle

parallel

$C subscript 1 end subscript$ is a circle of radius 1 touching the x -axis and y -axis. $text end text C subscript 2 end subscript$ is another circle of radius $greater than 1$ and touching the axes as well as circle $C subscript 1 end subscript. text Then the radius of end text C subscript 2 end subscript text end text text is end text$

$C subscript 1 end subscript$ is a circle of radius 1 touching the x -axis and y -axis. $text end text C subscript 2 end subscript$ is another circle of radius $greater than 1$ and touching the axes as well as circle $C subscript 1 end subscript. text Then the radius of end text C subscript 2 end subscript text end text text is end text$

PA and PB are tangents to a circle S touching S at points A and B.C is a point on S in between A and B as shown in the figure. LCM is a tangent to S intersecting PA and PB in points L and M respectively.Then the perimeter of the triangle PLM depends on

PA and PB are tangents to a circle S touching S at points A and B.C is a point on S in between A and B as shown in the figure. LCM is a tangent to S intersecting PA and PB in points L and M respectively.Then the perimeter of the triangle PLM depends on

The centres of two circles are $5 square root of 2$ units apart. The circles are orthogonal and their radii are integers $not equal to$ 1. The area of the region, in square units, common to the two circles, is

The centres of two circles are $5 square root of 2$ units apart. The circles are orthogonal and their radii are integers $not equal to$ 1. The area of the region, in square units, common to the two circles, is

parallel

If two chords, each bisected by the x - axis can be drawn to the circle, $2 open parentheses x to the power of 2 end exponent plus y to the power of 2 end exponent close parentheses minus 2 a x minus b y equals 0 left parenthesis a not equal to 0 comma b not equal to 0 right parenthesis text end text$ from the point $text end text left parenthesis a comma b divided by 2 right parenthesis text end text$ then :

If two chords, each bisected by the x - axis can be drawn to the circle, $2 open parentheses x to the power of 2 end exponent plus y to the power of 2 end exponent close parentheses minus 2 a x minus b y equals 0 left parenthesis a not equal to 0 comma b not equal to 0 right parenthesis text end text$ from the point $text end text left parenthesis a comma b divided by 2 right parenthesis text end text$ then :

The radius of the least circle passing through the point (8, 4) and cutting the circle $x to the power of 2 end exponent plus y to the power of 2 end exponent equals 40$ orthogonally is

The radius of the least circle passing through the point (8, 4) and cutting the circle $x to the power of 2 end exponent plus y to the power of 2 end exponent equals 40$ orthogonally is

P(3,2) is a point on the circle $x to the power of 2 end exponent plus y to the power of 2 end exponent equals 13$ Two points A, B are on the circle such that $P A equals P B equals square root of 5$ The equation of chord AB is

P(3,2) is a point on the circle $x to the power of 2 end exponent plus y to the power of 2 end exponent equals 13$ Two points A, B are on the circle such that $P A equals P B equals square root of 5$ The equation of chord AB is

parallel

Statement – 1: Two circles of radii $square root of 3 & 1$ cut orthogonally then area of common region is $fraction numerator 5 pi minus 6 square root of 3 over denominator 6 end fraction$ square unit.
Statement -2: Area $text end text left parenthesis A union B right parenthesis equals text AreaA end text plus text Area end text left parenthesis B right parenthesis minus text Area end text left parenthesis A intersection B right parenthesis$ , where A & B represents two regions

Statement – 1: Two circles of radii $square root of 3 & 1$ cut orthogonally then area of common region is $fraction numerator 5 pi minus 6 square root of 3 over denominator 6 end fraction$ square unit.
Statement -2: Area $text end text left parenthesis A union B right parenthesis equals text AreaA end text plus text Area end text left parenthesis B right parenthesis minus text Area end text left parenthesis A intersection B right parenthesis$ , where A & B represents two regions

Statement (I) : 27, 8 and 12 can be three terms of G.P. as well as an A.P
Statement (II) : Three non-zero real numbers can always be three terms of an A.P

Statement (I) : 27, 8 and 12 can be three terms of G.P. as well as an A.P
Statement (II) : Three non-zero real numbers can always be three terms of an A.P

The value of $blank to the power of n end exponent C subscript 1 end subscript minus open parentheses 1 plus fraction numerator 1 over denominator 2 end fraction close parentheses blank to the power of n end exponent C subscript 2 end subscript plus open parentheses 1 plus fraction numerator 1 over denominator 2 end fraction plus fraction numerator 1 over denominator 3 end fraction close parentheses blank to the power of n end exponent C subscript 3 end subscript minus horizontal ellipsis horizontal ellipsis horizontal ellipsis. plus left parenthesis negative 1 right parenthesis to the power of n minus 1 end exponent open parentheses 1 plus fraction numerator 1 over denominator 2 end fraction plus fraction numerator 1 over denominator 3 end fraction plus horizontal ellipsis horizontal ellipsis horizontal ellipsis times fraction numerator 1 over denominator n end fraction close parentheses blank to the power of n end exponent C subscript n end subscript text is end text$

The value of $blank to the power of n end exponent C subscript 1 end subscript minus open parentheses 1 plus fraction numerator 1 over denominator 2 end fraction close parentheses blank to the power of n end exponent C subscript 2 end subscript plus open parentheses 1 plus fraction numerator 1 over denominator 2 end fraction plus fraction numerator 1 over denominator 3 end fraction close parentheses blank to the power of n end exponent C subscript 3 end subscript minus horizontal ellipsis horizontal ellipsis horizontal ellipsis. plus left parenthesis negative 1 right parenthesis to the power of n minus 1 end exponent open parentheses 1 plus fraction numerator 1 over denominator 2 end fraction plus fraction numerator 1 over denominator 3 end fraction plus horizontal ellipsis horizontal ellipsis horizontal ellipsis times fraction numerator 1 over denominator n end fraction close parentheses blank to the power of n end exponent C subscript n end subscript text is end text$

parallel

If $text end text open parentheses 1 plus x plus x to the power of 2 end exponent close parentheses to the power of n end exponent equals a subscript 0 end subscript plus a subscript 1 end subscript x plus a subscript 2 end subscript x to the power of 2 end exponent plus horizontal ellipsis plus a subscript 2 n end subscript x to the power of 2 n end exponent comma text then end text a subscript 0 end subscript a subscript 1 end subscript minus a subscript 1 end subscript a subscript 2 end subscript plus a subscript 2 end subscript a subscript 3 end subscript minus a subscript 3 end subscript a subscript 4 end subscript plus horizontal ellipsis$ is equal to

If $text end text open parentheses 1 plus x plus x to the power of 2 end exponent close parentheses to the power of n end exponent equals a subscript 0 end subscript plus a subscript 1 end subscript x plus a subscript 2 end subscript x to the power of 2 end exponent plus horizontal ellipsis plus a subscript 2 n end subscript x to the power of 2 n end exponent comma text then end text a subscript 0 end subscript a subscript 1 end subscript minus a subscript 1 end subscript a subscript 2 end subscript plus a subscript 2 end subscript a subscript 3 end subscript minus a subscript 3 end subscript a subscript 4 end subscript plus horizontal ellipsis$ is equal to

Total number of divisors of $n equals 2 to the power of 5 end exponent times 3 to the power of 5 end exponent times 5 to the power of 10 end exponent times 7 to the power of 2 end exponent$ that are of the form $4 lambda plus 2 comma lambda greater or equal than 1$ is equal to

Total number of divisors of $n equals 2 to the power of 5 end exponent times 3 to the power of 5 end exponent times 5 to the power of 10 end exponent times 7 to the power of 2 end exponent$ that are of the form $4 lambda plus 2 comma lambda greater or equal than 1$ is equal to

If the sum of the coefficients in the expansion of $left parenthesis q plus r right parenthesis to the power of 20 end exponent left parenthesis 1 plus left parenthesis p minus 2 right parenthesis x right parenthesis to the power of 20 end exponent$ is equal to square of the sum of the coefficients in the expansion of $left square bracket 2 r q x minus left parenthesis r plus q right parenthesis times y right square bracket to the power of 10 end exponent text , where end text p comma r comma q$ are positive constants, then

If the sum of the coefficients in the expansion of $left parenthesis q plus r right parenthesis to the power of 20 end exponent left parenthesis 1 plus left parenthesis p minus 2 right parenthesis x right parenthesis to the power of 20 end exponent$ is equal to square of the sum of the coefficients in the expansion of $left square bracket 2 r q x minus left parenthesis r plus q right parenthesis times y right square bracket to the power of 10 end exponent text , where end text p comma r comma q$ are positive constants, then

parallel

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