Maths-
General
Easy

Question

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

  1. x to the power of 2 end exponent plus y to the power of 2 end exponent equals 4 a to the power of 2 end exponent    
  2. x to the power of 2 end exponent plus y to the power of 2 end exponent equals 2 a x    
  3. x to the power of 2 end exponent plus y to the power of 2 end exponent equals 2 a y    
  4. x to the power of 2 end exponent plus y to the power of 2 end exponent minus 2 a x minus 2 a y equals 0    

The correct answer is: x to the power of 2 end exponent plus y to the power of 2 end exponent equals 2 a x

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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

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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 textat 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 textat an angle

maths-General
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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

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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

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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

maths-General
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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 textfrom the point text end text left parenthesis a comma b divided by 2 right parenthesis text end textthen :

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 textfrom the point text end text left parenthesis a comma b divided by 2 right parenthesis text end textthen :

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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

maths-General
General
maths-

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

maths-General
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maths-

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

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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

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Statement (II) : Three non-zero real numbers can always be three terms of an A.P

maths-General
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maths-

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

maths-General
General
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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

maths-General
parallel
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maths-

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

maths-General
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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

maths-General
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If text end text stretchy sum from r equals 0 to n of   open curly brackets a subscript r end subscript left parenthesis x minus y plus 2 right parenthesis to the power of r end exponent minus b subscript r end subscript left parenthesis y minus x minus 1 right parenthesis to the power of r end exponent close curly brackets equals 0 for all n element of N comma text  then  end text b subscript n end subscript text end textis equal to

If text end text stretchy sum from r equals 0 to n of   open curly brackets a subscript r end subscript left parenthesis x minus y plus 2 right parenthesis to the power of r end exponent minus b subscript r end subscript left parenthesis y minus x minus 1 right parenthesis to the power of r end exponent close curly brackets equals 0 for all n element of N comma text  then  end text b subscript n end subscript text end textis equal to

maths-General
parallel

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