Maths-
General
Easy
Question
For all values of m ÎR the line y-mx + m-1 = 0 cuts the circle
at an angle
The correct answer is: ![fraction numerator pi over denominator 2 end fraction](data:image/png;base64,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)
Related Questions to study
maths-
is a circle of radius 1 touching the x -axis and y -axis.
is another circle of radius
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](data:image/png;base64,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)
is a circle of radius 1 touching the x -axis and y -axis.
is another circle of radius
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](data:image/png;base64,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)
maths-General
maths-
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
![](data:image/png;base64,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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
![](data:image/png;base64,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)
maths-General
maths-
The centres of two circles are
units apart. The circles are orthogonal and their radii are integers
1. The area of the region, in square units, common to the two circles, is
The centres of two circles are
units apart. The circles are orthogonal and their radii are integers
1. The area of the region, in square units, common to the two circles, is
maths-General
maths-
If two chords, each bisected by the x - axis can be drawn to the circle,
from the point
then :
If two chords, each bisected by the x - axis can be drawn to the circle,
from the point
then :
maths-General
maths-
The radius of the least circle passing through the point (8, 4) and cutting the circle
orthogonally is
The radius of the least circle passing through the point (8, 4) and cutting the circle
orthogonally is
maths-General
maths-
P(3,2) is a point on the circle
Two points A, B are on the circle such that
The equation of chord AB is
P(3,2) is a point on the circle
Two points A, B are on the circle such that
The equation of chord AB is
maths-General
maths-
Statement – 1: Two circles of radii
cut orthogonally then area of common region is
square unit.
Statement -2: Area
, where A & B represents two regions
Statement – 1: Two circles of radii
cut orthogonally then area of common region is
square unit.
Statement -2: Area
, where A & B represents two regions
maths-General
maths-
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
maths-General
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](data:image/png;base64,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)
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](data:image/png;base64,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)
maths-General
maths-
If
is equal to
If
is equal to
maths-General
maths-
Total number of divisors of
that are of the form
is equal to
Total number of divisors of
that are of the form
is equal to
maths-General
maths-
If the sum of the coefficients in the expansion of
is equal to square of the sum of the coefficients in the expansion of
are positive constants, then
If the sum of the coefficients in the expansion of
is equal to square of the sum of the coefficients in the expansion of
are positive constants, then
maths-General
maths-
If
is equal to
If
is equal to
maths-General
chemistry-
Statement-1 : Silicones are resistant to heat, oxidation and most chemicals
Statement-2 : The silicones(a) have stable silica-like six electron owing to high bond energy of Si – O bond and (b) have high strength of Si – C
Statement-1 : Silicones are resistant to heat, oxidation and most chemicals
Statement-2 : The silicones(a) have stable silica-like six electron owing to high bond energy of Si – O bond and (b) have high strength of Si – C
chemistry-General
chemistry-
Statement-1 : Boron forms only covalent compounds
Statement-2 : Due to small size of boron, the sum of its first three ionisation enthalpies very high
Statement-1 : Boron forms only covalent compounds
Statement-2 : Due to small size of boron, the sum of its first three ionisation enthalpies very high
chemistry-General