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Maths-

General

Easy

Question

If r1, r2, r3 in a triangle be in H.P. then the sides are in -

A.P.
G.P.
H.P.
None of these

The correct answer is: A.P.

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$open parentheses fraction numerator 1 over denominator r end fraction minus fraction numerator 1 over denominator r subscript 1 end subscript end fraction close parentheses open parentheses fraction numerator 1 over denominator r end fraction minus fraction numerator 1 over denominator r subscript 2 end subscript end fraction close parentheses open parentheses fraction numerator 1 over denominator r end fraction minus fraction numerator 1 over denominator r subscript 3 end subscript end fraction close parentheses$ =

$open parentheses fraction numerator 1 over denominator r end fraction minus fraction numerator 1 over denominator r subscript 1 end subscript end fraction close parentheses open parentheses fraction numerator 1 over denominator r end fraction minus fraction numerator 1 over denominator r subscript 2 end subscript end fraction close parentheses open parentheses fraction numerator 1 over denominator r end fraction minus fraction numerator 1 over denominator r subscript 3 end subscript end fraction close parentheses$ =

In an equilateral triangle, the in-radius, circum-radius and one of the ex- radii are in the ratio-

In an equilateral triangle, the in-radius, circum-radius and one of the ex- radii are in the ratio-

If r1 = r2 + r3 + r, then the  is -

If r1 = r2 + r3 + r, then the  is -

parallel

(r1 + r2) (r2 + r3) (r3 + r1) =

(r1 + r2) (r2 + r3) (r3 + r1) =

r2 r3 + r3 r1 + r1 r2 =

r2 r3 + r3 r1 + r1 r2 =

If the sides be a, b, c then $fraction numerator r subscript 1 end subscript minus r over denominator a end fraction plus fraction numerator r subscript 2 end subscript minus r over denominator b end fraction$ =

If the sides be a, b, c then $fraction numerator r subscript 1 end subscript minus r over denominator a end fraction plus fraction numerator r subscript 2 end subscript minus r over denominator b end fraction$ =

parallel

In any ABC, cosA + cosB + cosC =

In any ABC, cosA + cosB + cosC =

In any ABC, sinA + sinB + sinC =

In any ABC, sinA + sinB + sinC =

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A wire of diameter $1 m m$ breaks under a tension of $1000 blank N$ . Another wire, of same material as that of the first one, but of diameter $2 blank m m$ breaks under a tension of

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If S is stress and Y is Young’s modulus of material of a wire, the energy stored in the wire per unit volume is

If S is stress and Y is Young’s modulus of material of a wire, the energy stored in the wire per unit volume is

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A solid sphere of radius r made of a material of bulk modulus K is surrounded by a liquid in a cylindrical container. A massless piston of area a floats on the surface of the liquid. When a mass m is placed on the piston to compress the liquid, the fractional change in the radius of the sphere (dr/r) is

A solid sphere of radius r made of a material of bulk modulus K is surrounded by a liquid in a cylindrical container. A massless piston of area a floats on the surface of the liquid. When a mass m is placed on the piston to compress the liquid, the fractional change in the radius of the sphere (dr/r) is

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Which of the following rods of same material undergoes maximum elongation when subjected to a given force?

Which of the following rods of same material undergoes maximum elongation when subjected to a given force?

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A tensile force of $2 cross times 10 to the power of 3 end exponent N$ doubles the length of a rubber band of cross-sectional area $2 cross times 10 to the power of negative 4 end exponent m to the power of 2 end exponent.$ The Young’s modulus of elasticity of the rubber band is

A tensile force of $2 cross times 10 to the power of 3 end exponent N$ doubles the length of a rubber band of cross-sectional area $2 cross times 10 to the power of negative 4 end exponent m to the power of 2 end exponent.$ The Young’s modulus of elasticity of the rubber band is

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parallel

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