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Maths-

General

Easy

Question

Assertion : The locus of the centre of a circle which touches the circles $open vertical bar z minus z subscript 1 end subscript close vertical bar equals a$ and $open vertical bar z minus z subscript 2 end subscript close vertical bar equals b$ externally (z, $z subscript 1 end subscript$ and $z subscript 2 end subscript$ are complex numbers) will be hyperbola
Reason : $open vertical bar z minus z subscript 1 end subscript close vertical bar minus open vertical bar z minus z subscript 2 end subscript close vertical bar less than open vertical bar z subscript 2 end subscript minus z subscript 1 end subscript close vertical bar$
$not stretchy rightwards double arrow$ z lies on hyperbola

If both (A) and (R) are true, and (R) is the correct explanation of (A)
If both (A) and (R) are true but (R) is not the correct explanation of (A)
If (A) is true but (R) is false
If (A) is false but (R) is true

The correct answer is: If both (A) and (R) are true, and (R) is the correct explanation of (A)

Related Questions to study

Assertion : Consider an ellipse having its foci at A( $z subscript 1 end subscript$ ) and B( $z subscript 2 end subscript$ ) in the Argand plane. If the eccentricity of the ellipse be 'e' and it is known that origin is an interior point of the ellipse then
$e element of$ $open parentheses negative fraction numerator vertical line z subscript 1 end subscript plus z subscript 2 end subscript vertical line over denominator vertical line z subscript 1 end subscript vertical line plus vertical line z subscript 2 end subscript vertical line end fraction comma fraction numerator vertical line z subscript 1 end subscript plus z subscript 2 end subscript vertical line over denominator vertical line z subscript 1 end subscript vertical line plus vertical line z subscript 2 end subscript vertical line end fraction close parentheses$
Reason : If $Z subscript 0 end subscript$ is the point interior to curve $open vertical bar z minus z subscript 1 end subscript close vertical bar plus open vertical bar z minus z subscript 2 end subscript close vertical bar equals lambda rightwards double arrow open vertical bar z subscript 0 end subscript minus z subscript 1 end subscript close vertical bar plus open vertical bar z subscript 0 end subscript minus z subscript 2 end subscript close vertical bar less than lambda$

Assertion : Consider an ellipse having its foci at A( $z subscript 1 end subscript$ ) and B( $z subscript 2 end subscript$ ) in the Argand plane. If the eccentricity of the ellipse be 'e' and it is known that origin is an interior point of the ellipse then
$e element of$ $open parentheses negative fraction numerator vertical line z subscript 1 end subscript plus z subscript 2 end subscript vertical line over denominator vertical line z subscript 1 end subscript vertical line plus vertical line z subscript 2 end subscript vertical line end fraction comma fraction numerator vertical line z subscript 1 end subscript plus z subscript 2 end subscript vertical line over denominator vertical line z subscript 1 end subscript vertical line plus vertical line z subscript 2 end subscript vertical line end fraction close parentheses$
Reason : If $Z subscript 0 end subscript$ is the point interior to curve $open vertical bar z minus z subscript 1 end subscript close vertical bar plus open vertical bar z minus z subscript 2 end subscript close vertical bar equals lambda rightwards double arrow open vertical bar z subscript 0 end subscript minus z subscript 1 end subscript close vertical bar plus open vertical bar z subscript 0 end subscript minus z subscript 2 end subscript close vertical bar less than lambda$

If $alpha$ and $beta$ are different complex numbers with | $beta$ | = 1, then $open vertical bar fraction numerator beta minus alpha over denominator 1 minus stack alpha with ̄ on top beta end fraction close vertical bar$ is equal to

If $alpha$ and $beta$ are different complex numbers with | $beta$ | = 1, then $open vertical bar fraction numerator beta minus alpha over denominator 1 minus stack alpha with ̄ on top beta end fraction close vertical bar$ is equal to

What is the maximum value of the force F such that the block shown in the arrangement does not move? $open parentheses g equals 10 m divided by s to the power of 2 end exponent close parentheses$

What is the maximum value of the force F such that the block shown in the arrangement does not move? $open parentheses g equals 10 m divided by s to the power of 2 end exponent close parentheses$

physics-General

parallel

A block of mass $m subscript 1 end subscript$ rests on a rough horizontal plane relative to which the coefficient of friction is $mu.$ . A light string attached to the body passes over a light pulley and carries at its other end a mass $m subscript 2 end subscript$ and the system just begins to move. The value of $mu$ .

A block of mass $m subscript 1 end subscript$ rests on a rough horizontal plane relative to which the coefficient of friction is $mu.$ . A light string attached to the body passes over a light pulley and carries at its other end a mass $m subscript 2 end subscript$ and the system just begins to move. The value of $mu$ .

physics-General

With what acceleration 'a' should the box of figure moving up so that blocks of mass M exerts a force 7Mg/4 on the floor of the box?

With what acceleration 'a' should the box of figure moving up so that blocks of mass M exerts a force 7Mg/4 on the floor of the box?

physics-General

If $alpha$ and $beta$ are different complex numbers with
| $beta$ | = 1, then $open vertical bar fraction numerator beta minus alpha over denominator 1 minus alpha beta end fraction close vertical bar$ is equal to

If $alpha$ and $beta$ are different complex numbers with
| $beta$ | = 1, then $open vertical bar fraction numerator beta minus alpha over denominator 1 minus alpha beta end fraction close vertical bar$ is equal to

parallel

Let z₁ and z₂ be complex numbers, then $open vertical bar z subscript 1 end subscript plus z subscript 2 end subscript close vertical bar to the power of 2 end exponent plus open vertical bar z subscript 1 end subscript minus z subscript 2 end subscript close vertical bar to the power of 2 end exponent$ is equal to

Let z₁ and z₂ be complex numbers, then $open vertical bar z subscript 1 end subscript plus z subscript 2 end subscript close vertical bar to the power of 2 end exponent plus open vertical bar z subscript 1 end subscript minus z subscript 2 end subscript close vertical bar to the power of 2 end exponent$ is equal to

Let z = 1 – t + i $square root of t to the power of 2 end exponent plus t plus 2 end root$ , where t is a real parameter. The locus of z in the Argand plane is

Let z = 1 – t + i $square root of t to the power of 2 end exponent plus t plus 2 end root$ , where t is a real parameter. The locus of z in the Argand plane is

For all complex number z₁, z₂ satisfying $open vertical bar z subscript 1 end subscript close vertical bar$ = 12 and $open vertical bar z subscript 2 end subscript minus 3 minus 4 i close vertical bar equals 5$ , the minimum value of $open vertical bar z subscript 1 end subscript minus z subscript 2 end subscript close vertical bar$ is -

For all complex number z₁, z₂ satisfying $open vertical bar z subscript 1 end subscript close vertical bar$ = 12 and $open vertical bar z subscript 2 end subscript minus 3 minus 4 i close vertical bar equals 5$ , the minimum value of $open vertical bar z subscript 1 end subscript minus z subscript 2 end subscript close vertical bar$ is -

parallel

A pedigree is shown below for a disease that is autosomal dominant. The genetic make up of the first generation is

A pedigree is shown below for a disease that is autosomal dominant. The genetic make up of the first generation is

Let the complex number z satisfy the equation |z + 4i| = 3. Then the greatest and least values of |z + 3| are -

Let the complex number z satisfy the equation |z + 4i| = 3. Then the greatest and least values of |z + 3| are -

In the arrangement shown in figure $m subscript A end subscript equals m subscript B end subscript equals 2 k g.$ String is massless and pulley is frictionless. Block B is resting on a smooth horizontal surface, while friction coefficient between blocks A and B is $mu equals 0.5.$ The maximum horizontal force F can be applied so that blocks A does not slip over the blocks B is $open parentheses g equals 10 m divided by s to the power of 2 end exponent close parentheses$

In the arrangement shown in figure $m subscript A end subscript equals m subscript B end subscript equals 2 k g.$ String is massless and pulley is frictionless. Block B is resting on a smooth horizontal surface, while friction coefficient between blocks A and B is $mu equals 0.5.$ The maximum horizontal force F can be applied so that blocks A does not slip over the blocks B is $open parentheses g equals 10 m divided by s to the power of 2 end exponent close parentheses$

physics-General

parallel

Blocks A and B in the figure are connected by a bar of negligible weight. If mass of A and B are 170 kg each and $mu subscript A end subscript equals 0.2$ and $mu subscript B end subscript equals 0.4 comma$ where $mu subscript A end subscript$ and $mu subscript B end subscript$ are the coefficient of limiting friction between blocks and plane, calculate the force in the bar. $open parentheses g equals 10 m divided by s to the power of 2 end exponent close parentheses$

Blocks A and B in the figure are connected by a bar of negligible weight. If mass of A and B are 170 kg each and $mu subscript A end subscript equals 0.2$ and $mu subscript B end subscript equals 0.4 comma$ where $mu subscript A end subscript$ and $mu subscript B end subscript$ are the coefficient of limiting friction between blocks and plane, calculate the force in the bar. $open parentheses g equals 10 m divided by s to the power of 2 end exponent close parentheses$

physics-General

Two spheres of equal masses are attached to a string of length 2 m as shown in figure. The string and the spheres are then whirled in a horizontal circle about O at a constant rate. The value of the ratio
$open parentheses fraction numerator text Tensioninthestringbetween end text P text and end text Q over denominator text Tension isthestringbetween end text P text and end text O end fraction close parentheses$ is

Two spheres of equal masses are attached to a string of length 2 m as shown in figure. The string and the spheres are then whirled in a horizontal circle about O at a constant rate. The value of the ratio
$open parentheses fraction numerator text Tensioninthestringbetween end text P text and end text Q over denominator text Tension isthestringbetween end text P text and end text O end fraction close parentheses$ is

physics-General

A pedigree is shown below for a disease that is autosomal recessive. The genetic makeup of the first generation

A pedigree is shown below for a disease that is autosomal recessive. The genetic makeup of the first generation

parallel

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