Maths-
General
Easy

Question

Statement‐I :: If a point open parentheses x subscript 1 end subscript comma blank y subscript 1 end subscript close parentheses lies in the shaded region fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction minus fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction equals 1, show in the figure, then fraction numerator x subscript 1 end subscript superscript 2 end superscript over denominator a to the power of 2 end exponent end fraction minus fraction numerator y subscript 1 end subscript superscript 2 end superscript over denominator b to the power of 2 end exponent end fraction less than 0
Statement‐II :: P left parenthesis x subscript 1 end subscript comma blank y subscript 1 end subscript right parenthesis lies outside the hyperbola fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction minus fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction equals 1, then fraction numerator x subscript 1 end subscript superscript 2 end superscript over denominator a to the power of 2 end exponent end fraction minus fraction numerator y subscript 1 end subscript superscript 2 end superscript over denominator b to the power of 2 end exponent end fraction less than 1.

  1. Statement‐I is true, Statement‐II is true; Statement‐II is correct explanation for Statement‐I.    
  2. Statement‐I is true, Statement‐II is true ; Statement‐II is NOT a correct explanation for statement‐I.    
  3. Statement‐I is true, Statement‐II is false.    
  4. Statement‐I is false, Statement‐II is true.    

The correct answer is: Statement‐I is false, Statement‐II is true.

Related Questions to study

General
Maths-

Statement‐I The ellipse fraction numerator x to the power of 2 end exponent over denominator 16 end fraction plus fraction numerator y to the power of 2 end exponent over denominator 9 end fraction equals 1 and fraction numerator x to the power of 2 end exponent over denominator 9 end fraction plus fraction numerator y to the power of 2 end exponent over denominator 16 end fraction equals 1 are congruent.
Statement‐II The ellipse fraction numerator x to the power of 2 end exponent over denominator 16 end fraction plus fraction numerator y to the power of 2 end exponent over denominator 9 end fraction equals 1 and fraction numerator x to the power of 2 end exponent over denominator 9 end fraction plus fraction numerator y to the power of 2 end exponent over denominator 16 end fraction equals 1 have the same eccentricity.

For such questions, we should know properties of ellipse. We should know all the formulas related to ellipse. The axis which is larger is always the major axis.

Statement‐I The ellipse fraction numerator x to the power of 2 end exponent over denominator 16 end fraction plus fraction numerator y to the power of 2 end exponent over denominator 9 end fraction equals 1 and fraction numerator x to the power of 2 end exponent over denominator 9 end fraction plus fraction numerator y to the power of 2 end exponent over denominator 16 end fraction equals 1 are congruent.
Statement‐II The ellipse fraction numerator x to the power of 2 end exponent over denominator 16 end fraction plus fraction numerator y to the power of 2 end exponent over denominator 9 end fraction equals 1 and fraction numerator x to the power of 2 end exponent over denominator 9 end fraction plus fraction numerator y to the power of 2 end exponent over denominator 16 end fraction equals 1 have the same eccentricity.

Maths-General

For such questions, we should know properties of ellipse. We should know all the formulas related to ellipse. The axis which is larger is always the major axis.

General
Maths-

The minimum area of triangle formed by tangent to the ellipse fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction plus fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction equals 1 and coordinate axes‐

The minimum area of triangle formed by tangent to the ellipse fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction plus fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction equals 1 and coordinate axes‐

Maths-General
General
Maths-

An ellipse has OB as semi minor axis, F and F to the power of † end exponent its focii and the angle FBF’ is a right angle Then the eccentricity of the ellipse is‐

Therefore, the eccentricity of the ellipse isspace space fraction numerator 1 over denominator square root of 2 end fraction

An ellipse has OB as semi minor axis, F and F to the power of † end exponent its focii and the angle FBF’ is a right angle Then the eccentricity of the ellipse is‐

Maths-General

Therefore, the eccentricity of the ellipse isspace space fraction numerator 1 over denominator square root of 2 end fraction

parallel
General
Maths-

The number of values of c such that the straight line y=4x+c touches the curve left parenthesis x to the power of 2 end exponent divided by 4 right parenthesis plus y to the power of 2 end exponent equals 1 is‐

Therefore, there are two values of c.

The number of values of c such that the straight line y=4x+c touches the curve left parenthesis x to the power of 2 end exponent divided by 4 right parenthesis plus y to the power of 2 end exponent equals 1 is‐

Maths-General

Therefore, there are two values of c.

General
Maths-

Let P be any point on any directrix of an ellipse Then the chords of contact of point P with respect to the ellipse and its auxiliary circle intersect at

Let P be any point on any directrix of an ellipse Then the chords of contact of point P with respect to the ellipse and its auxiliary circle intersect at

Maths-General
General
maths-

An ellipse having foci at (3, 3) and (-4,4) and passing through the origin has eccentricity equal to‐

An ellipse having foci at (3, 3) and (-4,4) and passing through the origin has eccentricity equal to‐

maths-General
parallel
General
maths-

Normals A O comma A A subscript 1 end subscript comma A A subscript 2 end subscript are drawn to parabola y to the power of 2 end exponent equals 8 x from the pointA (h, 0) If triangle O A subscript 1 end subscript A subscript 2 end subscript( O being the origin) is equilateral, then possible value of h’ is

Normals A O comma A A subscript 1 end subscript comma A A subscript 2 end subscript are drawn to parabola y to the power of 2 end exponent equals 8 x from the pointA (h, 0) If triangle O A subscript 1 end subscript A subscript 2 end subscript( O being the origin) is equilateral, then possible value of h’ is

maths-General
General
maths-

Given: A circle, 2 x to the power of 2 end exponent plus 2 y to the power of 2 end exponent equals 5 and a parabola, y to the power of 2 end exponent equals 4 square root of 5 x
Statement‐I:: An equation of a common tangent to these curves is y equals x plus square root of 5.
Statement‐II:: If the line, y equals m x plus fraction numerator square root of 5 over denominator m end fraction left parenthesis m not equal to 0 right parenthesis is their common tangent, then m satisfies m to the power of 4 end exponent minus 3 m to the power of 2 end exponent plus 2 equals 0.

Given: A circle, 2 x to the power of 2 end exponent plus 2 y to the power of 2 end exponent equals 5 and a parabola, y to the power of 2 end exponent equals 4 square root of 5 x
Statement‐I:: An equation of a common tangent to these curves is y equals x plus square root of 5.
Statement‐II:: If the line, y equals m x plus fraction numerator square root of 5 over denominator m end fraction left parenthesis m not equal to 0 right parenthesis is their common tangent, then m satisfies m to the power of 4 end exponent minus 3 m to the power of 2 end exponent plus 2 equals 0.

maths-General
General
maths-

In any equilateral capital delta, three circles of radii one are touching to the sides given as in the figure then area of the capital delta is

In any equilateral capital delta, three circles of radii one are touching to the sides given as in the figure then area of the capital delta is

maths-General
parallel
General
maths-

If the sides a, b, c of a triangle are such that a : b : c : : 1 : square root of 3 : 2, then the A : B : C is -

If the sides a, b, c of a triangle are such that a : b : c : : 1 : square root of 3 : 2, then the A : B : C is -

maths-General
General
physics-

A block placed on a rough inclined plane of inclination (theta =30°) can just be pushed upwards by applying a force "F" as shown. If the angle of inclination of the inclined plane is increased to (theta = 60°), the same block can just be prevented from sliding down by application of a force of same magnitude. The coefficient of friction between the block and the inclined plane is

A block placed on a rough inclined plane of inclination (theta =30°) can just be pushed upwards by applying a force "F" as shown. If the angle of inclination of the inclined plane is increased to (theta = 60°), the same block can just be prevented from sliding down by application of a force of same magnitude. The coefficient of friction between the block and the inclined plane is

physics-General
General
physics-

The tube AC forms a quarter circle in a vertical plane. The ball B has an area of cross–section slightly smaller than that of the tube, and can move without friction through it. B is placed at A and displaced slightly. It will

The tube AC forms a quarter circle in a vertical plane. The ball B has an area of cross–section slightly smaller than that of the tube, and can move without friction through it. B is placed at A and displaced slightly. It will

physics-General
parallel
General
physics-

A small cube with mass M starts at rest at point 1 at a height 4R, where R is the radius of the circular part of the track. The cube slides down the frictionless track and around the loop. The force that the track exerts on the cube at point 2 is nearly _____ times the cube's weight Mg.

A small cube with mass M starts at rest at point 1 at a height 4R, where R is the radius of the circular part of the track. The cube slides down the frictionless track and around the loop. The force that the track exerts on the cube at point 2 is nearly _____ times the cube's weight Mg.

physics-General
General
physics-

A bob attached to a string is held horizontal and released. The tension and vertical distance from point of suspension can be represented by.

A bob attached to a string is held horizontal and released. The tension and vertical distance from point of suspension can be represented by.

physics-General
General
physics-

A ball whose size is slightly smaller than width of the tube of radius 2.5 m is projected from bottommost point of a smooth tube fixed in a vertical plane with velocity of 10 m/s. If N1 and N2 are the normal reactions exerted by inner side and outer side of the tube on the ball

A ball whose size is slightly smaller than width of the tube of radius 2.5 m is projected from bottommost point of a smooth tube fixed in a vertical plane with velocity of 10 m/s. If N1 and N2 are the normal reactions exerted by inner side and outer side of the tube on the ball

physics-General
parallel

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