The number of solutions of the equation , where a > 0, and has least value is :

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## Dispersive powers of materials used in lenses of an achromatic doublet are in the ratio 5:3. If the ….

Dispersive powers of materials used in lenses of an achromatic doublet are in the ratio 5:3. If the focal length of concave lens is 15 cm, then the focal length of the other lens will be

## When a train is at a distance of 2km, its engine sounds a whistle. A man near the railway track hear….

When a train is at a distance of 2km, its engine sounds a whistle. A man near the railway track hears the whistle directly and by placing his ear against the track of the train. If the two sounds are heard at an interval of 5.2 s, find the...

## In an acute – angled triangle ABC, points D, E and F are the feet of the perpendiculars from A, B an….

In an acute – angled triangle ABC, points D, E and F are the feet of the perpendiculars from A, B and C onto BC, AC and AB, respectively. H is the orthocentre of ∆ABC . If sin A = 3/5 and BC = 39, then the length of...

## The locus of the midpoints of the chords of the circle which are tangents to the hyperbola is….

The locus of the midpoints of the chords of the circle which are tangents to the hyperbola is

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## Find θ ∈ π 2 , 3 π 2 satisfying 2 cos 2 θ + sin θ ≤ 2 …..

Find θ ∈ π 2 , 3 π 2 satisfying 2 cos 2 θ + sin θ ≤ 2 .

## If one of the diagonal of a square is along the line x = 2y and one of its vertices is (3, 0), then ….

If one of the diagonal of a square is along the line x = 2y and one of its vertices is (3, 0), then its sides through this vertex are given by, the equations

## There are 4 white and 3 black balls in a box. In another box there are 3 white and 4 black balls. An….

There are 4 white and 3 black balls in a box. In another box there are 3 white and 4 black balls. An unbiased dice is rolled. If it shows a number less than or equal to 3 then a ball is drawn from the first box but if...

## Suppose then f ‘ (1/4) is equal to….

Suppose then f ‘ (1/4) is equal to

## If x = 9 is the chord of contact of the hyperbola , then the equation of the corresponding pair of….

If x = 9 is the chord of contact of the hyperbola , then the equation of the corresponding pair of tangents is

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