A particle is confined to move in circular path with decreasing speed. Which of the following is correct.

(1)Angular momentum is constant

(2) Only the direction of L is constant

(3) Acceleration is always directed towards the centre

(4) Particle moves in spiral path.

A satellite is revolving in a circular orbit at a height ‘$$h$$’ from the earths surface (radius of earth $$R$$; $$h < < R$$). The minimum increase in its orbital velocity required, so that the satellite could escape from the earths gravitational field, is close to : (Neglect the effect of atmosphere.)

1) $$\sqrt{2gR}$$
2) $$\sqrt{gR}$$
3) $$\sqrt{gR/2}$$
4) $$\sqrt{gR}\left(\sqrt{2}-1\right)$$

If α,β are the roots of x²+px+q=0 and γ,δ are the roots of x²+px+r=0, then

$$ \left(\alpha -\gamma \right) \left(\alpha -\delta \right)/\left(\beta -\gamma \right) \left(\beta -\delta \right) =$$

1) 1

2) q

3) r

4) q + r

The number of real roots of the equation |x|² – 3|x| + 2 = 0 is

1) 4

2) 3

3) 2

4) 1

I. H—C—H angle in CH₄
II. Cl—B—CI angle in BCl₃
III. F—I—F angle in IF₇ in a plane 
IV. I—I—I angle in I^-₃
Increasing order of above bond angles is

1) I < II < III < IV
2) II < I < III < IV
3) III < I < II < IV
4) IV < II < I < III

 A wire tension 225 N produces 6 beats per second when it tuked with a fork, when the tension changed to 256 N, it again tuned with the same tuning fork to no. of beats remained unchanged, the frequency of tuning fork will be

(1) 186 

(2) 280

(3) 225

(4) 256

In a simple metre-bridge circuit, the gaps are bridged by coils P and Q having the smaller resistance. A balance is obtained when the jockey key makes contact at a point of the bridge wire 40 cm from the P end. On shunting the coi1 Q with a resistance of 50 ?, the balance point is moved through 10 cm. The resistance P and Q are

$$\dfrac{dy}{dx}=e^{-2y},x=5\Rightarrow y=0,$$ then &#160;$$y=3,find\ the\ value\ of\ 2x$$.

1) e⁵ + 9
2) e⁶ + 9
3) e⁸ + 9
4) e⁴ + 9
.

An open vessel containing air at 27^oC is heated to 127^oC. The fraction of air originally present in the bottle that is expelled is:

1) 50%
2) 25%
3) 40%
4) 33%

Nine-fifth of the temperature in centrigrade (C) of a body plus 32^o is equal to the temperature of the same body in Fahrenheit (F). Find F, when C=55^o

1) 131^o

2) 1201^o

3) 140^o

4) 166^o