The area (in sq. units) of the smaller portion enclosed between the curves, x2 + y2 = 4 and y2 = 3x, is :

The following statement $$\left(p\to q\right)\to \left[\left(\sim p\to q\right)\to q\right]$$ is :

Contrapositive of the statement ‘If two numbers are not equal, then their squares are not equal’, is :

The proposition $$\left(\sim p\right)\vee \left(p\wedge \sim q\right)$$ is equivalent to :

Time (T), velocity (C) and angular momentum (h) are chosen as fundamentalquantities instead of mass, length and time. In terms of these, the dimensions of mass would be :

A physical quantity P is described by the relation P = a$${}^{\text{raise}0.5ex1/\text{lower}0.25ex2}$$ b2 c3 d$$-$$4 If the relative errors in the measurement of a, b, c and d respectively, are 2%, 1%, 3% and 5%, then the relative error in P will be :

The following observations were taken for determining surface tension T of water by capillary method: diameter of capillary, D = 1.25 $$\times$$ 10-2 m rise of water, h = 1.45 $$\times$$ 10-2m Using g = 9.80 m/s2 and the simplified relation T = {{rhg} \over 2} \times {10^3}N/m, the possible error in surface tension is closest to :

Let the refractive index of a denser medium with respect to a rarer medium be n12 and its critical angle be θC . At an angle of incidence A when light is travelling from denser medium to rarer medium, a part of the light is reflected and the rest is refracted and the angle between reflected and refracted rays is 90o. Angle A is given by :

In an experiment a convex lens of focal length 15 cm is placed coaxially on an optical bench in front of a convex mirror at a distance of 5 cm from it. It is found that an object and its image coincide, if the object is placed at a distance of 20 cm from the lens. The focal length of the convex mirror is :

A diverging lens with magnitude of focal length 25 cm is placed at a distance of 15cm from a converging lens of magnitude of focal length 20cm. A beam of parallel light falls on the diverging lens. The final image formed is:

Which of the following statements is false?

The figure shows three circuits I, II and III which are connected to a 3V battery. If the powers dissipated by the configurations I, II and III are P1 , P2 and P3 respectively, then :

In a meter bridge experiment resistances are connected as shown in the figure. Initially resistance P = 4 $$\Omega$$ and the neutral point N is at 60 cm from A. Now an unknown resistance R is connected in series to P and the new position of the neutral point is at 80 cm from A. The value of unknown resistance R is :

A uniform wire of length 1 and radius r has a resistance of 100 $$\Omega$$. It is recast into a wire of radius {r \over 2}. The resistance of new wire will be :

A 9 V battery with internal resistance of 0.5 $$\Omega$$ is connected across an infinite network as shown in the figure. All ammeters A1, A2, 3 and voltmeter V are ideal. Choose correct statement.

A potentiometer PQ is set up to compare two resistances as shown in the figure. The ammeter A in the circuit reads 1.0 A when two way key K3 is open. The balance point is at a length $$\ell$$1 cm from P when two way key K3 is plugged in between 2 and 1, while the balance point is at a length $$\ell$$2 cm from P when key K3 is plugged in between 3 and 1. The ratio of two resistances {{{R_1}} \over {{R_2}}}, is found to be :

In the given circuit, the current in each resistance is:

When a current of 5 mA is passed through a galvanometer having a coil of resistance 15$$\Omega$$, it shows full scale deflection. The value of the resistance to be put in series with the galvanometer to convert it into a voltmeter of range 0 – 10V is:

Two particles A and B of equal mass M are moving with the same speed $$\upsilon$$ as shown in the figure. They collide completely inelastically and move as a single particle C. The angle $$\theta$$ that the path of C makes with the X-axis is given by :

Two tubes of radii r1 and r2, and lengths l1 and l2 , respectively, are connected in series and a liquid flows through each of them in stream line conditions. P1 and P2 are pressure differences across the two tubes. If P2 is 4P1 and l2 is {{{1_1}} \over 4}, then the radius r2 will be equal to :