List of practice Questions

The blue colour of the sky is due to ?

\(4x^2+hxy+y^2\) = 0 represent coincident lines. Find h = ?

Sum of first 20 terms: 5, 11, 19, 29, 41

When 2 gm magnesium reasts with excess of HCl and H₂ gas is produced then the volume of H₂ gas produced is ____ × 10^–2liter at STP. (Nearest Integer)

Consider the following molecules : Br₃O₈, F2O, H2S4O6, H₂S₅O₆, and C₃O₂. Count the number of atoms existing in their zero oxidation state in each molecule. Their sum is _______.

A plain polarized blue light ray is incident on a prism such that there is no reflection from the surface of the prism. The angle of deviation of the emergent ray is \(\delta\) = 60\(^{\circ}\) (figure 1). The angle of min. deviation for red light from the same prism is min \(\delta_{min}\) = 30\(^{\circ}\) (figure 2). If the refractive index of prism material for blue light is √3, then which of the following options is correct?

PPBL = Plane Polarized Blue Light PPRL = Plane Polarized Red Light

S₁ & S₂ are sources of the sound of frequency 656 Hz. S₁ is moving along OP and S₂ is moving on the circle in an anticlockwise direction with a constant speed of 4√2 m\s. P is a detector that is fixed. Select the correct options (V_sound=300m\s)

A thin conducting rod MN of mass 20 gm, length 25 cm, and resistance 10Ω is held on frictionless long perfectly conducting vertical rails as in the figure. There is the uniform magnetic field B₀=4T directed perpendicular to the plane of the rod-rail arrangement. the rod is released from rest at time t=0 and it moves down along the rails assuming air drag is negligible. Match each quantity in L-I with an appropriate value from L-II and choose the correct options(g=10ms\(^{-2}\) and e\(^{-1}\)=0.4)

	List-I		List-II
(P)	At t=0.2s, the magnitude of induced emf in volt	(1)	0.08
(Q)	At t=0.2s, the magnitude of magnetic force in N	(2)	0.14
(R)	At t=0.2s, the power dissipated at heat in watt	(3)	1.20
(S)	The magnitude terminal velocity of the rod in ms\(^{-1}\)	(4)	0.12
		(5)	2.00

The liquid is raising at a rate of 250\(cm^3s^{-1}\) in the container. Value of the capacitance of the container after 10 sec.? (\(\varepsilon_0=9 \times10^{12}C^2N^{-1}m^{-2}\))

The system's center of mass is suspended by a steel wire of torsional spring

Two small particles of mass 20 gm and 30 gm are connected with a rigid massless rod of length of 10 cm. The system's center of mass is suspended by a steel wire of torsional spring constant \(c=1.2\times 10^{-8}\) N.m/rad. If the system is slightly rotated in its plane and the angular frequency of its oscillations in rad/sec is \(n\times 10^{-3}\), then write the value of n.

The Ratio of gravity field due to the earth at high h_P and h_Q from the earth's surface is \(\frac{g_{P}}{g_{Q}}=\frac{36}{25}.\) If \(h_P=\frac{R}{2}\), then the value of h_Q will be