Inequalities L-10 | Wavy Curve Method (Part B) | By Naman Agarwal | JEE Mains and Advanced | CBSE

A capacitor with capacitance 6 xx 10^(-5) F is charged by connecting it to a 12 -V battery. The capacitor is disconnected from the battery and connected across an inductor with L = 1.50 H . a. What are the angular frequency omega of the electrical oscillations and the period of these oscillations (the time for one oscillation)? b. What is the intial charge on the capacitor? c. How much energy is intially stored in the capacitor? d. What is the charge on the capacitor 0.0230 s after the connecting to the inductor is made? Interpret the sign of the your answer. e. At the times given in part (d), what is the current in the inductor? Interpret the sign of your answer. f. At the time given in part (d), how much electrical energy is stored in the capactior and how much is stored in the inductor?

The equation of a curve passing through (1,0) for which the product of the abscissa of a point P and the intercept made by a normal at P on the x-axis equal twice the square of the radius vector of the point P is (a) ( b ) (c) (d) x^(( e )2( f ))( g )+( h ) y^(( i )2( j ))( k )=( l ) x^(( m )4( n ))( o ) (p) (q) (b) ( r ) (s) (t) x^(( u )2( v ))( w )+( x ) y^(( y )2( z ))( a a )=2( b b ) x^(( c c )4( d d ))( e e ) (ff) (gg) (c) ( d ) (e) (f) x^(( g )2( h ))( i )+( j ) y^(( k )2( l ))( m )=4( n ) x^(( o )4( p ))( q ) (r) (s) (d) None of these

In a Young's double slit experiment, the light sources is at distance l_1 = 20mu m and l_2 = 40 mu m form the main slit. The light of wavelength lambda = 500nm is incident on slits separated at a distance 10mu m . A screen is placed at a distance D = 2 away from the slits as shown in figure. Find (a) the values of theta relative to the central line where maxima appear on the screen? (b) how many maxima will appear on the screen? what should be the minimum thickness of a slab of refractive index 1.5 placed on the path of one of the ray so that minima occurs at C ? .

A curved glass vessel full of water upto a height of 10 cm has a bottom of area 10 cm^(2) , top of area 30 cm^(2) and volume 1 L. (i) Find the force exerted by the water on the bottom. (ii) Find the resultant force exerted by the sides of the glass on the water. (iii) If the glass vessel is covered by a jar and the air inside the jar is completely pumped out, what will be the answers to parts (a) and (b) (iv) If a glass vessel of different shape is used provided the height, the bottom area and the volume are unchanged, will the answers to parts (a) and (b) change. (Take, g=10 ms^(-2) , density of water = 10^(3) kgm^(-2) and atmospheric pressure =1.01xx10^(5)Nm^(-2))

A block A of mass 2 kg is placed over another block B of mass 8 kg and supported by a ledge L fixed on block B on its smooth surface as its extended part. If a force F=100 N is applied on block B , it starts moving on a smooth horizontal surface. Find the force exerted by block B on is 25 N . (Take g=10m//s^(2) )

The electric field part of the electromagnetic wave in vacuum is given by E= 6 cos [1.2 ("rad")/(m) y + 3.6 xx 10^(8) ("rad")/(s) t ] l (N)/(C ) , then find (a) Frequency of propagation (f) (b) Wavelength (lambda) (c) Direction of propagation (d) Amplitude of magnetic field in electromagnetic wave (e) An expression for magnetic field part of the wave.

Figure shows a conducting rod of length l = 10 cm , resistance R and mass m = 100 mg moving vertically downward due to gravity. Other parts are kept fixed. Magnetic filed is B = 1 T . MN and PQ are vertical, smooth, the capacitor is C = 10mF . The rod is released from rest. Find the maximum current (in mA) in the circuit.

Figure shows a conducting rod of length l = 10 cm , resistance R and mass m = 100 mg moving vertically downward due to gravity. Other parts are kept fixed. Magnetic filed is B = 1 T . MN and PQ are vertical, smooth, the capacitor is C = 10mF . The rod is released from rest. Find the maximum current (in mA) in the circuit.

The formula in which a certain integral involving some parameters in connected with some integrals of lower order is called a reduction formula. In most of the cases the reduction formula is obtained by the process of integrating by parts. Of course, in some cases the methods of differentiation are adopted.Now answer the question:If I_(m,p)=intx^m(a+bx^n)^pdx and I_(m,p)=(x^(m+1)(a+bx^n)^p)/(m+1)-f(m,n,p,b)I_(m+n,p-1) , then the value of f(1,2,3,4) is equal to (A) 8 (B) 10 (C) 12 (D) none of these