List of practice Questions

A solid cylinder rolls up an inclined plane of inclination $\theta$ with an initial velocity $v$. How far does the cylinder go up the plane?
A solenoid of length 50 cm and a radius of cross-section 1 cm has 1000 turns of wire wound over it. If the current carried is 5 A, the magnetic field on its axis, near the centre of the solenoid is approximately (permeability of free space $\mu _0=4 \pi \times 10^{-7} T-mA^{-1}) $
A soap film is formed on a rectangular frame of length 0.07m dipping in soap solution. The frame hangs from the arm of a balance. An extra weitht of $0.38 \times 10^{-3}$ kg is to be placed in opposite pan to balance the pull on the frame.The surface tension of the soap solution. $(g = 9.8 m/s^2)$
A solenoid has an inductance of $10$ henry and a resistance of $2$ ohm. It is connected to a $10$ volt battery. How long will it take for the magnetic energy to reach $1/4$ of its maximum value?
A solenoid is connected to a battery so that a steady current flows through it. If an iron core is inserted into the solenoid, the current will
A solenoid of length 0.4 m and having 500 turns of wire carries a current of 3.0 A. A thin coil having 10 turns of wire and of radius 0.01 m carries a current of 0.4 A. Calculate the torque required to hold the coil in the middle of the solenoid with its axis perpendicular to the axis of the solenoid.
A small telescope has an objective lens of focal length $144\, cm$ and an eye piece of focal length $6.0\, cm$. What is the separation between the objective and the eye piece?
A small town with a demand of $800\,kW$ of electric power at $220\,V$ is situated $15\,km$ away from an electric plant generating power at $440\,V$. The resistance of the two wire line carrying power is $0.5\,\Omega$. per $km$. The town, gets power from the line through a $4000-220\,V$ step down transformer at a substation in the town. The line power loss in the form of heat is
A small block of mass $M$ moves on a frictionless surface of an inclined plane, as shown in the figure. The angle of the incline suddenly changes from $60^?$ to $30^?$ at point $B$.
The block is initially at rest at $A$. Assume that collisions between the block and the incline are totally inelastic, the speed of the block at point $C$, immediately before it leaves the second incline is
A small hole is made at the centre of the magnet then its magnetic moment
A small square loop of wire of side $l$ is placed inside a large square loop of wire of side $L ( L > > l)$ . The loops are coplanar and their centres coincide . The mutual inductance of the system is proportional to
A slit of width a is illuminated by white light. The first minimum for red light $\left(\lambda = 6500 ?\right) $ will fall at $\theta = 30^{\circ}$ when $a$ will be
A small angle prism $(\mu = 1.62)$ gives a deviation of $4.8^{\circ}$ . The angle of prism is
A signal which can be green or red with probability $\frac{4}{5} $ and $ \frac{1}{5} $ respectively, is received by station A and then transmitted to station B. The probability of each station receiving the signal correctly is $\frac{ 3}{4} $ If the signal received at station B is green, then the probability that the original signal green is
A simple microscope consists of a concave lens of power 10D and a convex lens of power 15 D. Its magnification at near point is (least -distance-of distinct vision, D = 25 cm)
A simple pendulum of length 1 m has a wooden bob of mass $ 1 \,kg $ . It is struck by a bullet of mass $ 10^{-2}\, kg $ moving with a speed of $ 2 \times 10^2\, ms^{-1} $ . The height to which the bob rises before swinging back is (Take $ g = 10 \,ms^{-2} $ )
A set contains $k$ elements. The power set of this set contains_______ elements.
A set of atoms in an excited state decays
A sex gland which contributes fluid containing sugar fructose that provides spermatozoa energy for swimming and hormone prostaglandins that stimulate contractions in the female reproductive tract to aid sperm-ovum interaction is
A shopkeeper sells three types of flower seeds $A_{1}$, $A_{2}$ and $A_{3}$. They are sold as a mixture, where the proportions are $4:4:2$, respectively. The germination rates of the three types of seeds are $45\%$, $60\%$ and $35\%$. calculate the probability $(i)$ of a randomly chosen seed to germinate. $(ii)$ that it will not germinate given that the seed is of type $A_{3}$. $( iii)$ that it is of the type $A_{2}$ given that a randomly chosen seed does not germinate.
A set contains (2n + 1) elements. If the number of subsets of this set which contain at most n elements is 4096, then the value of n is
The range of the function $f\left(x\right)=\frac{x^{2}-x+1}{x^{2}+x+1}$ where $x \in R$
Which of the following are not equivalence relations on I?
A sequence containing a finite number of terms is called a...................
A set A has 3 elements and another set B has 6 elements. Then