List of practice Questions

Generally the path of a projectile from the earth is parabolic but it is elliptical for projectile going to a very large height. Up to ordinary height the projectile moves under a uniform gravitational force, but for great heights, projectile moves under a variable force.
One-fourth length of a spring of force constant k is cut away. The force constant of the remaining spring will be
A cyclist rides up a hill at a constant velocity. Determine the power developed by the cyclist if the length of the connecting rod of the pedal is $r = 25 \,cm$, the time of revolution of the rod is $t = 2 \,s$ and the mean force exerted by his foot on the pedal is $F = 15\, kgf$.
If $E=at+bt^2, $ what is the neutral temperature?
The output form of a full wave rectifier is
Genetically engineered bacteria are being employed for production of
A capillary tube of radius $r$ is immersed in water and water rises in it to a height $h$. The mass of water in the capillary tube is $5\,g$. Another capillary tube of radius $2\,r$ is immersed in water. The mass of water that will rise in this tube is
$ {A (C10H_18O) ->[{HCL}] P}$
Degree of unsaturation of $A = 2$, it contains no double or triple bonds.
A bullet of mass $m$ moving with velocity $v$ strikes a suspended wooden block of mass $M$. If the block rises to a $S$ height the initial velocity of the block will be
A body falls freely from the top of a tower. It covers $36\%$ of the total height in the last second before striking the ground level. The height of the tower is
Rhizophora is a characteristic component of
The term biosystematics was coined by
The fungus commonly known as bread mould is
The fundamental frequency of a closed pipe is $220 \,Hz$. If $\frac{1}{4}$ of the pipe is filled with water, the frequency of the first overtone of the pipe now is
A battery is connected to a uniform resistance wire $AB$ and $B$ is earthed. Which one of the graphs below shows how the current density $J $ varies along $AB$?
A winding wire which is used to frame a solenoid can bear a maximum $10\, A$ current. If length of solenoid is $80\, cm$ and its cross-sectional radius is $3\, cm$ then required length of winding wire is $(B=0.2\, T)$
An inductor $ L,\,\,a $ capacitor of $ 20\mu F $ and a resistor of $ 10\Omega $ are connected in series with an $AC$ source of frequency $ 50\,Hz $ . If the current is in phase with the voltage, then the inductance of the inductor is
A rifle shoots a bullet with a muzzle velocity of $ 500\,m{{s}^{-1}} $ at a small target $ 50\,m $ away. To hit the target the rifle must be aimed (take$ g=10\,m{{s}^{-2}}) $
In an $ AC $ circuit the potential difference V and current i are given respectively by $ V=100\sin (100t) $volt and $ i=100\sin \left( 100t+\frac{\pi }{3} \right)mA $ The power dissipated in the circuit will be
Let $f : R \to R$ be a positive increasing function with $\displaystyle \lim_{x \to \infty} \frac{f\left(3x\right)}{f\left(x\right)} =1$ Then $\displaystyle \lim_{x \to\infty} \frac{f\left(2x\right)}{f\left(x\right)} = $
If the vectors $\vec{a} = \hat{i}- \hat{j}+2 \hat{k}, \vec{b} = 2\hat{i}+4 \hat{j}+ \hat{k}$ and $\vec{c} = \lambda\hat{i}+ \hat{j}+\mu \hat{k}$ are mutually orthogonal, then $\left(\lambda, \mu\right) = $
A particle is moving with velocity $\vec{v} = k\left(y\hat{i} + x\hat{j}\right),$ where $k$ is a constant. The general equation for its path is
A block of mass $10\, kg$ is moving in $x$-direction with a constant speed of $10\, m / s$. It is subjected to a retarding force $F=-0.1 \times J / m$ during its travel from $x=20\, m$ to $x=30\, m$. Its final kinetic energy will be :
A $12\, HP$ motor has to be operated $8\, h /$ day. How much will it cost at the rate of $50$ paise/kWh in 10 days?
When an ideal monoatomic gas is heated at consant pressure, fraction of heat energy supplied which increases the internal energy of gas, is