List of practice Questions

A gardener is digging a plot of land. As he gets tired, he works more slowly. After $' t '$ minutes he is digging at a rate of $\frac {2} {\sqrt {t}} $square metres per minute. How long will it take him to dig an area of $40$ square metres ?
Two concentric hollow spherical shells have radii $ r $ and $ R \left(R\,>>\,r\right) $ . A charge $ Q $ is distributed on them such that the surface charge densities are equal. The electric potential at the centre is
A steady current flows in a long wire. It is bent into a circular loop of one turn and the magnetic field at the centre of the coil is $ B $ . If the same wire is bent into a circular loop of $ n $ turns, the magnetic field at the centre of the coil is
A balloon with mass m is descending down with an acceleration a (where a < g). How much mass should be removed from it so that it starts moving up with an acceleration $a$?
Which property of colloids is not dependent on the charge on colloidal particles?
Which of the following will be most stable diazonium salt $(R\, N^{+}_{2}\,X^{-})$ ?
Which of the following will not be soluble in sodium hydrogen carbonate?
If $x+y\leq2,x \geq 0,y \geq 0$ the point at which maximum value of $3x + 2y$ attained will be
If the function $f(x)$ defined by $\frac {x^{100}}{100}+\frac {x^{99}}{100}+\dots \frac {x^2}{100}+x+1$ then $f'(0)$ is equal to
The general solution of the differential equation $\frac {dy}{dx}+\frac {y}{x}=3x$ is
Given $0 \leq x \leq \frac {1}{2}$ then the value of $\tan \left[\sin^{-1}\left\{\frac{x}{\sqrt {2}}+\frac {\sqrt {1-x^2}} {\sqrt {2}}\right\}-\sin^{-1}x\right]$ is
A stone of mass $0.05 \,kg$ is thrown vertically upwards. What is the direction and magnitude of net force on the stone during its upward motion ?
When longitudinal wave propagates, what happens in the region of compressions and rarefactions?
Energy of one mole of photons of radiation whose frequency is $ 5\times 10^{14}\,Hz $ is
A crystalline solid $X$ reacts with $dil. HCl$ to liberate a gas $Y.Y$ decolourises acidified $KMnO_4$. When a gas $'Z'$ is slowly passed into an aqueous solution of $Y$, colloidal sulphur is obtained. $X$ and $Z$ could be, respectively
A metallic oxide reacts with water to form its hydroxide, hydrogen peroxide and also liberates oxygen. The metallic oxide could be
The equivalent resistance of two resistors connected in series is $6\, \Omega$ and their parallel equivalent resistance is $\frac{4}{3} \Omega$. What are the values of resistances ?
Period of geostationary satellite is
If the line px + qy = 0 coincides with one of the lines given by $ax^2 + 2hxy + by^2 = 0$, then
A 150 watt bulb emits light of wavelength 6600 $?$ and only 8% of the energy is emitted as light. How many photons are emitted by the bulb per second?
Schottky defect in crystals is observed when
The radius of an atom is $300\,pm$. If it crystallizes in a face-centered cubic lattice, length of the edge of the unit cell is
In the following sets of ions, which one is not isoelectronic with the rest of the species? $ { O^{2-}, F^- , Na, Mg^{2+}, Al^{3+}, Ne} $
The subtangent at $x = \pi/2$ on the curve $y = x \sin x $ is
If the circle $x^2+y^2+2\,gx+2fy+=0,$ and $x^2+y^2+2g'x+2f'y$ touch each other, then