List of practice Questions

If a$_1$ = 4 and $a_{n+1}=a_{n}+4n\quad for\quad n\ge1. $ then the value of a$_{100}$ is

If $a$ is positive and if $A$ and $G$ are the arithmetic mean and the geometric mean of the roots of $ {{x}^{2}}-2ax+{{a}^{2}}=0 $ respectively, then

Three point charges q, - 2q and - 2q are placed at the vertices of an equilateral triangle of side a. The work done by some external force to in crease their separation to 2a will be

As per this diagram a point charge +q is placed at the origin O. Work done in taking another point charge -Q from the point A [co-ordinates (0,a)] to another point B [coordinates (a,0)] along the straight path AB is:
 

A solid cylinder rolls down an inclined plane of height 3 m and reaches the bottom of plane with angular velocity, of 2 $ \sqrt {2} rads ^{-1} $ . The radius of cylinder must be (Take g = 10 $ ms ^{-2}$ )

A wire of natural length $ l, $ Youngs modulus $ Y $ and area of cross-section $ A $ is extended by $ x $ . Then the energy stored in the wire is given by

The element with atomic number 117 has not been discovered yet. In which family would you place this element if discovered?

Which one of the following is not a sulphide ore?

A ray of light passes through an equilateral prism such that an angle of incidence is equal to the angle of emergence and the latter is equal to $ \frac{3}{4} $ th the angle of prism. The angle of deviation is:

A sample of phosphorus trichloride $(PCl_3)$ contains 1.4 moles of the substance. How many atoms are there in the sample ?

A transverse wave is described by the equation $ y={{y}_{0}}\sin 2\pi \left( ft-\frac{x}{\lambda } \right). $ The maximum particle velocity is equal to four times the wave velocity, if

After terminal velocity is reached, the acceleration of a body falling through a fluid is

Aldehydes that do not undergo aldol condensation are (1) propanal (2) trichloroethanal (3) methanal (4) ethanal (5) benzaldehyde

Cetyltrimethylammonium bromide is a popular

Disaccharide in milk is

For two isomorphous crystals $A$ and $B$, the ratio of density of $A$ to that of $B$ is $1.6$ while the ratio of the edge length of $B$ to that of $A$ is $2$. If the molar mass of crystal $B$ is $200\,g\,mol^{-1}$, then that of crystal $A$ is

Gabriel synthesis is used for the synthesis of:

Homolytic fission of a covalent bond leads to the formation of

Identify the product and its colour when $MnO_2$ is fused with solid $KOH$ in the presence of $O_2$

The carbonate that will not decompose on heating is

The charge on the central metal ion in the complex $[Ni(CO)_4]$ is

The correct order of boiling points of $2, 2-dimethylpropane$, $2-methylbutane$ and $n-pentane$ is

The dihalogen derivative $'X'$ of a hydrocarbon with three carbon atoms reacts with alcoholic $ KOH $ and produces another hydrocarbon which forms a red precipitate with ammoniacal $ C{{u}_{2}}C{{l}_{2}} $ . $ 'X' $ gives an aldehyde on reaction with aqueous $ KOH $ . The compound $'X'$ is

A particle of mass $m$ and charge $q$ with an initial velocity $v$ is subjected to a uniform magnetic field $B$ along the vertical direction. The particle will

A particle of mass m is moving along the x-axis under the potential $V (x) = \frac{kx^2}{2} + \frac{\lambda}{x}$, where $k $ and $\lambda$ are positive constants of appropriate dimensions. The particle is slightly displaced from its equilibrium position. The particle oscillates with the angular frequency $\omega$ given by