List of practice Questions

A differential equation $ \frac{dy}{dx}= \left(y+4x -4\right)^{2} $ is given. At $ x = 0, y = 4 $ the solution of this differential equation is given by

The values of $ x $ for which $ 4^x + 4^{1-x} - 5 < 0 $ , is given by

In which of the following intervals, the function $ y(x) = x^3 - 3x^2 - 9x + 5 $ is always decreasing?

The number of principal solutions of $\tan 2 \theta = 1$ is

The Tyndall effect is observed only when following conditions are satisfied (a) The diameter of the dispersed particles is much smaller than the wavelength of the light used. (b) The diameter of the dispersed particle is not much smaller than the wavelength of the light used (c) The refractive indices of the dispersed phase and dispersion medium are almost similar in magnitude (d) The refractive indices of the dispersed phase and dispersion medium differ greatly in magnitude

The number of $S=O$ and $S-OH$ bonds present in peroxodisulphuric acid and pyrosulphuric acid respectively are :

The de-Broglie wavelength of a neutron in thermal equilibrium with heavy water at a temperature $T$ (Kelvin) and mass $m$, is :

A particle is executing simple harmonic motion with a time period $T$. At time $t = 0$, it is at its position of equilibrium. The kinetic energy - time graph of the particle will look like :

A solid rectangular sheet has two different coefficients of linear expansion $\alpha_{1}$ and $\alpha_{2}$ along its length and breadth respectively. The coefficient of surface expansion is (for $\alpha_{1} t < < 1, \alpha_{2} t < < 1$)

A parallel beam of light is incident on a glass prism in the shape of a quarter cylinder of radius $R \,= \,0.05\, m$ and refractive index n = $1.5$ placed on a horizontal table as shown in the figure. Beyond the cylinder, a patch of light is found whose nearest distance $x$ from the cylinder is

Consider the following reaction,

X is

The volume of water to be added to 100 cm³ of 0.5 N H₂SO₄ to get decinormal concentration i

In which of the following the oxidation number of oxygen has been arranged in increasing order ?

Which of the following region is coldest ?

A solid AB has NaCl structure. If the radius of cation A⁺ is 170 pm, then the maximum possible radius of the anion B^- is

A first order reaction is 50% completed in 1.26 × 10¹⁴ How much time would it takes for 100% completion ?

Flux is used to

Sulphur reacts with chlorine in 1 : 2 ratio and forms X. Hydrolysis of X gives a sulphur compound Y. The hybridization of central atom in the anion Y is

Aqueous 10% NaHCO₃ solution is used as a reagent for identifying 'A'. Which of the following compounds yield 'A' on hydrolysis ?

Which of the following fibres is made of polyamides ?

Match the type of series given in Column I with the wavelength range given in Column II and choose the correct option.

Column I		Column II
A.	Lyman	1.	Ultraviolet
B.	Paschen	2.	Near infrared
C.	Balmer	3.	Far infrared
D.	Pfund	4.	Visible

The electrons identified by quantum numbers n and l, are as follows
(I) n = 4, l = 1
(II) n = 4, l = 0
(III) n = 3, l = 2
(IV) n = 3, l = 1
If we arrange them in order of increasing energy, i.e. from lowest to highest, the correct order is

In the cyanide extraction process of silver from argentite ore, the oxidizing and reducing agents are respectively:

The product of acid hydrolysis of (P) and (Q) can be distinguished by

Clemmensen reaction of ketone is carried out in the presence of: