List of practice Questions

$\frac{1}{e^{3 x}}\left(e^{x}+e^{5 x}\right)=a_{0}+a_{1} x +a_{2} x^{2}+\ldots$ $\Rightarrow 2 a_{1}+2^{3} a_{3}+2^{5} a_{5}+\ldots$ is equal to

The roots of $(x-a)(x-a-1)+(x-a-1)(x-a-2) +(x-a)(x-a-2)=0, a \in R$ are always

Atomic mass of $ {{^{13}}_{6}}C $ is 13.00335 amu and its ea-s number is 13.0. If 1 amu = 931 MeV, binding energy of the neutrons present in the nucleus is

For a first order reaction at 27$^{\circ}$C, the ratio of time required for 75% completion to 25% completion of reaction is

The dissociation constants for acetic acid and $HCN$ at $25^{\circ} C$ are $1.5 \times 10^{-5}$ and $4.5 \times 10^{-10}$ respectively. The equilibrium constant for the equilibrium $CN ^{-}+ CH _{3} COOH \rightleftharpoons HCN + CH _{3} COO ^{-}$ would be :

Which one of the elements with the following outer orbital configurations may exhibit the largest number of oxidation states?

A glass slab of thickness 8 cm contains the same number of waves as 10 cm long path of water when both are traversed by the same monochromatic light. If the refractive index of water is $ \frac{4}{3} $ , the refractive index of glass is

The main difference between formic acid and acetic acid is that formic acid is

If $A$ and $B$ are square matrices of the same order such that $(A + B) (A -B) = A^2-B^2$ then $(ABA^{-1} )^2=$

Compared to blood our lymph has

The negation of $p{\land}(q \to \sim r)$ is

Which one of the following is the correct matching of the events occurring during menstrual cycle?

A bar magnet having a magnetic movement of $2 \times 10^{4} JT ^{-1}$ is free to rotate in a horizontal plane. A horizontal magnetic field $B =6 \times 10^{-4}$ T exists in the space. The work done in taking the magnet slowly from a direction parallel to the field to a direction $60^{\circ}$ from the field is :

Adipic acid is used in the preparation of

Which one of the following is the correct quadratic form of the Ostwald's dilution law equation?

When the cold and hot junctions of a thermocouple are interchanged, the thermo emf

The one which decreases with dilution is

The ore that is concentrated by Froth Floatation process is

The characteristic not related to alkali metal is

A covalent molecule $AB_3$ has pyramidal structure. The number of lone pair and bond pair electrons in the molecule are respectively

In electrophillic aromatic substitution reaction, the nitro group is meta directing because it

If $'n '$ is a positive integer, then $n^3 + 2n$ is divisible by

On the set of integers $Z$. define $f: Z \to Z$ as $ f(n) = \begin{cases} n/2 & \quad \text{if } n \text{ is even}\\ 0 & \quad \text{if } n \text{ is odd}\\ \end{cases} $ then $'f'$ is

$_6C^{14}$ and $7_N^{15}$ are examples of