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Consider the following statements: (A) Propanal and propanone are functional isomers; (B) Ethoxyethane and methoxypropane are metamers; (C) But-2-ene shows optical isomerism; (D) But-1-ene and but-2-ene are functional isomers; (E) Pentane and 2,2-dimethylpropane are chain isomers. The correct statements are:

$C_{6}H_{12}O_{3}$ gives positive iodoform test. On hydrolysis with dilute acid, the product formed gives both Tollens' test and iodoform test. Find the correct structure.

Two mechanical waves travel on strings of equal length L and equal tension T. The linear mass densities are in ratio $\frac{\mu_{1}}{\mu_{2}}=\frac{1}{2}$. Find the ratio of time taken for a wave pulse to travel from one end to the other.

Find the change in internal energy of a gas if its temperature changes by 10K. Moles=10, $C_{p}=7 cal K^{-1}mol^{-1}$, $R=2~cal~K^{-1}mol^{-1}$.

In the binomial expansion of $(ax^{2}+bx+c)(1-2x)^{26}$, the coefficients of $x$, $x^{2}$, $x^{3}$ are 56, 0 and 0 respectively. Then the value of $(a+b+c)$ is:

If the domain of the function $\cos^{-1}(\frac{2x-5}{11x-7})+\sin^{-1}(2x^{2}-3x+1)$ is $[a,b]$, then the value of $\frac{1}{ab}$ is:

Out of the following, how many compounds have tetrahedral geometry? $NH4^{+}$, $XeF4$, $[NiCl4]^{2-}$, $[PtCl4]^{2-}$, $[Cu(NH3)4]^{2+}$, $BF3$, $[Ni(CO)4]$

1 g of $AB_{2}$ is dissolved in 50 g of a solvent such that $\Delta T_{f}=0.689~K.$ When 1 g of AB is dissolved in 50 g of the same solvent, $\Delta T_{f}=1.176~K$. Find the molar mass of $AB_{2}$. (Report to nearest integer).

Two rods of equal length 60 cm each are joined together end to end. The coefficients of linear expansion are $24\times10^{-6\circ}C^{-1}$ and $1.2\times10^{-5\circ}C^{-1}$. Initial temperature $30^{\circ}C$ is increased to $100^{\circ}C$. Find final length (in cm).

A wave propagates whose electric field is given by $\vec{E}=69~\sin(\omega t-kx)\hat{j}$. Find the direction of the magnetic field.

If $f(3)=18$, $f'(3)=0$ and $f''(3)=4$ then the value of $\lim_{x\rightarrow1}\ln(\frac{f(x+2)}{f(3)})^{\frac{18}{(x-1)^{2}}}$ is:

The value of $\int_{\frac{\pi}{6}}^{\pi}\frac{\pi+4x^{11}}{1-\sin(|x|+\frac{\pi}{6})}dx$ is:

If O is the vertex of the parabola $x^{2}=4y,$ Q is a point on the parabola. If C is the locus of the point which divides OQ in the ratio $2:3,$ then the equation of the chord of C which is bisected at the point (1,2) is: (Duplicate Question)

Which of the following resonating structures is the most stable?

Given below are two statements. Statement I: All the pairs of molecules $(PbO,PbO_{2})$; $(SnO,SnO_{2})$ and $(GeO,GeO_{2})$ contain amphoteric oxides. Statement II: $AlCl_{3}$, $BH_{3}$, $BeH_{2}$ and $NO_{2}$ all have incomplete octet.

An ideal solenoid is kept with its axis vertical. A current $I_{0}$ is flowing in the solenoid. A charge q is thrown vertically downward inside the solenoid. The acceleration of the charged particle is:

Find the volume flow rate in the Venturi meter shown below in which water is flowing. Given $\frac{A}{a}=2$, $A=\sqrt{3}m^{2}$, difference in levels is 5 cm and $\rho=1000~kg~m^{-3}$.

If $A=\{1,2,3,4,5,6\}$ and $B=\{1,2,3,...,9\}$, then the number of strictly increasing functions $f:A\rightarrow B$ such that $f(i)\ne i$ for all $i$ is:

If the mean and variance of observations $x, y, 12, 14, 4, 10, 2$ is 8 and 16 respectively, where $x>y$, then the value of $3x-y$ is:

Ellipse E: $\frac{x^{2}}{36}+\frac{y^{2}}{16}=1$. A hyperbola is confocal with the ellipse and the eccentricity of the hyperbola is equal to 5. If the principal axis of the hyperbola is the x-axis, then the length of the latus rectum of the hyperbola is: