List of practice Questions

C5H10 \(\xrightarrow{h\nu}\) possible structural isomers?
The sum of the coefficients of \(x^{499}\) and \(x^{500}\) in \[ (1+x)^{1000}+x(1+x)^{999}+x^2(1+x)^{998}+\cdots+x^{1000} \] is:
A block of mass \(5\) kg is moving on an inclined plane which makes an angle of \(30^\circ\) with the horizontal. The coefficient of friction between the block and the inclined plane surface is \(\dfrac{\sqrt{3}}{2}\). The force to be applied on the block so that the block moves {down the plane without acceleration is ________ N. (\( g = 10 \, \text{m s}^{-2} \))}
Let $a_1,a_2,a_3,a_4$ be an A.P. of four terms such that each term of the A.P. and its common difference are integers. If $a_1+a_2+a_3+a_4=48$ and $a_1^2a_2a_3a_4+1^4=361$, then the largest term of the A.P. is equal to
Let \( f \) be a polynomial function such that \[ f(x^2+1)=x^4+5x^2+2,\quad \text{for all } x\in\mathbb{R}. \] Then \[ \int_0^3 f(x)\,dx \] is equal to:
The number of isoelectronic species among S2−, C4−, Mn2+, Co3+ and Fe3+ is ‘n’.

If ‘n’ moles of AgCl is formed during the reaction of the complex with formula
CoCl2(en)2NH3
with excess AgNO3 solution, then the number of electrons present in the t2g orbital of the complex is ________.

Write the correct order of rate of reaction of following with PhN$_2$Cl

 

For first order reaction, rate constant at 27°C and t°C is $1.5 \times 10^3$ and $4.5 \times 10^3$ respectively. If the activation energy of the reaction is 60 kJ, then find the temperature $t$.
An alkane on complete combustion required 8 moles of O2. Find out the number of carbon and hydrogen in the alkane.
Compound of molecular formula C5H10 can not decolorize Baeyer's reagent, how many monohalo products (structural) are obtained by all isomers of C5H10.
For Diatomic gas, find the ratio of \(\Delta Q : \Delta U : W\) for an isobaric process.
The correct increasing order of bond length among the following is
The time period of a simple harmonic oscillator is \[ T=2\pi\sqrt{\frac{m}{k}}. \] Measured value of mass \(m\) has an accuracy of \(10%\) and time for 50 oscillations of the spring is found to be \(60\,\text{s}\) using a watch of 2 s resolution. Percentage error in determination of spring constant \(k\) is:
The nuclides of $^{197}_{79}\mathrm{Au}$ and $^{196}_{80}\mathrm{Hg}$ are called ______ of each other
An organic compound undergoes first order decomposition. The time taken for decomposition to \(\dfrac{1}{8}\) and \(\dfrac{1}{10}\) of its initial concentration are \(t_{1/8}\) and \(t_{1/10}\) respectively. Find the value of \[ \frac{t_{1/8}}{t_{1/10}}\times10 \] (Given: \(\log 2 = 0.3\))

The magnetic field at the centre of a current carrying circular loop of radius \(R\) is \(16\,\mu\text{T}\). The magnetic field at a distance \(x=\sqrt{3}R\) on its axis from the centre is ____ \(\mu\text{T}\).

Which of the following best represents the temperature versus heat supplied graph for water, in the range of \(-20^\circ\text{C}\) to \(120^\circ\text{C}\)? 

For two identical cells each having emf \(E\) and internal resistance \(r\), the current through an external resistor of \(6\,\Omega\) is the same when the cells are connected in series as well as in parallel. The value of the internal resistance \(r\) is ________ \(\Omega\).
Given below are two statements: Statement I: A plane wave after passing through a prism remains a plane wave, but passing through a small pin hole may become a spherical wave. Statement II: The curvature of a spherical wave emerging from a slit will increase for increasing slit width. In the light of the above statements, choose the correct answer:
The magnitudes of power of a biconvex lens (refractive index \(1.5\)) and that of a plano-convex lens (refractive index \(1.7\)) are same. If the curvature of the plano-convex lens exactly matches with the curvature of the back surface of the biconvex lens, then the ratio of radii of curvature of the front and back surfaces of the biconvex lens is:
Let \( y = y(x) \) be the solution of the differential equation \[ x\frac{dy}{dx} - \sin 2y = x^3(2 - x^3)\cos^2 y,\; x \ne 0. \] If \( y(2) = 0 \), then \( \tan(y(1)) \) is equal to:
The largest value of $n$, for which $40^n$ divides $60!$, is
Two iron solid discs of negligible thickness have radii $R_1$ and $R_2$ and moment of inertia $I_1$ and $I_2$, respectively. For $R_2 = 2R_1$, the ratio of $I_1$ and $I_2$ would be $1/x$, where $x =$ _____.
A wooden cubic block of relative density $0.4$ is floating in water. Side of cubic block is $10\ \text{cm}$. When a coin is placed on the block the block dips $0.3\ \text{cm}$ in equilibrium. Weight of coin is
If \( y = f(x) \) is the solution of the differential equation \( (1 + \sin x) \frac{dy}{dx} + \cos x = 0 \), such that \( f(0) = 0 \), then \( f\left( \frac{\pi}{2} \right) \) is equal to