List of top Questions asked in BITSAT- 2026

Evaluate the definite integral: $\int_{0}^{2026} \frac{x^5}{x^5 + (2026 - x)^5} \, dx$

In how many ways can the letters of the word COCHIN be arranged such that the two 'C's are never separated by any other letter?

A current of $2.0\text{ A}$ is passed for 5 hours through an electrolytic cell containing an aqueous solution of a metal salt, depositing $12.0\text{ g}$ of the metal at the cathode. If the atomic mass of the metal is $193\text{ g mol}^{-1}$, find the oxidation state of the metal ion in the solution. (Take Faraday's constant $F = 96500\text{ C mol}^{-1}$).

In an analytical laboratory, a $20.0\text{ mL}$ sample of an aqueous solution containing oxalic acid ($\text{H}_2\text{C}_2\text{O}_4$) requires exactly $16.0\text{ mL}$ of a $0.05\text{ M}$ potassium permanganate ($\text{KMnO}_4$) solution for complete oxidation in a hot, acidic medium ($\text{H}_2\text{SO}_4$). Calculate the molarity of the oxalic acid solution.

During the structural analysis of an unknown aldohexose, a chemist treats a sample with periodic acid ($\text{HIO}_4$). If the carbohydrate is completely cleaved to yield five molecules of formic acid ($\text{HCOOH}$) and one molecule of formaldehyde ($\text{HCHO}$), this diagnostic breakdown directly proves the presence of:

An octahedral coordination complex with the electronic configuration $t_{2g}^4 e_g^0$ is expected to exhibit which of the following magnetic properties and d-d transition characteristics?

The elastic potential energy stored per unit volume (energy density) in a stretched string under a longitudinal tension stress $\sigma$ and material Young's modulus $Y$ is expressed as:
Two wires $X$ and $Y$ of the same material have lengths in the ratio $1:2$ and diameters in the ratio $2:1$. If they are subjected to the same stretching force, the ratio of the elongation produced in wire $X$ to that in wire $Y$ ($\Delta L_X : \Delta L_Y$) is:
A particle moves in a circle of radius $R$ such that its linear speed varies with time $t$ as $v = kt$, where $k$ is a positive constant. The angle $\theta$ between the net acceleration vector and the velocity vector at time $t$ is given by:
A wire of length $L$ and cross-sectional area $A$ is made of a material of Young's modulus $Y$. If it is stretched by an amount $x$, the elastic potential energy stored in the wire is:
The sum of the series $\left(x + \frac{1}{x}\right)^2 + \left(x^2 + \frac{1}{x^2}\right)^2 + \left(x^3 + \frac{1}{x^3}\right)^2 \dots\dots\dots$ up to $n$ terms is:
General solution of $\tan 5\theta = \cot 2\theta$ is:
The distance from the origin to the image of $(1, 1)$ with respect to the line $x + y + 5 = 0$ is:
If $p$ and $q$ be the longest and the shortest distance respectively of the point $(-7, 2)$ from any point $(\alpha, \beta)$ on the curve whose equation is $x^2 + y^2 - 10x - 14y - 51 = 0$, then find the Geometric Mean (G.M.) of $p$ and $q$.
Using the standard electrode potential, find out the pair between which redox reaction is not feasible. \[ \text{E}^\ominus \text{ values: } \text{Fe}^{3+}/\text{Fe}^{2+} = +0.77\text{ V}; \quad \text{I}_2/\text{I}^- = +0.54\text{ V}; \quad \text{Cu}^{2+}/\text{Cu} = +0.34\text{ V}; \quad \text{Ag}^+/\text{Ag} = +0.80\text{ V} \]

A current of $4.0\text{ A}$ is passed through $0.5\text{ L}$ of $0.2\text{ M NaCl}$ solution for $1200\text{s}$. Calculate the $\text{pH}$ of the solution after electrolysis.

Titration of $0.1467\text{ g}$ of primary standard $\text{Na}_2\text{C}_2\text{O}_4$ required $28.85\text{ mL}$ of $\text{KMnO}_4$ solution. Calculate the molar concentration of $\text{KMnO}_4$ solution.

Balance the following redox reaction in acidic medium and determine the stoichiometric coefficient of $\text{H}_2\text{O}$ in the final balanced equation.

\[\text{MnO}_4^-(aq) + \text{Fe}^{2+}(aq) \rightarrow \text{Mn}^{2+}(aq) + \text{Fe}^{3+}(aq)\]

The de-Broglie wavelength of an electron accelerated from rest through a potential difference of $100\text{ V}$ is approximately:

The stopping potential for photoelectrons emitted from a surface illuminated by light of wavelength $\lambda$ is $\text{V}_s$. If the intensity of the incident light is doubled while keeping wavelength identical, the stopping potential will be:

The focal length of a convex lens is $f$ in air. When it is completely immersed in water of refractive index $\frac{4}{3}$, its focal length becomes (take refractive index of glass = 1.5):

A particle moves along a circle of radius $R$ with a constant angular acceleration $\alpha$. If the initial angular velocity is zero, the total acceleration of the particle at time $t$ is:
Let \(\text{L}_1\) be the length of the common chord of the curves \(x^2 + y^2 = 9\) and \(y^2 = 8x\), and \(\text{L}_2\) be the length of the latus rectum of \(y^2 = 8x\), then:
The eccentricity of the ellipse whose major axis is three times the minor axis is:
If the eccentricity and length of latus rectum of a hyperbola are \(\frac{\sqrt{13}}{3}\) and \(\frac{10}{3}\) units respectively, then what is the length of the transverse axis?