List of top Questions asked in BITSAT

Let \( [x] \) denote the greatest integer \( \leq x \). If \( f(x) = [x] \) and \( g(x) = |x| \), then the value of:
\[ f \left( g \left( \frac{8}{5} \right) \right) - g \left( f \left( \frac{-8}{5} \right) \right) \] is:
Let the function \( g: (-\infty, 0) \rightarrow \left(-\frac{\pi}{2}, \frac{\pi}{2}\right) \) be given by \( g(u) = 2 \tan^{-1}(e^u) - \frac{\pi}{2} \). Determine the properties of \( g \).

Evaluate the following limit: $ \lim_{n \to \infty} \prod_{r=3}^n \frac{r^3 - 8}{r^3 + 8} $.

In a binomial distribution, the mean is 4 and variance is 3. Then, its mode is:
If the arithmetic mean of two distinct positive real numbers \(a\) and \(b\) (where \(a>b\)) is twice their geometric mean, then \(a : b\) is:
The coefficient of \(x^n\) in the expansion of \[\frac{e^{7x} + e^x}{e^{3x}}\] is:
Number of solutions of equations \(\sin(9\theta) = \sin(\theta)\) in the interval \([0,2\pi]\) is:
The Boolean expression: \[ \neg (p \vee q) \vee (\neg p \wedge q) \] is equivalent to:
From the top of a cliff 50 m high, the angles of depression of the top and bottom of a tower are observed to be \(30^\circ\) and \(45^\circ\). The height of the tower is:
The system of equations:
\[ x - y + 2z = 4 \] \[ 3x + y + 4z = 6 \] \[ x + y + z = 1 \] has:
If \( \cot(\cos^{-1} x) = \sec \left( \tan^{-1} \left( \frac{a}{\sqrt{b^2 - a^2}} \right) \right) \), then:
If the angle made by the tangent at the point \((x_0, y_0)\) on the curve \(x = 12(t + \sin t \cos t)\), \(y = 12(1 + \sin t)^2\), with \(0<t<\frac{\pi}{2}\), with the positive x-axis is \(\frac{\pi}{3}\), then \(y_0\) is equal to:
The value of \( \int_0^\infty \frac{dx}{(x^2 + a^2)(x^2 + b^2)} \) is:
If \( \vec{a} = 2\hat{i} + \hat{j} + 2\hat{k} \), then the value of \( |\hat{i} \times (\vec{a} \times \hat{i})| + |\hat{j} \times (\vec{a} \times \hat{j})| + |\hat{k} \times (\vec{a} \times \hat{k})|^2 \) is equal to:}
The probability of getting 10 in a single throw of three fair dice is:
Thermal decomposition of lithium nitrate gives:
Which of the following is not correct about Grignard reagent?
The sol formed in the following unbalanced equation is:
\[ As_2O_3 + H_2S \rightarrow {?} \]

A tetrapeptide is made of naturally occurring alanine, serine, glycine, and valine. If the C-terminal amino acid is alanine and the N-terminal amino acid is chiral, the number of possible sequences of the tetrapeptide is: 
 

The combustion of benzene (L) gives CO\(_2\) (g) and H\(_2\)O (L). Given that heat of combustion of benzene at constant volume is -3263.9 kJ/mol at 25°C, heat of combustion (in kJ/mol) of benzene at constant pressure will be: (R = 8.314 J\(K^{-1}\) \(mol^{-1}\))
What is the stoichiometric coefficient of SO$_2$ in the following balanced reaction? \[ {MnO}_4^-(aq) + {SO}_2(g) \rightarrow {Mn}^{2+}(aq) + {HSO}_4^-(aq) \] (in acidic solution)

The major product X in the following given reaction is: 
 

The major product of the reaction between CH$_3$CH$_2$ONa and (CH$_3$)$_3$CCl in ethanol is:
Calculate the molarity of a solution containing 5 g of NaOH dissolved in the product of H$_2$ – O$_2$ fuel cell operated at 1 A current for 595.1 hours.(Assume F = 96500C/mol of electron and molecular weight of NaOH as 40 g/mol).
When the same quantity of electricity is passed through the aqueous solutions of the given electrolytes for the same amount of time, which metal will be deposited in maximum amount on the cathode?