List of top Questions asked in BITSAT

The area enclosed between the curve \( y = \log_e(x + e) \) and the coordinate axes is:
If \( \vec{a} = \hat{i} + \hat{j} + \hat{k} \), \( \vec{a} \cdot \vec{b} = 1 \) and \( \vec{a} \times \vec{b} = \hat{j} - \hat{k} \), then \( \vec{b} \) is:
Find: \( \lim_{x \to 0} \frac{| \sin x |}{x} \)
The lines \[ \frac{x - 2}{1} = \frac{y - 3}{1} = \frac{z - 4}{-k} \] and \[ \frac{x - 1}{k} = \frac{y - 4}{2} = \frac{z - 5}{1} \] are coplanar if:
Negation of the Boolean expression \( p \Leftrightarrow (q \Rightarrow p) \) is:
The maximum value of \( z = 5x + 2y \) subject to the constraints: \[ x + y \leq 7, \quad x + 2y \leq 10, \quad x, y \geq 0 \]
Find the mean deviation about the mean for the data: \( 4, 7, 8, 9, 10, 12, 13, 17 \)
Bag P contains 6 red and 4 blue balls, and bag Q contains 5 red and 6 blue balls. A ball is transferred from bag P to bag Q and then a ball is drawn from bag Q. What is the probability that the ball drawn is blue?
Find the value of \[ \tan^{-1}\left(\frac{1}{4}\right) + \tan^{-1}\left(\frac{2}{9}\right) \]
The middle term in the expansion of \( \left(\frac{10}{x} + \frac{x}{10}\right)^{10} \) is:
The equation of a common tangent to the parabolas \( y = x^2 \) and \( y = -(x - 2)^2 \) is:
A circle touches both the y-axis and the line \( x + y = 0 \). Then the locus of its center is:
The function \( f(x) = \tan^{-1}(\sin x + \cos x) \) is an increasing function in:
Simplify \( i^{57} + \frac{1}{i^{25}} \) and find its value:
If one root of the equation \( x^2 + px + 12 = 0 \) is \( 4 \), while the equation \( x^2 + px + q = 0 \) has equal roots, then the value of \( q \) is:
Evaluate the integral: \[ I = \int \frac{x + 3}{(x + 4)^2} e^x \,dx \]
The shortest distance between the lines \[ \frac{x - 3}{2} = \frac{y - 2}{3} = \frac{z - 1}{-1} \] and \[ \frac{x + 3}{2} = \frac{y - 6}{1} = \frac{z - 5}{3} \] is:
If \( P(B) = \frac{3}{5} \), \( P(A \mid B) = \frac{1}{2} \), and \( P(A \cup B) = \frac{4}{5} \), then the value of \( P(A \cup B)' + P(A' \cup B) \) is:
In a Young's double slit experiment, the intensities at two points, for the path difference \( \frac{\lambda}{4} \) and \( \frac{\lambda}{3} \) (\( \lambda \) being the wavelength of light used) are \( I_1 \) and \( I_2 \) respectively. If \( I_0 \) denotes the intensity produced by each one of the individual slits, then \( \frac{I_1 + I_2}{I_0} \) is equal to:

The energy levels of an atom are shown in the figure. Which one of these transitions will result in the emission of a photon of wavelength 124.1 nm? Given \( h = 6.62 \times 10^{-34} \) Js. 

Frenkel and Schottky defects are:

The Bohr orbit radius for the hydrogen atom (\(n = 1\)) is approximately 0.530 \({Å}\). The radius for the first excited state (\(n = 2\)) 
orbit is (in \({Å}\)): 
 

Select the figure from among the given Option that can replace the question mark (?) in the following series. 

Identify the Venn diagram that best represents the relationship among classes given below: Profit, Dividend, and Bonus.

How many triangles are there in the following figure?