List of top Questions asked in BITSAT- 2025

Calculate the electric field at a point due to a uniformly charged spherical shell.
Two circles with centers $O_1$ and $O_2$ touch externally. The radius of the first circle is 4 cm and the second is 9 cm. The distance between their centers is 13 cm. Find the length of the direct common tangent.
The equation of the line passing through the point $ (2, 3) $ and making equal intercepts on the coordinate axes is:
Find the coordinates of the point which divides the line segment joining \((2, -3)\) and \((7, 9)\) in the ratio \(3:2\).
In triangle $ ABC $, the length of sides are $ AB = 7 $, $ BC = 10 $, and $ AC = 5 $. What is the length of the median drawn from vertex $ B $?
The area of a triangle with vertices at points $ A(1,2) $, $ B(4,6) $, and $ C(k, 8) $ is 5. Find the value of $ k $.
If the distance between the points \( (2, -1) \) and \( (k, 3) \) is 5, then the possible values of \( k \) are:
The equation of the circle passing through the points (1,2), (4,3), and (2,–1) is:
Evaluate the integral: $$ \int_0^{\pi/4} \frac{\ln(1 + \tan x)}{\cos x \sin x} \, dx $$
Find the value of the integral: \[ \int_0^\pi \sin^2(x) \, dx. \]
Evaluate the integral \( \int_0^1 \frac{\ln(1 + x)}{1 + x^2} \, dx \)
If \( z = 2(\cos 60^\circ + i \sin 60^\circ) \), find the value of \( z^3 \).
If \( z = x + iy \) is a complex number such that \( |z - 1| = |z + 1| \), then the locus of \( z \) represents:
Find the slope of the line passing through the points $ (1, 2) $ and $ (3, 6) $:
The equation of a straight line is given by \( y = 3x + 4 \). What is the slope of the line?
How many different 4-letter words can be formed from the letters of the word "BINARY" without repetition?
Maximize \( z = 5x + 2y \) subject to \( 2x + y \leq 8 \), \( x \geq 0 \), \( y \geq 0 \). What is the maximum value of \( z \)?
If the word "BITS" is coded using \( A=1, B=2, \ldots, Z=26 \), and the code is the sum of the squares of each letter's value, what is the code for the word?
From the top of a 60 m high building, the angles of depression to two points on the ground on the same side of the building are \( 30^\circ \) and \( 60^\circ \). What is the distance between the two points?
Maximize \( z = 3x + 4y \) subject to \( x + y \leq 4 \), \( x \geq 0 \), \( y \geq 0 \). What is the maximum value of \( z \)?
Find the sum of the series \( 1 + 3 + 5 + \ldots + 99 \).
If the word "GIFT" is coded using A=1, B=2, ..., Z=26, and each letter’s value is squared, what is the sum of the coded values?
If $ x + \frac{1}{x} = 2 \cos \theta $, find the value of \[ x^5 + \frac{1}{x^5} \] in terms of $\theta$.
From the top of a 50 m tall building, the angles of depression to two points on the ground are \( 45^\circ \) and \( 30^\circ \). Find the distance between the two points.
Two numbers are selected at random (without replacement) from the first 6 natural numbers. What is the probability that the difference of the numbers is less than 3?