List of top Mathematics Questions asked in BITSAT

Find the variance of the data given below \[ \text{Size of item:} \quad 3.5, 4.5, 5.5, 6.5, 7.5, 8.5, 9.5 \\ \text{Frequency:} \quad 3, 7, 22, 60, 85, 32, 8 \]

The determinant \[ \left| \begin{matrix} 1 & x & x^2 \\ 1 & x^3 & x^4 \\ 1 & x^5 & x^6 \end{matrix} \right| \] vanishes for

If \( f(x) = \begin{cases} \frac{x^2 + 3x - 10}{x^2 + 2x - 15}, & x \neq -5 \\ a, & x = -5 \end{cases} \) is continuous at \( x = -5 \), then the value of \( a \) will be

A shopkeeper wants to purchase two articles A and B of cost price \( 4 \) and \( 3 \) respectively. He thought that he may earn 30 paise by selling article A and 10 paise by selling article B. He has not to purchase total articles worth more than \( 24 \). If he purchases the number of articles of A and B, \( x \) and \( y \) respectively, then linear constraints are

For \( k = 1, 2, 3 \), the box \( B_k \) contains red balls and \( (k+1) \) white balls. Let \( P(B_1) = \frac{1}{2}, P(B_2) = \frac{1}{3}, P(B_3) = \frac{1}{6} \). A box is selected at random and a ball is drawn from it. If a red ball is drawn, then the probability that it came from box \( B_2 \) is

The probability of India winning a test match against West Indies is \( \frac{1}{2} \). Assuming independence from match to match, the probability that in a 5 match series India’s second win occurs at the third test is

An object is observed from the points A, B and C lying in a horizontal straight line which passes directly underneath the object. The angular elevation at A is \( \theta \), at B is \( 2\theta \), and at C is \( 3\theta \). If AB = a, BC = b, and the height of the object is h, then the height of the object is

The coordinates of the point where the line through the points \( A(3, 4, 1) \) and \( B(5, 1, 6) \) crosses the \( XY \)-plane are

If vectors \( 2i + j + k \), \( 2j - 3k \), and \( 3i + j + 5k \) are coplanar, then the value of \( a \) is

Find the angle between the two planes \( 2x + y - 2z = 5 \) and \( 3x - 6y - 2z = 7 \).

The general solution of the differential equation \[ \frac{dy}{dx} + \sin(x + y) = \sin(x - y) \] is

The solution to the differential equation \[ \frac{dy}{dx} = \frac{yf'(x) - y^2}{f(x)} \] where \( f(x) \) is a given function is

The area intercepted by the curves \( y = \cos x \), \( x \in [0, \pi] \) and \( y = \cos 2x \), \( x \in [0, \pi] \), is

Evaluate \[ \int_0^{\frac{\pi}{2}} \frac{\sin x}{1 + \cos^2 x} \, dx \] is

If \( \mathbf{a}, \mathbf{b}, \mathbf{c} \) are three unit vectors such that \[ \mathbf{a} + \mathbf{b} + \mathbf{c} = \mathbf{0}, \quad \mathbf{a} \cdot \mathbf{b} = \mathbf{b} \cdot \mathbf{c} = \mathbf{c} \cdot \mathbf{a} \] then the value of \( \mathbf{a} \cdot \mathbf{a} \) is

\[ \int \frac{1}{(x^2 + 1)^{\frac{3}{4}}} \, dx \] is equal to

If the lines \( \ell_1 : \ell m + mn + n = 0 \), \( \ell_2 : mn + m + n = 0 \) are concurrent then

If \( a^2 x^4 + b^2 y^4 = c^4 \), then the maximum value of \( xy \) is

The function \( f(x) = (x(x - 2))^2 \) is increasing in the set

If \( y = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \dots + \infty \), then

The equation of all lines having slope 2 which are tangent to the curve \( y = \frac{1}{x - 3} \), is

If the value of mode and mean is 60 and 66 respectively, then the value of median is

The value of \[ \frac{1}{2} \cos^{-1} \left( \cos \left( \frac{\pi}{3} - \frac{\sqrt{63}}{8} \right) \right) \] is

The greatest and least values of \( \left( \sin(x) \right)^2 + \left( \cos(x) \right)^2 \) are respectively

Let \( R \) be the relation on the set \( \mathbb{R} \) of all real numbers, defined by \( aRb \) if \( |a - b| \leq 1 \). Then, \( R \) is