List of top Mathematics Questions asked in BITSAT

If \(y^x = e^{y - x}\), then \(\frac{dy}{dx}\) is equal to:

The point of inflexion for the curve \(y = (x - a)^n\), where \(n\) is an odd integer and \(n \ge 3\) is:

The domain of the function \(f(x) = \sqrt{x - \sqrt{1 - x^2\) is:}

The value of \(\lim_{n \rightarrow \infty} \prod_{r=3}^{n} \frac{r^3 - 8}{r^3 + 8}\) equals to:

The line \(y = mx\) bisects the area enclosed by the lines \(x = 0\), \(y = 0\), \(x = \frac{3}{2}\) and the curve \(y = 1 + 4x - x^2\). Then, the value of \(m\) is:

If \(\vec{a} = 2\hat{i} + \hat{j} + 2\hat{k}\), then the value of \(|\hat{i} \times (\vec{a} \times \hat{i})|^2 + |\hat{j \times (\vec{a} \times \hat{j})|^2 + |\hat{k} \times (\vec{a} \times \hat{k})|^2\) is equal to:}

The shortest distance between the lines \[ x = y + 2 = 6z - 6 \] and \[ x + 1 = 2y = -12z \] is:

If \( x = \sqrt{2^{\text{cosec}^{-1} t}} \) and \( y = \sqrt{2^{\text{sec}^{-1} t}} (|t| \ge 1) \), then dy/dx is equal to :

If \( f(x) = \int_0^x t(\sin x - \sin t)dt \) then :

Let P be a point on the parabola, \( x^2 = 4y \). If the distance of P from the centre of the circle, \( x^2 + y^2 + 6x + 8 = 0 \) is minimum, then the equation of the tangent to the parabola at P, is :

The value of x is maximum for

If \(a > 0, \, b > 0, \, c > 0\) and \(a, b, c\) are distinct, then \((a + b)(b + c)(c + a)\) is greater than

If \(|z_1| = 2, |z_2| = 3, |z_3| = 4\) and \(|2z_1 + 3z_2 + 4z_3| = 4\), then absolute value of \(8z_2z_3 + 27z_3z_1 + 64z_1z_2\) equals

The locus of the mid-point of a chord of the circle \( x^2 + y^2 = 4 \), which subtends a right angle at the origin is

The equation of a plane passing through three non-collinear points is determined using:

Let \( A = \begin{bmatrix} 1 & 0 & 0 0 & 1 & 0 3 & 2 & 1 \end{bmatrix} \). Find \( A^{100} \).

Let the foot of perpendicular from a point \( P(1,2,-1) \) to the straight line \( L: \frac{x}{1} = \frac{y}{0} = \frac{z}{-1} \) be \( N \). Let a line be drawn from \( P \) parallel to the plane \( x + y + 2z = 0 \) which meets \( L \) at point \( Q \). If \( \alpha \) is the acute angle between the lines PN and PQ, then \( \cos \alpha \) is equal to

The magnitude of projection of line joining (3, 4, 5) and (4, 6, 3) on the line joining (−1, 2, 4) and (1, 0, 5) is

If \( \vec{a} = 2\hat{i} + \hat{j} + 2\hat{k} \), then the value of \( |\hat{i} \times (\vec{a} \times \hat{i})|^2 + |\hat{j} \times (\vec{a} \times \hat{j})|^2 + |\hat{k} \times (\vec{a} \times \hat{k})|^2 \) is equal to

The value of \( \int e^{\tan \theta} (\sec \theta - \sin \theta) \, d\theta \) is

The area of the region bounded by the curves \( x = y^2 - 2 \) and \( x = y \) is

Find the equation of the normal to a parabola which is perpendicular to a given line. This involves:

The angle between two lines in 3D space can be found using:

In a Linear Programming Problem (LPP), the objective function Z is minimized subject to constraints. Where does the minimum value occur?

Find the term independent of \( x \) in the expansion of \( (1 + x)^{n} (1 + \frac{1}{x})^{n} \).