List of top Mathematics Questions asked in BITSAT

Let \[ A = \begin{pmatrix} 1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1 \end{pmatrix}, \quad 10B = \begin{pmatrix} 4 & 2 & 2 \\ -5 & 0 & \alpha \\ 1 & -2 & 3 \end{pmatrix} \] If $ B $ is the inverse of $ A $, then the value of $ \alpha $ is:

If $ x \in \left( 0, \frac{\pi}{2} \right) $, then the value of $ \cos^{-1} \left( \frac{7}{2} (1 + \cos 2x) + \sqrt{(\sin^2 x - 48\cos^2 x)\sin x} \right) $ is equal to:

For each parabola $ y = x^2 + px + q $, meeting the coordinate axes at three distinct points, if circles are drawn through these points, then the family of circles must pass through:

If the sum of the coefficients in the expansion of $ (x + y)^n $ is 1024, then the value of the greatest coefficient in the expansion is:

The number of ways of arranging the letters of the word HAVANA so that V and N do not appear together is:

If $\hat{u}$ and $\hat{v}$ are two non-collinear unit vectors such that $\left| \frac{\hat{u} + \hat{v}}{2} + \hat{u} \times \hat{v} \right| = 1$, then the value of $\left| \hat{u} \times \hat{v} \right|$ is equal to:

In order to solve the differential equation $x \cos x \frac{d y}{d x}+y(x \sin x+\cos x)=1$ the integrating factor is:

Equation of two straight lines are $\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}$ and $\frac{x-4}{5}=\frac{y-1}{2}=z$ .Then

A bag contains $2n$ coins out of which $n-1$ are unfair with heads on both sides and the remaining are fair. One coin is picked from the bag at random and tossed. If the probability that head falls in the toss is $\frac{41}{56}$, then the number of unfair coins in the bag is

The equation of the curve passing through the point $\left(a, -\frac{1}{a}\right)$ and satisfying the differential equation $y-x \frac{dy}{dx}=a\left(y^{2}+\frac{dy}{dx}\right)$ is

Consider $\frac{x}{2}+\frac{y}{4} \ge1,$ and $\frac{x}{3}+\frac{y}{4} \le1, x, y \ge0.$ Then number of possible solutions are :

If $a_{1}, a_{2}, a_{3}, \ldots, a_{n}$ are in A.P. where $a_{i}>0$ for all $i$, then $\frac{1}{\sqrt{a_{1}}+\sqrt{a_{2}}}+\frac{1}{\sqrt{a_{2}}+\sqrt{a_{3}}}+\ldots .+$ $\frac{1}{\sqrt{a_{n-1}}+\sqrt{a_{n}}}$ is?

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

For the following feasible region, the linear constraints are

With the usual notation $\displaystyle \int_1^2 ([x^2]-[x]^2)dx$ is equal to

The coefficient of $x^2$ term in the binomial expansion of $\left(\frac{1}{3}x^{1/2}+x^{-1/4}\right)^{10}$ is :

What is the slope of the normal at the point (at, 2at) of the parabola y = 4ax ?

If $f(x)=3 x^{4}+4 x^{3}-12 x^{2}+12,$ then f(x) is

$\displaystyle\lim_{x\to0} \sqrt{\frac{x-\sin x}{x+\sin^{2}x}} $ is equal to

The number of ways in which first, second and third prizes can be given to $5$ competitors is

The coefficient of $x^3$ in the expansion of $\left(x -\frac{1}{x}\right)^{7}$ is :

The value of $\displaystyle\lim_{n \to\infty} \frac{1+2+3+...n}{n^{2}+100}$ is equal to :

If $ \hat{i} + \hat{j}, \hat{j} + \hat{k}, \hat{i} + \hat{k}$ are the position vectors of the vertices of a triangle $ABC$ taken in order, then $\angle A$ is equal to

The equation of the circle which passes through the point $(4, 5)$ and has its centre at $(2, 2)$ is

In how many ways can $12$ gentlemen sit around a round table so that three specified gentlemen are always together?