List of top Mathematics Questions asked in BITSAT

Let \(A\), \(B\) and \(C\) are the angles of a triangle and \(\tan \frac{A}{2} = 1/3\), \(\tan \frac{B}{2} = \frac{2}{3}\). Then, \(\tan \frac{C}{2}\) is equal to:

The coefficient of the highest power of \(x\) in the expansion of \((x + \sqrt{x^2 - 1})^8 + (x - \sqrt{x^2 - 1})^8\) is:

Given a real-valued function \( f \) such that: \[ f(x) = \begin{cases} \frac{\tan^2\{x\}}{x^2 - \lfloor x \rfloor^2}, & \text{for } x > 0 \\ 1, & \text{for } x = 0 \\ \sqrt{\{x\} \cot\{x\}}, & \text{for } x < 0 \end{cases} \] Then:

From a point A(0,3) on the circle \[ (x + 2)^2 + (y - 3)^2 = 4 \] a chord AB is drawn and extended to a point Q such that AQ = 2AB. Then the locus of Q is:

A(3,2,0), B(5,3,2), C(-9,6,-3) are three points forming a triangle. AD, the bisector of angle $BAC$ meets BC in D. Find the coordinates of D:

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:

If the focus of the parabola \[ (y - k)^2 = 4(x - h) \] always lies between the lines \(x + y = 1\) and \(x + y = 3\) then:

If \( p \) and \( q \) be the longest and the shortest distance respectively of the point (-7,2) from any point (\(\alpha, \beta\)) on the curve whose equation is \[ x^2 + y^2 - 10x - 14y - 51 = 0 \] then the geometric mean (G.M.) of \( p \) is:

The locus of the point of intersection of the lines \(x = a(1 - t^2)/(1 + t^2)\) and \(y = 2at/(1 + t^2)\) (t being a parameter) represents:

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

The coefficient of \(x^n\) in the expansion of \[\frac{e^{7x} + e^x}{e^{3x}}\] is:

If the straight line $2x + 3y - 1 = 0$, $x + 2y - 1 = 0$ and $ax + by - 1 = 0$ form a triangle with origin as orthocentre, then $(a,b)$ is equal to:

If \[ y = \tan^{-1} \left( \frac{1}{x^2 + x + 1} \right) + \tan^{-1} \left( \frac{1}{x^2 + 3x + 3} \right) + \tan^{-1} \left( \frac{1}{x^2 + 5x + 7} \right) + \cdots { (to n terms)} \], then \(\frac{dy}{dx}\) is:

The distance from the origin to the image of $(1,1)$ with respect to the line $x + y + 5 = 0$ is:

Let \( f(x) = \sin x \), \( g(x) = \cos x \), and \( h(x) = x^2 \). Then, evaluate: \[ \lim\limits_{x \to 1} \frac{f(g(h(x))) - f(g(h(1)))}{x - 1} \]

If \( x \) is a complex root of the equation
\[ \begin{vmatrix} 1 & x & x \\ x & 1 & x \\ x & x & 1 \end{vmatrix} + \begin{vmatrix} 1 - x & 1 & 1 \\ 1 & 1 - x & 1 \\ 1 & 1 & 1 - x \end{vmatrix} = 0, \] then \( x^{2007} + x^{-2007} \) is:

Let \( p, q, r \) be three logical statements. Consider the compound statements: \[ S_1: (\neg p \vee q) \vee (\neg p \vee r) \] \[ S_2: p \rightarrow (q \vee r) \] Which of the following is NOT true?

Let R be the relation "is congruent to" on the set of all triangles in a plane. Is R:

Consider the following two propositions: \[ P_1: \neg (p \rightarrow \neg q) \] \[ P_2: (p \wedge \neg q) \wedge ((\neg p) \vee q) \] If the proposition \( p \rightarrow ((\neg p) \vee q) \) is evaluated as FALSE, then:

Number of subsets of set of letters of word 'MONOTONE' is:

Suppose \( p, q, r \neq 0 \) and the system of equations:
\[ (p + a)x + by + cz = 0 \] \[ ax + (q + b)y + cz = 0 \] \[ ax + by + (r + c)z = 0 \] has a non-trivial solution, then the value of \[ \frac{a}{p} + \frac{b}{q} + \frac{c}{r} \] is:

If matrix \( A = \begin{bmatrix} 3 & -2 & 4 \\ 1 & 2 & -1 \\ 0 & 1 & 1 \end{bmatrix} \) and \( A^{-1} = \frac{1}{k} adj(A) \), then \( k \) is

If \( A = \frac{1}{3} \begin{bmatrix} 1 & 2 & 2 \\ 2 & 1 & -2 \\ a & 2 & b \end{bmatrix} \) is an orthogonal matrix, then

If the variance of the data \( 2,3,5,8,12 \) is \( \sigma^2 \) and the mean deviation from the median for this data is \( M \), then \( \sigma^2 - M \) is: