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:

Consider the following statements:
$ A $: Rishi is a judge.
$ B $: Rishi is honest.
$ C $: Rishi is not arrogant.
The negation of the statement "If Rishi is a judge and he is not arrogant, then he is honest" is:

The sum of all values of $x$ in $[0, 2\pi]$, for which $x + \sin(2x) + \sin(3x) + \sin(4x) = 0$ is equal to:

If $ p $: 2 is an even number, $ q $: 2 is a prime number, and $ r $: $ 2 + 2 = 2^2 $, then the symbolic statement $ p \rightarrow (q \vee r) $ means:

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:

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 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:

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:

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

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:

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
$ p $: It is raining today,
$ q $: I go to school,
$ r $: I shall meet my friends,
and $ s $: I shall go for a movie, then which of the following represents:
"If it does not rain or if I do not go to school, then I shall meet my friend and go for a movie?"

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 $x^n$ 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 the 17th and the 18th terms in the expansion of $(2 + a)^{50}$ are equal, then the coefficient of $x^{35}$ in the expansion of $(a + x)^{-2}$ 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 R be the relation "is congruent to" on the set of all triangles in a plane. Is R:

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

In an examination, 62% of the candidates failed in English, 42% in Mathematics and 20% in both. The number of those who passed in both the subjects is:

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:

The variance of 20 observations is 5. If each observation is multiplied by 2, then the new variance of the resulting observation is: