List of top Mathematics Questions asked in BITSAT

Minimise $Z=\displaystyle\sum_{j=1}^{n} \displaystyle\sum_{i=1}^{m} c_{i j} \cdot x_{i j}$ Subject to $\displaystyle\sum_{ i =1}^{ m } x _{ ij }= b _{ j }, j =1,2, \ldots \ldots n$ $\displaystyle\sum_{j=1}^{n} x_{i j}=b_{j}, j=1,2, \ldots \ldots, m$ is a LPP with number of constraints
The angle of intersection of the two circles $x^2 + y^2 - 2x - 2y = 0$ and $x^2 + y^2 = 4$, is
If \[ \begin{vmatrix} p & q - y & r - z \\ p - x & q & r - z \\ p - x & q - y & r \end{vmatrix} = 0, \] then the value of \(\dfrac{p}{x} + \dfrac{q}{y} + \dfrac{r}{z}\) is
Let \( f:\mathbb{R} \to \mathbb{R} \) be a function defined by \( f(x) = \dfrac{x - m}{x - n} \), where \( m \neq n \). Then
If \(\begin{bmatrix} \alpha & \beta \\ \gamma & -\alpha \end{bmatrix}\) is a square root of identity matrix of order 2, then
Let \[ f(x)= \begin{cases} (x-1)\sin\!\left(\dfrac{1}{x-1}\right), & x \neq 1 \\ 0, & x = 1 \end{cases} \] Then which one of the following is true?
The coefficient of \(x^4\) in the expansion of \((1 + x + x^2 + x^3)^{11}\) is:
If the \((2p)^{\text{th}}\) term of a H.P. is \(q\) and the \((2q)^{\text{th}}\) term is \(p\), then the \(2(p+q)^{\text{th}}\) term is:
\(\displaystyle \lim_{x \to 0} \left(\csc x\right)^{\frac{1}{\log x}}\) is equal to:
Let \( R = \{(3,3), (6,6), (9,9), (12,12), (6,12), (3,9), (3,12), (3,6)\} \) be a relation on the set \( A = \{3,6,9,12\} \). Then, the relation is:
Through the vertex \(O\) of parabola \(y^2=4x\), chords OP and OQ are drawn at right angles to one another. The locus of the midpoint of PQ is
Let \[ f(x)= \begin{cases} \dfrac{1-\sin^3 x}{3\cos^2 x}, & x < \dfrac{\pi}{2} \\ [6pt] p, & x = \dfrac{\pi}{2} \\ [6pt] \dfrac{q(1-\sin x)}{(\pi-2x)^2}, & x > \dfrac{\pi}{2} \end{cases} \] If \(f(x)\) is continuous at \(x=\dfrac{\pi}{2}\), then \((p,q)=\)
A coin is tossed 7 times. Each time a man calls head. Find the probability that he wins the toss on more occasions.
The equation of the right bisector plane of the segment joining \((2,3,4)\) and \((6,7,8)\) is
Consider \(\dfrac{x}{2}+\dfrac{y}{4}\ge1\) and \(\dfrac{x}{3}+\dfrac{y}{2}\le1,\; x,y\ge0\). Then number of possible solutions are
If \(A=\begin{bmatrix}1 & 1 \\ 1 & 1\end{bmatrix}\), then \(A^{100}\) is
Find the angle between the line \[ \frac{x+1}{2}=\frac{y}{3}=\frac{z-3}{6} \] and the plane \(10x+2y-11z=3\).
A bag contains \(n+1\) coins. It is known that one of these coins shows heads on both sides, whereas the other coins are fair. One coin is selected at random and tossed. If the probability that toss results in heads is \(\frac{7}{12}\), then the value of \(n\) is
The angle between any two diagonals of a cube is
Solution of differential equation \[ x^2-1+\left(\frac{x}{y}\right)^{-1}\frac{dy}{dx} +\frac{x^2}{2!}\left(\frac{dy}{dx}\right)^2 +\frac{x^3}{3!}\left(\frac{dy}{dx}\right)^3+\cdots=0 \] is
If the middle points of sides BC, CA and AB of triangle ABC are respectively D, E, F. If the position vectors of A, B, C are \(\hat{i}+\hat{j},\;\hat{j}+\hat{k},\;\hat{k}+\hat{i}\) respectively, then the position vector of the centre of triangle DEF is
The area bounded by the x-axis, the curve \(y=f(x)\) and the lines \(x=1,\;x=b\) is equal to \(\sqrt{b^2+1}-\sqrt{2}\) for all \(b > 1\). Then \(f(x)\) is
The value of \(\lambda\), for which the lines \(3x-4y=13\), \(8x-11y=33\) and \(2x-3y+\lambda=0\) are concurrent is
Evaluate: \[ \int \frac{1}{1+3\sin^2 x+8\cos^2 x}\,dx \]
The fuel charges for running a train are proportional to the square of the speed generated in miles per hour and cost $48 per hour at 16 miles per hour. The most economical speed if the fixed charges (i.e., salaries etc.) amount to $30 per hour is: