List of top Mathematics Questions asked in BITSAT

An observer on the top of a tree finds the angle of depression of a car moving towards the tree to be 30°. After 3 minutes this angle becomes 60°. After how much more time will the car reach the tree?

The function \(f(x) = x - |x - x^2|\), \(-1 \le x \le 1\) is continuous on
If
\[ \frac{4^n}{n+1} < \frac{(2n)!}{(n!)^2}, \]
then \(P(n)\) is true for
If a system of equations
\[ a x + y + z = 0, \quad x - b y + z = 0, \quad x + y - c z = 0 \quad (a, b, c \ne -1) \]
has a non-zero solution, then
\[ \frac{1}{1+a} + \frac{1}{1+b} + \frac{1}{1+c} = \]
The value of
\[ \lim_{x \to \infty} \left(a_1^{1/x} + a_2^{1/x} + \cdots + a_n^{1/x}\right)^{n x}, \quad a_i > 0 \]
A random variable \(X\) has the probability distribution given. For the events \(E = \{X \text{ is a prime}\}\) and \(F = \{X < 4\}\), then \(P(E \cup F)\) is
The number of roots of the equation \(\cos x + \cos 3x = 0\) in \(0 \le x \le 2\pi\) is
The area under the curve \(y = |\cos x - \sin x|\), for \(0 \le x \le \frac{\pi}{2}\), and above the x-axis is
If
\[ f(x) = \begin{cases} \dfrac{x \log(\cos x)}{\log(1 + x^2)}, & x \ne 0 \\[2mm] 0, & x = 0 \end{cases} \]
then \(f(x)\) is
The maximum value of \(z = 3x + 2y\) subject to \(x + 2y \ge 2\), \(x + 2y \le 8\), \(y \ge 0\) is
A cylindrical gas container is closed at the top and open at the bottom. If the iron plate of the top is \(\frac{5}{4}\) times as thick as the plate forming the cylindrical sides, the ratio of the radius to the height of the cylinder using minimum material for the same capacity is
Let \(A, B, C\) be finite sets. Suppose that \(n(A) = 10\), \(n(B) = 15\), \(n(C) = 20\), \(n(A \cap B) = 8\), and \(n(B \cap C) = 9\). Then the possible value of \(n(A \cup B \cup C)\) is
If \(f(z) = \frac{7 - z}{1 - z^2}\), where \(z = 1 + 2i\), then \(|f(z)|\) is equal to
If
\[ f(x) = \cos^{-1} \left[ \frac{1 - (\log x)^2}{1 + (\log x)^2} \right], \]
then the value of \(f'(e)\) is equal to
If
\[ R(t) = \begin{pmatrix} \cos t & \sin t \\ -\sin t & \cos t \end{pmatrix}, \]
then \(R(s)R(t)\) equals
If
\[ \int x \log\left(1 + \frac{1}{x}\right) \, dx = f(x) \log(x+1) + g(x) x^2 + Lx + C, \]
then
Let \(\mathbf{a}, \mathbf{b}, \mathbf{c}\) be non-coplanar unit vectors equally inclined to one another at an acute angle \(\theta\). Then \(|\mathbf{a} \cdot (\mathbf{b} \times \mathbf{c})|\) in terms of \(\theta\) is equal to
\(\frac{2^1}{4} \cdot \frac{2^2}{8} \cdot \frac{2^3}{16} \cdot \frac{2^4}{32} \cdots\) is equal to
If \(\sum_{r=0}^{n} \binom{n}{r} \frac{r + 3}{r} = \frac{3}{a+3}\), then \(a - n\) is equal to

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

The ratio in which the line joining the points \( (2,1,5) \) and \( (3,4,3) \) is divided by the plane \( x + y - z = \dfrac{1}{2} \) is:
Value of \( \displaystyle \int_{0}^{\pi/2} \dfrac{\sqrt{\sin x}}{\sqrt{\sin x} + \sqrt{\cos x}} \, dx \) is:
The dot product of a vector with the vectors \( \mathbf{i} + \mathbf{j} - 3\mathbf{k} \), \( \mathbf{i} + 3\mathbf{j} - 2\mathbf{k} \) and \( 2\mathbf{i} + \mathbf{j} + 4\mathbf{k} \) are 0, 5 and 8 respectively. The vector is:
An urn contains five balls. Two balls are drawn and found to be white. The probability that all the balls are white is
The angle between the two lines whose intercepts on the axes are a,-b and b,-a respectively is