List of top Questions asked in BITSAT

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:

Two plano-concave lenses (1 and 2) of glass of refractive index 1.5 have radii of curvature 25 cm and 20 cm. They are placed in contact with their curved surfaces towards each other and the space between them is filled with liquid of refractive index 4/3. The combination is 

Two concentric conducting spherical shells A and B having radii rA and rB (rB>rA) are charged to +2q and -q respectively. The electric field along a line passing through the centre is 

Two conducting shells of radius a and b are connected by a conducting wire as shown in the figure. The capacity of the system is 

One mole of an ideal gas is taken from state A to state B by three different processes, 
(i) ACB (ii) ADB (iii) AEB as shown in the P–V diagram. The heat absorbed by the gas is 

A meter bridge is set up as shown to determine an unknown resistance X using a standard 10 ohm resistor. The galvanometer shows null point at 52 cm mark. The end corrections are 1 cm and 2 cm respectively for the ends A and B. The determined value of X is 

On a hypotenuse of a right angled prism of liquid is placed as shown in the figure. Light is allowed to fall normally on the short face of the prism. In order that the ray of light may be totally reflected, the maximum value of refractive index is