List of top Questions asked in BITSAT- 2017

A mercury drop of radius 1 cm is sprayed into \(10^6\) drops of equal size. The energy expressed in joules is (surface tension of mercury is \(460 \times 10^{-3} \, \text{N/m}\)).
When \({}^{235}\text{U}\) undergoes fission, 0.1% of its original mass is changed into energy. How much energy is released if 1 kg of \({}^{235}\text{U}\) undergoes fission?

Two projectiles, A and B, are thrown with speeds in the ratio 1:√(2) and acquire the same heights. If A is thrown at an angle of 45° with the horizontal, the angle of projection of B will be

A disk of radius \(a/4\) having a uniformly distributed charge \(6\,\text{C}\) is placed in the x-y plane with its centre at \((-a/2, 0, 0)\). A rod of length \(a\) carrying a uniformly distributed charge \(8\,\text{C}\) is placed on the x-axis from \(x = a/4\) to \(x = 5a/4\). Two point charges \(-7\,\text{C}\) and \(3\,\text{C}\) are placed at \((a/4, -a/4, 0)\) and \((-3a/4, 3a/4, 0)\) respectively. Consider a cubical surface formed by six surfaces \(x = \pm a/2\), \(y = \pm a/2\), \(z = \pm a/2\). The electric flux through this cubical surface is

A steel wire of length L at 40°C is suspended from the ceiling and carries a mass m from its free end. The wire is cooled from 40°C to 30°C to regain its original length L. The coefficient of linear expansion is 10⁻⁵/°C, Young’s modulus of steel is 10¹¹ N m⁻², and the radius of the wire is 1 mm. The value of m in kg is nearly

For the reaction
\(\text{H}_2(g) + \text{Br}_2(g) \to 2 \text{HBr}(g)\),

the experimental data suggest the rate law
\(\text{Rate} = k[\text{H}_2][\text{Br}_2]^{1/2}\).
The molecularity and order of the reaction are respectively

Which of the following relations represents the correct relation between standard electrode potential and equilibrium constant?

I. \(\log K = \frac{n F E^\circ}{2.303 R T}\)

II. \(K = e^{\frac{n F E^\circ}{R T}}\)

III. \(\log K = -\frac{n F E^\circ}{2.303 R T}\)

IV. \(\log K = 0.4342 \frac{n F E^\circ}{R T}\)

Choose the correct statements.

The standard electrode potentials are:
\(E^\circ(\text{Zn}^{2+}/\text{Zn}) = -0.76 \, \text{V}, \quad E^\circ(\text{Cu}^{2+}/\text{Cu}) = +0.34 \, \text{V}\).
The equilibrium constant for the reaction
\(\text{Zn} + \text{Cu}^{2+} \rightleftharpoons \text{Cu} + \text{Zn}^{2+}\)
at \(25^\circ \text{C}\) is of the order of
Specific conductance of 0.1 M \(HA\) is \(3.75 \times 10^{-4} \, \Omega^{-1} \text{cm}^{-1}\). If \(\Lambda_m^\infty (HA) = 250 \, \Omega^{-1} \text{cm}^2 \text{mol}^{-1}\), the dissociation constant \(K_a\) of \(HA\) is

My father gave me (a) a pair of binoculars (b)  on my birthday. (c) No error. (d)

The teacher as well as his students, (a)  all left (b)  for the trip. (c)  No error. (d)

If \(\sum_{k=1}^{n} k(k+1)(k-1) = p n^4 + q n^3 + t n^2 + s n\), where \(p, q, t, s\) are constants, then the value of \(s\) is equal to
The integer just greater than \((3 + \sqrt{5})^{2n}\) is divisible by
The domain of the function
\[ f(x) = \sin^{-1} \!\left( \log_2 \left( \frac{1}{2} x^2 \right) \right) \]
is
If \(A, B, C\) are the angles of a triangle and
\[ e^{iA}, \; e^{iB}, \; e^{iC} \]
are in A.P., then the triangle must be

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