List of top Questions asked in BITSAT- 2017

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

Correct formula of the complex formed in the brown ring test for nitrates is
If $\displaystyle\sum^n_{R = 0} (-1)^r \; \frac{^{n}C_{r}}{^{r+3}C_{r}} = \frac{3}{a+3} $ , then a - n is equal to
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
The equation of one of the common tangents to the parabola y²=8x and x²+y²-12x+4=0 is
The length of the semi-latus rectum of an ellipse is one third of its major axis. Its eccentricity would be
The value of
\[ \lim_{x \to \infty} \left(a_1^{1/x} + a_2^{1/x} + \cdots + a_n^{1/x}\right)^{n x}, \quad a_i > 0 \]
If \(f(z) = \frac{7 - z}{1 - z^2}\), where \(z = 1 + 2i\), then \(|f(z)|\) is equal to
An equilateral triangle is inscribed in the circle x²+y²=a² with one of the vertices at (a,0). What is the equation of the side opposite to this vertex?
Given the system of straight lines a(2x+y-3)+b(3x+2y-5)=0, the line of the system situated farthest from the point (4,-3) has the equation
The angle between the two lines whose intercepts on the axes are a,-b and b,-a respectively is
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
\[ f(x) = \begin{cases} \dfrac{x \log(\cos x)}{\log(1 + x^2)}, & x \ne 0 \\[2mm] 0, & x = 0 \end{cases} \]
then \(f(x)\) is
How many different nine digit numbers can be formed from the number 223355888 by rearranging its digits so that odd digits occupy even positions?
Statement–1: A five digit number divisible by 3 is to be formed using the digits 0,1,2,3,4 and 5 with repetition. The total number formed are 216. Statement–2: If sum of digits of any number is divisible by 3 then the number must be divisible by 3.
If \(\sum_{r=0}^{n} \binom{n}{r} \frac{r + 3}{r} = \frac{3}{a+3}\), then \(a - n\) is equal to
If x is real number, then (x)/(x²-5x+9) must lie between
The integer just greater than \((3 + \sqrt{5})^{2n}\) is divisible by
One mapping is selected at random from all mappings of the set S=1,2,3,… ,n into itself. The probability that it is one–one is (3)/(32). Then the value of n is
An urn contains five balls. Two balls are drawn and found to be white. The probability that all the balls are white is
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 value of cot⁻17+cot⁻18+cot⁻118 is

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?

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