List of top Mathematics Questions asked in BITSAT

In an examination, 62% of the candidates failed in English, 42% in Mathematics and 20% in both. The number of those who passed in both the subjects is:

If $ \vec{a} = 2\hat{i} + \hat{j} + 2\hat{k} $, then the value of $ |\hat{i} \times (\vec{a} \times \hat{i})| + |\hat{j} \times (\vec{a} \times \hat{j})| + |\hat{k} \times (\vec{a} \times \hat{k})|^2 $ is equal to:}

If a function $ f: \mathbb{R} \setminus \{1\} \rightarrow \mathbb{R} \setminus \{m\} $ is defined by $ f(x) = \frac{x+3}{x-2} $, then $ \frac{3}{l} + 2m = $

Let $ [x] $ denote the greatest integer $ \leq x $. If $ f(x) = [x] $ and $ g(x) = |x| $, then the value of:
\[ f \left( g \left( \frac{8}{5} \right) \right) - g \left( f \left( \frac{-8}{5} \right) \right) \] is:

The function f: R$\rightarrow$ R is defined by \[ f(x) = \frac{x}{\sqrt{1 + x^2}} \] is:

If matrix $ A = \begin{bmatrix} 3 & -2 & 4 \\ 1 & 2 & -1 \\ 0 & 1 & 1 \end{bmatrix} $ and $ A^{-1} = \frac{1}{k} adj(A) $, then $ k $ is

If $ p $: 2 is an even number, $ q $: 2 is a prime number, and $ r $: $ 2 + 2 = 2^2 $, then the symbolic statement $ p \rightarrow (q \vee r) $ means:

The coefficient of the highest power of $x$ in the expansion of $(x + \sqrt{x^2 - 1})^8 + (x - \sqrt{x^2 - 1})^8$ is:

The coefficient of $x^2$ term in the binomial expansion of $\left(\frac{1}{3}x^{\frac{1}{3}} + x^{-\frac{1}{4}}\right)^{10}$ is:

If the variance of the data $ 2,3,5,8,12 $ is $ \sigma^2 $ and the mean deviation from the median for this data is $ M $, then $ \sigma^2 - M $ is:

From a point A(0,3) on the circle \[ (x + 2)^2 + (y - 3)^2 = 4 \] a chord AB is drawn and extended to a point Q such that AQ = 2AB. Then the locus of Q is:

From the top of a cliff 50 m high, the angles of depression of the top and bottom of a tower are observed to be $30^\circ$ and $45^\circ$. The height of the tower is:

If the function $ f(x) $, defined below, is continuous on the interval $[0,8]$, then: \[ f(x) = \begin{cases} x^2 + ax + b, & 0 \leq x < 2 \\ 3x + 2, & 2 \leq x \leq 4 \\ 2ax + 5b, & 4 < x \leq 8 \end{cases} \]

Evaluate the integral: \[ \int_{5}^{9} \frac{\log 3x^2}{\log 3x^2 + \log (588 - 84x + 3x^2)} dx \]

Evaluate the following limit: $ \lim_{n \to \infty} \prod_{r=3}^n \frac{r^3 - 8}{r^3 + 8} $.

For two events A and B, if $P(A) = P(A/B) = \frac{1}{4}$ and $P(B/A) = \frac{1}{2}$, then which of the following is not true?

A book contains 1000 pages. A page is chosen at random. The probability that the sum of the digits of the marked number on the page is equal to 9, is

Given below is the distribution of a random variable $X$:
\[ \begin{array}{|c|c|} \hline X = x & P(X = x) \\ \hline 1 & \lambda \\ 2 & 2\lambda \\ 3 & 3\lambda \\ \hline \end{array} \] If $\alpha = P(X<3)$ and $\beta = P(X>2)$, then $\alpha : \beta = $

The probability that certain electronic component fails when first used is 0.10. If it does not fail immediately, the probability that it lasts for one year is 0.99. The probability that a new component will last for one year is

In a binomial distribution, the mean is 4 and variance is 3. Then, its mode is:

The probability of getting 10 in a single throw of three fair dice is:

If the number of available constraints is 3 and the number of parameters to be optimised is 4, then