List of top Mathematics Questions asked in BITSAT

The point of inflexion for the curve \(y = (x - a)^n\), where \(n\) is odd integer and \(n \ge 3\), is:

The maximum volume (in cu. units) of the cylinder which can be inscribed in a sphere of radius 12 units is:

If \( x\sqrt{1 + y} + y\sqrt{1 + x} = 0 \), then find \( \frac{dy}{dx} \).

The value of definite integral \( \int_0^{\pi/2} \log(\tan x) dx \) is:

The function \[ f(x) = \frac{\cos x}{\left\lfloor \frac{2x}{\pi} \right\rfloor + \frac{1}{2}}, \] where \( x \) is not an integral multiple of \( \pi \) and \( \lfloor \cdot \rfloor \) denotes the greatest integer function, is:

The value of \( \int e^{\tan \theta} (\sec \theta - \sin \theta) \, d\theta \) is:

If \( y = \tan^{-1}\left( \frac{\sqrt{x} - x}{1 + x^{3/2}} \right) \), then \( y'(1) \) is equal to:

The value of \( \int_0^\infty \frac{dx}{(x^2 + a^2)(x^2 + b^2)} \) is:

Consider the function \( f(x) = \frac{|x-1|{x^2} \). Then \( f(x) \) is:}

Evaluate the integral: \[ \int \frac{x^3 - 1}{x^3 + x} dx \]

Evaluate the integral: \[ \int \sqrt{x + \sqrt{x^2 + 2}} \, dx. \]

If \( f: \mathbb{R} \to \mathbb{R} \), \( g: \mathbb{R} \to \mathbb{R} \) are defined by \( f(x) = 5x - 3 \), \( g(x) = x^2 + 3 \), then \( g \circ f^{-1}(3) \) is equal to

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

The population \( p(t) \) at time \( t \) of a certain mouse species satisfies the differential equation:
\[ \frac{d p(t)}{dt} = 0.5p(t) - 450. \] If \( p(0) = 850 \), then the time at which the population becomes zero is:

At \( x = \frac{\pi^2}{4} \), \( \frac{d}{dx} \left( \tan^{-1}(\cos\sqrt{x}) + \sec^{-1}(e^x) \right) = \)

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

The line \(y = mx\) bisects the area enclosed by lines \(x = 0\), \(y = 0\), and \(x = \frac{3}{2}\) and the curve \(y = 1 + 4x - x^2\). Then, the value of \(m\) is:

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

The value of \( \int_0^{\frac{\pi}{2}} \frac{\sin\left( \frac{\pi}{4} + x \right) + \sin\left( \frac{3\pi}{4} + x \right)}{\cos x + \sin x} \, dx \) is:

Evaluate the integral: \[ \int \frac{x^2 (x \sec^2 x + \tan x)}{(x \tan x + 1)^2} dx \]

The number of solutions of the differential equation \[ \frac{dy}{dx} = \frac{y+1}{x-1} \] when \( y(1) = 2 \) is:

Number of words from the letters of the word BHARAT in which B and H will never come together is:

Bag P contains 6 red and 4 blue balls, and bag Q contains 5 red and 6 blue balls. A ball is transferred from bag P to bag Q and then a ball is drawn from bag Q. What is the probability that the ball drawn is blue?