List of top Mathematics Questions asked in BITSAT

If $\log a, \log b$, and $\log c$ are in A.P. and also $\log a-\log 2 b, \log 2 b-\log 3 c, \log 3 c-\log a$ are in A.P., then

If $\sin^{-1} \left(\frac{2a}{1+a^{2}}\right) -\cos^{-1} \left(\frac{1-b^{2}}{1+b^{2}}\right) = \tan^{-1} \left(\frac{2x}{1-x^{2}}\right) , $ then what is the value of x?

The curve $y = xe^x$ has minimum value equal to

If $\sum\limits^{n}_{r=0} \frac{r+2}{r+1} \,^{n}C_{r} = \frac{2^{8}-1}{6} $, then $n =$

The number of values of $r$ satisfying the equation $^{39}C_{3r-1} - ^{39}C_{r^{2}} = ^{39}C_{r^{2}-1} - ^{39}C_{3r} $ is

The locus of the point of intersection of two tangents to the parabola $y^2 = 4ax$, which are at right angle to one another is

All the words that can be formed using alphabets $A, H, L, U$ and $R$ are written as in a dictionary (no alphabet is repeated). Rank of the word RAHUL is

A ray of light coming from the point $(1, 2)$ is reflected at a point $A$ on the $x$-axis and then passes through the point $(5, 3)$. The co-ordinates of the point $A$ is

The number of integral values of $\lambda$ for which $x^2 + y^2 + \lambda x + (1 - \lambda )y + 5 = 0 $ is the equation of a circle whose radius cannot exceed $5$, is

Let $f (x) = \frac{ax+ b}{cx + d} $ , then $fof(x) = x$, provided that :

At an extreme point of a function $f (x)$, the tangent to the curve is

Consider the following statements in respect of the function $f(x)=x^{3}-1, x \in[-1,1]$ I. $f(x)$ is increasing in $[-1,1]$ II. $f(x)$ has no root in $(-1,1)$. Which of the statements given above is/are correct?

The lengths of the tangent drawn from any point on the circle $15x^2 +15y^2 - 48x + 64y = 0$ to the two circles $5x^2 + 5y^2 - 24x + 32y + 75 = 0$ and $5x^2 + 5y^2 - 48x + 64y + 300 = 0$ are in the ratio of

The line joining $(5,0)$ to $((10 \cos \theta, 10 \sin \theta)$ is divided internally in the ratio $2: 3$ at $P$. If $q$ varies, then the locus of $P$ is

If three vertices of a regular hexagon are chosen at random, then the chance that they form an equilateral triangle is :

The average age of 8 men is increased by 2 years when one of them whose age is 20 years is replaced by a new man. What is the age of the new man?

If \(\rho=\{(x,y)\mid x^2+y^2=1;\ x,y\in\mathbb R\}\), then \(\rho\) is

Let \(f(x)\) be a polynomial of degree three satisfying \(f(0)=-1\) and \(f'(0)=0\). Also, 0 is a stationary point of \(f(x)\). If \(f(x)\) does not have an extremum at \(x=0\), then the value of \[ \int \frac{f(x)}{x^3-1}\, dx \] is

If in a binomial distribution \(n=4\), \(P(X=0)=\frac{16}{81}\), then \(P(X=4)\) equals

A line makes the same angle \(\theta\) with each of the X and Z-axes. If the angle \(\beta\) which it makes with Y-axis is such that \(\sin^2\beta=3\sin^2\theta\), then \(\cos^2\theta\) equals

Let \(f:\mathbb R\to\mathbb R\) be a function such that \(f(x+y)=f(x)+f(y)\) for all \(x,y\in\mathbb R\). If \(f(x)\) is differentiable at \(x=0\), then which one of the following is incorrect?

If binomial coefficients of three consecutive terms of \((1+x)^n\) are in H.P., then the maximum value of \(n\) is

If complex numbers \(z_1,z_2\) and \(0\) are vertices of an equilateral triangle, then \(z_1^2+z_2^2-z_1z_2\) is equal to

Area of the circle in which a chord of length \(\sqrt{2}\) makes an angle \(\pi/2\) at the centre is

If \(\dfrac{\cos A}{\cos B}=n,\ \dfrac{\sin A}{\sin B}=m\), then the value of \(m^2-n^2\) is