List of top Mathematics Questions asked in BITSAT

For $| x | < 1$, the constant term in the expansion of $\frac{1}{x -1^2 x - 2}$ is

$\cos \, A \, \cos \, 2A \, \cos \, 4A ... \cos \, 2^{n -1} A$ equals

If \(\begin{vmatrix}1&-1&x\\1&x&1\\x&-1&1\end{vmatrix}\) has no inverse, then the real value of \(x\) is

The roots of $ (x- a) (x - a-1) + (x - a -1) (x - a - 2) + (x - a) (x - a - 2) = 0 , a \in R$ are always

Let $f(x) = x^2 + ax + b,$ where $a, b \in R$. If $ f(x) = 0$ has all its roots imaginary, then the roots of $ f(x) + f' (x) + f" (x) = 0$ are

The period of $\sin^4 \, x + \cos^4 \, x$ is

The image of the point $(3, 2, 1)$ in the plane $2x-y+3z = 7$ is

If $m_1, m_2, m_3$ and $m_4$ are respectively the magnitudes of the vectors $a_1 = 2i - j + k, a_2 = 3i - 4j - 4 k $ $a_3 = i + j - k$ and $a_4 = - i + 3j + k , $ then the correct order of $m_1, m_2, m_3 $ and $m_4$ is

The locus of centre of a circle which passes through the origin and cuts off a length of $4$ unit from the line $x = 3$ is

If $x, y, z$ are all positive and are the $p^{th}, q^{th}$ and $r^{th}$ terms of a geometric progression respectively, then the value of the determinant $\begin{vmatrix} \log x & p & 1 \\ \log y & q & 1 \\ \log z & r & 1 \end{vmatrix} = 0 $ equals

The locus of $z$ satisfying the inequality $\frac{z + 2i}{2z + i} < 1$ , where $z = x + iy$, is

If one of the roots of $\begin{vmatrix} 3 &5 & x \\ 7 & x & 7 \\ x & 5 & 3 \end{vmatrix} = 0 $ is -10,then the other roots are

The inverse of the point $(1, 2)$ with respect to the circle $x^2 + y^2 - 4x - 6y + 9 = 0$, is

A pair of perpendicular straight lines passes through the origin and also through the point of intersection of the curve $x^2 + y^2 = 4$ with $x + y = a$. The set containing the value of '$a$' is

If $f : R \rightarrow R$ is defined by $f(x) = \begin{cases} \frac{\cos \ 3x - \cos \ x}{x^2} &, \text{for } x \neq 0 \\ \lambda &, \text{for } x = \end{cases}$ and if $f$ is continuous at $x = 0,$ then $\lambda$ is equal to

If $f(2) = 4$ and $f'(2) = 1$, then $\displaystyle\lim_{x \to 2} \frac{xf (2) - 2 f (x) }{x -2}$ is equal to

The solution of the differential equation $\frac{dy}{dx} = \frac{xy + y}{xy + x}$ is

In $\triangle A B C$ the mid points of the sides $A B, B C$ and $C A$ are respectively $(1,0,0),(0$, $m , 0)$ and $(0,0, n )$. Then, $\frac{A B^{2}+B C^{2}+C A^{2}}{l^{2}+m^{2}+n^{2}}$ is equal to

If $f: R \rightarrow R$ is defined by $f(x)=[x-3]+|x-4|$ for $x \in R$, then $\displaystyle\lim _{x \rightarrow 3} f(x)$ is equal to

The distance between the foci of the hyperbola $x^2 - 3y^2 - 4x - 6y -11 = 0$ is

The radius of the circle with the polar equation $r^2 - 8r( \sqrt{3} \, \cos \, \theta + \sin \, \theta) + 15 = 0$ is

If $2x + 3y + 12 = 0$ and $x - y + 4 \lambda = 0$ are conjugate with respect to the parabola $y^2 = 8x$, then $\lambda$ is equal to

If $A$ and $B$ are independent events of a random experiment such that $P(A \cap B) = \frac{1}{6} $ and $P(A \cap B) = \frac{1}{3}$, then $P(A)$ is equal to (Here, $E$ is the complement of the event $E$)

If the lines $2x - 3y = 5$ and $3x - 4y = 7$ are two diameters of a circle of radius $7$, then the equation of the circle is

The solution of the differential equation $\frac{d y}{d x}+\frac{2 y x}{1+x^{2}}=\frac{1}{1+x^{22}}$ is