List of top Mathematics Questions asked in BITSAT

If $2 i + j - k$ and $i -4 j +\lambda k$ are perpendicular to each other, then $\lambda$ is equal to:

The length of the latus rectum of the parabola $169\left[(x-1)^{2}+(y-3)^{2}\right]=(5 x-12 y+ 17) ^{2}$ is:

$\int \frac{\sin 2 x}{\sin ^{4} x+\cos ^{4} x}$ is equal to:

A bag contains $3$ white and $5$ black balls. One ball is drawn at random. Then the probability that it is white is:

Equation of the bisector of the acute angle between lines $3x + 4y + 5 = 0$ and $12x -5y - 7 = 0$ is

The value of $\begin{vmatrix}1&2&3\\ -4&3&6\\ 2&-7&9\end{vmatrix} $ is

Which one of the following is the unit vector perpendicular to both $\vec{a}=-\hat{i}+\hat{j}+\hat{k}$ and $\vec{b}=\hat{i}-\hat{j}+\hat{k}$ ?

If $f(x)=\frac{x}{\sqrt{1+x^{2}}}$, then (fof of) ( $x$ ) is

If $A = \begin{bmatrix}1&3\\ 3&2\\ 2&5\end{bmatrix}$ and $ B = \begin{bmatrix}-1&-2\\ 0&5\\ 3&1\end{bmatrix} $ and $A + B - D = 0$ (zero matrix), then $D$ matrix will be -

The area of the region bounded by the curve $y=x |x|, x$-axis and the ordinates $x=1, x=$ $-1$ is given by:

In a polygon no three diagonals are concurrent. If the total number of points of intersection of diagonals interior to the polygon be $70$ then the number of diagonals of the polygon is

The value of $\cos^{-1}x + \cos^{-1} \left(\frac{x}{2} + \frac{1}{2} \sqrt{3-3x^{2}}\right) ; \frac{1}{2} \le x \le 1 $ is

With $17$ consonants and $5$ vowels the number of words of four letters that can be formed having two different vowels in the middle and one consonant, repeated or different at each end is

The function $f(x) = \tan x - 4x$ is strictly decreasing on

If $m$ arithmetic means are inserted between $1$ and $31$ so that the ratio of the $7^{th}$ and $(m - 1)^{th}$ means is $5 : 9$, then find the value of m.

The slope of the tangent to the hyperbola $2x^2 - 3y^2 = 6$ at $(3, 2)$ is

If $I_{m}=\int\limits_{1}^{e}(\ln x)^{m} d x$, where $m \in N$, then $I_{10}+10 I_{9}$ is equal to -

Mean of $25$ observations was found to be $78.4$. But later on it was found that $96$ was misread $69$. The correct mean is

The solution of differential equation $2x \frac{dy}{dx} - y = 3$ represents a family of

The coefficient of $x^{24}$ in the expansion of $(1 + x^2)^{12} (1 + x^{12}) (1 + x^{24})$ 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

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

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