List of top Mathematics Questions asked in BITSAT

If $A = \begin{bmatrix}1&1\\ 1&1\end{bmatrix}$ then $A^{100}$ :

If $\begin{bmatrix}\alpha&\beta\\ \gamma&-\alpha\end{bmatrix}$ is square root of identity matrix of order $2$ then

In how many ways can a committee of $5$ made out $6$ men and $4$ women containing atleast one woman?

Let $a \in R$ and let $f: R \rightarrow R$ be given by $f(x)=x^{5}-5 x+a$, then

If $P_1$ and $P_2$ be the length of perpendiculars from the origin upon the straight lines $x \sec \theta + y cosec \theta = a$ and $x \cos \theta - y \sin \theta = a \cos 2 \theta$ respectively, then the value of $4P_1{^2} + P_2{^2}$.

The angle of intersection of the two circles $x^2 + y^2 - 2x - 2y = 0$ and $x^2 + y^2 = 4$, is

If $T_0, T_1, T_2.....T_n$ represent the terms in the expansion of $ (x + a)^n$, then $(T_0 -T_2 + T_4 - .......)^2 + (T_1 - T_3 + T_5 - .....)^2 =$

Let $f(x)=\left(x^{5}-1\right)\left(x^{3}+1\right), g(x)=\left(x^{2}-1\right)\left(x^{2}-x+1\right)$ and let $h(x)$ be such that $f(x)=g(x) h(x)$. Then $\displaystyle\lim _{x \rightarrow 1} h(x)$ is

If the line $2x - 3y = k$ touches the parabola $y^2 = 6x$, then find the value of $k$.

A box contains two white balls, three black balls and four red balls. In how many ways can three balls be drawn from the box if at least one black ball is to be included in the draw?

If $4a^2 + b^2 + 2c^2 + 4ab - 6ac - 3bc = 0$, the family of lines $ax + by + c = 0$ is concurrent at one or the other of the two points-

If x satisfies $| 3 x - 2 | + | 3x - 4 | + | 3x - 6 | \ge 12$, then

Find the variance of the data given below

Occurance $(x_i)$	Frequency $(f_i)$	Freq $\ast (x_i)$	$(x_i-mean)$	$(x_i-mean)^2$	$f_i(x_i-mean)^2$
3.5	3	10.5	-3.59	12.887	38.661
4.5	7	31.5	-2.59	6.707	46.952
5.5	22	121	121	2.528	55.609
6.5	60	390	-0.59	0.348	20.876
7.5	85	637.5	0.41	0.168	14.298
8.5	32	272	1.41	1.988	63.632
9.5	8	76	2.41	5.809	46.47
Total	217	1538.5	-	-	286.498

A pair of tangents are drawn from the origin to the circle $x^2 + y^2+ 20 (x + y) + 20 = 0$, then the equation of the pair of tangent are

An ellipse has $OB$ as semi-minor axis, $F$ and $F$ are its foci and the $\angle FBF$, is a right angle. Then, the eccentricity of the ellipse is

A class has $175$ students. The following data shows the number of students obtaining one or more subjects. Mathematics $100$, Physics $70$, Chemistry $40$; Mathematics and Physics $30$, Mathematics and Chemistry $28$, Physics and Chemistry $23$; Mathematics, Physics and Chemistry $18$. How many students have offered Mathematics alone?

If $1.0$ mole of $I_{2}$ is introduced into $1.0$ litre flask at $1000\, K$, at equilibrium $\left(K_{c}=10^{-6}\right)$, which one is correct?

For the reaction $CO ( g )+\left(\frac{1}{2}\right) O _{2}( g ) \longrightarrow CO _{2}( g ), K _{ p } / K _{ c }$ is

Let $R$ be the relation on the set $R$ of all real numbers, defined by $aRb$ If $|a - b| \le 1$. Then, $R$ is

The value of $\cos \left[ \frac{1}{2} \cos^{-1}\left(\cos\left(\sin^{-1} \frac{\sqrt{63}}{8}\right)\right)\right] $ is -

The coefficient of the middle term in the expansion of $(2 + 3x)^4$ is :

For $k=1,2,3$ the box $Bk$ contains $k$ red balls and $(k+1)$ white balls. Let $P\left(B_{1}\right)=\frac{1}{2}, P\left(B_{2}\right)=\frac{1}{3}=\frac{1}{3}$ and $P\left(B_{3}\right)=\frac{1}{6} .$ A box is selected at random and a ball is drawn from it. If a red ball is drawn, then the probability that it has come from box $B_{2}$, is

In the truth table for the statement $(p \wedge q) \rightarrow(q \vee \sim p)$, the last column has the truth value in the following order is

$S$ and $T$ are the foci of an ellipse and $B$ is an end of the minor axis. If $STB$ is an equilateral triangle, then the eccentricity of the ellipse is