List of top Mathematics Questions asked in BITSAT

The number of real roots of the equation \[ e^{x-1}+x-2=0 \] is

Universal set, \[ U=\{x\mid x^5-6x^4+11x^3-6x^2=0\}; \quad A=\{x\mid x^2-5x+6=0\}; \quad B=\{x\mid x^2-3x+2=0\}. \] What is \((A\cap B)'\)?

If \[ \frac{e^x+e^{5x}}{e^{3x}}=a_0+a_1x+a_2x^2+a_3x^3+\cdots, \] then the value of \(2a_1+2^3a_3+2^5a_5+\cdots\) is

Let \(\vec a,\vec b,\vec c\) be three vectors satisfying \(\vec a\times\vec b=\vec a\times\vec c\), \(|\vec a|=|\vec c|=1\), \(|\vec b|=4\) and \(|\vec b\times\vec c|=\sqrt{15}\). If \(\vec b-2\vec c=\lambda \vec a\), then \(\lambda\) equals

If \(\cos^{-1}x-\cos^{-1}\frac{y}{2}=\alpha\), then \(4x^2-4xy\cos\alpha+y^2\) is equal to

The total number of 4-digit numbers in which the digits are in descending order is

The line which is parallel to X-axis and crosses the curve \(y=\sqrt{x}\) at an angle \(45^\circ\) is

The area of the region \(R=\{(x,y):|x|\le |y| \text{ and x^2+y^2\le1\}\) is

If \(\phi(x)\) is a differentiable function, then the solution of the differential equation \[ dy+y\phi'(x)-\phi(x)\phi'(x)\,dx=0 \] is

A bag contains \((2n+1)\) coins. It is known that \(n\) of these coins have a head on both sides, whereas the remaining \((n+1)\) coins are fair. A coin is picked up at random from the bag and tossed. If the probability that the toss results in a head is \(\frac{31}{42}\), then \(n\) is equal to

If a function \(f(x)\) is given by \[ f(x)=\frac{x}{1+x}+\frac{x}{(x+1)(2x+1)}+\frac{x}{(2x+1)(3x+1)}+\cdots+\infty, \] then at \(x=0\), \(f(x)\)

The period of \(\tan 3\theta\) is

If \(g\) is the inverse of function \(f\) and \(f'(x)=\sin x\), then \(g'(x)\) is equal to

The value of \[ \frac34+\frac{15}{16}+\frac{63}{64}+\cdots \text{ up to } n \text{ terms is} \]

If \(\omega\) is the complex cube root of unity, then the value of \[ \omega+\omega\!\left(\frac12+\frac38+\frac{9}{32}+\frac{27}{128}+\cdots\right) \] is

The root of the equation \[ 2(1+i)x^2-4(2-i)x-5-3i=0 \] which has greater modulus is

\(\displaystyle \lim_{x\to\infty}\frac{\int_{0}^{2x} x e^{x^{2}}\,dx}{e^{4x^{2}}}\) equals

The mean square deviation of a set of $n$ observation $x_{1}, x_{2},... x_{n}$ about a point $c$ is defined as $\frac{1}{n} \displaystyle\sum_{i=1}^{n}\left(x_{i}-c\right)^{2}$.The mean square deviations about $- 2$ and $2$ are $18$ and $10$ respectively, the standard deviation of this set of observations is

The number of real roots of the equation $e^{x-1} + x - 2 = 0$ is

Let $M$ be a $3 \times 3$ non-singular matrix with $det(M)=\alpha$. If $\left[M^{-1} adj(adj(M)]=K I\right.$, then the value of $K$ is

A bag contains $3$ red and $3$ white balls. Two balls are drawn one by one. The probability that they are of different colours is.

The arithmetic mean of the data $0,1,2, \ldots \ldots, n$ with frequencies $1,{ }^{n} C_{1},{ }^{n} C_{2}, \ldots,{ }^{n} C_{n}$ is

Let $S$ be the focus of the parabola $y ^{2}=8 x$ and let $PQ$ be the common chord of the circle $x^{2}+y^{2}-2 x-4 y=0$ and the given parabola. The area of the $\Delta PQS$ is

If a function $f(x)$ is given by $f(x)=\frac{x}{1+x}+\frac{x}{(x+1)(2 x+1)}+\frac{x}{(2 x+1)(3 x+1)}+\ldots \infty$ then at $x =0$, $f(x)$

The total number of $4$-digit numbers in which the digits are in descending order, is