List of top Mathematics Questions asked in BITSAT

The domain of the function \[ f(x)=\frac{\sin^{-1}(x-3)}{\sqrt{9-x^2}} \] is
Area of the circle in which a chord of length \(\sqrt{2}\) makes an angle \(\pi/2\) at the centre is
The degree of the differential equation satisfying \[ \sqrt{1-x^2}+\sqrt{1+y^2}=a(x-y) \] is
If \(0 < x < \dfrac{\pi}{2}\), then
If \(\displaystyle \lim_{x\to\infty}x\sin\!\left(\frac1x\right)=A\) and \(\displaystyle \lim_{x\to0}x\sin\!\left(\frac1x\right)=B\), then which one of the following is correct?
If \(y=\left(x+\sqrt{1+x^2}\right)^n\), then \((1+x^2)\dfrac{d^2y}{dx^2}+x\dfrac{dy}{dx}\) is
If \(a\) and \(b\) are non-zero roots of \(6x^2+ax+b=0\), then the least value of \(x^2+ax+b\) is
The eccentricity of an ellipse, with its centre at origin, is \(1/2\). If one of the directrices is \(x=4\), then the equation of the ellipse is
Let \(M\) be a \(3\times3\) non-singular matrix with \(\det(M)=\alpha\). If \(|M^{-1}\operatorname{adj}(M)|=K\), then the value of \(K\) is
The function \(f(x)=\dfrac{x}{2}+\dfrac{2}{x}\) has local minimum at
Tangents are drawn from the origin to the curve \(y=\cos x\). Their points of contact lie on
The slope of the tangent to the curve \(y=e^x\cos x\) is minimum at \(x=\alpha,\;0\le\alpha\le2\pi\). Then the value of \(\alpha\) 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
Two lines \(L_1:\;x=5,\; \dfrac{y}{3-\alpha}=\dfrac{z}{-2}\) \(L_2:\;x=\alpha,\; \dfrac{y}{1}=\dfrac{z}{2-\alpha}\) are coplanar. Then \(\alpha\) can take value(s)
Let \(S\) be the focus of the parabola \(y^2=8x\) and \(PQ\) be the common chord of the circle \(x^2+y^2-2x-4y=0\) and the given parabola. The area of \(\triangle PQS\) is
The mean square deviation of a set of observations \(x_1,x_2,\ldots,x_n\) about point \(c\) is defined as \[ \frac1n\sum_{i=1}^n(x_i-c)^2. \] The mean square deviations about \(-2\) and \(2\) are 18 and 10 respectively. The standard deviation of the set of observations is
In a \(\triangle ABC\), the lengths of the two larger sides are 10 and 9 units respectively. If the angles are in A.P., then the length of the third side can be
The number of real roots of the equation \[ e^{x-1}+x-2=0 \] is
Minimise \( Z=\sum_{i=1}^{n}\sum_{j=1}^{m} c_{ij}x_{ij} \) subject to \[ \sum_{i=1}^{m} x_{ij}=b_j,\; j=1,2,\ldots,n, \] \[ \sum_{j=1}^{n} x_{ij}=b_i,\; i=1,2,\ldots,m. \] This is an LPP with number of constraints equal to
The arithmetic mean of the data \(0,1,2,\ldots,n\) with frequencies \(1,{}^nC_1,{}^nC_2,\ldots,{}^nC_n\) 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
If \(\cos^{-1}x-\cos^{-1}\frac{y}{2}=\alpha\), then \(4x^2-4xy\cos\alpha+y^2\) is equal to
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
The total number of 4-digit numbers in which the digits are in descending order is