List of top Mathematics Questions asked in BITSAT

A line makes the same angle \(\theta\) with each of the X and Z-axes. If the angle \(\beta\) which it makes with Y-axis is such that \(\sin^2\beta=3\sin^2\theta\), then \(\cos^2\theta\) equals
Let \(f:\mathbb R\to\mathbb R\) be a function such that \(f(x+y)=f(x)+f(y)\) for all \(x,y\in\mathbb R\). If \(f(x)\) is differentiable at \(x=0\), then which one of the following is incorrect?
If binomial coefficients of three consecutive terms of \((1+x)^n\) are in H.P., then the maximum value of \(n\) is
If complex numbers \(z_1,z_2\) and \(0\) are vertices of an equilateral triangle, then \(z_1^2+z_2^2-z_1z_2\) is equal to
If the lines \(p_1x+q_1y=1\), \(p_2x+q_2y=1\) and \(p_3x+q_3y=1\) are concurrent, then the points \((p_1,q_1), (p_2,q_2)\) and \((p_3,q_3)\) are
If \(\dfrac{\cos A}{\cos B}=n,\ \dfrac{\sin A}{\sin B}=m\), then the value of \(m^2-n^2\) is
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 \(\displaystyle \lim_{x\to\infty}x\sin\!\left(\frac1x\right)=A\) 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
If \(0 < x < \dfrac{\pi}{2}\), then
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 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
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
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)
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
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 number of real roots of the equation \[ e^{x-1}+x-2=0 \] 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 arithmetic mean of the data \(0,1,2,\ldots,n\) with frequencies \(1,{}^nC_1,{}^nC_2,\ldots,{}^nC_n\) is