List of top Mathematics Questions asked in Assam CEE

The eccentricity of the hyperbola which is the locus of a point moving in a plane such that the difference of its distances from the points \[ (-5,0) \quad\text{and}\quad (5,0) \] is equal to \(8\), is
If \(P\) is any point on the ellipse \[ \frac{x^2}{a^2}+\frac{y^2}{b^2}=1 \] with major axis \(AA'\), and \(N\) is the foot of the perpendicular drawn from \(P\) upon \(AA'\), then
If the straight line \[ lx+my+n=0 \] touches the parabola \[ y^2=4ax, \] then
The area of the region bounded by the \(x\)-axis, the line \(x=4\) and the curve \[ f(x)= \begin{cases} x^2, & 0\le x\le 1\\ \sqrt{x}, & x\gt 1 \end{cases} \] is
The value of \[ \int_{\alpha}^{\beta} \sqrt{(x-\alpha)(\beta-x)}\,dx, \qquad \alpha\ne\beta \] is
The value of \[ \int \frac{dx}{\sin x\,(2+3\cos x)} \] is
If \[ x=f(t), \qquad y=g(t), \] then \[ \frac{d^2y}{dx^2} \] equals
A milkman has \(250\) litres of milk containing \(5\%\) fat. How many litres of milk containing \(15\%\) fat should he add to his stock so that the fat content in the mixture would be more than \(7\%\) but less than \(10\%\)?
If \[ \arg\left(\frac{z-1}{z+1}\right)=\frac{\pi}{4}, \] then the locus of the point \(P(z)\) on the Argand plane is a
If \[ y=\left(\frac{a+x}{b+x}\right)^{a+b+2x}, \] then \[ \left.\frac{dy}{dx}\right|_{x=0} \] is
If a coin is tossed \(10\) times, the probability of getting head at least two times but at most five times is
If \(A\) is a \(3\times3\) matrix with \[ |A|=-1, \] then \[ \left|\,3(\operatorname{adj}(A^T))A^2\,\right| \] equals
How many license plates can be made if the license plates contain 6 characters out of which the first two characters are distinct digits and the remaining 4 characters are distinct capital letters of the English alphabet?
The range of the function \[ f:\mathbb{R}-\{-1,1\}\to\mathbb{R}, \qquad f(x)=\frac{x^2}{1-x^2} \] is
If a machine is correctly set up, it produces \(90\%\) acceptable items. If it is incorrectly set up, it produces \(40\%\) acceptable items. Past experience shows that \(80\%\) of the setups are correctly done. If after a certain setup, the machine produces \(2\) acceptable items, then the probability that the machine is correctly set up is
For a linear programming problem, which one is correct?
If \(\vec a,\vec b,\vec c\) are three vectors such that \[ |\vec a|=a,\qquad |\vec b|=b,\qquad |\vec c|=c \] and each one of them is perpendicular to the sum of the other two, then \[ |\vec a+\vec b+\vec c| \] equals
Assuming that the straight line works as a plane mirror for a point, the image of the point \((1,2)\) in the line \[ x-3y+4=0 \] is
The equations of two circles which touch the coordinate axes and whose centres lie on the line \[ x-2y=3 \] are
The orthocentre of the triangle formed by the following straight lines is \[ y=x,\qquad x-2y+1=0,\qquad 3x-4y-1=0 \]
Which of the following functions is differentiable on the set of real numbers?
Which of the following functions is not continuous on the set of real numbers?
\(f(x)\) is a polynomial of degree \(3\) such that \[ f(0)=f(3)=f(-3)=0 \] \[ f(1)=-8 \] The maximum and minimum values of \(f(x)\) are respectively
The function \[ y=\frac{\sin x+2\cos x}{3\sin x+4\cos x} \] is
The value of \[ \sin\left[\cos^{-1}\left(\frac{3}{5}\right)+\tan^{-1}(-2)\right] \] is