List of top Questions asked in Assam CEE

For what value of \(x\), will the two vectors \[ \vec A=\hat i+4\hat j-2\hat k \] \[ \vec B=-2\hat i+x\hat j-x^2\hat k \] be mutually perpendicular?

In the equation \[ X=\frac12 E_rYZ^2 \] \(Z\) has the dimensions of \[ \frac12 LI^2 \] and \(X\) has the dimensions of energy. \(L\) stands for coefficient of self-induction and \(I\) for electric current. What are the dimensions of \(Y\)?

An astronomical telescope in normal adjustment has magnifying power \(5\) for distant objects. The separation between the objective and the eyepiece is \(36\) cm. The focal lengths of the objective and the eyepiece are respectively

Two coherent monochromatic light beams of intensities \(I\) and \(4I\) are superposed. What are the maximum and minimum possible intensities in the resulting beam?

A double convex lens is made of a certain material. The refractive index of the material of the lens is \(1.55\) for violet rays and \(1.50\) for red rays. If the focal length of the lens is \(20\) cm for violet rays, then the focal length of the lens for red rays is

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 \[ y=x,\qquad x-2y+1=0,\qquad 3x-4y-1=0 \]