List of top Questions asked in AP ECET

If $A = \begin{bmatrix}k/2&0&0\\ 0&1/3&0\\ 0&0&m/4\end{bmatrix} $ and $A^{-1} = \begin{bmatrix}1/2&0&0\\ 0&1/3&0\\ 0&0&1/4\end{bmatrix}$ then $ k + l + m = $

A random variable X has the following probability distribution The variance of this random variable is

For the matrix $A = \begin{pmatrix}3&-3&4\\ 2&-3&4\\ 0&-1&1\end{pmatrix}, A^{-1} = $

If $x^{2}+\alpha y^{2}+2 \beta y=a^{2} \quad$ represents a pair of perpendicular lines, then $\beta$ equals to

The condition for the lines $l x+m y+n=0$ and $l_{1} x+m_{1} y+n_{1}=0$ to be conjugate with respect to the circle $x^{2}+y^{2}=r^{2}$, is

The slopes of the focal chords of the parabola $y^{2}=32 x$, which are tangents to the circle $x^{2}+y^{2}=4$, are

Wires $ A $ and $ B $ have resistivities $ \rho_{A} $ and $ \rho_{B} $ , $ (\rho_{B}=2\rho_{A}) $ and have lengths $ l_{A} $ and $ l_{B} $ . If the diameter of the wire $ B $ is twice that of $ A $ and the two wires have same resistance, then $ \frac{l_{B}}{l_{4}} $ is

The point at which the circles $x^{2}+y^{2}-4 x-4 y+7=0 $ and $x^{2}+y^{2}-12 x -10 y+45=0$ touch each other, is

If a normal chord at a point $t$ on the parabola $y^{2}=4 \,a \,x$ subtends a right angle at the vertex, then $t$ equals to

The length of the common chord of the two circles $x^{2}+y^{2}-4 y=0 $ and $x^{2}+y^{2}-8 x - 4 y+11=0$, is

A circle with centre at $(2,4)$ is such that the line $x+y+2=0$ cuts a chord of length $6$ . The radius of the circle is

The locus of the centre of the circle, which cuts the circle $x^{2}+y^{2}-20 x+4=0$ orthogonally and touches the line $x=2$, is

The area (in s units) of the triangle formed by the lines $x^{2}-3 x y+y^{2}=0$ and $x+y+1=0$, is

The shortest distance between the skew lines $\bar{r}=(i+2\bar{j}+3\bar{k})+t(i+3\bar{j}+2\bar{k}) $ and $\bar{r}=(4i+5\bar{j}+6\bar{k})+t(2i+3\bar{j}+\bar{k})$ is

If a line $l$ passes through $(k, 2 k),(3 k, 3 k)$ and $(3,1), k \neq 0$, then the distance from the origin to the line $l$ is

A convex lens has its radii of curvature equal. The focal length of the lens is $f$. If it is divided vertically into two identical plano-convex lenses by cutting it, then the focal length of the plano-convex lens is $(\mu=$ the refractive index of the material of the lens $)$

A thin converging lens of focal length $ f = 25\, cm $ forms the image of an object on a screen placed at a distance of $ 75\, cm $ from the lens. The screen is moved closer to the lens by a distance of $ 25\, cm $ . The distance through which the object has to be shifted, so that its image on the screen in sharp again is

Three resistances of equal values are arranged in four different configurations as shown below. Power dissipation in the increasing order is

Four resistors $A, B, C$ and $D$ form a Wheatstones bridge. The bridge is balanced, when $C=100 \Omega$. If $A$ and $B$ are interchanged, the bridge balances for $C=121 \Omega$. The value of $D$ is

Three rods of same dimensions have thermal conductivities 3 K, 2 K and K. They are arranged as shown below:What will be the temperature T of the junction?

A ball of mass 0.6 kg attached to a light inextensible string rotates in a vertical circle of radius 0.75 m such that it has a speed of $ 5\text{ }m{{s}^{-1}} $ when the string is horizontal. Tension in string when it h horizontal on other side is $ (g=10m{{s}^{-}}2) $

Of the vectors given below, the parallel vectors are, $ A = 6 \hat i + 8 \hat j$ $30mm B = 210 \hat i + 280 \hat k$ $ C = 0.3 \hat i + 0.4 \hat j$ $ D = 3.6 \hat i + 6 \hat j + 4.8 \hat k$

The rate constant of a reaction at temperature 200 K is 10 times less than the rate constant at 400 K. What is the activation energy $ E_a$ of the reaction? (R = Gas constant)

Reduction of nitrobenzene in the presence of $ \text{Zn/N}{{\text{H}}_{\text{4}}}\text{Cl} $ gives: