List of top Questions asked in COMEDK UGET- 2007

A set $A$ has $5$ elements. Then the maximum number of relations on $A$ (including empty relation) is

If $A, B, C, D$ are four points and $\vec{AB} = \vec{DC}$ , then $\vec{AC} + \vec{BD} = $

The vectors $\vec{a} = x \hat{i} + (x +1) \hat{j} + ( x +2 ) \hat{k} $ $\vec{b} = (x + 3) \hat{i} + (x +4) \hat{j} + ( x + 5 ) \hat{k} $ , and $\vec{c} = (x + 6) \hat{i} + (x + 7 ) \hat{j} + ( x + 8) \hat{k} $ are co-planar for

The derivative of $\cos^{-1}\left(\frac{1-x^{2}}{1+x^{2}}\right) $ with respect to $\cot^{-1} \left(\frac{1-3x^{2}}{3x-x^{3}}\right)$ is

Let $f(x) = \begin{cases} -2 \sin x, &x \leq - \pi /2 \\ a \sin x +b, & - \pi /2 < x < \pi /2 \\ \cos \, x , & x \geq \pi /2 \end{cases}$ then the? values of a and b so that $f(x)$ is continuous are

If $x^y = \log x$ , then $\frac{dy}{dx} $ at the point where the curve cuts the $x-axis$ is

If $a= 5, b = 13 , c = 12$ in $\Delta ABC$, then $\tan \frac{B}{4}$ is

If $y = \tan^{-1} ( \sec x - \tan x) $, then $ \frac{dy}{dx} = $

The value of $[ \vec{a} - \vec{b} \,\,\,\,\,\, \vec{b} - \vec{c} \,\,\,\,\,\, \vec{c} - \vec{a} ]$ where $|\vec{a}| = 1 , |\vec{b} | = 5 , |\vec{c}| = 3 $

If $\sqrt{1-x^{2} } + \sqrt{1- y^{2}} =x -y $, then $\frac{dy}{dx} = $

The function $f(x) = \begin{cases} x^2 & \quad \text{for } x < 1\\ 2 - x & \quad \text{for } x \geq 1 \end{cases}$ is

0.3 g of an acid is neutralised by 40 $cm^3$ of 0.125 N NaOH. Equivalent mass of the acid is

Which one of the following is not ferromagnetic?

Oxygen molecule is

Fog is a colloid consisting of

A process is spontaneous at a given temperature if

5 g of $CaCO_3$ completely reacts with

Coordination number of caesium in caesium chloride is

An example for a face centred cubic lattice is

Bakelite is manufactured by using a mixture of

Which one of the following is a homogeneous catalysis?

A spring balance carries a load. When the load is pulled aside so that the balance makes an angle of $30^{\circ}$ with the vertical, the balance reads $4 \, kg\, wt$. The mass of the load is

A bulb is kept at a depth h inside water of refractive index $' n' $. Area of the bright patch on the water surface is

The ratio of forces between two point charges in the two cases when their separation is halved and when it is doubled, is

If the diameter of a capillary tube is doubled, the rate of flow ofliquid increases