List of practice Questions

In the circuit, the potential difference across $PQ$ will be nearest to

The relation between voltage sensitivity $\left(\sigma_{ v }\right)$ and current sensitivity $\left(\sigma_{1}\right)$ of a moving coil galvanometer is (resistance of galvanometer is G).

Which of the following statements is true?

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

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

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

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

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 $a= 5, b = 13 , c = 12$ 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

A process is spontaneous at a given temperature if

Fog is a colloid consisting of

5 g of $CaCO_3$ completely reacts with

Coordination number of caesium in caesium chloride is

Bakelite is manufactured by using a mixture of

An example for a face centred cubic lattice is

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