List of practice Questions

1 gm of organic compound gave 1.32g $\text{CO}_2$, 0.53g of same compound gave 0.75g AgBr. If molecular formula of compound is $\text{C}_x\text{H}_y\text{Br}_z$ then calculate percentage of hydrogen in the given compound.

Calculate pH of 10 mM weak acid (HA) dissociated in water. Assume $\alpha$ to be negligible. Given $\text{pK}_a = 4$

Ice is heated from $-20^\circ C$ to $200^\circ C$. Which of the following temperature (T) vs heat (Q) graph is correct ?

If nothing is kept between jaws, zero of Vernier scale lies right of 0 cm of main scale and $4^{th}$ line of Vernier scale matches perfectly with any line of main scale. An object is kept between jaws and zero of Vernier scale crosses $15^{th}$ division of main scale and $5^{th}$ division of Vernier scale exactly matches with any line of main scale. (Least count = 0.1 mm and 1 MSD = 1mm). Find dimension of object :

Two wires of cross sectional area $1 \text{ cm}^2$ and $2 \text{ cm}^2$ and lengths 20 cm and 30 cm are connected to the same load. If their extensions are same, find the ratio of their Young's modulus :

In the system of two discs and a rod of mass 600 g each, a torque of magnitude $43 \times 10^5$ dyne-cm is applied along the axis of rotation as shown in figure. Find the approx angular acceleration about given axis :

As shown in the figure, radius of gyration about the axis shown in $\sqrt{n}$ cm for a solid sphere. Find 'n'.

Consider the following changes : $\text{SnO}_2 \rightarrow \text{SnO}$ $\Delta G_1^o$ and $\text{PbO}_2 \rightarrow \text{PbO}$ $\Delta G_2^o$. Select the correct option

One of the pots does not belong to the group of pots shown below. What is the number written on that pot?

Let x be the number of 9 digit numbers formed by taking digits from first 9 natural numbers, where only one digit is repeated twice & y be the number of 9 digit numbers formed from first 9 natural numbers, such that exactly 2 digits repeated twice then

The value of $\lim_{x \to 0} \frac{\ln(\sec(ex) \cdot \sec(e^2x) \dots \sec(e^{10}x))}{e^2 - e^{2\cos x}}$ is :

If $\vec{a}, \vec{b} \& \vec{c}$ are unit vectors such that $(\vec{a}-\vec{b})^2 + (\vec{b}-\vec{c})^2 + (\vec{c}-\vec{a})^2 = 9$. Find positive k if $|2\vec{a} + k\vec{b} + k\vec{c}| = 3$ :

Find possible no. of triplets (b, c, d), such that $x^2 + 2$ is divisor of $x^3 + bx^2 + cx + d$ & b, c, d $ \le $ 20 & b, c, d $ \in $ N :

Let $f(x)$ be a differentiable function satisfying \[ f(x)=e^x+\int_0^1 (y+xe^x)f(y)\,dy \] Find $f(0)+e$, where $e$ is Napier's constant.

If $f(a)$ is the area bounded in the first quadrant by $x=0$, $x=1$, $y=x^2$ and $y=|ax-5|-|1-ax|+ax^2$, then find $f(0)+f(1)$.

Find the number of solutions of the equation \[ \tan(x+100^\circ)=\tan(x+50^\circ)\tan(x-50^\circ) \] where $x\in(0,\pi)$.

The correct order of electron gain enthalpy (magnitude only) for group 16 elements is:

Resistance of each side is $R$. Find equivalent resistance between two opposite points as shown in the figure.

In case of meter bridge experiment balance length for $2\Omega$ and $3\Omega$ is $\ell$ and for $x\Omega$ and $3\Omega$ is $(\ell + 10)$ cm. Find $x$.

When rod becomes horizontal find its angular velocity. It is pivoted at point A as shown.

On a surface, if photon of wavelength $\lambda$ is incident, the stopping potential is $3.2$ V. If the wavelength incident is $2\lambda$, stopping potential is $0.7$ V. Find $\lambda$.

An electron makes transition from higher energy orbit to lower energy orbit in $Li^{2+}$ ion such that $n_1 + n_2 = 4$ and $n_2 - n_1 = 2$. Determine the wavelength of emitted photon in transition (in cm).

In a vernier calipers 50 VSD are equal to 48 MSD. 1 MSD is equal to $0.05$ mm. Find least count of this vernier calipers.

In YDSE, slit separation $d = 2$ mm, distance between slits and screen $D = 10$ m. Wavelength of light is $\lambda = 6000$\AA. If intensity of light through each slit is $I_0$, find intensity at point directly in front of one of the slits.

A solid cylinder of radius $\dfrac{R}{3}$ and length $\dfrac{L}{2}$ is removed along the central axis. Find ratio of initial moment of inertia and moment of inertia of removed cylinder.