List of practice Questions

A blue lamp emits light of mean wavelength 4500${Å}$. The lamp is rated at 150 W and 8% efficiency. Then the number of photons are emitted by the lamp per second.

Which of the following alkenes does not undergo anti-Markovnikov addition of HBr?

Match the following

What are X and Y respectively in the following reactions?

If the slope of one of the pair of lines represented by $ 2x^2 + 3xy + Ky^2 = 0 $ is 2, then the angle between the pair of lines is:

If $\cos \alpha + \cos \beta + \cos \gamma = \sin \alpha + \sin \beta + \sin \gamma = 0,$ then evaluate $(\cos^3 \alpha + \cos^3 \beta + \cos^3 \gamma)^2 + (\sin^3 \alpha + \sin^3 \beta + \sin^3 \gamma)^2 =$

Evaluate the infinite series: \[ 1 + \frac{1}{3} + \frac{1.3}{3.6} + \frac{1.3.5}{3.6.9} + \dots \text{ to } \infty = \]

Evaluate the integral: \[ I = \int_{-3}^{3} |2 - x| dx. \]

The general solution of the differential equation $$ (y^2 + x + 1) \, dy = (y + 1) \, dx $$ is:

When the temperature of a gas is raised from 27°C to 90°C, the increase in the rms velocity of the gas molecules is:

Two spheres A & B of radii 4 cm & 6 cm are given charges of 80 µC & 40 µC respectively. If they are connected by a fine wire, the amount of charge flowing from one to the other is:

In the given circuit the currents are $ I_1 = 5A $, $ I_4 = 10A $, and $ I_5 = 15A $. Analyzing the circuit using Kirchhoff’s laws, then $ I_2 $, $ I_3 $, and $ I_6 $ values are:

If the matrix is:
$\left| \begin{array}{ccc} a & 1 & 1 \\ 1 & b & 1 \\ 1 & 1 & c \end{array} \right|>0, \text{ then } abc>?$

The set of all real values of $x$ satisfying the inequality $\frac{7x^2 - 5x - 18}{2x^2 + x - 6}<2$ is

For $|x|<\frac{1}{\sqrt{2}}$ the coefficient of $x$ in the expansion of $\frac{(1-4x)^2(1-2x^2)^{1/2}}{(4-x)^{3/2}}$ is

If $ P $ is a point which divides the line segment joining the focus of the parabola $ y^2 = 12x $ and a point on the parabola in the ratio 1:2, then the locus of $ P $ is:

Let $ [P] $ denote the greatest integer $ \leq P $. If $ 0 \leq a \leq 2 $, then the number of integral values of $ a $ such that $ \lim_{x \to a} [x^2] - [x]^2 $ does not exist is:

Find the domain of $ f(x) $ given: \[ \int \frac{\sin x \cos x}{\sqrt{\cos^4 x - \sin^4 x}} dx = -\frac{f(x)}{2} + C. \] then domain of f{x) is

Two light waves of intensities $ I $ and $ 2I $ superimpose on each other. If the path difference between the light waves reaching a point is 12.5% of the wavelength of the light, then the resultant intensity at the point is (Both the light waves have the same wavelength)

Hydrolysis of XeF$_4$ gives HF, O$_2$, Xe and 'X'. The structure of 'X' is

The energy released in the fission of one $_{92}^{235}{U}$ nucleus is 200 MeV. The energy released in the fission of 235 g of $_{92}^{235}{U}$ is nearly:

A lens with refractive index $ \frac{3}{2} $ has a power of +5 diopters in air. If it is completely immersed in water, its power is (in diopters).
The refractive index of water is $ \frac{4}{3} $