List of practice Questions

Simplify the expression: $ 4 + \frac{1}{4 + \frac{1}{4 + \frac{1}{4 + \cdots}}} $

Find the domain of the real valued function: \[ f(x) \;=\; \sqrt{\cos(\sin x)} + \cos^{-1}\left(\frac{1+x^2}{2x}\right). \]

The equation $ 2x^2 - 3xy - 2y^2 = 0 $ represents two lines $ L_1 $ and $ L_2 $. The equation $ 2x^2 - 3xy - 2y^2 - x + 7y - 3 = 0 $ represents another two lines $ L_3 $ and $ L_4 $. Let $ A $ be the point of intersection of lines $ L_1 $ and $ L_3 $, and $ B $ be the point of intersection of lines $ L_2 $ and $ L_4 $. The area of the triangle formed by the lines $ AB $, $ L_3 $, and $ L_4 $ is: .

A coil of two turns is made of a wire length L and another coil of four turns is made from same length L. When the same current is flowing in two coils, then the ratio of magnetic inductions at their centres is:

If the work done $W$, length $L$ and time $T$ are considered as the fundamental quantities, the dimensional formula for mass is:

Equation of the line touching both parabolas $ y^2 = 4x $ and $ x^2 = -32y $ is:

The point $(p, q)$ is the point of intersection of a latus rectum and an asymptote of the hyperbola $9x^2 - 16y^2 = 144$. If $p>0$ and $q>0$, then $q = \ldots$

If $ \log y = y^{\log x} $, then $ \frac{dy}{dx} $ is:

The relation between the force (F in newton) acting on a particle executing simple harmonic motion and the displacement of the particle (y in metre) is given by: \[ 500F + \pi^2 y = 0 \] If the mass of the particle is 2 g, the time period of oscillation of the particle is:

For the displacement current through the plates of a parallel plate capacitor of capacitance 30 µF to be 150 µA, the potential difference across the plates of the capacitor has to vary at the rate of:

The RMS value of the electric field of an electromagnetic wave emitted by a source is $ 660 $ N/C. The average energy density of the electromagnetic wave is:

निम्नांकित शब्दों को इस क्रम में जमाइए कि लोकोक्ति का स्वरूप प्राप्त कर लें-

उचित सम्बन्ध जोड़िए-

(a) व्याकरण सम्मत वाक्य अशुध्द उच्चारण करने पर अपूर्ण माना जाता है।
(b) किसी भी भाषा के उच्चारण हेतु चार स्तर निर्धारित है ध्वनि, शब्द, वाक्य एवं प्रान्तीय।

"मैनेजर ने कहा तुम्हे घर घर जाकर सूचनाएँ इकट्ठी करनी होगी" उपर्युक्त वाक्य के लिए उचित विराम चिह्न वाले वाक्य का चयन कीजिए।

A Circle S passes through the points of intersection of the circles $ x^2 + y^2 - 2x + 2y - 2 = 0 $ and $ x^2 + y^2 + 2x - 2y + 1 = 0 $. If the centre of this circle S lies on the line $ x - y + 6 = 0 $, then the radius of the circle S is:

The length of the tangent from a point 15 cm away from the centre of a circle of radius 9 cm is:

The focal length of double concave lens having refractive index 1.5 kept in air with two spherical surfaces of radii $ R_1 = 20 \, \text{cm} $ and $ R_2 = 80 \, \text{cm} $ is

What is the kinetic energy (in $ {J/mol} $) of one mole of an ideal gas (molar mass = $0.01 \, {kg/mol}$) if its rms velocity is $4 \times 10^2 \, {m/s}$?

The value of $p$, for which the pair of equations $3x + 4y + 2 = 0$ and $9x + py + 8 = 0$ represents parallel lines, is:

The value of $\log_6 2 + \log_6 3$ is:

H.C.F. of 2023, 2024, 2025 is:

tan 9$^\circ$ - tan 27$^\circ$ - tan 63$^\circ$ + tan 81$^\circ$ =

The bond lengths of diatomic molecules of elements X, Y, and Z respectively are 143, 110, and 121 pm. The atomic numbers of X, Y, and Z respectively are: