List of practice Questions

A certain volume of a gas at 300 K expands adiabatically until its volume is doubled. The resultant fall in temperature of the gas is nearly (The ratio of the specific heats of the gas is 1.5)

If $ (a, \beta) $ is the orthocenter of the triangle with the vertices $ A(2, 5), B(1, 5), C(1, 4) $, then $ a + \beta = $:

At STP $x$ g of a metal hydrogen carbonate (MHCO$_3$) (molar mass $84 \, {g/mol}$) on heating gives CO$_2$, which can completely react with $0.02 \, {moles}$ of MOH (molar mass $40 \, {g/mol}$) to give MHCO$_3$. The value of $x$ is:

A tightly wound coil of 200 turns and of radius 20 cm carrying current 5 A. Magnetic field at the centre of the coil is.

If the pair of lines represented by \[ 3x^2 - 5xy + P y^2 = 0 \] and \[ 6x^2 - xy - 5y^2 = 0 \] have one line in common, then the sum of all possible values of $ P $ is:

If $ a $ is a rational number, then the roots of the equation $ x^2 - 3ax + a^2 - 2a - 4 = 0 $ are:

Evaluate the integral $$ I = \int_1^5 \left( |x - 3| + |1 - x| \right) \, dx $$

A body of mass 4 kg is moving with a velocity 6 ms$^{-1}$ on a smooth surface. If it is brought to rest in 4 s, the force applied is:

If $ x $ is real and $ \alpha, \beta $ are maximum and minimum values of $ \frac{x^2 - x + 1}{x^2 + x + 1} $ respectively, then $ \alpha + \beta = $:

The following data is obtained for coagulating a positively charged sol in 2 hours:

What is the coagulating value of electrolyte for this sol?

Pseudocyesis is found in:

Three particles of each mass $ m $ are kept at the three vertices of an equilateral triangle of side $ 1 $. The moment of inertia of the system of the particles about any side of the triangle is:

Which of the following molecules is not having glycosidic linkage?

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:

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