List of practice Questions

Which of the following tetrahalides does not exist?
The correct order of acidity of the following is:
order of acidity
Identify the reaction/process in which the entropy increases.
Output of the following logic circuit is:
logic circuit
Lithium shows diagonal relationship with element X and aluminum with element Y. Identify X and Y respectively.
If the average power per unit area delivered by an electromagnetic wave is \( 9240 \, \text{Wm}^{-2} \), what is the amplitude of the magnetic field in the wave?
The metal which has the highest work function in the following is:
For a hydrogen atom, the energy of a stationary electron is given by \( E_n = -\frac{13.6}{n^2} \, \text{eV} \). The energy required to excite the electron to the second excited state and to the ionized state are:
Two positive charges of 10 \( \mu \text{C} \) and 12 \( \mu \text{C} \) are 10 cm apart. What is the work done in bringing them 6 cm closer?
Current density in a cylindrical wire of radius \( R \) varies with radial distance as \( \beta (r + r^2) \). What is the current through the shaded section (sector angle \( \pi/6 \)) of the wire as shown in the figure?
Current density in a cylindrical wire of radius R
A compass needle oscillates 20 times per minute at a location with dip \( 45^\circ \) and magnetic field \( B_1 \). It oscillates 30 times per minute at another location where dip is \( 30^\circ \) and field is \( B_2 \). Find the ratio \( \frac{B_1}{B_2} \).
A car engine has a power of 20 kW and runs for 1 hour. If the thermal efficiency is 40\% and ambient temperature is 300 K, then what is the energy generated by fuel combustion?
Electrostatic force between two identical charges placed at a distance \( r \) is \( F \). A slab of width \( \frac{r}{5} \) and dielectric constant 9 is inserted between them. Then, the new force between the charges is:
Two rectangular blocks of masses 40 kg and 60 kg are connected by a string on a frictionless table. A force of 1000 N is applied on the 60 kg block away from the 40 kg block. Find the tension in the string.
A bead of mass 400 g is moving along a straight line under a force delivering constant power 1.2 W. If the bead is initially at rest, the speed attained after 6 seconds is (in \( \text{ms}^{-1} \))
At any point \( (x, y) \) on a curve, if the length of the subnormal is \( (x - 1) \) and the curve passes through \( (1, 2) \), then the curve is a conic. A vertex of the curve is:
The function \( y = Ae^x + Be^{-2x} \) satisfies which of the following differential equations?
A car travels with a speed of 40 km/h. Rain drops fall vertically but the traces on the side window make an angle of \( 30^\circ \) with the vertical. Find the magnitude of rain’s velocity with respect to the car.
If \( I_n = \int \tan^n x \, dx \), and \( I_0 + I_1 + 2I_2 + 2I_3 + 2I_4 + I_5 + I_6 = \sum_{k=1}^n \frac{\tan^k x}{k} \), then \( n = \)
The parametric form of a curve is \( x = \frac{t^3}{t^2 - 1},\ y = \frac{t}{t^2 - 1} \), then \( \int \frac{dx}{x - 3y} = \)
Let \( \alpha \) and \( \beta \) (\( \alpha<\beta \)) be roots of \( 18x^2 - 9\pi x + \pi^2 = 0 \), \( f(x) = x^2, g(x) = \cos x \). Then
\[ \int_{\alpha}^{\beta} x (g \circ f(x)) \, dx = ? \]
\( \int_0^{\pi} x \left( \sin^2(\sin x) + \cos^2(\cos x) \right) dx = \)
The x-intercept of a plane $\pi$ passing through the point $(1, 1, 1)$ is $\dfrac{5}{2}$ and the perpendicular distance from the origin to the plane $\pi$ is $\dfrac{5}{7}$. If the y-intercept of the plane $\pi$ is negative and the z-intercept is positive, then its y-intercept is
If $\displaystyle \lim_{x \to \infty} x^n \log_e x = 0$, then $\log_e 12 =$
The pole of the line $\dfrac{x}{a} + \dfrac{y}{b} = 1$ with respect to the circle $x^2 + y^2 = c^2$ is