List of practice Questions

If $\lambda_1$ and $\lambda_2$ are the wavelengths of de-Broglie waves for electrons in first and second Bohr orbits in hydrogen atom, then $\left(\dfrac{\lambda_1}{\lambda_2}\right)$ is equal to (Energy in 1st Bohr orbit = $-13.6\,\text{eV}$)

In Searle's method to find Young's modulus of a wire, when a force of $1.5$ kg-wt is applied at its free end, the length of wire is $a$. When force of $2.5$ kg-wt is applied, the length of wire is $b$. What would be its original length?

Kirchhoff's current law and voltage law respectively are based on the law of conservation of

Focal length of a convex lens will be maximum for

An electromagnetic wave of wavelength $\lambda$ is incident on a photosensitive surface of negligible work function. If the photoelectrons emitted from this surface have the de-Broglie wavelength $\lambda_1$, then

A pipe open at both ends has length 1 m. The air column in the pipe cannot resonate for a frequency (Neglect end correction, speed of sound in air = 340 m/s)

If three vectors have equal magnitude i.e. $A = B = C$, then the angle between $\vec{A$ and $\vec{C}$ is $\alpha$. If $\vec{A} + \vec{B} + \vec{C} = 0$, then the angle between $\vec{A}$ and $\vec{C}$ is $\beta$, then $\dfrac{\alpha}{\beta}$ is}

The parametric equations of the line passing through \( A(3, 4, -7) \), \( B(1, -1, 6) \) are

A bus is moving with a velocity of 5 m/s towards a wall. The driver blows the horn of frequency 165 Hz. If the speed of sound in air is 335 m/s, then after reflection of the sound wave, the number of beats per second heard by the passengers in the bus will be

A graph of magnetic flux ($\phi$) versus current ($I$) is shown for four inductors A, B, C and D. Larger value of self-inductance is for inductor

Evaluate the integral: \[ \int \frac{dx}{\cos x \sqrt{\cos 2x}}. \]

The equation of a plane containing the point \( (1, -1, 1) \) and parallel to the plane \[ 2x + 3y - 4z = 17 \text{ is} \]

The angle between the line \[ \frac{x - 1}{2} = \frac{y + 3}{1} = \frac{z + 7}{2} \] and the plane \[ \mathbf{r} \cdot (6\hat{i} - 2\hat{j} - 3\hat{k}) = 5 \] is

The auxiliary equation of the lines passing through the origin and having slopes \[ \sqrt{3} + 1 \quad \text{and} \quad \sqrt{3} - 1 \quad \text{is} \]

If \[ \frac{\sin(A + B)}{\sin(A - B)} = \frac{\cos(C + D)}{\cos(C - D)}, \] then \( \tan A \cot B = \)

The particular solution of the differential equation \[ \sin^2 y \frac{dx}{dy} + x = \cot y \quad \text{when} \quad x = 0 \quad \text{and} \quad y = \frac{3\pi}{4} \text{ is} \]

If \[ f(x) = |x - 2|, \quad x \in [0, 4], \quad \text{then the Rolle's theorem cannot be applied to the function because} \]

If \[ y = 3e^{5x} + 5e^{3x}, \quad \text{then} \quad \frac{d^2 y}{dx^2} - 8 \frac{dy}{dx} = \]

If \( \theta \) is a parameter, then the parametric equations of the circle \[ x^2 + y^2 - 6x + 4y - 3 = 0 \] are given by

If \[ | \mathbf{a} \times \mathbf{b} \times \mathbf{c} | = 4, \] then the volume of the parallelepiped with coterminous edges \[ \mathbf{a} + 2\mathbf{b}, \quad \mathbf{b} + 2\mathbf{c}, \quad \mathbf{c} + 2\mathbf{a} \] is

If \[ \mathbf{a} = \frac{1}{\sqrt{10}} (3i + k), \quad \mathbf{b} = \frac{1}{7} (2i + 3j - 6k), \quad \text{then the value of} \] \[ (2\mathbf{a} - \mathbf{b}) \cdot \left[ (\mathbf{a} \times \mathbf{b}) \times (\mathbf{a} + 2\mathbf{b}) \right] \]

If \( \cos 2\theta = \sin \alpha \), then \( \theta = \)

The maximum value of the function \[ y = e^{5 + \sqrt{3} \sin x + \cos x} \]

Which among the following elements has the lowest density and is lightest?

What is the value of radius ratio of ionic crystal having coordination number six?