List of top Physics Questions on Mathematical Methods

The divergence of a 3-dimensional vector \(\frac{𝑟̂}{𝑟^3}\) (𝑟̂ is the unit radial vector) is:

In the x-y plane, a vector is given by
\(\overrightarrow𝐹 (𝑥, 𝑦) = \frac{−𝑦𝑥̂ + 𝑥𝑦̂}{𝑥^ 2 + 𝑦^2} . \)
The magnitude of the flux of \(\overrightarrow∇ ×\overrightarrow 𝐹\) , through a circular loop of radius 2, centered at the origin, is:

Two positive charges Q and 2Q are kept at points A and B, separated by a distance 2d, as shown in the figure. MCL is a semicircle of radius 2d centered at the origin O. If Q=2C and d=10cm, the value of the line integral \(∫^L_M{\overrightarrow{E}}.{\overrightarrow{dl}}\) (where \(\overrightarrow{E}\) represents electric field) along the path MCL will be____V.

In the Taylor expansion of function, 𝐹(𝑥)=𝑒^𝑥 sin 𝑥, around 𝑥 = 0, the coefficient of 𝑥⁵ is ______. (Rounded off to three decimal places)

Two sides of a triangle OAB are given by:
\(\overrightarrow{𝑂𝐴} = 𝑥̂ + 2𝑦̂ + 𝑧̂ \)
\(\overrightarrow{𝑂B}= 2𝑥̂ − 𝑦̂ + 3𝑧̂ \)
The area of the triangle is _______. (Rounded off to one decimal place)

Which of the following matrices is Hermitian as well as unitary?

The value of the line integral for the vector,
\(\overrightarrow𝑣=2𝑥̂ +𝑦𝑧 ^2𝑦̂ +(3𝑦+𝑧 ^2 )𝑧̂ \)
along the closed path OABO (as shown in the figure) is: 

(Path AB is the arc of a circle of unit radius)

A vector field is expressed in the cylindrical coordinate system (s, ϕ, z) as,
\(\overrightarrow𝐹=\frac{𝐴}{𝑠} 𝑠̂+ \frac{𝐵}{𝑠} 𝑧̂. \)
If this field represents an electrostatic field, then the possible values of A and B, respectively, are:

The roots of the polynomial, 𝑓(𝑧)=𝑧 ⁴-8𝑧 ³+27𝑧 ²-38𝑧+26, are 𝑧₁, 𝑧₂, 𝑧₃,& 𝑧₄, where 𝑧 is a complex variable. Which of the following statements is correct?

The sum of three binary numbers, 10110.10, 11010.01, and 10101.11, in decimal system is:

The co-ordinate system (x,y,z) is transformed to the system (u,v,w), as given by:
𝑢 = 2𝑥 + 3𝑦 − 𝑧 
𝑣 = 𝑥 − 4𝑦 + 𝑧 
𝑤 = 𝑥 + 𝑦 
The Jacobian of the above transformation is ________.

Which of the following fields has non-zero curl ?

The plot of the function f(x) = ||x| - 1| is

Inverse of the matrix \(\begin{bmatrix} 1 & 1 & 0 \\ 2 & 3 & 0 \\ 1 & 0 & 1 \end{bmatrix}\) is

The absolute error in the value of sin𝜃 if approximated up to two terms in the Taylor’s series for 𝜃 = 60∘ is ___________ (rounded off to three decimal places).

The sum of the x-components of unit vectors 𝑟̂ ̇ and 𝜃̂̇ for a particle moving with angular speed 2 rad s ^-1 at angle 𝜃 = 215° is__________ (rounded off to two decimal places)

Unit vector normal to the equipotential surface of 𝑉(𝑥, 𝑦, 𝑧) =4𝑥²+𝑦² + 𝑧 at (1,2,1) is given by (𝑎𝑖̂+ 𝑏𝑗̂+ 𝑐𝑘̂). The value of |𝑏| is (rounded off to two decimal places).

A rectangular pulse of width 0.5 cm is travelling to the right on a taut string (shown by full line in the figure) that has mass per unit length 𝜇1. The string is attached to another taut string (shown by dashed line) of mass per unit length 𝜇2. If the tension in both the strings is the same, and the transmitted pulse has width 0.7 cm, the ratio 𝜇1⁄𝜇2 is _______(rounded off to two decimal places)

The sum of the eigenvalues 𝜆₁ and 𝜆₂ of matrix 𝐵 = 𝐼+𝐴+𝐴² , where
\( \left[ {\begin{array}{cc}  2&1 \\     -0.5 &0.5 \\   \end{array} } \right]\)
 is_____ (rounded off to two decimal places).

The Jacobian matrix for transforming from (x, y) to another orthogonal coordinates system (u, v) as shown in the figure is

The equation \(z^2+\bar{z}^2=4\) in the complex plane (where \(\bar{z}\) is the complex conjugate of z) represents

A rocket (S') moves at a speed \(\frac{c}{2}\)m/s along the positive x-axis, where c is the speed of light. When it crosses the origin, the clocks attached to the rocket and the one with a stationary observer (S) located at x = 0 are both set to zero. If S observes an event at (x, t), the same event occurs in the S' frame at

The resultant of the binary subtraction 1110101-0011110 is

The function f(x) = e^sinx is expanded as a Taylor series in x, around x = 0, in the form f(x) = \(\sum^{\infin}_{n=0}a_nx^n\). The value of a₀ + a₁ + a₂ is

Consider a unit circle C in the xy plane, centered at the origin. The value of the integral \(\oint\)[(sin x - y)dx - (sin y - x)dy] over the circle C, traversed anticlockwise, is