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CSIR NET-JRF Physical Sciences Quiz

Authored by Satyam Ruhela

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12th Grade

CSIR NET-JRF Physical Sciences Quiz
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31 questions

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1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

A set of 100 data points yields an average x̄ = 9 and a standard deviation σx = 4. The error in the estimated mean is closest to

3.0

0.4

4.0

0.3

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

An integral is given by ∬ exp(-2xy + a) dx dy, where a is a real parameter. The full range of values of a for which the integral is finite, is

a < -2

-2 < a < 2

-1 < a < 1

-1 ≤ a ≤ 1

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Vorticity of vector field B is defined as V = ∇ × B. Given B = kxyz, where k is a constant, which one of the following is correct?

Vorticity is a null vector for all finite x, y, z

Vorticity is parallel to the vector field everywhere

The angle between vorticity and vector field depends on x, y, z

Vorticity is perpendicular to the vector field everywhere

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

The matrix A is given by A = [[1, 2, 3], [0, 3, 2], [0, 0, 2]]. The eigenvalues of A^3 + 5A^2 + 6A + 2I, where I is the identity matrix, are

4, 9, 27

1, 9, 44

1, 110, 8

4, 110, 10

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Probability density function of a variable x is given by P(x) = δ(x - a) + δ(x + a). The variance of x is

2a

0

2a^2

2a^2

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

An integral transform F of a function f(x) can be regarded as a result of applying an operator F to the function such that F(f(x)) = ∫ f(y) e^(-ixy) dy. If I is the identity operator, then the operator F is given by

(4/2)I

(2/2)I

I

(2/2)I

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

The integral I = ∫ (1/(x^2 + 1)) dx from 0 to 2 is estimated using Simpson's 1/3rd rule with a grid value of h = 0.5. The difference (I_estimated - I_exact) is closest to

0.007

0.001

0.0007

-0.005

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