Let 𝑦̂=5.5+3.2 𝑥 be an estimated regression equation using a large sample. The 95% confidence interval of the coefficient of 𝑥 is [0.26, 6.14] and 𝑅 2 = 0.26. The standard error of the estimated coefficient is ______

Consider a thick biconvex lens (thickness t=4cm and refractive index n=1.5) whose magnitudes of the radii of curvature R1 and R2, of the first and second surfaces are 30cm and 20cm, respectively. Surface 2 is silvered to act as a mirror. A point object is placed at point A on the axis (OA= 60cm) as shown in the figure. If its image is formed at point Q, the distance d between O and Q is_____ cm. (Rounded off to two decimal places)
a thick biconvex lens

IIT JAM - 2024
Wave optics

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

IIT JAM - 2024
Mathematical Methods

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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:

IIT JAM - 2024
Mathematical Methods

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The P-V diagram of an engine is shown in the figure below. The temperatures at points 1, 2, 3 and 4 are T₁, T₂, T₃ and T₄, respectively. 1→2 and 3→4 are adiabatic processes, and 2→3 and 4→1 are isochoric processes

Identify the correct statement(s).
[γ is the ratio of specific heats C_p (at constant P) and C_v (at constant V)]

IIT JAM - 2024
Thermodynamics

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A time dependent magnetic field inside a long solenoid of radius 0.05m is given by \(\overrightarrow𝐵\)(𝑡) = 𝐵₀ sin 𝜔𝑡 \(\^z\). If 𝜔=100rad/s and 𝐵₀= 0.98Weber/m² , then the amplitude of the induced electric field at a distance of 0.07m from the axis of the solenoid is ______V/m. (Rounded off to two decimal places)

IIT JAM - 2024
Magnetism and Maxwell's Equations

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Let 𝑦̂=5.5+3.2 𝑥 be an estimated regression equation using a large sample. The 95% confidence interval of the coefficient of 𝑥 is [0.26, 6.14] and 𝑅² = 0.26. The standard error of the estimated coefficient is _______ (round off to 1 decimal place).

Correct Answer: 1.4

Solution and Explanation

Top Questions on Correlation and regression

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𝑌	2	5	9	14
𝑋	2	4	6	8

Let 𝑦̂=5.5+3.2 𝑥 be an estimated regression equation using a large sample. The 95% confidence interval of the coefficient of 𝑥 is [0.26, 6.14] and 𝑅2 = 0.26. The standard error of the estimated coefficient is _______ (round off to 1 decimal place).

Correct Answer: 1.4

Solution and Explanation

Top Questions on Correlation and regression

Questions Asked in IIT JAM exam

Let 𝑦̂=5.5+3.2 𝑥 be an estimated regression equation using a large sample. The 95% confidence interval of the coefficient of 𝑥 is [0.26, 6.14] and 𝑅² = 0.26. The standard error of the estimated coefficient is _______ (round off to 1 decimal place).