If \( S_n = 3n^2 + 5n \) represents the sum of \( n \) terms of an A.P., find the \(10^{th}\) term \( (a_{10}) \).

• (A) \(60\)
• (B) \(62\)
• (C) \(64\)
• (D) \(66\)

Find the distance of the point \( (1,-2,3) \) from the \(yz\)-plane.

• (A) \(0\)
• (B) \(1\)
• (C) \(2\)
• (D) \(3\)

Evaluate the integral \( \displaystyle \int \frac{1}{x\log x}\,dx \).

• (A) \( \log|x| + C \)
• (B) \( \log|\log x| + C \)
• (C) \( \frac{1}{\log x} + C \)
• (D) \( \frac{\log x}{x} + C \)

Calculate the de Broglie wavelength of an electron accelerated through a potential difference of \(100V\).

• (A) \(0.1227\,\AA\)
• (B) \(1.227\,\AA\)
• (C) \(12.27\,\AA\)
• (D) \(0.01227\,\AA\)

Find the electric flux through one face of a cube if a charge \(q\) is placed at its center.

• (A) \( \frac{q}{\epsilon_0} \)
• (B) \( \frac{q}{2\epsilon_0} \)
• (C) \( \frac{q}{6\epsilon_0} \)
• (D) \( \frac{q}{12\epsilon_0} \)

A coil has a self-inductance of \(2H\); find the induced EMF if the current changes from \(5A\) to \(2A\) in \(0.1\) seconds.

• (A) \(30V\)
• (B) \(40V\)
• (C) \(50V\)
• (D) \(60V\)

Identify the monomer units used in the preparation of Nylon-6,6.

• (A) Adipic acid and Hexamethylenediamine
• (B) Terephthalic acid and Ethylene glycol
• (C) Caprolactam
• (D) Styrene

Which of the following noble gas compounds has a square planar geometry: \(XeF_2\), \(XeF_4\), or \(XeF_6\)?

• (A) \(XeF_2\)
• (B) \(XeF_4\)
• (C) \(XeF_6\)
• (D) None of these

If `ORANGE' is coded as `PSBOHF', how is `GRAPES' coded?

• (A) \(HSBQFT\)
• (B) \(HRBQFT\)
• (C) \(HSBQFS\)
• (D) \(GSBQFT\)

Point out the antonym of the word `Vague'.

• (A) Ambiguous
• (B) Uncertain
• (C) Precise
• (D) Confusing