The combination of the gates shown in the following figure yields

• (A) NAND gate
• (B) OR gate
• (C) NOT gate
• (D) XOR gate

A series LCR circuit consists of \(R = 80 \, \Omega\), \(X_L = 100 \, \Omega\), and \(X_C = 40 \, \Omega\). The input voltage is \(2500 \cos(100\pi t)\) V. The amplitude of current in the circuit is

• (A) 25 A
• (B) 50 A
• (C) 75 A
• (D) 100 A

The critical angle of a medium for a specific wavelength, if the medium has relative permittivity 3 and relative permeability \(\frac{4}{3}\) for this wavelength, will be:

• (A) \(15^\circ\)
• (B) \(30^\circ\)
• (C) \(45^\circ\)
• (D) \(60^\circ\)

Two lighter nuclei combine to form a comparatively heavier nucleus by the relation
\({}_1^2X + {}_1^2X = {}_2^4Y\)

The binding energies per nucleon of \({}_1^2X\) and \({}_2^4Y\) are 1.1 MeV and 7.6 MeV respectively. The energy released in this process is

• (A) 26 MeV
• (B) 56 MeV
• (C) 78 MeV
• (D) 108 MeV

A given ray of light suffers minimum deviation in an equilateral prism P. Additional prisms Q and R of identical shape and of same material as that of P are now combined as shown in the figure. The ray will now suffer

• (A) greater deviation
• (B) no deviation
• (C) same deviation as before
• (D) total internal reflection

Which of the following gases has the highest rate of diffusion?

• (A) \(O_2\)
• (B) \(CO_2\)
• (C) \(H_2\)
• (D) \(N_2\)

What is the IUPAC name of the compound: \(CH_3 - CH_2 - CH(CH_3) - CH_2 - CH_3\)

• (A) 3-Methylpentane
• (B) 2-Methylpentane
• (C) 3-Methylbutane
• (D) 2-Methylbutane

A first-order reaction is 25% complete in 30 minutes. How much time will it take for the reaction to be 75% complete?

• (A) 90 min
• (B) 60 min
• (C) 120 min
• (D) 150 min

Which of the following substances does not undergo hydrolysis in aqueous solution?

• (A) Sodium acetate
• (B) Ammonium chloride
• (C) Sodium carbonate
• (D) Sodium chloride

How many moles of oxygen are required to completely combust 1 mole of propane (\(C_3H_8\))?

• (A) 4 moles
• (B) 5 moles
• (C) 6 moles
• (D) 3 moles

The area of the region bounded by the curves \(x = y^2 - 2\) and \(x = y\) is

• (A) \(\frac{9}{4}\)
• (B) 9
• (C) \(\frac{9}{2}\)
• (D) \(\frac{9}{7}\)

The value of \(\int e^{\tan\theta} (\sec\theta - \sin\theta) d\theta\) is

• (A) \(e^{\tan\theta} \sec\theta + c\)
• (B) \(e^{\tan\theta} \sin\theta + c\)
• (C) \(e^{\tan\theta} (\sec\theta + \sin\theta) + c\)
• (D) \(e^{\tan\theta} \cos\theta + c\)

If \(\vec{a} = 2\hat{i} + \hat{j} + 2\hat{k}\), then the value of \(|\hat{i} \times (\vec{a} \times \hat{i})|^2 + |\hat{j} \times (\vec{a} \times \hat{j})|^2 + |\hat{k} \times (\vec{a} \times \hat{k})|^2\) is equal to

• (A) 17
• (B) 18
• (C) 19
• (D) 20

The magnitude of projection of line joining (3, 4, 5) and (4, 6, 3) on the line joining (1, 2, 4) and (1, 0, 5) is

• (A) \(\frac{4}{3}\)
• (B) \(\frac{2}{3}\)
• (C) \(\frac{8}{3}\)
• (D) \(\frac{1}{3}\)

Let the foot of perpendicular from a point \(P(1, 2, -1)\) to the straight line \(L : \frac{x}{1} = \frac{y}{0} = \frac{z}{-1}\) be \(N\). Let a line be drawn from \(P\) parallel to the plane \(x + y + 2z = 0\) which meets \(L\) at point \(Q\). If \(\alpha\) is the acute angle between the lines \(PN\) and \(PQ\), then \(\cos\alpha\) is equal to

• (A) \(\frac{1}{\sqrt{5}}\)
• (B) \(\frac{\sqrt{3}}{2}\)
• (C) \(\frac{1}{\sqrt{3}}\)
• (D) \(\frac{1}{2\sqrt{3}}\)