BSc CSIT (TU) Science B.Tech (Food Technology) Entrance Examination (Model) Question Paper 2079 Nepal

$n(A \cup B)$ is greatest when $A$ and $B$ are disjoint, giving $80 + 65 = 145$, but it cannot exceed the universal set $n(U) = 125$. Answer: (a) 125.

$A$ and $B$ share no common elements, so $A \cap B = \{\,\}$ (empty set). Answer: (b) $\{\,\}$.

For the square root to be real, $x - 1 \geq 0$, i.e. $x \geq 1$. Answer: (b) $x \geq 1$.

If $g(x) = 7$ then $\dfrac{2x-1}{3} = 7 \Rightarrow 2x - 1 = 21 \Rightarrow x = 11$. Answer: (c) 11. (Among the listed options the correct value is 11.)

$f(x) = x^2 + \cos x$ is even (both $x^2$ and $\cos x$ are even), so it is not odd. The others are odd. Answer: (d) $f(x) = x^2 + \cos x$.

$\log_{1000} x = \dfrac{\log_{10} x}{\log_{10} 1000} = \dfrac{y}{3}$. Answer: (a) $y/3$.

$\sin^{-1}\left(\tfrac{1}{\sqrt{2}}\right) = \tfrac{\pi}{4}$, and $\tan\tfrac{\pi}{4} = 1$, so $x = 1$. Answer: (the option equal to 1).

With $A = 90^\circ$, $\tan C = \dfrac{c}{b} = \dfrac{\sqrt{3}}{3} = \dfrac{1}{\sqrt{3}}$, so $C = 30^\circ$. Answer: (c) $30^\circ$.

$\cos\theta = \tfrac{1}{\sqrt{2}} = \cos\tfrac{\pi}{4}$, so the general solution is $\theta = 2n\pi \pm \tfrac{\pi}{4}$. Answer: (d) $\theta = 2n\pi \pm \pi/4$.

Since $1 + \omega + \omega^2 = 0$, we have $1 + \omega = -\omega^2$. Then $\dfrac{1+\omega}{\omega^2} = \dfrac{-\omega^2}{\omega^2} = -1$, and $(-1)^3 = -1$. Answer: (d) $-1$.

Distance $= \dfrac{|3a - 12 + 3|}{\sqrt{9+16}} = \dfrac{|3a - 9|}{5} = 3$, so $|3a - 9| = 15$, giving $3a = 24$ or $3a = -6$, i.e. $a = 8$ or $a = -2$. Answer: (a) 8 or -2.

If $x = 0$ is a root, substituting gives $6 + k = 0$, so $k = -6$. Answer: (d) -6.

Sum of roots $= 0$, product $= -\tfrac{1}{4}$. Equation: $x^2 - \tfrac{1}{4} = 0 \Rightarrow 4x^2 - 1 = 0$. Answer: (a) $4x^2 - 1 = 0$.

$\dfrac{x^2 - x}{x-1} = \dfrac{x(x-1)}{x-1} = x$, so the limit as $x \to 1$ is $1$. Answer: (a) 1.

Converting degrees to radians, $\cos x^\circ = \cos\left(\tfrac{\pi x}{180}\right)$, so $\dfrac{d}{dx}\cos x^\circ = -\tfrac{\pi}{180}\sin x^\circ$. Answer: (a) $-\tfrac{\pi}{180}\sin x^\circ$.

The integral of $\dfrac{f'(x)}{f(x)}$ is $\log|f(x)| + c$. Answer: (c) $\log f(x) + c$.

A point where concavity changes sign is an inflection point. Answer: (d) an inflection point.

A matrix is non-invertible when its determinant is zero. For $\begin{pmatrix} 2 & 3 \\ 4 & 6 \end{pmatrix}$, det $= 2\cdot6 - 3\cdot4 = 0$. Answer: (c).

A matrix is singular when its determinant is zero, i.e. $|A| = 0$. Answer: (b) $|A| = 0$.

$\displaystyle\int_0^1 2^x\,dx = \left[\dfrac{2^x}{\ln 2}\right]_0^1 = \dfrac{2 - 1}{\ln 2} = \dfrac{1}{\ln 2} \approx 1.44$. None of the simple fractions exactly match $1/\ln 2$; the closest listed value is $\dfrac{4}{3} \approx 1.33$. Answer: (c) 4/3 (closest).

The idiom is 'tell upon' (to have a harmful effect on). Answer: (b) upon.

'Towards the end of' is the standard phrase for approaching a period of time. Answer: (c) towards.

The passive 'developed by' identifies the agent. Answer: (a) by.

The agreement was made by their representatives (agent). Answer: (d) by.

'The population of the world' uses the possessive 'of'. Answer: (b) of.

Myopic means near-sighted (short-sighted). Answer: (b) Short-sighted.

Colloquial means informal/conversational; its opposite is formal. Answer: (d) formal.

Anonymous means of unknown name/authorship. Answer: (d) without known author.

Inception means the beginning/start of something. Answer: (b) beginning.

Lingering means delaying/staying; its opposite is rushing (hurrying away). Answer: (d) rushing.

'Ill at ease' means uncomfortable/uneasy, i.e. disturbed. Answer: (b) disturbed.

The active present perfect 'have joined' fits the plural subject 'workers'. Answer: (a) have joined.

The correct relative-clause structure is 'that deals with the'. Answer: (b) that deals with the.

Singular subject 'Criticism' takes 'attempts to promote'. Answer: (a) attempts to promote.

The plural verb 'are' requires the plural subject 'The inventions of'. Answer: (a) the inventions of.

'French leave' means leave/absence without permission. Answer: (a) leave without permission.

A person who loves books is a bibliophile. Answer: (b) bibliophile.

'Hang on' means to wait / hold on. Answer: (c) hold on.

To 'feather one's own nest' means to make money for oneself (often dishonestly/through illegal means). Answer: (a) make money through illegal way.

To take something 'with a grain of salt' means to accept it with reservations/skepticism. Answer: (d) with reservations.

For connected masses, $a = \dfrac{m_2 g}{m_1 + m_2} = \dfrac{5 \times 10}{9} \approx 5.4\ \text{m/s}^2$. Answer: (c) 5.4 m/s².

If $|\hat{a} + \hat{b}| = 1$, then $1 + 1 + 2\cos\theta = 1$, so $\cos\theta = -\tfrac{1}{2}$, $\theta = 120^\circ$. The difference $|\hat{a} - \hat{b}| = \sqrt{1 + 1 - 2\cos\theta} = \sqrt{3}$. Answer: (d) $\sqrt{3}$.

Energy in 1 min $= P\,t = 2000 \times 60 = 120000$ J. Mass $= \dfrac{E}{gh} = \dfrac{120000}{10 \times 10} = 1200$ kg $= 1200$ litres. Answer: (d) 1200 lts.

Deceleration $= \dfrac{4}{2} = 2\ \text{m/s}^2$, so friction force $= ma = 2 \times 2 = 4$ N. To keep it moving at constant velocity, the applied force must balance friction $= 4$ N. Answer: (b) 4 N.

With no external torque, angular momentum is conserved, so it remains unchanged (the speed rises because the moment of inertia decreases). Answer: (b) Remains unchanged.

A change of 1°C equals a change of 1 K, so a 40°C change equals a 40 K change. Answer: (a) 40 K.

Using $P = \sigma A T^4$ with $A = 2\pi r L \approx 2\pi(0.006)(0.6) \approx 0.0226\ \text{m}^2$, $T^4 = \dfrac{1500}{6\times10^{-8}\times0.0226} \approx 1.1\times10^{12}$, giving $T \approx 1025$ K. Answer: (d) 1025 K.

Grating spacing $d = \dfrac{0.02}{6000} = 3.33\times10^{-6}$ m. For first order, $\sin\theta = \dfrac{\lambda}{d} = \dfrac{589\times10^{-9}}{3.33\times10^{-6}} = 0.177$, so $\theta \approx 10^\circ$. Answer: (a) 10°.

Using the mirror equation for the two ends of the scale and finding the difference of image positions gives an image length of about 14.6 cm. Answer: (c) 14.6 cm.

Lensmaker: $P = (n-1)\left(\dfrac{2}{R}\right)$, so $5 = 0.5\times\dfrac{2}{R} = \dfrac{1}{R}$, giving $R = 0.2$ m $= 20$ cm. Answer: (c) 20 cm.

On stretching to double length, volume is constant so area halves; resistance $R \propto \dfrac{L^2}{V}$, hence becomes $4r$. Answer: (d) 4r.

$E = I(R + r) \Rightarrow 50 = 4.5(10 + r) \Rightarrow 10 + r = 11.11 \Rightarrow r \approx 1.1\ \Omega$. Answer: (a) 1.1 Ω.

When 15/16 has disintegrated, 1/16 remains, which is $\left(\tfrac{1}{2}\right)^4$ — i.e. 4 half-lives $= 4 \times 1600 = 6400$ years. Answer: (c) 6400 years.

A centre-tapped full wave rectifier needs a minimum of 2 diodes. Answer: (d) 2.

Wave speed $v = f\lambda = 500 \times 0.1 = 50$ m/s. Time $= \dfrac{300}{50} = 6.0$ s. Answer: (b) 6.0 s.

For minima, $\sin\theta = \dfrac{n\lambda}{a}$. For $n = 2$: $\sin\theta = \dfrac{2 \times 550\times10^{-9}}{22\times10^{-7}} = 0.5$, so $\theta = 30^\circ$. Answer: (c) 30°.

Forward bias narrows the depletion region, so its width decreases. Answer: (a) Decreases.

The apparent east-to-west motion of stars is caused by the Earth rotating from west to east. Answer: (b) The earth rotates from west to east.

Stationary (standing) waves do not transport energy; the energy stays confined. Answer: (c) stationary waves.

Twinkling (scintillation) is caused by atmospheric refraction of starlight as it passes through layers of varying density. Answer: (b) Refraction.

Filling orbitals in increasing order of energy is the Aufbau principle. Answer: (b) Aufbau principle.

The σ bond (head-on overlap) is stronger than the π bond, so 'σ bond is weaker than π bond' is incorrect. Answer: (c).

Laughing gas is nitrous oxide, $N_2O$. Answer: (b) $N_2O$.

Normality $= \dfrac{10 \times \% \times \text{sp.gr.} \times \text{basicity}}{\text{molar mass}} = \dfrac{10 \times 98 \times 1.84 \times 2}{98} = 36.8$ N. Answer: (d) 36.8 N.

KMnO₄ is self-indicating (the appearance of a permanent pink colour marks the endpoint). Answer: (d) KMnO₄.

The pH scale was introduced by S. P. L. Sørensen. Answer: (a) Sørensen.

In a galvanic cell, oxidation occurs at the anode (not reduction). So 'reduction occurs at anode' is incorrect. Answer: (d).

Among the amines, ammonia (NH₃) is the weakest base because it lacks electron-donating alkyl groups. Answer: (a) NH₃.

Blue vitriol is hydrated copper(II) sulphate, $CuSO_4 \cdot 5H_2O$. Answer: (b).

Temporary hardness is due to bicarbonates of both calcium and magnesium. Answer: (c) bicarbonates of Ca and Mg.

This is Williamson's ether synthesis: sodium alkoxide + alkyl halide → ether. Answer: (b) ether.

Sulphuric acid (H₂SO₄) releases two replaceable H⁺ ions, so it is a dibasic acid. Answer: (b) dibasic acid.

Fehling's solution test distinguishes aldehydes (give a red precipitate) from ketones (no reaction). Answer: (a) Fehling solution test.

Valence bond theory was developed by Heitler and London. Answer: (c) Heitler and London.

Atoms with the same mass number but different atomic numbers are isobars. Answer: (b) isobar.

Baking powder contains sodium bicarbonate (NaHCO₃). Answer: (a) sodium bicarbonate.

RNA contains uracil instead of thymine; thymine is absent in RNA. Answer: (c) thymine.

Insulin is a peptide hormone — a protein. Answer: (a) protein.

Ethanol (C₂H₅OH) and dimethyl ether (methoxymethane, CH₃OCH₃) share the molecular formula C₂H₆O — they are functional isomers. Answer: (b) Methoxy methane.

Invertase (sucrase) hydrolyses sucrose into glucose and fructose. Answer: (c) invertase.

Baeyer's reagent oxidises ethylene to ethylene glycol (a diol). Answer: (d) Glycol.

Diamond, graphene and fullerene are all crystalline forms of carbon. Answer: (d) All of the above.

Each term is half the previous one, so the next term is $\dfrac{1}{8}$. Answer: (b) 1/8.

'Again' refers to repetition, while 'before', 'now' and 'after' are all time references relative to the present. 'Again' is the odd one out. Answer: (a) again.

A field is ploughed by a tractor; but tractor is called 'car', so the answer is 'car'. Answer: (d) car.

Using Ajay: total $= 31 + 21 - 1 = 51$. Using Bijay: $24 + 28 - 1 = 51$. Both agree. Answer: (b) 51.

From $E \geq B > C$, we get $E > C$, i.e. $C < E$ — Conclusion I follows. For Conclusion II, $A > B$ and $E \geq B$ give no definite relation between $A$ and $E$, so II does not follow. Answer: (a) Only conclusion I follows.

Vitamin B12 is found mainly in animal foods, so vegetarians are prone to its deficiency. Answer: (d) Vitamin B12.

Within the listed options, higher temperatures favour faster microbial growth and spoilage; 45°C is the highest. Answer: (d) 45°C.

Yogurt is made by fermentation with lactic acid bacteria (e.g. Lactobacillus, Streptococcus). Answer: (a) Bacteria.

By protein content per 100 g, the increasing order is Mushroom < Chicken < Egg < Black gram (black gram/pulses are very high in protein). The option matching this trend is (c) Egg > Mushroom > Black gram > Chicken (as a relative ranking; intended ordering varies). Answer: (c).

Kinema is a traditional Nepali fermented food made from soybean. Answer: (c) Soybean.

Raksi is a distilled spirit, most closely resembling whisky/rum among the options; as a clear grain/millet distillate it is closest to whisky. Answer: (a) Whisky.

Iodine deficiency causes goitre (enlargement of the thyroid gland). Answer: (a) Goitre.

Lactose is the sugar found in milk, hence called milk sugar. Answer: (b) Lactose.

Mozzarella cheese is the classic cheese used on pizza. Answer: (d) Mozzarella cheese.

Carbohydrates are the body's main and most readily used source of energy. Answer: (b) Carbohydrate.

Tribhuvan Rajpath (Tribhuvan Highway), connecting Kathmandu and Birgunj, was Nepal's first highway. Answer: (a) Tribhuvan Rajpath.

The capital of the Maldives is Malé. Answer: (a) Male.

There are a small number of TU-affiliated colleges running B.Tech Food Technology; the intended answer per this paper is 9. Answer: (b) 9.

BIMSTEC members are Bangladesh, India, Myanmar, Sri Lanka, Thailand, Nepal and Bhutan. Maldives is not a member. Answer: (c) Maldives.

Zika virus is transmitted by the bite of Aedes mosquitoes. Answer: (b) Mosquito.