BSc CSIT (TU) Science General B.Sc. Entrance Examination (Model) Question Paper 2079 Nepal

Answer: (a) H — ordinary hydrogen (protium, $^{1}_{1}\text{H}$) has one proton and no neutron.

Answer: (b) NH$_2$OH — in hydroxylamine, N has oxidation state $-1$ (H is $+1$, O is $-2$).

Answer: (a) 2 — oxygen ($1s^2 2s^2 2p^4$) has two unpaired electrons in its $2p$ orbitals.

Answer: (c) Curie — the curie (Ci) is a unit of radioactivity.

Answer: (d) NaCl — ionic chloride gives a white precipitate (AgCl) with AgNO$_3$, whereas covalent CCl$_4$, CHCl$_3$ and CH$_3$Cl do not ionise readily.

Answer: (b) Avogadro's law — equal volumes of gases at the same T and P contain equal numbers of molecules.

Answer: (d) 2 — by Graham's law, $\frac{r_{gas}}{r_{O_2}}=\sqrt{\frac{M_{O_2}}{M_{gas}}}=4$, so $M_{gas}=\frac{32}{16}=2$.

Answer: (d) 1/5 — mole fraction $=\frac{1}{1+4}=\frac{1}{5}$.

Answer: (b) +4 — with O at $-2$, $x + 2(-2) = 0 \Rightarrow x = +4$.

Answer: (b) Temperature — the equilibrium vapour pressure of a liquid depends only on its nature and temperature.

Answer: (d) Ge — germanium is Mendeleev's predicted 'eka-silicon'.

Answer: (d) CCl$_2$F$_2$ — dichlorodifluoromethane (Freon-12) is used as a refrigerant.

Answer: (d) Glycol — cold dilute alkaline KMnO$_4$ hydroxylates ethylene to ethylene glycol.

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

Answer: (b) Sulphide ore — froth flotation is used to concentrate sulphide ores.

Answer: (b) 0.1N — moles $=4/40=0.1$, so normality $=0.1$N.

Answer: (c) 1.0 — moles HCl $=3.65/36.5=0.1$ M, $[H^+]=0.1$, pH $=-\log(0.1)=1$.

Answer: (a) Temperature — the rate constant depends on temperature (Arrhenius equation), not on concentration.

Answer: (d) Fe — iron readily rusts (corrodes) in moist air; Cu, Ag and Au are far more resistant.

Answer: (d) Increase — melting increases disorder, so entropy increases.

Answer: (d) C — Lassaigne's test detects N, S and halogens; carbon is not detected by it.

Answer: (d) Alkane — methane (CH$_4$) is the simplest alkane.

Answer: (b) Benzene — three molecules of ethyne (acetylene) cyclically polymerise to benzene on passing through a red-hot tube.

Answer: (a) Benzoic acid — the methyl side-chain of toluene is oxidised to a carboxylic acid (benzoic acid).

Answer: (a) AlCl$_3$ — anhydrous aluminium chloride is the Lewis-acid catalyst for Friedel-Crafts reactions. (Option printed as 'AlCl'.)

Answer: (c) $(A \cup B) - (A \cap B)$ — this is the symmetric difference of the two sets.

Answer: (c) $[2,3]$ — adding 1: $4 \le 2x \le 6$, dividing by 2: $2 \le x \le 3$.

Answer: (b) 2 — by the chain rule of logs the product telescopes to $\log_3 9 = 2$.

Answer: (c) $\sec\theta = \tfrac{1}{2}$ — secant cannot lie between $-1$ and $1$, so $|\sec\theta|\ge 1$; $\sec\theta = 1/2$ is impossible.

Answer: (a) $\dfrac{3}{4}$ — using $\sin 3x \approx 3x$ and $\tan 4x \approx 4x$, the limit is $3/4$.

Answer: (d) $\pi/180$ — converting degrees to radians, $\sin x^\circ = \sin\!\left(\frac{\pi x}{180}\right)$, so the limit is $\pi/180$.

Answer: (c) $\dfrac{1}{x}$ — the derivative of $\log|x|$ is $1/x$.

Answer: (d) 12, 8 — maximising $x^3 y^2$ with $x + y = 20$ gives $x = 12$, $y = 8$ (the cubed part gets $\frac{3}{5}$ of 20).

Answer: (c) $e^{\tan^{-1}x} + C$ — with $u = \tan^{-1}x$, $du = \frac{dx}{1+x^2}$, so the integral is $\int e^u\,du = e^{\tan^{-1}x} + C$.

Answer: (a) 1 — $\int \log x\,dx = x\log x - x$; evaluating from 1 to e gives $(e - e) - (0 - 1) = 1$.

Answer: (a) $-i$ — $i^{4n} = 1$ and $i^3 = -i$, so $i^{4n+3} = -i$.

Answer: (d) $\dfrac{17}{12}$ — by the factor theorem $f(-3) = 0$: $-27 + 9k + 3k + 10 = 0 \Rightarrow 12k = 17 \Rightarrow k = 17/12$.

Answer: (d) 0 — with $w$ a cube root of unity ($1 + w + w^2 = 0$), this circulant determinant evaluates to 0.

Answer: (c) $x^2 + y^2 \pm 10x \pm 10y + 25 = 0$ — a circle of radius 5 touching both axes has centre $(\pm 5, \pm 5)$, giving $(x \pm 5)^2 + (y \pm 5)^2 = 25$, i.e. $x^2 + y^2 \pm 10x \pm 10y + 25 = 0$.

Answer: (a) 100 — the sum of the first $n$ odd numbers is $n^2 = 10^2 = 100$.

Answer: (d) 30 — 'madam' has 5 letters with 'm' twice and 'a' twice: $\frac{5!}{2!\,2!} = \frac{120}{4} = 30$.

Answer: (b) 28 — number of terms $= \binom{6+2}{2} = \binom{8}{2} = 28$.

Answer: (c) 2 — points $(2,1)$ and $(k,1)$ share $y = 1$, but $(4,5)$ has $y = 5$. For collinearity the area must be zero, which forces $k = 2$ (so $(k,1)$ coincides with $(2,1)$). Answer (c) 2.

Answer: (a) $(2, \pi/6)$ — $r = \sqrt{3+1} = 2$ and $\theta = \tan^{-1}(1/\sqrt{3}) = \pi/6$.

Answer: (a) $90^\circ$ — slopes are $2$ and $-1/2$; their product is $-1$, so the lines are perpendicular.

Answer: (d) 2 — dividing by 2: $x^2+y^2-1.5x+2.5y+4.5=0$. Length $=\sqrt{4+1-3-2.5+4.5}=\sqrt{4}=2$.

Answer: (a) $(2,3)$ — completing the square: $(y-2)^2 = 4(x-2)$, vertex $(2,2)$, $a=1$, so focus $=(2+1,2)=(3,2)$. The intended option matching this is (b) (3,2); however the source key here reads (a).

Answer: (a) $\pi/2$ — the tangents at the ends of the latus rectum of a parabola are perpendicular (they meet on the directrix at right angles).

Answer: (a) x-axis — the set of points with $y = 0$ and $z = 0$ is the x-axis.

Answer: (d) $|\vec{a} \times \vec{b}|$ — for unit vectors, $|\vec{a}\times\vec{b}| = |\vec{a}||\vec{b}|\sin\theta = \sin\theta$.

Answer: (c) Paleontology — palaeontology is the study of fossils.

Answer: (a) Pseudopodia — Amoeba moves using temporary cytoplasmic projections called pseudopodia.

Answer: (a) Three — insects have three pairs (six) of legs.

Answer: (b) Sex call for female — male frogs croak to attract females (mating call).

Answer: (b) Chitwan N P — Chitwan National Park is a UNESCO World Heritage Site.

Answer: (d) In the cheek wall — the lining of the cheek (buccal cavity) is simple squamous epithelium.

Answer: (b) Gastrula — the yolk plug appears during gastrulation at the blastopore.

Answer: (c) Peristalsis — rhythmic muscular contractions (peristalsis) propel food through the intestine.

Answer: (d) Residual volume — residual volume is the air that remains in the lungs after a maximal exhalation.

Answer: (a) 40 mm Hg — normal systolic ≈120 and diastolic ≈80, so pulse pressure ≈40 mm Hg.

Answer: (c) Brain and spinal cord both — the CNS comprises the brain and the spinal cord.

Answer: (c) Stomach — typhoid (caused by Salmonella typhi) infects the gastrointestinal tract (stomach/intestine).

Answer: (d) Cell wall — a (cellulose) cell wall is characteristic of plant cells; centrioles are usually absent in higher plants.

Answer: (c) Pachytene — crossing over (exchange of chromatid segments) occurs during the pachytene stage of prophase I.

Answer: (b) Protista — unicellular eukaryotes are placed in kingdom Protista.

Answer: (d) Archegonium — the venter is the swollen basal part of the archegonium (female sex organ).

Answer: (d) Pteridophytes — pteridophytes are seedless vascular plants (vascular cryptogams).

Answer: (b) Community — synecology is the ecological study of communities.

Answer: (c) Leaf — palisade parenchyma (chlorenchyma) lies beneath the upper epidermis of the leaf.

Answer: (b) Collenchyma — the hypodermis of a dicot stem is made of collenchyma (gives flexibility and support).

Answer: (a) Xylem — xylem conducts water and minerals upward from roots to leaves.

Answer: (c) Grana — the light reactions occur in the thylakoid membranes (grana) of the chloroplast.

Answer: (b) mRNA — a codon is a triplet of bases on mRNA that codes for an amino acid.

Answer: (c) Linkage — genes located on the same chromosome tend to be inherited together (linkage).

Answer: (b) Nutritive — the tapetum is the innermost nutritive layer of the anther that nourishes developing pollen grains.

Answer: (a) $[L]$ — a light-year is a distance, so its dimension is length $[L]$.

Answer: (d) K.E. — at constant speed the kinetic energy stays constant, while velocity, acceleration (direction changing) do not.

Answer: (c) Torque — angular motion is changed by torque, so torque is needed to stop rotation.

Answer: (b) Angle of shear — shearing strain is measured by the angle of shear (angular deformation).

Answer: (a) Concave — water wets glass, so its meniscus is concave upward.

Answer: (b) Pyrometer — a (radiation) pyrometer measures very high temperatures such as that of the Sun.

Answer: (c) 4°C — due to anomalous expansion, water has its maximum density (minimum volume) at 4°C.

Answer: (d) 70% — $\eta = 1 - \frac{T_2}{T_1} = 1 - \frac{300}{1000} = 0.70 = 70\%$.

Answer: (b) Refraction — twinkling is caused by atmospheric refraction of starlight through layers of varying density.

Answer: (b) Violet — violet light has the shortest wavelength, highest refractive index, hence maximum deviation.

Answer: (a) $J\,K^{-1}\,mol^{-1}$ — R is measured in joule per kelvin per mole.

Answer: (d) Convex lenses — hypermetropia (long sight) is corrected with converging (convex) lenses.

Answer: (c) Light year — the distance light travels in one year is the light-year.

Answer: (a) Zero — sound is a mechanical wave and cannot travel through a vacuum.

Answer: (a) Shrill sound — a mosquito's buzz is high-frequency, so it is a shrill (high-pitched) sound.

Answer: (a) Seebeck — the thermoelectric (Seebeck) effect was discovered by Thomas Seebeck.

Answer: (b) Coulomb forces — the electrostatic (Coulomb) attraction between the nucleus and electrons holds electrons in the atom.

Answer: (a) 13.6 eV — the ground-state (ionisation) energy of hydrogen is 13.6 eV (energy $-13.6$ eV).

Answer: (c) 1/12 (mass of one C atom) — 1 amu is defined as one-twelfth the mass of a carbon-12 atom.

Answer: (b) Fission — an atom (fission) bomb releases energy by nuclear fission.

Answer: (b) Potential energy — energy stored in a capacitor's electric field is electrostatic potential energy.

Answer: (d) right-hand thumb rule — Maxwell's right-hand thumb (grip) rule gives the direction of the magnetic field around a straight current-carrying conductor.

Answer: (a) Big-bang theory — the Big Bang theory is the most widely accepted explanation for the origin of the universe. (Printed as 'Big-band'.)

Answer: (b) $\pi/2$ — for wattless current the power factor $\cos\phi = 0$, so $\phi = \pi/2$.

Answer: (a) Ferromagnetic — ferromagnetic materials (e.g. steel) retain magnetisation and are used for permanent magnets.

Answer: (b) Innocuous — innocuous means harmless.

Answer: (c) Intangible — intangible means unable to be grasped/touched by the mind.

Answer: (c) Jockey — a jockey is a professional horse-race rider.

Answer: (d) Stupor — stupor is a state of near-unconsciousness/heavy unnatural sleep.

Answer: (c) Verbatim — verbatim means word for word.

Answer: (a) Antidote — an antidote counteracts the effects of poison.

Answer: (b) Teetotaller — a teetotaller completely abstains from alcohol.

Answer: (c) Loquacious — loquacious describes someone who talks a great deal.

Answer: (c) Fastidious — a fastidious person is very hard to please.

Answer: (d) Expiate — to expiate is to atone for one's sins.

Answer: (c) Indomitable — indomitable means impossible to subdue or defeat.

Answer: (b) Inexplicable — inexplicable means impossible to explain.

Answer: (b) Nursery — a nursery is where young plants are raised.

Answer: (a) Cobbler — a cobbler repairs shoes.

Answer: (b) Widower — a widower is a man whose wife has died.

Answer: (c) Pot-boiler — a pot-boiler is a work produced merely to earn money.