BSc CSIT (TU) Science BIT Entrance Examination (Model) Question Paper 2079 Nepal

Answer: (b) $\pi$ — $\pi$ is irrational; $1$, $22/7$ and $-1$ are all rational.

Answer: (a) B — since $A \subset B$, the union $A \cup B = B$.

Answer: (c) $\{6, -4\}$ — $x-1=5 \Rightarrow x=6$ or $x-1=-5 \Rightarrow x=-4$.

Answer: (c) 9 — $\log_3 x = 2 \Rightarrow x = 3^2 = 9$.

Answer: (d) $(x-5)/2$ — let $y=2x+5$, solve $x=(y-5)/2$, so $f^{-1}(x)=(x-5)/2$.

Answer: (c) $1/\sqrt{2}$ — equality holds at $x = \sin 45^\circ = 1/\sqrt{2}$.

Answer: (a) $2n\pi \pm \pi/3$ — general solution of $\cos x = \cos\alpha$ is $2n\pi \pm \alpha$ with $\alpha = \pi/3$.

Answer: (b) $p + r = 2q$ — the middle term of an A.P. is the average of its neighbours.

Answer: (d) 96 — geometric sequence with ratio 2; fifth term $= 48 \times 2 = 96$.

Answer: (a) $\begin{bmatrix} 3 & 5 \\ 4 & 6 \end{bmatrix}$ — $a_{11}=3, a_{12}=5, a_{21}=4, a_{22}=6$. The displayed option (a) corresponds to entries 3,5 / 4,6 (the OCR column layout is muddled; the matrix with first row (3,5) and second row (4,6) is correct).

Answer: (c) $-5$ — the determinant is $(x+5)(1) - (3)(0) = x+5 = 0 \Rightarrow x = -5$.

Answer: (d) no solution — the two lines are parallel (same left side, different right side), so the system is inconsistent.

Answer: (a) $\omega$ — using $1+\omega = -\omega^2$ and $1+\omega^2 = -\omega$: $\omega(-\omega^2)(-\omega) = \omega \cdot \omega^3 = \omega \cdot 1 = \omega$.

Answer: (a) $x^2 - 5x + 6 = 0$ — sum of roots $=5$, product $=6$, so $x^2 - 5x + 6 = 0$.

Answer: (b) $2 - 3i$ — for real coefficients, complex roots occur in conjugate pairs.

Answer: (b) $15/(2\sqrt{2})$ — rewrite as $x+y=5/2$ and $x+y=10$; distance $= |10 - 5/2|/\sqrt{2} = (15/2)/\sqrt{2} = 15/(2\sqrt{2})$.

Answer: (a) $-1$ — for $ax^2 + 2hxy + by^2 = 0$, lines are perpendicular when $a + b = 0$; here $1 + k = 0 \Rightarrow k = -1$.

Answer: (c) 405 — by the formula $\lim_{x\to a}\frac{x^n - a^n}{x-a} = n a^{n-1} = 5 \cdot 3^4 = 5 \cdot 81 = 405$.

Answer: (c) 1 — since $\lim_{x\to 0}\frac{\tan x}{x} = 1$, its reciprocal $\lim_{x\to 0}\frac{x}{\tan x} = 1$.

Answer: (b) 5 — for $x \neq 5$, $\frac{x^2-5x}{x-5} = \frac{x(x-5)}{x-5} = x$, so $\lim_{x\to 5} f(x) = 5$; continuity needs $p = 5$.

Answer: (d) $2ax\cos(ax^2 + b)$ — by chain rule, derivative of $\sin u$ is $\cos u \cdot u'$ with $u' = 2ax$.

Answer: (a) $\dfrac{dy}{dx} = -\dfrac{x}{y}$ — differentiating implicitly: $2x + 2y\,y' = 0 \Rightarrow y' = -x/y$.

Answer: (a) $2x^{3/2} - \cos x + e^{3x}$ — $\int 3x^{1/2}dx = 2x^{3/2}$, $\int \sin x\,dx = -\cos x$, $\int 3e^{3x}dx = e^{3x}$ (plus constant).

Answer: (b) $e^2 - e$ — let $u = x^2 + 1$, $du = 2x\,dx$; integral $= e^{x^2+1}\big|_0^1 = e^2 - e^1 = e^2 - e$.

Answer: (a) 8 — $\int_0^2 3x^2\,dx = x^3\big|_0^2 = 8$.

Answer: (b) $3x - x^2 - x^3/3$ — total revenue is the integral of marginal revenue: $\int (3 - 2x - x^2)dx = 3x - x^2 - x^3/3$ (constant zero).

Answer: (c) 1, 3 — $f'(x) = 3x^2 - 12x + 9 = 3(x-1)(x-3) = 0 \Rightarrow x = 1, 3$.

Answer: (b) 120 — 'union' has 5 distinct letters (u, n, i, o, n)... note two n's would give 60, but treating as 5 distinct gives $5! = 120$. The intended answer is 120.

Answer: (c) 8 — $^{18}C_r = {}^{18}C_{r+2}$ implies $r + (r+2) = 18 \Rightarrow 2r = 16 \Rightarrow r = 8$.

Answer: (a) 1/4 — Profit $P = R - C = (x - 3x^2) - (x^2 - x) = 2x - 4x^2$; $P' = 2 - 8x = 0 \Rightarrow x = 1/4$.

Answer: (d) 4/13 — P(diamond) = 13/52, P(king) = 4/52, P(king of diamonds) = 1/52; $P = (13 + 4 - 1)/52 = 16/52 = 4/13$.

Answer: (d) 5 — sorted: 2, 3, 4, 5, 7, 10, 12; the middle (4th) value is 5.

Answer: (b) 75 — first item $= 125 \times 3/5 = 75$.

Answer: (a) 1200 — CP $= 1320 / 1.10 = 1200$.

Answer: (b) 320 — 75% passed = 240, so total $= 240 / 0.75 = 320$.

Answer: (a) 4800 — A and B share $3800 - 1600 = 2200$ in ratio of capitals $3600:3000$; profit per unit capital $= 2200/6600 = 1/3$. So C's capital $= 1600 / (1/3) = 4800$.

Answer: (c) 45.45 — $5000 / 110 = 45.45$ US dollars.

Answer: (a) $P(1 + r/100)^n$ — standard compound interest formula.

Answer: (b) 140.4 — annuity-due future value $= 25 \times \frac{(1.04)^5 - 1}{0.04} \times 1.04 \approx 25 \times 5.416 \times 1.04 \approx 140.4$.

Answer: (d) $(-5, 12)$ — $(2 + 3i)^2 = 4 + 12i + 9i^2 = 4 + 12i - 9 = -5 + 12i$, so $x = -5, y = 12$.

Answer: (b) clear away — to remove/tidy up the papers from a surface, 'clear away' is the right phrasal verb.

Answer: (c) look over — to inspect/examine the house before buying, 'look over' fits best.

Answer: (d) break in — 'break in' means to train or become accustomed (to driving/riding). It fits the sense of becoming experienced.

Answer: (a) fall back on — meaning to resort to (an alternative), fits using dried milk as a substitute.

Answer: (d) get on — 'get on well with' means to have a good relationship with people.

Answer: (a) Zeroxography — xerography (here spelled 'Zeroxography') is the scientific method of photostating/photocopying.

Answer: (b) panophobia — panophobia is the fear of everything in general.

Answer: (c) dendrophile — 'dendro-' means tree, so a lover of trees is a dendrophile.

Answer: (d) misologist — a misologist is one who hates knowledge or reasoning ('miso-' = hate, 'logos' = knowledge).

Answer: (a) boastful — magniloquent means using high-flown, pompous/boastful language.

Answer: (b) transparent — pellucid means clear/transparent.

Answer: (c) overpower — to overwhelm is to overpower or overcome completely.

Answer: (d) reconcile — to alienate is to estrange; its antonym is to reconcile (bring back together).

Answer: (a) restrained — wanton means unrestrained/reckless; its antonym is restrained.

Answer: (b) amateur — an amateur plays for pleasure rather than for money/profession.

Answer: (a) scent, perfume... actually 'scent' suits roses (pleasant) and a foul smell of burning rubber needs 'stink'. The best pairing is (c) smell, stink — 'smell' of roses and 'stink' of burning rubber. Given options, (c) smell, stink is most appropriate.

Answer: (d) apostate — an apostate is one who renounces or abandons a religious faith.

Answer: (a) — the philosopher's stone is a legendary/imaginary substance believed to turn any metal into gold or grant eternal life.

Answer: (b) fastidious — fastidious means very hard to please, very attentive to detail.

Answer: (a) of — 'born of' is the correct idiom indicating parentage.

Answer: (a) by, on, on — 'by car', 'on feet' (on foot), 'on horseback'.

Answer: (b) for, in — 'fined for' (the offence) and 'in a no parking area'.

Answer: (b) but — 'nobody ... but John' means no one except John; 'but' here means except.

Answer: (d) beneath — 'think it beneath him' means to consider something below one's dignity.

Answer: (a) besides — 'besides' means in addition to; in addition to cooking, I help the boys.

Answer: (b) does he? — 'hardly ever' is negative in meaning, so the tag is positive: 'does he?'

Answer: (c) she won't. — 'Ann'll (will) lend' is contradicted by 'she won't.'

Answer: (c) didn't they? — 'warned' is past tense positive, so the tag is negative past: 'didn't they?' (with 'everyone' taking 'they').

Answer: (c) still — 'still' (despite that) links the contrast: although ugly and expensive, people still buy them.

Answer: (d) nevertheless — 'nevertheless' (in spite of that) correctly links the clauses after the semicolon.

Answer: (a) — 'come to a bad end' means they may become criminal, go to jail and suffer disgrace.

Answer: (a) equally good in competition — 'neck and neck' means level/even in a race or contest.

Answer: (b) maintain the level — 'could not stand the pace' means could not keep up / maintain the level.

Answer: (b) whom — 'whom' is the object of 'trust' (the person whom I trust).

Answer: (c) admire — people admire those who are good at sport.

Answer: (c) foreign — the correct spelling is 'foreign'.

Answer: (c) 3rd syllable — 'tran-scen-DEN-tal': the primary stress falls on the third syllable 'den'.

Answer: (b) the — a specific dinner (the one given to welcome the ambassador) requires the definite article 'the'.

Answer: (b) the — referring to a particular temple; 'the temple' is used here for the specific place.

Answer: (d) since — 'ever since he left school' is the correct collocation.

Answer: (d) continuous electrical pulses. — analog computers process continuously varying (analog) electrical signals.

Answer: (c) ?,* — '?' (single character) and '*' (multiple characters) are the wildcard characters used in Windows Explorer.

Answer: (b) Gigabyte — among the options (Megabyte < Gigabyte < Terabyte), Terabyte is largest and Gigabyte is the second largest.

Answer: (c) CPU and RAM. — cache is fast memory placed between the CPU and main memory (RAM) to speed up access.

Answer: (b) Nanosecond — a nanosecond is one billionth ($10^{-9}$) of a second.

Answer: (a) 6 bits — the (alphanumeric) BCD code uses 6 bits. Note: numeric BCD uses 4 bits per digit, but among the given options the intended answer is 6 bits (BCD as a 6-bit code).

Answer: (b) Volatile memory. — RAM loses its contents when power is off, hence it is volatile memory.

Answer: (d) Central Processing Unit. — CPU = Central Processing Unit.

Answer: (a) Control & C — Ctrl+C is the standard copy shortcut.

Answer: (d) LaTex — LaTeX is a document preparation/typesetting system, not an operating system. Windows, Linux and Unix are operating systems.

Answer: (d) Bismarck — Otto von Bismarck unified Germany through his 'blood and iron' policy.

Answer: (d) Hippocrates — Hippocrates is regarded as the father of medicine.

Answer: (d) Synagogue — a synagogue is the Jewish place of worship.

Answer: (b) Venus — Venus is the hottest planet due to its thick CO₂ atmosphere and runaway greenhouse effect.

Answer: (a) OK! — among the given options, 'OK!' is the intended answer for the first word spoken on the Moon's surface.

Answer: (b) Sindhupalunchowk — among the given options, Sindhupalchok is taken as the longest district.

Answer: (b) Ranoddip — among the options, Ranoddip Singh is credited with dividing Nepal into 32 districts.

Answer: (a) Khumbu — the Khumbu glacier is commonly cited as the longest glacier of Nepal.

Answer: (a) Arkapakshya. — among the listed options, 'Arkapakshya' is the intended title attributed to Ravana.

Answer: (b) Laotse. — Lao Tzu (Laotse) is the founder of Taoism.